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Gr 10 Applied TIPS Workbook

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1. TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 44 3 4 4 Rising and Running From a Point Continued Graph the following equations on the grids given below and check your graphs using the graphing calculator Note When you write the slope as a fraction any negative signs should be placed in the numerator only Slope Slope Rise Rise Run Run y intercept y intercept Describe how you graphed the line TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 45 3 4 4 Rising and Running From a Point Continued Graph the following equations on the grids given below and check your graphs using the graphing calculator Note When you write the slope as a fraction any negative signs should be placed in the numerator only y 2x y 3 Slope Slope Rise Rise Run Run y intercept y intercept Describe how you graphed the line Describe how you graphed the line TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 46 3 4 5 Graphic Organizer Definition in own words Rules Method Graphing by Hand Using the Slope and Y Intercept Non examples TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 47 3 5 1 Nspire CAS Handheld Manual Getting Started When you turn on the handheld press ace You will be asked whether you want to save the Do you want to save this document document
2. Equation s n Remember You need the slope and y intercept Use your knowledge to calculate these values 2 Use your equation to calculate the number of sides that 50 squares placed side by side would have 3 Use your equation to calculate how many squares you would have if you counted all the sides and got a number of sides equal to 256 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 78 3 9 3 Fm on your side Continued RECTANGLE INVESTIGATION otart by placing rectangles side by side as shown Note This arrangement of 4 rectangles has 13 sides 1 2 3 4 Equation s n Remember You need the slope and y intercept Use your knowledge to calculate these values 2 Use your equation to calculate the number of sides that 75 rectangles placed side by side would have 3 Use your equation to calculate how many rectangles you would have if you counted all the sides and got a number of sides equal to 724 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 79 3 9 3 Fm on your Side Continued HEXAGON INVESTIGATION Start by placing hexagons side by side as shown Note This arrangement of 2 hexagons has 11 sides Equation s n Remember You need the slope and y intercept Use your knowledge to calculate these values 2 Use your equation to calculate the number of sides that 76 hexagons placed side by side would have 3 Use your equation
3. Its price is 1 83 per linear meter Determine the cost of the irrigation system for the hedge Part C The Proposal Complete a proposal to Sham City Your proposal should be one paragraph Be sure to include the following The amount of sod and hedging needed in metric units The cost of the sod and hedging The cost of the entire irrigation system needed for the sod and hedge Summarize the proposal with a total cost Included with your proposal paragraph should be a drawing of the park labeled in metric units This will be handed in to the teacher to be assessed TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 20 7 5 2 Job Opportunity Rubric Thinking Reasoning and Proving Criteria Degree of clarity in explanations and justifications in reporting Making inferences conclusions and justifications Level 1 Explanations and justifications are partially understandable Justification of the answer presented has a limited connection to the problem solving process and models presented Level 2 Explanations and justifications are understandable by me but would likely be unclear to others Justification of the answer presented has some connection to the problem solving process and models presented Level 3 Explanations and justifications are clear for a range of audiences Justification of the answer presented has a direct connection to the problem
4. TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 8 7 3 3 Convertible Numbers Let s practice converting some numbers from metric to imperial units and vice versa How many meters are there in 13 yards Y This is a technique called the Ratio 1 yards meters Method of converting It consists of three steps 2 1 0 9144 1 Set up a ratio in words X BE x 13 2 Use the conversion table 3 13 3 Create equivalent ratio 0 9144 x 13 11 8872 Therefore there are about 11 89 meters in 13 yards Let s try another How many squared inches are there in 9 squared centimetres Ratio inches cm Conversion 1 645 Factor 23 x 1 395 Equivalent 9 Ratio _ R 1 x 1 395 1 395 in Therefore there are 1 395 in in 9 cm TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 3 3 Convertible Numbers Continued Try the following conversions using your conversion table and the Ratio Method or any method of your choice If you bought a 24 foot ladder how many meters would it be If a bag of salt holds 150 cubic inches how many cubic centimetres does it hold Joe is 1 75 meters tall How many feet tall is Joe How many squared feet is a house that measures 42 squared meters The length of a CFL football field is 160 yards from end zone to end zone How many met
5. Point of intersection What does the point of intersection mean in this catering problem Nick and Heather have invited 80 people to their wedding How much will it cost for each menu TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 Solve the system using elimination Point of intersection You used 3 different methods to solve the system what did you notice about the points of intersection Does this surprise you Heather prefers the Frugal Gourmet menu to Cookie s Catering How much more will she pay for her preference 4 49 4 7 5 3 Ways continued The student council is providing lunch and music for the grade 10 class They have two quotes from Lunch Express and Let s Do Lunch The costs for each were given as follow Lunch Express If 100 students attend it will cost 1 000 If 200 students attend it will cost 1 500 Let s Do Lunch If 50 students attend it will cost 700 If 150 students attend it will cost 1 350 Solve the system using the three different methods Equations for the companies Lunch Express Let s Do Lunch Lunch Express Let s Do Lunch Graphing Method Substitution Method 100 150 200 250 300 Point of intersection Point of intersection TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 50 4 7 5 3 Ways continued Elimination Method The student council has 1 800 in their budget for the lunch They prefer Let s Do Lunch what is th
6. STATION 1 Part A Using an Interactive White Board or laptop you will be investigating the volume of a rectangle GETTING STARTED i Open the website http www learner org interactives geometry ii Click on the Surface Area and Volume Tab iii Click on the tab labeled Volume Rectangles Read through the introduction and then answer the questions provided When finished scroll down and select the Find Volume of Another Prism option Fill in the chart provided below Part B Determine the volume of empty space that is in the box that holds exactly a basketball ball with a diameter of 18 inches TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 45 7 11 3 Shapes to Go Continued STATION 2 Your goal is to show how the volume of a cone is related to the volume of a cylinder Your task 1 Compare the base of the cone with the base of the cylinder What do you notice 2 Compare the height of the cone to the height of the cylinder What do you notice 3 How many times do you think you would be able to fill the cone with water and pour it into the cylinder before it overflows Fill in the blanks below Fill in the bolded components after you perform the experiment Guess Actual Therefore the volume of a cylinder is times greater than the volume of a cone LETS TRY IT i Fill the cone full with water ii Empty the water from the cone into t
7. The report should describe what the profession is all about Let us know what they do and what type of education is needed to enter that profession The report should also include a description of how trigonometry is used by the professional in their work What types of problems do they need trigonometry for Include one example of a problem that could be solved using trigonometry from the field of work you are researching A list of resources that you used must be included These may be articles books websites magazines etc The Presentation The presentation should provide a quick snapshot of your research Include visuals pictures graphics etc related to the profession The presentation can be a poster newspaper article created by you a brochure that you have created a skit an electronic presentation etc Your presentation should highlight e your chosen profession e education needed ie college university workplace and courses in high school e what kind of problems the professional will need to use trigonometry to solve Where do you get information The internet is a great place to start You can do a search using the title at the top of the page This will give you an idea of different professions and then you can investigate the specific one you pick If you know someone who actually is in one of those professions ask them The library is a great place to start and to get help on research Types of presentatio
8. How many hours must the mechanic work if she earns 1240 Can you build the 8 figure Explain TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 61 3 6 6 Practising Modelling Part A Complete the following table Equation in DN NEN NL MN A caterer charges a flat fee of Find the cost after 30 people 400 plus 15 person An internet package charges a flat fee of 10 plus 0 40 per hour Find the number of hours of internet usage if the cost is 200 A tree s diameter grows by 134 cm per year The tree s diameter is currently 12 cm Find how many years it will take have diameter 2034 cm A spring is 14 cm long with no mass on it and it grows by 3 cm per kg put on it Find how much weight was added if the spring is 35 cm long The temperature of hot water Find the temperature after 13 hours placed in the freezer is 80 C and itis decreasing at the rate of 8 C per hour Part B For each equation create a real world context Identify the independent variable x and dependent variable y for each 1 y 15x 2 y 2 0 05x 25 3 y 20x 100 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 62 3 7 1 Y the X Are You Intercepting Me On the grid paper on the next page plot and label all the points listed below Note Each point is labelled so you can refer to them later A 3 3 B 2 3 C 1 3 D 0 3 E 1 3 F 2 3 G 3 3 H 3 2 3 1
9. Now decide how you would start solving for x Perhaps you ve decided that adding 5 to both sides E of the equation is a good start Wonderful To do E this immediately press cs Notice that the handheld automatically inserts Ans What is this Ans stands for the last answer you found If you now DEG AUTO REAL press the key the handheld will add 5 to the left side and the right side of 6x 5 2 8 You will see this 9x 5 8 6x 2 8 result 6 x 5 8 5 6 x 13 Continue solving the equation You probably see that to finally isolate the x variable it is necessary to aoe E divide the equation by 6 on both sides Again just start typing the operation you want to perform Press 5 x 5 8 6 x 5 8 Ce The handheld will insert Ans for you Press NEIN 6x 13 to calculate the result 6x 13 13 As you can see the handheld reports that amp imr 13 X 6 Is this the result you expected To convert this result to its decimal equivalent press Now try to solve the following equations on your own Remember to start a new calculator screen for each one 3X 4z 2 7 7 2xX 4 2X 4 82 3x4 3 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 49 3 5 1 Nspire CAS Handheld Manual Continued How to Check a Solution to a One Variable Equation Say that you have solved the following equation 6x 5 8 and you believe the solution is x This would be ted
10. aR Targeted Implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MFM2P Unit 1 Similar Triangles COLO II A n C Z A X 9 D bu eel b v Student January 2009 Dufferin Peel Catholic District School Board Unit 1 Similar Triangles Section Acivity Page 122 ReviewofMetic Units 6 1 2 4 What s on the Menu Growing Shapes 9 KWL Chart Investigation TIPS4RM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 1 1 Its All About Me The last math course that took was The mark received in that course was The things like most about math are The things don t enjoy about math are am taking this course because hope to achieve a mark of am going to achieve this mark by doing the following After school I m involved in fill in the chart Sport Club Other would prefer to sit because If you need to call home you should speak to who is my because You should know that have allergies epilepsy diabetes Some other things you should know about me In 10 years hope to TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 3 1 1 2 What s on the Menu Teachers vs Students Adapted from About Teaching Mathematics by Marilyn Burns Math Solutions Publications
11. b What is the area of the silo that will be painted red 3 a What is the total surface area that will be painted red b What is the total surface area that will be painted white 4 a What would the answer to 3a be in squared feet b What would the answer to 3b be in squared feet TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 40 7 10 1 Old McDonald Continued 5 If one can of paint will cover a total of 1000 ft a How many cans of white paint will Old McDonald need to buy b How many cans of red paint will Old McDonald need to buy c How many paint cans will Old McDonald need to buy in total TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 41 7 10 2 Old McDonald Rubric Selecting Computational Strategies Selects and applies appropriate strategies Selects and applies the most appropriate strategies accurately Selects and applies appropriate strategies with major Selects and applies appropriate strategies with Select and use strategies to solve a problem errors omissions or mis sequencing minor errors omissions or mis sequencing Communicating accurately and logically sequenced and logically sequenced Communicating Ability to read and interpret mathematical language charts and graphs Correct use of mathematical symbols labels units and conventions
12. hypotenuse of ADEF _ Length of hypotenuse of ADEF _ Length of hypotenuse of NABC Length of hypotenuse of AGHK Length of shortest side of ADEF _ Length of shortest side of ADEF _ Length of shortest side of NABC Length of shortest side of AGHK Length of middle side of ADEF _ Length of middle side of ADEF _ Length of middle side of AABC Length of middle side of AGHK 8 What do you notice about the ratios you have calculated in each column State each ratio This ratio is called a scale factor TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 21 1 5 2 Finding Similar Triangles continued 9 What conclusions about the triangles can you draw based on the ratios calculated in question 7 Are they similar or not Explain 10 If you were given a triangle with side lengths specified and a scale factor how could you use this information to determine the side lengths of the similar triangle that would be created 11 Use your method above to solve the following triangles 10cm ocm 8 cm X 12 Try to recreate your original rectangle TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 22 1 5 2 Similar Triangles Practice 1 Calculate the missing information for the following pairs of similar triangles 16 b a a O1 5 5 15 C 18 TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 23 1 6 1 Let
13. 2000 Who will win the tug of war in round 3 7 X mm GRAZ ED E S T Round 1 On one side are four teachers each of equal strength On the other side are five students each of equal strength The result is dead even Round 2 On one side is Buddy a dog Buddy is put up against two of the students and one teacher The result once again is dead even Round 3 Buddy and three of the students are on one side and the four teachers are on the other side Who do you think will win the third round Explain Puzzling Fruit In the puzzle below the numbers alongside each column and row are the total of the values of the symbols within each column and row What should replace the question mark Make sure you provide a full and detailed solution 7o 9 20 3 TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 4 1 1 3 What s on the Menu continued Buddy s Hungry Buddy one of the teacher s dogs is very hungry Ms Jones stops at the pet store on her way home from school She is always looking for the most economical buy While at the pet store she notices the following prices of pet food Five 150 mL cans of Perfect Pet dog food for 1 26 Twelve 400 mL cans of Doggies Love It for 7 38 Ten 150 mL cans of Rover s Chow for 2 60 Six 400 mL cans of Man s Best Friend for a ms Which pet food should Ms Jones buy Explain in as many different ways as possible TIPS4RM Grade 10 App
14. August 2008 1 19 1 5 2 Finding Similar Triangles You and your partner will need e one sheet of legal size paper and one sheet of letter size paper e protractor e ruler e scissors 1 Measure and label the side lengths on your piece of paper Write a large signature across the back of your piece of paper You may need this later 2 Each rectangle has two diagonals Fold your paper along one of the diagonals Cut the paper along the diagonal 3 What do you notice about the two triangles that you have created 4 Take one of the two congruent triangles and set it aside Take the other one and using a ruler and protractor draw a line that is perpendicular to the hypotenuse and passes through the vertex of the right angle Cut the paper along this line You should now have three triangles Label the vertices of each triangle with appropriate letters Largest triangle is AABC Middle triangle is A DEF Smallest triangle is AGHJ Explore the relationship between the triangles by reorienting them and overlapping the three triangles so that corresponding angles are in the same place 5 Identify any triangles that you think are similar Explain TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 20 1 5 2 Finding Similar Triangles continued 6 Using a ruler and protractor complete the table below to determine whether the triangles are similar 7 Complete the following calculations Length of
15. Part 1 ACTIVITY 2 1 Select an object whose base is at right angles to the ground and whose height you cannot measure object 2 Measure the length of the shadow of the object Indicate units 3 Hold a metre yard stick at right angles to the ground and measure the length of its shadow Use the same units as in question 2 4 Draw similar triangles representing this situation in the space below Label the diagram and indicate all known measurements with units 5 Write the proportion needed to find the desired height 6 Calculate the height of the object Show your work TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 28 1 7 3 How High Part 2 ACTIVITY 3 1 Select an object whose height you cannot measure object 2 Lay a small mirror horizontally on the ground exactly 1 metre in front of the object 3 Slowly walk backwards until you can just see the top of the object in the mirror Measure your distance from the mirror 4 Measure the distance from the ground to your eye level 5 Draw similar triangles representing this situation in the space below Label the diagram and indicate all known measurements with units 6 Write the proportion needed to find the desired height 7 Calculate the height of the object Show your work TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 29 1 7 4 How High Part 3 ACTIVITY 4 1 6 Select an obje
16. You Lg EI will see this result 6 2 y218 6 x 2 y 18 6 x Continue solving the equation You probably see that to finally isolate the y variable it is necessary to divide the equation by 2 on both sides Again just start typing the operation you want to perform Press ci 2 The handheld will insert Ans for you Press to calculate the result As you can see the handheld reports that RAD AUTO REAL y 3 x 3 6x 2 y 18 6x E2 y 18 B Is this the result you expected Gxt 2 y 18 6 x 2 y 18 6 x Your teacher will discuss this with your class 2 y 18 6 x selle After the discussion use the space below to write your 2 own explanation of what this means TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 4 Nspire CAS Handheld Manual Continued How to Check a Solution to a Linear System Say that you have solved the following linear system 4x4 2y 24 8x 6y 18 and you believe the solution is 2 3 This would be tedious to check by pencil and paper but it is quick to check with the handheld Here is how to do it First be certain that you are on a Calculator page If you need help with this see the Getting Started section from earlier in this manual You are going to press the following keys to check the solution against the first equation POP B3VOPVPOWOPMO2 O MOOUOG This means Check this equation such that x and y Dont forget to press the key lower right corner of keypad b
17. e e 7 28 7 8 1 Pick a Square Any Square On the board you should see many different sized squares labelled with a unit For each of the items in the chart below select the square unit that you think would be best for describing the size of the item Once you have selected the square unit make an estimate as to how many squares you think could fit inside the item Classroom Floor Front of Math Textbook Thumbnail Blackboard Interactive White Board One Classroom Window Classroom Door Clock in Class Exchange your chart with a partner when instructed There is a chart below for your partners comments Partners Name Classroom Floor Front of Math Textbook Thumbnail Blackboard Interactive White Board One Classroom Window Classroom Door Clock in Class TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 29 7 8 2 Planter s Dilemma Aw Joe is going to paint his hanging flower pots Flower Pot Here is a close up look at one of the flower pots 5 inches 9 inches 9 inches How much paint would Joe need in square inches to paint the outside of ONE flower 1 pot Note You may need to referto 2 How many square feet of paint is needed one of your conversion tables that was made earlier in the unit 7 30 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 8 2 Planter s Dilemma Continued 3 If on
18. or down how many units do you need to reach the same level as point B 3 Only moving right how many units do you have to move your pencil to connect to point B 4 Given the equation for the graph state the slope and the y intercept Slope y intercept TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 42 3 4 3 Can Graphing Get Any Easier Continued Summary Discuss each question with your partner and both partners write answers 1 Looking at all three investigations can you relate the values from steps 2 and 3 with the slope or the y intercept Explain the relationship 2 Given the following equation Slope y ay 4 j 3 y intercept Describe a method to graph this equation by hand using the slope and the y intercept 2 3 Using the grid provided below graph the equation y 2 4 Write the steps you followed to the right of your graph 1 5 2 1U TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 43 3 4 4 Rising and Running From a Point Graph the following equations on the grids given below and check your graphs using the graphing calculator Note When you write the slope as a fraction any negative signs should be placed in the numerator only 2 4 x 4 x 2 a 173 Slope Slope Rise Rise Run Run y intercept y intercept Describe how you graphed the line Describe how you graphed the line
19. the square base and h is the height of pyramid If the base has a side length of 6 cm and the volume is 396 cm what is the height TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 59 7 13 3 Don t Feel Isolated Landscape Customer Architect Mrs Rose wants a rectangular Rectangle shaped garden planted off the back of her house She can only afford to plant flowers in an area of 15m She really wants the garden to be 5m in length How far from the house will the garden stick out School Sports School You are designing a flag for the Team Manager Council upcoming Football Game Tradition says that the flag must be triangular The base of the flag has to be 15 inches and you only have enough material to cover an area of 150 square inches Triangle A What will be the height of the flag according to these restrictions Packaging Candy A brand new sugary treat has been Cylinder Designer Manufacturer invented The volume of one candy is 1 6 cm and its radius is 1 cm How long would you need the cylindrical package of candy to be if you need 20 candies to fit in one tube Carpenter Contractor An entertainment unit needs to be Rectangular Prism built for a new home The cabinet has to have a volume of 1 01 m so it can hold the TV and stereo that the owners recent purchased In order to fit the space provided bot
20. 200 and 50 An internet package charges a flat fee of 10 for every audio system he sells plus 0 40 per hour Initial Value Initial Value TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 7 3 1 4 Reminiscing Old Relationships Continued A Runner s Time Cost of Renting a Bus s m Initial Value TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 8 3 1 4 Reminiscing Old Relationships Continued Running Up The Stairs Cost of Renting a Boat 0 10 2 3 Number of Days Initial Value TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 9 3 1 6 A Mathematical Spelling Bee Procedure 1 2 5 6 f You will work in partners where Partner A is the timer and Partner B is the recorder Create four quadrants by folding a piece a paper in half and fold in half again With a watch student A will signal student B to start printing the full word RUN down one of the paper quarters as many times possible in 10 seconds This is not a contest print at your normal printing speed After 10 seconds student B signals student A to stop printing Count all the legible words Record this value in the table below Repeat steps 1 6 for the words RATE VALUE CHANGE and INITIAL Recording Data 8 9 Record this value in the table below RATE VALUE CHANGE INITIAL What i
21. 3 36 3 4 1 Graphs Slopes Intercepts Equations and Check One partner will find the y intercept of each graph and the other partner will find the slope of each graph You will both then create an equation that represents the graph Finally you will check your equation using the graphing calculator use BLM 3 4 2 as a reference for your graphing calculator Partner A Slope Partner B y intercept Join both A and B to create an equation Equation Check you answer using the graphing calculator Partner B Slope Partner A y intercept Join both A and B to create an equation Equation Check you answer using the graphing calculator TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 37 3 4 1 Graphs Slopes Intercepts Equations and Check Continued Partner A Slope Partner B y intercept Join both A and B to create an equation Equation Check you answer using the graphing calculator Partner B Slope Partner A y intercept Join both A and B to create an equation Equation Check you answer using the graphing calculator TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 38 3 4 2 Graphs Slopes Intercepts Equations and Check Graphing Calculator Keystrokes 1 Prepare your calculator by either running a get ready program or resetting the graphing calculator 2 Press the button and set the window setting as sh
22. A quadratic relation forms a graph with shape of a c Below is a table of value determine if this relation is linear quadratic or neither The relation is d A linear relation has the equal and the equal to e A quadratic relation has the equal TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 28 6 11 2 Review of Quadratics continued 2 Features of a Quadratic Graph a A quadratic relation can be seen when b A quadratic relation can be seen when a ball is thrown in the air and the height a duck flies into the water catches a is measured versus time A sketch of fish and flies back out this graph might look This parabola is facing This parabola is facing and the vertex is a and the vertex is a C The key features of a quadratic graph are TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 29 6 11 2 Review of Quadratics continued 3 Forms of A Quadratic Standard Form y ax bx c a The y intercept is the or term b We can change factored into standard form by c There are three methods of expanding and _ d Example 1 Find the y intercept x intercepts of the following quadratic y x 4 x 5 The y intercept is The x intercepts are and Example 2 Expand the following y 2x 3x 4 TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Fo
23. Appropriate use of mathematical vocabulary Integration of narrative and mathematical forms of communication Misinterprets a major part of the information but carries on to make some otherwise reasonable statements Sometimes uses mathematical symbols labels and conventions correctly Sometimes uses mathematical vocabulary correctly when expected Either mathematical or narrative form is present but not both Misinterprets part of the information but carries on to make some otherwise reasonable statements Usually uses mathematical symbols labels and conventions correctly Usually uses mathematical vocabulary correctly when expected Both mathematical and narrative forms are present but the forms are not integrated Correctly interprets the information and makes reasonable statements Consistently uses mathematical symbols labels and conventions correctly Consistently uses mathematical vocabulary correctly when expected Both mathematical and narrative forms are present and integrated Correctly interprets the information and makes subtle or insightful statements Consistently and meticulously uses mathematical symbols labels and conventions recognizing novel opportunities for their use Consistently uses mathematical vocabulary correctly recognizing novel opportunities for its use A variety of mathematical forms and narrative are present integrated and wel
24. August 2008 6 34 l Targeted Implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MFM2P Unit 7 Surface Area and Volume REVISED August 2008 Dufferin Peel Catholic District School Board Student Unit 7 Surface Area and Volume Secion Acivity Page 721 Imperial Decisions 6 732 AQuesonofConvring 8 733 Convertible Numbers 9 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 2 Section Activiy Page TR Reflecting on My Learning 3 2 1 60 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 3 7 1 1 Imperial Measurements Refer to the many different measuring units on the board at the front of the room Your job is to take those measurement units and place them in the appropriate column below Don t forget to also write the name of an object that could be measured in that unit beside the unit TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 4 7 1 2 Measure This In the following table you will see many common school items Your job is to estimate what you think the measurement of that item will be and then measure the item with the devices that are provided It s important that you take a really good estimate before you measure To keep things simple you can estimate to the close
25. Complete the three columns of the table below 7 Press 2 Graph so that you can look at the tables of values for the two curves Discuss what you see and complete the table TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 3 6 2 1 Multiply a Binomial by a Binomial Part A Use algebra tiles to multiply binomials and simplify the following 1 y x 1 x 3 2 y x 2 x 3 7 Part B Use the chart method to multiply and simplify the following 1 y x 1 x 3 7 2 y x 2 x 3 7 3 y x 2 x 1 4 y x 2 x 3 7 o y x 1 x 1 6 y x 1 x 2 7 TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 4 6 2 1 Multiply a Binomial by a Binomial continued Part C Multiply and simplify the two binomials using the chart method and the distributive property 1 x 4 x 3 x 4 2 x 3 x 3 Oy ee 3 een 4 o3 A me n 4 3 Pp xt a o3 Log s an FB amp en X 3 Pp xt m R E o o Eo T 8 x 3 x 4 X a d TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 5 6 3 1 Finding the y Intercept of a Quadratic Equation Name 1 Use the graphing calculator to find the y intercept for each of the equations Note any patterns you see 2 How can you determine the y intercept by looking at a quadratic
26. Draw an example 0 What is the difference between A Draw A 2 on the left and draw A 6 on 2 and A 6 the right TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 28 3 3 2 Slopes and Stuff on TI 83 Investigation continued 6 When you are changing A what stayed the same 7 What happens when B 5 Draw an example 8 What happens when B 6 Draw an example 9 When you are changing B what stayed the same 10 In the equation y mx b what does letter A represent What about B TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 29 3 3 2 Slopes and Stuff on TI 83 Investigation continued Almost done But since we re finished with the Transform applications please help me uninstall it first before we move on Press APPS Scroll and find TRANSFRM Press ENTER Select UNINSTALL by pressing ENTER Using your equation that you got from your teacher type this into your graphing calculator Press Yz and enter the equations remember X is the button with X T n Press GRAPH You should see your graph on your screen Walk around the room and find a line that looks parallel to yours from another student If you want to see whether the lines are parallel type the equation from the student you found into your calculator as well Just repeat the above instructions and enter the second equation into Y Press GRAPH again Are they similar If t
27. J 3 0 K 3 1 L 3 2 M 3 3 N 3 2 O 3 1 P 3 0 Q 3 1 R 3 2 S 3 3 T 2 3 U 1 3 V 0 3 W 1 3 X 2 3 Now read the following carefully There are three columns given starting point ending point and slope a If you have the starting point and slope you have to state the ending point a If you have the ending point and slope you have to state the starting point a Ifyou have the starting point and ending point you have to state the slope Making the picture Connect each starting point to each ending point What type of shape is created State the y intercepts State the x intercepts TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 63 3 7 1 Y the X Are You Intercepting Me continued TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 64 3 7 3 Y the X Are You Intercepting Me Practice Answer the following questions based on the lines graphed below 1 Which lines have positive slopes 2 Which lines have negative slopes 3 Fill in the table by listing the coordinates for the x intercepts and y intercepts ttt tt w SS eT L A ttt tT tt tT u t SERRE Eee es NL LLL ee SR oh Ae tt tT eT co SAS eee E R es eee LEL Eo dy dlc PE TT TT T T T A UL LLLI SERRE See XM LLL 1l ATT WA E STT A LEI Pa w STT
28. Learning 3 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPS4RM Grade 10 Applied Unit 2 Trigonometry August 2008 2 22 2 RLS Reflecting on Learning Skills Students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the following questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future E Always G Sometimes S Need Improvement N Never Organization e EGSN came prepared for class with all materials e EGSN My work is submitted on time e EGSN keep my notebook organized o a Q ZZZzZ22Z2Z2 attempt all of my homework use my class time efficiently limit my talking to the math topic on hand am on time If am away ask someone what missed complete the work from the day that missed e o oe oe ooooooSgs E am an active participant in pairs group work co operate with others within my group respect the opinions of others e ee 4 Q oocoSg ZZZ lt QOQE ooooo0 Init IT ITI ITI TH amp ITI ITI TI S ITI ITI ITI ITI ITI ITI e N participate in class discussion lessons N When have difficulty seek extra help N After resolve my difficulties reattempt the problem N p G C C C review the daily lesson ideas conc
29. PD ve ae dd ae EE wl ae oe l Describe in your own words how you would calculate the slope of a line given two points without using a graph TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 71 3 8 3 Slopes A way 9 A 25 30 B 35 20 10 E 13 23 F 31 17 11 G 32 21 H 3 16 12 A 7 40 B 11 81 13 E 3 33 F 2 27 14 G 200 100 H 30 6 15 E 12 15 F 20 4 16 E 5 6 F 15 8 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 72 3 8 4 Writing Equations of Lines For each of the following questions Plot the points on the given grid Draw a line connecting the points and extend the line in both directions to the edge of the graph Calculate the slope rate of change using a formula Compare your answer with your graph Using the graph state the y intercept Write the equation of the line in slope y intercept form Verify your equation using a graphing calculator F2 E c x y intercept FERRER FREE EEE EEE SSSR 00 Se PEPPER equation E y intercept Equation fa D oD g ns p g ob D fa TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 73 3 8 4 Writing Equations of Lines continued For each of the following questions Plot the points on the given grid Draw a line connecting the points and extend the line in both
30. Select No To do this use the large circular navpad to move to the right then press the Yes button 1 Add Calculator Next select 1 Add Calculator To do this press the lt button Z 4dd Graphs amp Geometry 3wdd Lists amp Spreadsheet eave Nes You are now ready to use CAS on the handheld nAadd Data amp Statistics Some Helpful Shortcuts If you make a mistake at any point that you want to undo press G 2 If you undo something that you want back again press Q Y How to Solve for a One Variable Equation Example One say that you wish to solve the equation 3x 2 14 To do this first be certain that you are on a Calculator page If you need help with this see the Getting Started section above First type in the equation that you want to solve Use the number pad and the green letter keys the operations x are located on the right and the equals sign is in the top left corner of the keypad When you have typed in the equation press the key found in the bottom right corner DEG AUTO REAL The top of your screen will look something like this 3 x 2 14 3 x 2 14 Now decide how you would start in solving for x DEG AUTO REAL Perhaps you ve decided that subtracting 2 from both sides of the equation is a good start Wonderful To 3 x 2 14 3 x 2214 do this immediately press 25 Notice that the a andheld automatically inserts Ans What is t
31. Systems August 2008 Point of intersection Interpretation of the point Point of intersection Interpretation of the point 4 2 4 Does This Line Cross From the list of relations below determine which lines cross through the point 2 3 You may use the graph to assist you 1 y 22x43 2 y x l1 3 y 2 2x 7 4 y 3 5 X 2 6 y 2 Questions 1 Which of the lines passes through the point 2 3 2 Is there another way to determine if the line passes through the point other than graphing Explain 3 Without graphing how can you quickly determine if a horizontal or vertical line passes through a point 4 Other than the point 2 3 what are the other points of intersection on your graph 5 Is it possible for two lines to have more than one point of intersection with each other Discuss this with your partner TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 20 4 2 5 Is this Accurate 1 Find the point of intersection Solve the system using graphical method a y 2x 1 b y x 2 y 2x d y 5 Point of intersection Is Point of intersection Is TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 21 4 3 1 What s my POI e Each one of you will solve one of the systems of equations given below e Once you have solved the system you were assigned trade with your partner and check their solution Share your feedback with your partner
32. TTET T e l STA Aes Se eee eee 4 Write the equation for line 1 5 Write the equation for line 2 6 Write the equation for line 3 7 Write the equation for line 4 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 65 3 3 Y the X Are You Intercepting Me Practice continued 8 Calculate the x and y intercepts and graph each line on the graph paper on the next page a 3x 2y 6 0 b 5x 2y 10 0 c 3x y 9 0 d 2x 5y 14 0 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 66 3 7 3 Y the X Are You Intercepting Me Practice continued TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 67 3 8 1 Writing Equations of Lines Working with Another Form Some Review 1 What is the slope and y intercept for each line a y 3x 1 2 Using this information graph each of the equations on the grid below Use a different colour for each line and label each line 3 Let s look at another two equations a 3x y 1 0 b 3x 4y 12 20 What are two things you notice are different about these equations when you compare them to the equations in 1 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 68 3 8 1 Writing Equations of Lines continued 4 Calculate the x intercept and the y interce
33. The Descartes Publishing Company charges a flat fee 475 4 50x of 475 plus 4 50 per book School Memories charges a flat fee of y 550 plus 4 25 per book For what amount of books do the two y 550 4 25x companies charge the same amount am solving problem i TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 26 4 3 5 What s My Equation Part 2 continued 1 Looking at your problem how can you tell from the equation which company is cheaper before the point of intersection where the costs are equal 2 Looking at your problem how can you tell from the equation which company is cheaper after the point of intersection where the costs are equal 3 Is this true for all problems 4 Now that you ve solved the problems using two different methods which method do you prefer Why 5 When do you think solving by substitution would be preferable to solving by graphing TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 27 4 4 1 The Lowdown on Downloads Let s return to our music downloading problem Here s the problem again iTones and Music Mine are two online music providers Each company charges a monthly membership fee and then a per song download rate iTones charges 10 per month and 1 per song C x l10 Music Mine charges 7 per month and 1 50 per song C 1 5x 7 1 Find the number of songs that would need to download where the costs are the same for the
34. Which Method Continued Graphing For System C determine if you can solve the system using each of the three methods you have learned and if you can then solve y 2x 7 y 4x 5 Justify why you can or cannot Justification solve using this method Substitution Elimination Justification Justification TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 7 4 The Frayer Model Definition Facts Characteristics Non Examples TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 47 4 7 5 3 Ways Two catering companies provide food and the banquet hall for weddings proms and anniversaries Nick and Heather are getting married in September and they have two catering companies to choose from Cookie s Frugal Gourmet Catering Minestrone Cesaer Salad Soup Chicken Picatta Mixed green Roasted salad Potatoes Prime Rib Steamed Garlic Mashed Vegetables Potatoes Sherbert Asparagus Coffee or Tea Apple Pie Coffee or Tea The cost C for the different menu options Solve the system using the graphing includes the cost of the hall rental and method price per person n Cookie s Catering C 40n 500 Frugal Gourmet C 45n 350 Cookie s Catering Frugal Gourmet 10 20 30 40 50 BU S0 100 Point of intersection TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 48 4 7 5 3 Ways continued oolve the system using substitution
35. at the bottom of the page You need to put the steps under the correct equation in the correct order The steps should be listed in such a way that you would be able to isolate the variable by following these steps Equation 22 3x 7 Equation m 2 6 18 Equation 4k 5 25 Steps Subtract 3 Add 8 Multiply by 2 Subtract 9 Divide by 4 Divide by 6 Divide by 3 Subtract 7 Subtract 6 Divide by negative 8 Multiply by 4 Add 5 Equation 6t 8 34 Equation 21 3 8z Equation x 4 9 1 TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 54 7 13 2 Solving Measurement Problems The area of a rectangle is 72 cm The length is 3 cm What is the width Here is the formula for the area of a trapezoid A a b xh 2 If the Area is 19 5 cm a 7 cm and b 6 cm what is the height of the trapezoid The volume of a rectangular prism is 120 cm The length of the base is 6 cm and the height of the prism is 10 cm What is the width of the base of the prism The area of a triangle is 32 cm The base of the triangle is 4 cm What is the height The volume of a cylinder is given by the formula V rrr h If the radius of the cylinder is 8 inches and the volume is 2411 52 in what is the height of the cylinder The Volume of a square based pyramid is given by the formula 7s I x w x h where is the length of the square base w is the width of
36. axis again Select Translate from the Transform menu On the pop up menu you should have your prior numbers on there already If not translate this point the same as your last point Click Translate Again click on the Line Tool on the left hand side and create a new line with the two new points that you have Select the Arrow Tool on the left hand side click on any white space highlight the new line and Measure the Slope of the new line Click on any white space Answer question 11 on your worksheet Highlight Point A and Point B Measure the Coordinate Distance Click on any white space Measure the Coordinate Distance for Point A and B as well Click on any white space Answer the rest of the questions on your worksheet amp Picture source http www wiley com college musser CL 0471263796 S sketchpad sketchpad tutorial TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 32 3 3 5 Slopes and Stuff on GSP Optional Investigation Worksheet for GSP Describe the graph when the slope is Draw an example greater than 1 What is the difference between the Draw slope 2 on the left and draw slope slope 2 approximately and the 6 on the right slope 6 approximately What happens when slope 0 Draw an example Describe the graph when slope is less Draw an example than 0 What is the difference between slope Draw slope 2 on the left and draw slope 2 and slope 6
37. directions to the edge of the graph Calculate the slope rate of change using the formula Compare your answer with your graph Using the graph state the y intercept Write the equation of the line in slope y intercept form Verify your equation using a graphing calculator y intercept Equation 4 A 4 6 B 12 0 Rise Slope i Run y intercept Equation TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 74 3 8 4 Writing Equations of Lines continued For each of the following questions Plot the points on the given grid Draw a line connecting the points and extend the line in both directions to the edge of the graph Calculate the slope rate of change using the formula Compare your answer with your graph Using the graph state the y intercept Write the equation of the line in slope y intercept form Verify your equation using a graphing calculator gt lt N y intercept Equation E Ed ce a pars 5 m d ni a N M I E m un m y intercept N Equation E ELPI E ras L TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 75 3 9 2 Yes We got no Graph Paper Given points the slope and or the y intercept write the equation in y mx b form for each of the following Given Given slope 5 y intercept 5 M 2 b 3 Given Given Slope parallel to y 2x 7 with t
38. m and b TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 101 Unit 3 Equations of Lines Review continued 12 Draw rough s following lines PTET TTT tT EET TT mower TE triangle for each eee Pitt LL bal LLL tt Ll e EEE EEE b y x 2 oy ee aoe app eet oh d y gr 8 LLL LLL DLL LL LLLI pt Pe LLL LL LLL LL LLL LE Lal LLL LL LL Aidid Answer the following questions based on the lines graphed below 13 Which lines will have positive slopes 1 2 N E L x of L EN Sk 14 Which lines will have negative slopes TET T GB A Lu Tw 15 Fill in the table by listing the coordinates for 1 the x intercepts and y intercepts TST EII Seo eT ETT N B S eee EJ EJ F i E E N i a E E N EJ C E E EJ E LET VLLL eee eee MAE EET EST SEE JEN Eg ee a al w F ra A E E Nn Ms ui E E E ES m TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 102 Unit 3 Equations of Lines Review continued 16 How does knowing the x intercept and y intercept help you to graph a line 17 Graph the following lines by finding the x and y i 10l B 4 intercepts 1 naan i a 3x 2y 620 b 2a2x 5y 1420 Ld B al El E E 18 Find the equation of the line given the point and slope a 2 1 m 3 b 3 4 m 3 4 C 4 5 m 1 d 5 0 m 6 19 Find the equation of the
39. of the following e identify what information the equation tells you about the parabola e factor the equation and identify what the new form of the equation tells you e sketch the parabola using the information you have make sure you plot key points 1 y x 7x 10 4 y x 3 x 2 TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 21 6 9 2 Matching e For each equation in column A state the y intercept e For each equation in column B state the zeros or x intercepts e Each equation in column A has a matching equation in column B Draw an arrow Y x 3x 2 y intercept Y x 3x 10 y intercept Y 2x x 12 y intercept Y x 5x 6 y intercept Y x 6x 8 y intercept Y x 2x 8 y intercept Y x 3x 4 y intercept Y x x 6 y intercept Y 2 x 7x 10 y intercept Y x 3 x 2 x intercepts Y x 3 x 2 x intercepts Y x 4 x 2 x intercepts Y x 2 x 1 x intercepts Y x 3 x 4 x intercepts Y x 5 x 2 x intercepts Y x 5 x 2 x intercepts Y x A x 2 x intercepts Y x 4 x 1 x intercepts TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 22 6 9 3 Quick Sketches of Parabolas For each quadratic function given below dete
40. of the following nets below would create this prism Circle your choice b Explain how you know that you are right c Find the area of each shape in the net that you selected TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 25 7 7 2 Cuboid Creations You will be given 27 linking cubes Your mission is the following a Using all 27 linking cubes create three different rectangular prisms that can be made b Using the isometric dot paper provided draw each of your creations Please note that one of your creations will not be able to be drawn because of size limitations c Fill in the following table for your three creations d What do you notice about the 2 and 4 column e Write your own definition for Surface Area based on what you answered in d TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 26 7 7 3 Net Worth Take a look at the following net finding the area of a triangle is A bxh 2 a Number the shapes in the above net from 1 to 5 b Using the chart below calculate the area of each shape in the above net c What 3 D shape would be formed by this net d What would the surface area of this 3 D shape be TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 27 7 7 4 Isometric Dot Paper e TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 e e e e e e
41. s Do Proportions 1 State whether the ratios are proportional Give reasons to support your answers n 18 p Ll 912 12 27 102 17 8 16 2 Solve each proportion a Ze b es C 2 18 6 7 42 l4 k 3 Solve each proportion a mole b Py C sr 12 10 d 6 8 9 4 Create a proportion from each set of numbers Only use four 4 numbers from each set of numbers a 21 7 18 6 14 b 16 2 1 21 8 C 10 15 20 25 30 TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 24 1 6 2 Solving Those Proportions 1 Solve the following EA TEME C 1 5 3 y 10 d h 25 4 10 5 20 3 6 2 These are two similar triangles a Which proportion could be used to solve for x 24 32 b Now solve that proportion X 1 3 AB is parallel to DE Solve for h and k Hint Redraw the triangles so that the corresponding angles are in the same position B TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 25 1 6 3 Practice 1 Flagpole The flagpole casts a shadow 14 5 m long at the same time that a person 1 8m tall casts a shadow 2 5 m long Find the height of the flagpole Draw a diagram 2 CN Tower The CN Tower casts a shadow 845 8m long A 1 83m tall person standing near the tower casts a shadow 3 05m long How tall is the CN Tower 3 Communication lf two triangles are similar explain in your own words what that means 4 A triangle has sides whose lengths are 5 12 and 13 A similar trian
42. the selection tool then click on Measure and then click on AREA The area will be displayed on the screen Also under the Measure button is a command called TABULATE You can create a table that will allow you to calculate the total area of the rectangle and two circles File Edit Display Construct Transform Measure Graph File Edit Display Construct Transform Measure Graph Instructions gsp Instructions gsp TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 38 7 10 1 Old McDonald Old McDonald wants to paint his barn house and silo The entire barn house and silo will be painted red EXCEPT for the two doors those will be painted white Be aware that it is not possible to paint the bottom of the barn house and silo Here is what the barn house and silo looks like 8m The door of the barn house has dimensions of 5 m wide by 4 m tall Note A silo is a structure for storing bulk materials such as grain coal cement carbon black wood chips food products and sawdust eee eel 14 m The door of the silo has dimensions of 3 m wide by 5 m tall 1 a What is the area of the barn house door that will be painted white b What is the area of the barn house that will be painted red TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 39 7 10 1 Old McDonald Continued 2 a What is the area of the silo door that needs to be painted white
43. to hold the athletic banquet The Algebra Ballroom charges an 800 flat fee and 60 per person The Geometry Hall charges a 1000 flat fee and 55 per person Which location should the school council select for the athletic banquet To solve the question complete the table of values and the graph Algebra Ballroom Geometry Hall Algebra Ballroom vs Geometry Hall Cost 0 20 30 40 50 BO FO 80 390 100 Number of People 1 How can the flat fee and the per person cost be used to draw the graph 2 What is the point of intersection of the two lines What does it represent 3 Under what conditions is it best to go with Algebra Ballroom 4 Under what conditions is it best to go with Geometry Hall TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 11 4 1 2 What s My Equation Continued Problem C The yearbook club is considering two different companies to print the yearbook The Descartes Publishing Company charges a flat fee of 475 plus 4 50 per book School Memories charges a flat fee of 550 plus 4 25 per book Which company should the yearbook club select to print this year s yearbook To solve the question complete the table of values and the graph Descartes School Memories Descartes vs School Memories Number Cost Number Cost of Books of Books S000 vor dt dt oop LLL oot zc LO 150 0 150 Cost 50 10
44. top the first one creating a two layer plank bridge Place the empty cup in the middle of the bridge Repeat step 4 5 Repeat steps 6 8 for a 3 4 and 5 layer plank arch bridge c o0 oco TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 92 3 11 3 London Bridge Is Falling Down Instructions Continued London Bridge Is Falling Analysis Data Tables 1 Place the data from your investigation on the tables below Graphs 2 Use this grid for the questions below TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 93 3 11 3 London Bridge Is Falling Down Instructions Continued Calculations 3 What variable is the x variable independent Circle one Number of Planks or Number of Cubes 4 What variable is the y variable dependent Circle one Number of Planks or Number of Cubes 5 Create a scatter plot from the data of both bridges using a different colour for each data set Label axes with appropriately Create lines of best fit for both sets of data using a different colour for each line From the Beam Bridge line of best fit choose two points Calculate the slope using these two points m 8 Explain the significance of the slope in the context of this activity 9 Using the slope and coordinates of one of the two points calculate the y intercept by substituting into y mx b and solving for b b 10 Write the equation of the Beam Bridge TIPS4RM Grad
45. two music providers 2 Paris solved the problem and then made the following conclusion If you download less than 6 songs per month than choose iTones since the cost per song is less If you download more than 6 songs per month than choose Music Mine since the fixed cost is less If you download exactly 6 songs per month choose either Is the conclusion that Paris made correct If not underline the part s of her conclusion that are incorrect and then rewrite it so that it is correct TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 28 4 4 2 Putting the Pieces Together Continued solve the system y 10 2x and x 2y 10 The steps to the solution to this system are given in the pieces below Cut the pieces out and glue them in the correct order on a separate piece of paper Use the handheld to help you Hint There are 10 steps in the complete solution x 2 10 2x 10 X 20 X II O Point of Intersection 6 2 x 20 4x 10 y 10 12 X 10 2x 10 y 10 2 6 5x 10 20 x 30 5 x 10 10 5x 30 lt We ll No A X 20 X 20 4x 10 x l ho Point of Intersection 2 6 TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 m n O TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 30 4 4 3 An Interesting Problem Consider the following three systems of equations xX 2y S3and 4x 5y 6 2x y 4and 7x 10y 1
46. when expected Both mathematical and narrative forms are present but the forms are not integrated Connecting Makes simple connections Makes simple connections accurately and logically sequenced Correctly interprets the information and makes reasonable statements Consistently uses mathematical symbols labels and conventions correctly Consistently uses mathematical vocabulary correctly when expected Both mathematical and narrative forms are present and integrated Makes appropriate connections Makes appropriate connections TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 and logically sequenced Correctly interprets the information and makes subtle or insightful statements Consistently and meticulously uses mathematical symbols labels and conventions recognizing novel opportunities for their use Consistently uses mathematical vocabulary correctly recognizing novel opportunities for its use A variety of mathematical forms and narrative are present integrated and well chosen Makes strong connections Makes strong connections 7 9 1 Cylinder Nets Your Challenge Take a look at the three drawings below Only one of them can be cut out and turned into a cylinder Select the one that you think will form the cylinder Cut it out to see if you made the right choice If you did you should be able to assemble a cylinder Optio
47. will require two equations to solve it The equations that are needed to solve each problem appear at the bottom of the handout Match the equations with the problems and compare your answers with another student Note There are more equations than problems and all the equations use x for the independent variable and y for the dependent variable Problem A Equations Yasser is renting a car Zeno Car Rental charges 45 for the rental of the car and 0 15 per kilometre driven Erdos Car Rental charges 35 for the rental of the same car and 0 25 per kilometre driven Which company should Yasser choose to rent the car from Problem B Equations The school council is trying to determine where to hold the athletic banquet The Algebra Ballroom charges an 800 flat fee and 60 per person The Geometry Hall charges a 1000 flat fee and 55 per person Which location should the school council select for the athletic banquet Problem C Equations The yearbook club is considering two different companies to print the yearbook The Descartes Publishing Company charges a flat fee of 475 plus 4 50 per book School Memories charges a flat fee of 550 plus 4 25 per book Which company should the yearbook club select to print this year s yearbook Problem D Equations The school is putting on the play Algebra The Musical Adult tickets were sold at a cost of 8 and student tickets were sold at a cost of 5 A total of 220 tickets were sol
48. y 1 Work in pairs to consider the following linear systems Decide what operation addition or subtraction would result in the elimination of a variable You may use CAS on the handheld to help you decide OX y 4 3X y 50 X 6y 338 14x y 1 12x y 115 9x 6y 366 18x 5y 454 19x 2y 102 Lyx CY 323 12x DW S16 19x 2y 50 6x 8y 114 Ox 4y 235 7X 16y 441 5x 3y 188 15x 2y 409 7x 17y 476 6x lly 344 2 What needs to be true about a linear system so that a variable is eliminated when the equations are added or subtracted TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 35 4 5 3 Solving a Linear System by Elimination 1 How would you begin solving this linear system Addition or Subtraction 5X 4y 7 3x 4y 17 2 Solve the system 3 In your own words describe what you must do to solve a linear system by elimination 4 36 TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 6 1 What s the difference x 2y 6 Original equation The new equation is Multiply the equation by the constant Complete the table of values for your equation and plot the values on the grid provided dD AJAS a eee AAS A AAA Pee ASSAS Pee ASAS Pee ASST AAAA Pees AJS Ree ASA tt eee eee rte tt tt da EE ER RRR Lees ERR Pees ERR Ree Lees ot tT ttt da Tt ERR Ree Lees ptt tt tT da tT ilillill ot ttt ttt tr tt tT L
49. 0 1 3 2 Growing and Shrinking Triangles Investigation Find the area and perimeter of the triangle If another triangle of the same shape has a perimeter that is double what is the effect on the area If another triangle of the same shape has a perimeter that is half what is the effect on the area Hypothesis If one triangle of the same shape has double the perimeter of the original triangle the resulting area of the triangle would be Complete the investigation Show your work and explain your reasoning Generalize by stating the relationship between the perimeter and the area of similar triangles State a conclusion based on your work This conclusion may be based on your original hypothesis TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 11 1 4 1 What is Similarity What does it mean if we say that 2 objects are similar see if you can find out by using the clues below Hint Use a ruler and a protractor to make measurements Clue 1 These 2 objects are similar Clue 2 These 2 objects are not similar Clue 4 These 2 objects are not similar Clue 6 These 2 objects are not similar Clue 8 These 2 objects are not similar Did you get it What do you think similarity means Formal Definition of Similarity TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 12 1 4 1 What is Similarity continued In each question decide if the objects are similar yes or no and the
50. 0 150 200 250 300 350 400 450 500 Number of Books 1 How can the flat fee and the cost per book be used to draw the graph 2 What is the point of intersection of the two lines What does it represent 3 Under what conditions is it best to go with Descartes Publishing 4 Under what conditions is it best to go with School Memories TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 12 4 1 2 What s My Equation continued Problem D The school is putting on the play Algebra The Musical Adult tickets were sold at a cost of 8 and student tickets were sold at a cost of 5 A total of 220 tickets were sold to the premiere and a total of 1460 was collected from ticket sales How many adult and student tickets were sold to the premiere of the musical To solve the question complete the table of values and the graph Let x represent the of student tickets sold Let y represent the of adult tickets sold Algebra The Musical X X 40 40 Number of Adult Tickets 20 40 BO S0 100 120 140 160 180 200 Number of Student Tickets 1 What is the approximate point of intersection of the two lines What does it represent 2 Does the rest of the graph other than the POI give us any information about the number of tickets sold TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 13 4 1 3 Meaning of the Point of Intersection 1 Your family wants to rent a car for a weekend trip Ca
51. 10 Applied Unit 2 Trigonometry August 2008 2 14 2 6 3 Applications of Trigonometry Assignment continued Analysis 1 If you were to measure the height of a light sticking out from a post could you use today s method Explain why or why not LIGHT 2 Darla is standing 15 m from the base of a building and using a clinometer she measures the angle of elevation to be 37 If her eyes are 1 65 m above ground level find the height of the building TIPS4RM Grade 10 Applied Unit 2 Trigonometry August 2008 2 15 2 1 Applying Trigonometry Use BLM 2 7 2 to organize your solution steps Then solve the application questions Find angles to the nearest degree and distances to the nearest tenth of a unit 1 A ladder is leaning against a building and makes an angle of 62 with level ground If the distance from the foot of the ladder to the building is 4 feet find to the nearest foot how far up the building the ladder will reach 3 A ship on the ocean surface detects a sunken ship on the ocean floor at an angle of depression of 50 The distance between the ship on the surface and the sunken ship on the ocean floor is 200 metres If the ocean floor is level in this area how far above the ocean floor to the nearest metre is the ship on the surface TIPS4RM Grade 10 Applied Unit 2 Trigonometry August 2008 2 The Dodgers Communication Company must run a telephone line between two poles at opposite en
52. 2 92 ABMeWay a 433 Putting the Pieces Together J a The Sub Way 025 435 What s My Equation Part 2 26 44i The Lowdown on Downloads 2 442 Putting the Process Together An Interesting Problem 08 aaa Thesubseps i 3 451 ATiiptodimHorions a 452 An Elimination troduction 36 _ 98 89 OD NE NN 92 NE NEN Solving a Linear System by Elimination 37 Elimination Preparation Algebra the Musical Redux Two for You Two for You A65 Help an Absent Friend 466 Here stothe Crazy Ones Which Method ATS 3Wam 0 O oB 4S UmtSummay 2 AR Reflecting on My Learning 3 2 1 53 ARLS Reflecting on Learning Skills 5 TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 2 Nspire CAS Handheld Manual Getting Started When you turn on the handheld press C You will be asked whether you want to save the cu OW uer Wu eee ante Cio ie nie document Select No To do this use the large circular navpad to move to the right then press the Yes amp button in the middle of the navpad 1 Add Calculator Next select 1 Add Calculator To do this press the button again Z Add Graphs amp Geometry 3wdd Lists amp Spreadsheet eda Masi You are now ready to use CAS on the handheld pAdd Data amp Statistics Some Helpful Shortcuts If you make a mistake at any poin
53. 3 5x 3y 1 and x 3y 5 1 In order to solve these systems by substitution we need to first isolate one variable in one equation Circle the variable in each system that would require just one step to isolate Compare your choice with a neighbour 2 Using your handheld to help you isolate the variable you selected in 1 for each system 3 Assign each system to one person in your group and solve the system assigned to you in the space below Use your handheld to help solve and check am solving system 4 Compare your solution to the rest of the group What do you notice TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 31 4 4 3 An Interesting Problem Continued 5 The chart below lists out only the numbers that appear in each system What do you notice about the numbers in each system SystemA SystemB 1 2 9 4 5 0 22 1 4 7 10 13 5 35 T 1 3 5 6 Let s see if this works with more systems Each system below has only one equation given Assign each system to one person in the group and create a second equation that will give the solution 1 2 when solved SystemA SystemB Equation 1 x 6y 11 Equation 1 14x 9y 4 Equation 1 9x 7y 2 5 Equation 2 Equation 2 Equation 2 7 Share your equation with everyone in the group and copy down the equations from the rest of the group Review the equations created and make sure they follow the rul
54. 6 Quadratic Relations of the Form y ax bx c August 2008 6 17 6 7 1 Investigate Relations of the Form y ax D continued 6 Fillin the following table Clear the y screen on one of the four calculators enter the factored form of the four equations and graph Are these graphs the same as the ones in your sketch If yes continue to question 8 If no revise and check Ask your teacher for assistance if needed 8 Can the equations in the third column of your table be simplified Explain 9 Record the simplified versions of your relation in factored form TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 18 6 7 2 Factoring x bx Consider the outer portion of the algebra tile representation as the length and width of a room The rectangle is the carpet Colour in as many cells as required for each example to form a rectangle To factor form a rectangle using the tiles then determine the length and width of the room xX 2x Example 1 Example 2 x 3x factored form the coordinates of the x intercepts of y xX 2x and the coordinate of the y intercept _ Use your algebra tiles to factor the following 1 x 4x factored form the coordinates of the x intercepts of y x Ax and the coordinate of the y intercept 3 x 5x _ factored form the coordinates o
55. 6 on the right TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 33 3 3 5 Slopes and Stuff on GSP Optional Investigation continued 6 When you are changing the slope what stayed the same What happens when the y ordinate Draw an example What happens when the y ordinate Draw an example 6 When you are changing the y ordinate what stayed the same 10 In the equation y mx b which letter does slope represent What about the y ordinate TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 34 3 3 5 Slopes and Stuff on GSP Optional Investigation continued 11 What do you notice about these two lines 12 What do you notice about the two Write down the two coordinate distances coordinate distances here 13 Because the two coordinate distances Was your hypothesis correct from question are the same what does that mean 11 about the two lines TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 35 3 3 6 Slopes and Stuff Practice From the graph below label each point with a name A B etc name each slope state whether the slope is positive or negative calculate the slope and state any parallel slopes 15 Distane Time h Slope Slope Slope Slope Slope Parallel slopes TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008
56. 8 7 33 7 8 4 Planter s Dilemma Rubric Selecting Computational Strategies Selects and applies appropriate strategies Selects and applies the most appropriate strategies accurately Selects and applies appropriate strategies with major Selects and applies appropriate strategies with Select and use strategies to solve a problem Ability to read and interpret mathematical language charts and graphs Correct use of mathematical symbols labels units and conventions Appropriate use of mathematical vocabulary Integration of narrative and mathematical forms of communication Make connections among mathematical concepts and procedures Relate mathematical ideas to situations drawn from other contexts errors omissions or mis sequencing Misinterprets a major part of the information but carries on to make some otherwise reasonable statements Sometimes uses mathematical symbols labels and conventions correctly Sometimes uses mathematical vocabulary correctly when expected Either mathematical or narrative form is present but not both Makes weak connections Makes weak connections minor errors omissions or mis sequencing Communicating Misinterprets part of the information but carries on to make some otherwise reasonable statements Usually uses mathematical symbols labels and conventions correctly Usually uses mathematical vocabulary correctly
57. M Grade 10 Applied Unit 3 Equation of Lines November 2008 3 106 3 5 Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit Summary TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 107 3 R Reflecting on My Learning 3 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 108 3 RLS Reflecting on Learning Skills Students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the following questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future E Always G Sometimes S Need Improvement N Never Organization e EGSN came prepared for class with all materials e EGSN My work is submitted on time e EGSN keep my notebook organized o a em Q ZZZZ22Z2Z2 attempt all of my homework use my class time efficiently limit my talking to the math topic on hand am on time If am away ask someone what missed complete the work from the day that missed ii LE oodoooogsSg D Q x e ITI FTH ITI mae ITI ITI ITI Ss TI ITI TTI TI TI TTI am an active participant in pairs group work co operate with others within my group respect the opinions of oth
58. M2P Unit 6 Quadratic Relations of the Form y ax bx c Dufferin Peel Catholic District School Board a Unit 6 Quadratic Relations of the Form y ax bx c Section Activity Graphing Quadratic Relations Multiply a Binomial by a Binomial 04 6 3 1 Finding the Y intercept of a Quadratic m Equation Quadratic Equations Finding the X intercepts of a Quadratic Eu Equation Making Connections to the Graph Match f Use Intercepts to Graph It 6 7 1 Investigating Relations of the Form 17 y ax b Graphing Relations of the Form yex a 6 9 3 Quick Sketches of Parabolas 23 ve eRe a Investigating Parabolas FRAME Function Representation And a Model Sahin 6R Reflecting on My Leaning 8 2 1 33 TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 2 6 1 2 Graphing Quadratic Equations Name 1 Obtain a pair of equations from your teacher 2 Press the Zoom button and press 6 for ZStandard to set the window to make the max and min on both axes go from 10 to 10 3 Press the y button and key in your two equations into Y4 and Y To change the graph of Y to animation Move the cursor to the left of Y2 Press Enter four times to toggle through different graph styles available You shoul 5 Press Graph First the Y quadratic will appear then the Y quadratic will appear and be traced by an open circle 6
59. Sham City has been carefully reviewed They were so impressed with the plan that they have decided to also have you install an irrigation system throughout the park They need a cost proposal from you to see if they can afford this drip and soaker system in addition to the cost of the sod and hedges Note You will need to refer to your answers from the previous lesson activity for Sham City to complete this cost proposal Part A The SOD 1 There is a by law in Sham City that states that all city parks must have an underground drip sprinkler system The city gives you the design below that indicates approximately where the plastic underground pipes must go EN a If pipes come in 5 m lengths how many pipes need to be purchased for the underground sprinkler system oprinkler Pipe b What will the cost be if each length costs 7 19 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 19 7 5 1 Job Opportunity Continued c The sod requires plenty of water for optimal growth The ratio of 1 m of water for every 25 m of sod is needed daily How many cubic meters of water are required daily for the sod to grow d If it costs the city 0 03 ft of water how much will it cost to water the park daily Part B The Hedge 1 To make sure the hedge receives enough water the city needs to place an underground irrigation system that is made specifically for hedges called a soaker line
60. WN 22229 et ow Ze ooeoos ee oe o I rm m m x G C C Yes No know all the different ways available in my school where can seek extra help Yes No tried my best What will do differently in the next unit to improve TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 37 TIPS4RM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 38 TIP 0 Targeted Implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MFM2P Unit 2 Trigonometry Dufferin Peel Catholic District School Board REVISED August 2008 Unit 2 Trigonometry Section Activity What s My Ratio Group Activity What s My Ratio Individual Heflection 241 What sMyTriangle 6 251 GongtheWrongWay B 252 TangentorSomething 9 Assignment oll alle 3 Assignment TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 2 ly Fill in each of the columns with information for your triangle IVI What s My Ratio Group Acti 2 1 2 juaovnlpo asnuajodAy asnuajodAy azisoddo juaov ipo ajsoddo S33e d euro p 044 0 ONLI 21 23UTULI2 9 3prs ju22e pe Jo ysu apis 33150d do ysu asnuajodAy Jo ysu 43333 3335 V 2 3 TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 1 3 What s My Ratio Individual Reflection 1 If you hav
61. aphs with your work Definition Facts Characteristics Parabola Non examples TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 11 5 4 2 Quadratic Power Modelling Canada s Baby Boom Your Task The Baby Boom occurred right after World War II Determine if a parabola can be a useful model for the number of births per year for this post war Baby Boom period Procedure To access Canada s Baby Boom data 1 Open the E STAT website at http estat statcan ca 2 Select your language of choice Click Accept and Enter at the bottom of the screen 3 Click Search CANSIM on the left side bar and then click Search by Table Number 5 In the blank box type 053 0001 to retrieve Table 053 0001 Vital statistics births deaths and marriages quarterly 5 On the subset selection page choose as follows e Under Geography select Canada e Under Estimates select Births e Under From select Jan 1950 e Under To select Dec 1967 6 Click the Retrieve as Individual Time Series button 7 Inthe Output specification screen under output format selection click the down arrow and select Plain Text Table Time as Rows 8 From The frequency of the output data will be pull down menu select Converted to Annual Sum 9 Press the Go button Year Births 10 Record the data on a sheet of paper using the following headings Year and Births Graphing Calculator Analysis 1 Create a B
62. are horizontal Underline the equations of lines that are vertical a x 7 b y 3 C X 3 d y 5 e y 3x 6 f y 2 5 Complete the sentences by filling in the blanks Horizontal Lines a The equations of all horizontal lines are of the form b The slope of a horizontal line is c Horizontal lines do not cross the axis Vertical Lines a The equations of all vertical lines are of the form b The slope of a vertical line is c Vertical lines do not cross the axis TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 99 Unit 3 Equations of Lines Review continued Write the equation of each line Graph and label the lines A x 3 B y 6 C y 5 8 a When the equation of a line has the form y mx b m is the of the line and b is the b State the slope and coordinates of the y intercept for each i y x 4 i y 3x ii y 2x 5 9 Write the equation of each line given a slope 5 and y intercept 3 b b 7 m 12 c slope of 2 and passing through A 0 4 d slope parallel to y 3x 7 with same y intercept as y 8x 19 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 100 Unit 3 Equations of Lines Review continued 10 Find the equation of each line a b a b c V db c d x 11 State two possible equations for each line y y a b X X 1 1 2 2 C Justify your choices for
63. at is the slope What does the b represent TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 2 2 Exploring an MB Eh continued What does the equation tell you y 4x 1 y 7 X 2 yx y 2X y x 10 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 2 4 Why Mr Y depends on the independent Ms X Complete the tables on the next two pages that compare and contrast terms equations tables of values and graphs between grade 9 and grade 10 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 24 3 2 4 Why Mr Y depends on the independent Ms X Continued TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 25 3 2 4 Why Mr Y depends on the independent Ms X Continued Complete the following table for each equation given Provide a different context for each row if possible travels C 2 50d 5 C represents Y225x45 2 50 km 5 starting fee COStando represents distance a cab T m H om TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 26 3 3 1 Slopes and Stuff on TI 83 Instructions for TI 83 Ok if you follow this step by step it will be fool proof Let s start Press ON Press APPS Scroll and find TRANSFRM Press ENTER Select UNINSTALL by pressing ENTER Press APPS again Scroll and find TRANSFRM Press ENTER Now the screen shoul
64. bic feet Are there any lengths that need to be converted If so convert them TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 51 7 12 1 Pumping Up the Volume Continued 5 Calculate the volume for each section Use the space below to organize your work Object A Object B Object C Object D Object E Object F E MEME 6 Determine the total volume of the swimming pool in cubic feet TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 52 7 12 2 Pool Management The building code indicates that when filling swimming pools there must be a 6 inch gap between the water level and the top of the pool at ground level Using your results from 7 11 1 Pumping Up the Volume calculate the volume of water that is needed to fill the pool so that it can meet the building code Steps 1 Sketch the volume of the space that will not have water 2 Label the dimensions needed 3 Calculate the total volume of water that will be in the pool if the building code is to be followed 4 The chlorine to water ratio is 130 grams to 10 OOOL If chlorine is purchased in 130 gram bags determine the amount of chlorine that is needed in kilograms to chlorinate the pool 1 ft 28 3168 Litres TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 53 7 13 1 Feeling Isolated Look at the following equations Next look at the steps that are
65. ct whose height you cannot measure Person 1 Walk at least 20 large steps away from the object Place your eye as close to the ground as possible and close your top eye Your job will be to line up the top of the metre stick with the top of the object Person 2 Place the metre stick between Person 1 and the object The metre stick must be kept at a 90 angle with the ground Slowly move the metre stick towards or away from the object on the instructions of Person 1 Hold still when Person 1 has lined up the objects Persons 3 and 4 Measure the distance from Person 1 to the metre stick Then measure the distance from Person 1 to the object Draw similar triangles representing this situation in the space below Label the diagram and indicate all known measurements with units Write the proportion needed to find the desired height 7 Calculate the height of the object Show your work TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 30 1 8 1 Eye eye eye Hurricanes are violent storms which form over the warm waters of the oceans Each year hurricanes cause millions dollars of damage when they hit coastal areas Hurricanes can produce winds with speeds up to 241 or more kilometres per hour The centre of a hurricane is called the EYE Inside the eye of a hurricane there is almost NO WIND The air is perfectly calm and just outside the eye are the most violent winds of the storm How far across is the eye of thi
66. d say PRESS ANY KEY so press any key to continue Your screen will say DONE Press Yz grey button white font top left You now need to enter AX B Do you see all the green letters on the calculator You can get to them by pressing the ALPHA button green button white font So to get A you need to press ALPHA then MATH See X is the button to the right of the ALPHA button the button with X T n The sign you can find for sure and can you figure out how to type B So now you should have AX B entered on the screen A few more steps and we re ready to graph Press WINDOWS ocroll up once so that SETTINGS is highlighted Scroll down and change A to 1 change B to 1 and change Step to 1 Ok you re ready Press GRAPH Scroll right and left to see what happens to A If you want to play with B scroll down once so that the equal sign for B is highlighted and then scroll right and left as well to change B Picture Source http education ti com educationportal sites US productCategory us_graphing html TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 27 3 3 2 Slopes and Stuff on TI 83 Investigation Worksheet for graphing calculator 1 Describe the graph when A is greater Draw an example than 1 What is the difference between A 2 Draw A 2 on the left and draw A 6 on and A 6 the right What happens when A 0 Draw an example Describe the graph when A is less than
67. d to the premiere and a total of 1460 was collected from ticket sales How many adult and student tickets were sold to the premiere of the musical EQUATIONS 1 y 4 50 475x 2 60 800x y 3 y 1000 55x 4 x 45 0 15x 5 Y 1000x 55 6 y 45 0 15x 7 X y 220 8 5x 8y 220 9 y 4 25x 550 10 y2 550x 4 25 11 y 800 60x 12 x y 1460 13 y 2 0 25x 35 14 y 2 4 50x 475 15 y 2 85x 0 25 16 5x 8y 1460 TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 9 4 1 2 What s My Equation Continued Problem A Yasser is renting a car Zeno Car Rental charges 45 for the rental of the car and 0 10 per kilometre driven Erdos Car Rental charges 35 for the rental of the same car and 0 25 per kilometre driven Which company should Yasser choose to rent the car from To solve the question complete the table of values and the graph Zeno vs Erdos Zeno Erdos Cost 10 20 30 40 50 60 F70 60 90 100 Kilometers Driven 1 How can the car rental cost and the cost per kilometre be used to draw the graph 2 What is the point of intersection of the two lines What does it represent 3 Under what conditions is it best to rent from Zeno Car Rental 4 Under what conditions is it best to rent from Erdos Car Rental TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 10 4 1 2 What s My Equation Continued Problem B The school council is trying to determine where
68. ds of a lake as shown below The length and width of the lake is 75 feet and 30 feet respectively tt Pole 1 What is the distance between the two poles to the nearest foot 4 Draw and label a diagram of the path of an airplane climbing at an angle of 11 with the ground Find to the nearest foot the ground distance the airplane has traveled when it has attained an altitude of 400 feet 2 16 2 7 2 Trigonometry Getting it together Use the following chart to analyze the applications given in the problems on BLM 2 7 1 What is given What angle and side measurements are stated in the problem What is required What angle and side measurements do you need to find What tools can be used to solve the problem Name a trigonometric ratio li TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 17 2 3 Applying Trigonometry Solve the application questions Draw a diagram where necessary Find angles to the nearest degree and distances to the nearest tenth of a unit Buffalo 280 miles Albany poh Dame a T im j i 470 miles E it New York City 1 lf an engineer wants to design a highway to connect New York City directly to Buffalo at what angle x would she need to build the highway Find the angle to the nearest degree To the nearest mile how many miles would be saved by travelling directly from New York City to Buffalo rather than by travelling
69. dure 1 Build the following sequence of models using the cubes Note The pool is the shaded square the tiles are white 2 Build the next model in the sequence 35 Mathematical Models Complete the table including first and second differences j Make a scatter plot and a line of best fit 29 20 TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 4 5 1 3 Going Around the Curve Experiment C A particular mould grows in the following way If there is one blob of mould today then there will be 3 tomorrow and 6 the next day Model this relationship using linking cubes Purpose Find the relationship between the number of cubes in the bottom row and the total number of cubes Hypothesis What type of relationship do you think exists between the number of cubes in the bottom row and the total number of cubes Procedure 1 Build the following sequence of models using the cubes SE Bs ER 2 Build the next model in the sequence Mathematical Models Complete the table including first and second differences Make a scatter plot and a line of best fit TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 5 5 1 4 Going Around the Curve Experiment D Luisa is designing an apartment building in a pyramid design Each apartment is a square She wants to know how many apartments can be built in this design as the number of apartments on th
70. e ground floor increases Model this relationship using linking cubes Purpose Find the relationship between the number of cubes in the bottom row and the total number of cubes Hypothesis What type of relationship do you think exists between the number of cubes in the bottom row and the total number of cubes Procedure 1 Build the following sequence of models using the cubes Ej 2 Build the next model in the sequence Mathematical Models 24 Complete the table including first and second differences 22 Make a scatter plot and a line of best fit TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 6 5 1 5 Going Around the Curve Experiment E Liz has a beautiful pond in her yard and wants to build a tower beside it using rocks She is unsure how big she will make it and how many rocks she will need She is particularly concerned to have the nicest rocks showing Model the relationship comparing the length of the base to the number of visible rocks using linking cubes Purpose Find the relationship between the number of cubes on the side of the base and the total number of unhidden cubes Hypothesis What type of relationship do you think exists between the length of the side of the base and the number of visible cubes Procedure 1 Build the following sequence of models using the cubes 2 Build the next model in the sequence 24 Mathematical Models 22 Complete
71. e 10 Applied Unit 3 Equation of Lines November 2008 3 90 3 11 3 London Bridge Is Falling Down Instructions Continued 4 Place the first bridge plank such that the ends of each plank touch the masking tape as shown below 5 Next place the plastic cup in the middle of the Beam Bridge 6 Place a linking cube into the cup gently Continue placing one linking cube at a time until the bridge collapses The bridge must touch the desk for it to be considered a collapse 7 Record this data on the data collection sheet provided 8 Place another plank over top the first one creating a two layer plank bridge as ole E a 9 Place the empty cup in the middle of the bridge 10 Repeat step 6 7 11 Repeat steps 8 10 for a 3 4 and 5 layer plank beam bridge TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 91 3 11 3 London Bridge Is Falling Down Instructions Continued 1 The next design is to create an arch bridge Using the same textbooks and setup as the last bridge place the unfolded piece of paper between the textbooks to form an arch as shown below 2 Place one of the planks from the last activity on top of the arch making sure the ends of the plank coincide with the tape 3 Place the empty cup in the middle of the plank 4 Add linking cubes one at a time until the bridge collapses Record this data on the data collection sheet provided Place another plank over
72. e 10 Applied Unit 3 Equation of Lines November 2008 3 94 3 11 3 London Bridge Is Falling Down Instructions Continued 11 From the Arch Bridge line of best fit choose two points Calculate the slope from these two points 12 Explain the significance of the slope in the context of this activity 13 Using the slope and coordinates of one of the two points calculate the y intercept by substituting into y mx b and solving for b TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 95 3 11 3 London Bridge Is Falling Down Instructions Continued 14 Write the equation of the Arch Bridge 15 You want to be sure that a bridge can hold 100 cars at one time If each car is represented by a linking cube how many planks would your bridge need Show work below 16 You recently saw two bridges hold 250 cars at once How many planks would be required to hold those cars for both bridges Show work below TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 96 3 11 3 London Bridge Is Falling Down Instructions Continued Reflection 17 What are the x intercepts of both graphs Interpret their significance in the context of this activity 18 Which bridge presents a better design Offer mathematical proof using data you collected and calculations you did 19 One of your friends says the she constructed an amazing bridge but the plans were lost The only thing left was the e
73. e Form y ax bx c August 2008 6 12 6 4 3 Factoring Using Algebra Tiles and Making Connections to the Graph continued 3 standard form y x 6xt 5 factored form 3 y intercept first x intercept second x intercept 4 standard form y xt 4x 4 factored form 3 y intercept first x intercept second x intercept 5 In what way is the last example different from the others TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 13 6 5 2 Factored Form and x Intercepts Name Use algebra tiles to find the length and width for each given area Use the graphing calculator to find the x intercepts of the corresponding quadratic relation Graph both the area model and factored form of the quadratic relation to check that these are the same before finding the x intercepts X 4x 3 X 5x 6 X 6x48 X6 Tx 12 1 What do you notice about the constant term in the length and width expressions and the coefficient of the x term in the area expressions 2 What do you notice about the constant term in the length and width expressions and the constant term in the area expressions 3 Ifan area is expressed as X 10x 21 what must be true of the constant terms in the length and width expressions 4 Ifthe standard form of a quadratic relation is y X bx c and it has x intercepts of rand s then the same relation would then be y
74. e Once you have shared your feedback and are confident in the solutions to the systems post your point of intersection under the appropriate heading on the class list Point of Intersection Point of Intersection TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 22 4 3 2 A Better Way Solve the following systems of equations algebraically Use your CAS handheld to solve and check if needed 1 Equation 1 y 2 10 and Equation2 x y 12 Point of intersection 2 Equation 1 3x 2y 33 and Equation 2 2x X 7 Point of intersection In each of the systems you solved above which equation did you choose to solve first Why did you select that equation in each case TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 23 4 3 3 Putting the Pieces Together System 1 y 2x and y 3x 4 Record the line that results once you have substituted and then solve the equation using your CAS handheld Resulting equation and my solution Don t forget to solve for both variables Check your solution using the CAS handheld Compare your solution to someone else in the class System 2 2x y 2 0 and x y 12 Record the line that results once you have substituted and then solve the equation using your CAS handheld Resulting equation and my solution Don t forget to solve for both variables Check your solution using the CAS handheld Compare your s
75. e a fifth triangle that is similar to your four triangles what would your hypothesis be about the following ratios Explain opposite _ adjacent _ opposite _ hypotenuse hypotenuse adjacent Explanation Explanation 2 Identify a relationship between the ratios in the chart for opposite nd adjacent hypotenuse hypotenuse i 3 Identify a relationship if you divide the ratio for CORO E for one of the angles TIPS4RM Grade 10 Applied Unit 2 Trigonometry August 2008 hypotenuse Explanation adjacent hypotenuse 2 4 2 3 1 Who Uses Trigonometry Project Content Choose a career of interest that uses trigonometry Suggestions Aerospace Archaeology Astronomy Building Carpentry Chemistry Engineering Geography Manufacturing Navigation Architecture Optics Physics Sports Surveying Process Decide how you will learn more about the use of trigonometry in your chosen career Suggestions Internet research text research interview job shadow job fair Product Select the way you will share what you learn Suggestions skit newspaper story brochure poster electronic presentation photo essay verbal presentation report Personal Selection Chart Teacher s comments and suggestions e Your final submission must include the following the career activity investigated a brief description of your process description of the career activity including how trigonometry plays a role list of s
76. e build html Before a bridge is constructed engineers design models to ensure that the bridge can withstand the stress of the load from cars and people In today s activity you will be working in groups of three Your group will construct two bridge designs out of paper the Plank Bridge and the Arch Bridge Using linking cubes you will record the number of cubes needed to make each bridge collapse at various paper thicknesses Group Member Responsibilities Name 9 Minds On Card Appointed Job y mx b Data Recorder Records information from the activity Slope and Y intercept Materials Manager Collects all the materials needed Prepares paper and books Standard Form Model Designer Creates each bridge model and adds the load to the bridge model TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 89 3 11 3 London Bridge Is Falling Down Instructions 1 Have the materials manager collect 30 linking cubes a piece of masking tape a plastic cup and 6 pieces of paper Your teacher may have already cut the paper for you by cutting a standard sheet of 8 5 x 11 in half as shown below 2 Fold 5 pieces of paper as shown below These will be call you bridge planks 2 cmt SO teen SS 8 5 3 Place a piece of masking take 2 cm from the edge of two textbooks Make sure the spines of each book are facing outside as shown below MALHEOWER ERIPIIITETTRERTT TIPSARM Grad
77. e crazy co workers are calling for their cup o joe Unfortunately since the morning fix hasn t arrived yet no one can remember how much a small or extra large coffee costs including yourself You need to find out how much each size costs to collect the correct amount of money for the Wednesday coffee run 1 Let s be the number of small coffees ordered on a single day Let e be the number of extra large coffees ordered on a single day As a class can we decide on an equation to represent the purchases made on Monday and an equation to represent the purchases made on Tuesday Monday s equation Tuesday s equation 2 Now we have a linear system Take a few minutes to solve the linear system using substitution in the space below Then pair with another student to discuss your solution 3 What problems if any did you encounter TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 34 4 5 2 An Elimination Introduction You know that two integers can be added or subtracted 5 15 To 6 12 9 In the same way equations can be added or subtracted 3x 2y 19 10x 20y 80 t 5x 2y 5 10x 15y 25 8x 24 SY 22 Notice that by adding the equations in the first linear system the y variable was eliminated there were Oy which makes it possible to solve for x By subtracting the equations in the second linear system the x variable was eliminated there were Ox which makes it possible to solve for
78. e greatest number of grade 10 students they can have at the lunch Point of intersection What does the ordered pair 25 750 mean on the Lunch Express line TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 51 4 S Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit Summary TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 52 4 R Reflecting on My Learning 3 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 RLS Reflecting on Learning Skills students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the following questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future E Always G Sometimes S Need Improvement N Never Organization e EGSN came prepared for class with all materials e EGSN My work is submitted on time e EGSN keep my notebook organized o a em Q ZZZZ22Z2Z2 attempt all of my homework use my class time efficiently limit my talking to the math topic on hand am on time If am away ask someone what missed complete the work from the day that missed e oe oe oe eO NNNnNHnHHnHASG x am an active participant in pa
79. e is how to do this on a handheld First be certain that you are on a Calculator page If you need help with this see the Getting Started section from earlier in this manual Press the following keys 35 552500 53 P 00 DP What you have typed should look like this RAD AUTO REAL Press the key The handheld will display the result RAD AUTO REAL i Now we havea system that we 6x 15y 21 can begin to solve by subtracting the equations 3 2 3 5 y 3 7 6 x 15 y 21 f TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 6 4 1 1 Working on Commission Nahid works at Euclid s Electronics She is paid a salary of 200 per week plus a commission of 5 of her sales during the week The equation P 0 05s 200 represents Nahid s pay for the week where P represents the total pay for the week and s represents her total sales If Nahid earned 290 in a week use the Euclid s Electronics Wages equation to algebraically determine how S00 much she sold Use your handheld to help you solve Refer to the user manual if you need to review how to solve using the handheld Week s Pay 1000 1500 2000 2500 Total Value of Sales Nahid is offered another job at Fermat s Footwear where the pay is a salary of 100 per week and 1096 commission on all sales The graph below represents the Pay vs Sales for this job Which of the following equations do you think represents pay for one week at Fermat s Foo
80. e quart of paint is enough to paint 10 ft how many quarts will Joe need to buy in order to paint his 10 flower pots 4 Joe has some other decisions to make about his flower pots Take a look at two of the other flower pots that Joe could have bought Open top 9 inches 9 inches What would the height of the each of these two flower pots have to be in order to need exactly TWICE as much paint as one of Joe s current flower pots TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 31 7 8 2 Planter s Dilemma Continued 4 continued Square Based Prism Square Based Pyramid TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 32 7 8 3 Applications 1 Find the area of the floor and the amount of glass used to build the latest addition to the entrance of the Louvre the world famous museum in Paris France Its base measures 116 ft long http www quide to symbols com pyramid 2 A tent that has a square base and a height of 6 5 ft needs a canvas cover a Identify the base b and the slant height hg b Is there another calculation you need to complete prior to using the surface area formula for square based pyramids Explain c Calculate the h for the tent e Determine the amount of canvas needed to cover the tent Hint The floor of the tent is not made of canvas TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 200
81. e sketch of the graph 1 Ball type Stee EEEE LIT L3 B A Times s Height cm cu TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 15 5 5 2 Ball Bouncing Activity continuea 2 Balltype 3 Ball type 5 16 TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 W Definition Page Second Differences Parabola Vertex Maximum Minimum Value Axis of Symmetry Zeroes TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 17 5 S Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit Summary TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 18 5 R Reflecting on My Learning 3 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 19 5 RLS Reflecting on Learning Skills Students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the following questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future E Always G Sometimes S Need Improvement N Never Organization e EGSN came prepared for class with all materials e EGSN My work
82. e that you noted in 5 You will solve these three systems as a part of your home activity TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 32 4 4 4 The Sub Steps Solving using the method of substitution requires five steps The steps are given below in the text boxes Discuss with your partner what you think the correct order is for the steps and then write the steps in the space provided Solve the system in the chart as model of solving by substitution Check using your handheld State the point of intersection Solve the resulting equation Substitute the isolated expression into Substitute your solution into an original the other equation equation to solve for the other variable Isolate for a variable The easiest variable to isolate for has a coefficient of 1 m Example Solve Steps for Solving by Substitution 4x y 6and 2x 3y 10 TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 33 4 5 1 A Trip to Jim Hortons Its summer vacation Ah sweet freedom The only problem is that you re the designated coffee gopher at the office where you have a summer job On Monday you were sent out to Jimmies to pick up five small coffees and seven extra large coffees You remember that the total cost was 14 95 including tax On Tuesday you were sent out to get three small coffees and seven medium coffees You recall that the total came to 12 75 with tax Its Wednesday morning and your coffe
83. e the following linear system by elimination 6x 2y 2 12x 4y 4 6 Did you encounter any results that are unusual Explain what is different compared to questions you have already solved 7 Re arrange each equation from the linear system into y mx b form then graph a fal E EJ i a E E IE L a 0 a a a E a E a E a 8 What do you notice about the slope and y intercept in each equation that you re arranged What do you notice about how the two lines visually relate to each other Is there a solution to this linear system If so how many TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 43 4 7 3 Which Method Graphing For System A determine if you can solve the system using each of the three methods you have learned and if you can then solve 2x 3y 10 4x 5y 2 Justify why you can or cannot Justification solve using this method Substitution Elimination Justification Justification TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 44 4 7 3 Which Method Continued Graphing For System B determine if you can solve the system using each of the three methods you have learned and if you can then solve y x 2 x 5y 4 Justify why you can or cannot Justification solve using this method Substitution Elimination Justification Justification TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 7 3
84. ed to the west by fire fighters at a rate of 2 km hr e Both fires can only change east or west They will not get wider or narrower The picture below shows how the fires looked at the moment you arrived Note Each square 1 km FIRE 2 Direction of Receding Fire at 2 km hr Did you read carefully The first fire is on the bottom TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 54 3 6 2 Can You Stop The Fire Continued Questions 1 Use the linking cubes to create models that represent the area of both fires at 0 1 2 and 3 hours Each cube represents 1 km Use different colours for the contained fire model and the spreading fire model 2 Complete the tables below 3 What variable is the x variable independent Circle one Time or Area 4 What variable is the y variable dependent Circle one Time or Area 5 Whatis the y intercept initial value of both fires a y intercept of Fire 1 b y intercept of Fire 2 6 For both sets of data graph the time vs the Area of the fires on the grid on the next page and draw lines of best fit for each set of data Use different colours for each line Label both axes and each line TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 55 3 6 2 Can You Stop The Fire Continued 7 Using the graphs or the tables determine the slope rate of change of both fires a Slope of Fire 1 b Slope of F
85. een the height of something or someone flying through the air and time 1 A football player kicks a ball of a football tee The height of the ball h in metres after t seconds can be modelled using the formula h 5f 20t a Graph the relationship using your graphing calculator Remember that you need to set your window settings Record the window settings you used Sketch your graph in the window at right Make sure to label your axes You can get the table of values for this relationship TABLE SETUP Press and to access the table setup TblStart H screen Make sure your screen looks like the one given Now press and GRAPH Fill in the window with the values you see A Y For which times does the height not make sense CRM Why z E Au What is the initial height of the ball a Where do you look in the table and the graph to determine the answer Why does this make sense TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 25 6 10 2 Applying Quadratic Relationships continued i What is the maximum height of the ball j Where do you look in the table and the graph to determine the answer k When does the ball hit the ground Where do you look in the table and the graph to determine the answer m When is the ball more 10 m above the ground You may need to give approximate answers Playing Football on Mars 2 The force of gra
86. efore and after the ANO Here is what it will look like on your handheld screen RAD AUTO REAL To have the handheld check the solution press the key If the solution is correct the handheld will return the result true If the solution is not correct the handheld will report false You should find that the handheld reports that d J is a correct solution for the first equation Remember it is necessary to check the solution in the second equation as well It works the same way as before but you can save RAD AUTO REAL some typing Use the circular navpad and press up N twice The first command you entered is highlighted 4 2 224 amp k and y 3 Now press the key The handheld copies the command down to the line you are working on You 9 can now use the navpad to move left until the cursor me is behind the D symbol It looks like this Press the key to erase the first equation then type the second equation Then press Giz 9 As you can see E f J is a correct solution for the 2 B x 6 y 18lx and y 3 second equation as well Since the solution is correct for both equations from the linear system we know it must be the right answer TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 5 Nspire CAS Handheld Manual Continued How to Add or Subtract Two Equations The elimination method for solving a linear system involves adding or subtracting the given equati
87. ents Consistently uses mathematical symbols labels and conventions correctly Consistently uses mathematical vocabulary correctly when expected TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 Correctly interprets the information and makes subtle or insightful statements Consistently and meticulously uses mathematical symbols labels and conventions recognizing novel opportunities for their use Consistently uses mathematical vocabulary correctly recognizing novel opportunities for its use 1 21 7 6 1 Is the NET Up or Down Some say the surface area of a square based pyramid is equal to the sum of the areas of a square and four identical triangles Let s Investigate Part A The NET 1 Examine the following net Identify amp label the square and the 4 identical triangles 2 To calculate the area of this 2 dimensional net we need to a First find the area of the square using A length width square 5 ft b Second find the area of one triangle using _ lendth of base height of triangle 6 ft A FCO sy iangle m 2 c The next step is to multiply the area of the triangle by 4 Explain why you think this step is necessary d Finally the total area of the net is the sum of the areas of the square and the triangles Determine the total area TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 22 7 6 1 Is the NET Up
88. epts O TI TI ITI ITI o ndependently attempt the work on my own try before seeking help If have difficulties ask others but stay on task am committed to tasks at hand oocoocoaoG ooo0 G C N N N N e e e Yes No know all the different ways available in my school where can seek extra help Yes No tried my best What will do differently in the next unit to improve TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 23 TIPS4RM Grade 10 Applied Unit 2 Trigonometry August 2008 2 24 Targeted implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MFM2P Unit 3 Equations of Lines REVISED January 2009 Unit 3 Equations of Lines Secion Acivity Page 4 7 3 2 4 Why Mr Y Depends c on the desee 3 Ms X Slopes and Stuff on the TI 83 Slopes and Stuff on the TI 83 Investigation Slopes and Stuff on GSP Optional Slopes and Stuff on GSP Optional Investigation Slopes and Stuff Practice L3 Graphs Slopes Intercepts Graphs ad 8 Check Graphs Slopes Intercepts Graphs Check Graphing Calculator Keystrokes 343 Can Graphing Get Any Easier 40 Investigation EMA I DEL NEN NE Can the Graphing Calculator Stop the a Fire 3 6 4 Modelling Problems Algebraically 60 TIPS4RM Grade 10 A
89. equation 3 Which form of the quadratic equation is easiest to use to determine the y intercept Explain your choice 4 Using your conclusion from question 2 state the y intercept of each and check using a graphing calculator Does it check 5 Explain the connection between the y intercept and the value of y when x 0 TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 6 6 3 2 Quadratic Equations Name 1 Find the y intercept for each of the following quadratic equations given in factored form Write the equations in standard form Show your work a y x 5 x 2 standard form H y intercept b y x 4 x 3 standard form y intercept c y x 4y standard form y intercept d y x 5 standard form y intercept 2 Find the y intercept for each of the following quadratic equations a y x 4 x 2 b y x 6 y intercept y intercept TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 7 6 4 1 Finding the x Intercepts of a Quadratic Equation Name To find the x intercepts 1 Enter the equation in Y4 y2x x 6 2 Press ZOOM and 6 Zstandard to set the scale for your graph The calculator will then show the parabola 3 minimum maximum gsintenrsect dud oJ CxIdx 4 LeftEound W 2 446009 Y 2 4336004 5 You will be asked to enter a left bound You can move the cu
90. ers o oocoSg ZZZ 0002 ooooQ00 Init e N participate in class discussion lessons N When have difficulty seek extra help N After resolve my difficulties reattempt the problem N p G C C C review the daily lesson ideas concepts O T ITI ITI ITI x o ndependently attempt the work on my own try before seeking help If have difficulties ask others but stay on task am committed to tasks at hand oococoo ooo0 G C C C N N N N e e e Yes No know all the different ways available in my school where can seek extra help Yes No tried my best What will do differently in the next unit to improve TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 109 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 110 Targeted implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MFM2P Unit 4 Linear Systems Go 1 g ZN Quantity Dufferin Peel Catholic District School Board August 2008 Unit 4 Linear Systems Section Activity BEEN Nspire CAS Manual 0838 7 442 What s My Equation 213 Meaning of he Point of Intersection 421 AVisual Gell Phone Problem 7 Where Do We Meet Does This Line Cross Is This Accurate 43 100 What s My POI OO T O 9 _ __ d _ 20 8
91. ers long is the field One can of paint is enough to paint 500 squared feet How many squared meters can you paint with this one can TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 4 1 Placemat Perimeter and Area Perimeter For more information examples and support on how to administer a placemat activity refer to either of the following resources Think Literacy Cross Curricular Approaches Grades 7 10 Small Group Discussions Place Mat MATHEMATICS pgs 66 71 http oame on ca main files thinklit PlaceMat2 pdf TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 11 7 4 2 Let s Convert Part A Complete the conversions in the chart below TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 4 3 Proposing the Park Sham City has asked your landscaping company to submit a Sidewalk proposal estimating the cost of completing the construction of a memorial park Your company needs PARK to sod the park as well as plant a small hedge along the inside of the paved sidewalk that is located around the parks perimeter Project A The Sod Below is a sketch of the park with its corresponding dimensions Note that the uniform paved sidewalk surrounding the green space is 1 5 yards wide 8 yards g 20 yards 24 feet 19 yards To determine the amount of sod required you will need to find
92. etres 2 4Olitres dekalitres 3 600 milligrams grams 4 5 kilometres hectometres 5 70 centimetres metres 6 900 decilitres dekalitres 7 John s pet python measured 600 centimetres long How many metres long was the snake 8 Faith weighed 5 kilograms at birth How many grams did she weigh 9 Jessica drank 4 litres of tea today How many decilitres did she drink 10 Fill in the blanks with the correct units a 10 km 10000 b 50000 mm 50 c 85 8500 cm TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 8 1 2 4 What s on the Menu Growing Shapes Materials Needed Ruler Problem For the triangle drawn below make another triangle that has exactly the same shape and whose a Perimeter is twice as long b Perimeter is half as long c Determine the area of the three triangles original double half d Determine the relationship between the side length and the area of the triangle For example what happens to the area when side length is doubled show your work and reasoning in each case TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 9 1 3 1 Tri Matching These Triangles Match the triangles on the right with the name on the left by connecting with a line Equilateral LZN yo A A TIPS4RM Grade 10 Applied Unit 1 Similar Triangles August 2008 4 49 Grade 10 Applied Unit 1 Similar Triangles August 2008 1 1
93. f the x intercepts of y X 5y and the coordinate of the y intercept _ factored form the coordinates of the x intercepts of y xX 3x and the coordinate of the y intercept _ 2 X 1x factored form the coordinates of the x intercepts of y X 1x and JX the coordinate of the y intercept 4 x _ factored form the coordinates of the x intercepts of y X x and the coordinate of the y intercept _ TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 19 6 8 1 Graphing Relations of the Form y x a Name 1 Working with a partner and one graphing calculator set your Window Xmin 10 Xmax 10 Xscl 1 Ymin 36 Ymax 10 Yscl 1 Xres 1 Complete the following table Consider your results from question 1 and answer the following questions 2 What is the same about the relations 3 What is the same about the graphs 4 What is the same about the vertex of each graph 5 What do you notice about the rand s values of each relation 6 Solve this puzzle How can you find the y intercept and the x intercepts of the graph of a quadratic relation of the form y X a TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 20 6 9 1 Quick Review of Factoring and Graphing For each
94. find ZC Solve for ZC C B 20 cm A TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 7 2 5 1 Going the Wrong Way There are two problems shown below For each problem the answer provided is incorrect Partner A will identify the errors in the given solutions Partner B will write a correct solution to the problem Solve for the missing side labelled x Solve for the missing side labelled x D hypotenuse i opposite 52 mm adjacent Solve for the missing side x j 20 32 X 1424 x 2 41424 X 3 4 TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 8 2 5 2 Tangent or Something else 1 Decide whether to the use tangent ratio or the Pythagorean relationship to find x Solve for x A 35 cm y B C 2 Decide whether to use the tangent ratio or the Pythagorean relation to find ZA Solve for ZA A 35 cm B 60 cm C 3 Decide whether to the use tangent ratio or the Pythagorean relationship to find x Solve for x A X 30 mm N aN B 40 mm C 4 Decide whether to use the tangent ratio or the Pythagorean relation to find ZC Solve for ZC A 51 5 mm 25 mm B 45 mm C TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 9 2 5 3 Who Uses Trigonometry Research Assignment You are to investigate someone who uses trigonometry in their professional lives You will be responsible for submitting e a report e a presentation The Report
95. first to Albany and then to Buffalo 3 An8mlong ramp reaches up a vertical height of 1m What angle does the ramp make with the ground TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 In order to safely land the angle that a plane approaches the runway should be no more than 10 A plane is approaching Pearson airport to land It is at an altitude of 850 m It is a horizontal distance of 5 km from the start of the runway Is it safe for the plane to land 4 Atree casts a shadow 42 m long when the sun s rays are at an angle of 38 to the ground How tall is the tree 2 18 2 8 1 Who Uses Trigonometry Organizer Visit two other project presentations and collect information to return to your home groups The type of education they They use trigonometry in their The most interesting thing is need is job by Include a description example or diagram One thing I ll remember is I m still wondering about Someone who think would be good at this job is TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 19 2 W Definition Page Pythagorean Formula Clinometer Angle of Elevation TIPS4RM Grade 10 Applied Unit 2 Trigonometry August 2008 2 20 2 5 Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit Summary TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 21 2 R Reflecting on My
96. form linear regression to determine the equation of the line of best fit Enter the data into the list of the calculator be pressing for into L1 and the area of the fire into L2 To determine the equation for the line of best fit press Press ES a1 ED to state the two lists to use Your screen will look like ENTER Now press to generate the equation Your screen will show results similar but with different values as below Note a represents the slope In this case your equation would be y 1x 50ry xXx 5 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 58 3 6 3 Can The Graphing Calculator Stop the Fire Continued Determining the Equation of a Line 8 To view the graph of the data and graph you must first enter the equation of the line in Y1 by pressing clas 9 Next enter the equation from above into Y1 fory x 5 10 Change the window seitings as illustrated below be pressing 11 Now to view the graph press 12 Compare with the graph you made earlier by hand If they are different check for errors TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 59 3 6 4 Modelling Problems Algebraically Piggy Bank Math Patterns in Area Consider the following patterns created with unit Little Johnny has three dollars to put into his cubes brand new piggy bank He will deposit his entire two dollar per week allowance into his piggy bank a Create a table tha
97. gle could have sides with lengths of Give side lengths of two 2 different similar triangles TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 26 1 7 1 How Far ACTIVITY 1 Your arm is about ten times longer than the distance between your eyes Verify Arm length cm Distance between eyes cm Ratio of arm length to distance between eyes cm 1 Select an object from which you want to determine the distance object 2 Estimate the width of the object cm 3 Hold one arm straight out in front of you elbow straight thumb pointing up Close one eye and align one side of your thumb with a particular spot on the front of the object Without moving your head or arm sight with the other eye Your thumb will appear to jump sideways a Approximate the number of widths of the object your thumb appeared to move b Whatis the distance the image moved cm Distance the image moved In the diagram T is the position of your thumb AT represents the length of your arm TB represents the distance from your thumb to the object a Indicate all known measurements on the diagram Include units b Identify which triangles are similar Label the triangle vertices Write the proportion needed to find the distance the object is from you c Determine the distance the object is from you using two different methods TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 27 1 7 2 How High
98. h the height and length of the unit have to be1 2 m How far will the unit stick out from the wall when complete TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 56 7 W Definition Page Imperial Measurement Metric Measurement Conversion Factor Perimeter Area Composite Shape 3D Solid Volume Net Surface Area TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 57 7 W Definition Page Continued Slant Height Triangular Prism Cylinder TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 58 7 S Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit summary TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 59 7 R Reflecting on My Learning 3 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 60 7 RLS Reflecting on Learning Skills Students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the following questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future E Always G Sometimes S Need Improvement N Never Organization e EGSN came prepared for c
99. he cylinder iii Repeat until the cylinder is completely full keep track of how many times it takes 4 From your findings come up with a formula for the volume of a cone using the volume of a cylinder as a base TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 46 7 11 3 Shapes to Go Continued STATION 3 Your goal is to show how the volume of a square based pyramid is related to the volume of a cube Your task 1 Compare the base of the cube with the base of the pyramid What do you notice 2 Compare the height of the cube to the height of the pyramid What do you notice 3 How many times do you think you would be able to fill the pyramid with water and pour it into the cube before it overflows Fill in the blanks below Fill in the bolded components after you perform the experiment Guess Actual Therefore the volume of a cube is times greater than the volume of a pyramid LETS TRY IT i Fill the pyramid full with water ii Empty the water form the pyramid into the cube ii Repeat until the cube is completely full keep track of how many times it takes 4 From your findings come up with a formula for the volume of a pyramid using the volume of a cube as a base TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 47 7 11 3 Shapes to Go Continued STATION 4 Imagine a steaming hot summers day and you run into the house after a lo
100. he same y Slope parallel to x 5 going through point A intercept as y 4x 10 2 5 Slope is 0 y intercept 5 slope 4 Point A 0 3 Work Shown Work Shown Given Given Point A 4 3 Point B 1 3 Point A 0 1 Point B 4 8 Work Shown Work Shown Given Given 5 3 Slope z Point 5 7 M PE Point A 5 0 Work Shown Work Shown TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 76 3 9 2 Yes We got no Graph paper Continued Given two points the slope and or the y intercept write the equation in y mx b form for each of the following Given Given Point A 10 19 Point B 18 31 Point A 4 6 Point B 7 15 Work Shown Work Shown Given Given Point A 5 0 Point B 0 200 Point A 0 5 Point B 200 0 Work Shown Work Shown Given Given Point A 1 5 6 5 Point B 1 5 2 5 Point A 1 8 50 Point B 4 28 50 Work Shown Work Shown TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 77 3 9 3 l m on your side You will be assigned one of four shapes Your job is to find the equation relating the number of shapes and the number of sides and then answer some other questions SQUARE INVESTIGATION Start by placing squares side by side as shown Note This arrangement of 4 squares has 13 ides sides 1 2 3 4 CLEC 9 8 7 6 1 Complete the following table relating the number of squares and total number of sides
101. hey are compare the two equations What is the same What can you conclude about parallel lines Check this by finding another pair of students and discuss your conclusions briefly with them Write down your conclusion below TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 30 3 3 4 Slopes and Stuff on GSP Optional Student Instructions for GSP Ok Geometer s Sketchpad is a great way to see just how the slope and y intercepts work Follow these instructions and they will help you create what you need in order for you to start investigating Good luck First let s launch Geometer s Sketchpad on the computer Click on any white space to get rid of the logo Let s see some grid Select Show Grid from the Graph menu Great now we re ready to create a line Select Plot Points from the Graph menu Enter O left text box and 1 right text box Click Plot Click Done Click on the Point Tool on the left hand side menu Create a point anywhere you want Click and hold the Line Tool on the left hand side menu until a line with arrows on both ends appear and select that option Click on point 0 1 and click on the point that you created to create a line Click on the Arrow Tool on the left hand side menu and click on any white space Now click on the line so that only the line is highlighted Select Slope from the Measure menu Click on any white space Click on the line If you point your curso
102. his Ans stands for the last answer you found If you now DEG AUTO REAL press the Gi key the handheld will subtract 2 from the left side and the right side of 3x 2 14 You xr2 H4 x 2 14 will see this result I33 2 14 2 aee Continue solving the equation You probably see that to finally isolate the x variable it is necessary to E AUR e divide the equation by 3 on both sides Again just start typing the operation you want to perform Press x 2 14 Sxt2 4 G gt The handheld will insert Ans for you Press 3 4 9 14 2 eye i to calculate the result uMMM g 2 Ax 12 x 4 As you can see the handheld reports that xz4 3 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 48 3 5 1 Nspire CAS Handheld Manual Continued How to Solve for a Variable Example Two Say that you wish to solve the equation 6x 5 8 for the variable y To do this first be certain that you are on a Calculator page If you need help with this see the Getting Started section above First type in the equation that you want to solve Use the number pad and the green letter keys the operations x are located on the right and the equals sign is in the top left corner of the keypad When you have typed in the equation press the key found in the bottom right corner The top of your screen will look something like this eS 6 x 5 8 6 x 5 8
103. ht of horses My HAND INCHES Length from point of bent elbow to middle fingertip Egyptian pyramids Noah s ark My CUBIT INCHES BRACCIO Italian for an arm s length Da Vinci s parachute FATHOM PACE My BRACCIO INCHES From the Anglo Saxon word for embrace it was the length of rope held between two hands with the arms outstretched sailors My FATHOM INCHES Length of a single step In Roman times one pace was a double step and our MILE came from the Latin mille passuum meaning 1000 paces My PACE INCHES TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 7 7 3 2 A Question of Converting Centimetres to Inches How many cm are in ONE inch Centimetres to Inches How many cm are in ONE inch Decimetre to Feet How many dm are in ONE foot Meters to Yards How many meters are in ONE yard Cubic centimetres to Cubic inches How many cubic cm are in ONE cubic inch Meters to Feet How many meters are in ONE foot Meters to Yards How many meters are in ONE yard Squared centimetres to Square inches How many squared cm are in ONE square inch Squared meters to Squared feet How many squared meters are in ONE square foot Squared meters to Squared yards How many squared meters are in ONE Squared yard Meters cubed to Yards cubed How many cubic meters are in ONE cubic yard Cubic decimetres to Cubic feet How many cubic dm are in ONE cubic foot
104. ies charge a monthly flat fee plus an additional cost for each minute of time used The graph below shows the Time vs Cost relationship for one month Cell Phone Costs ALLLLLLLIEFELLL LLLLLLBMA GAIIL x LLLLLSLLLLIL LLLLAELLLLLL Talk More We Talk Cost 200 400 E00 sou 1000 1200 Time minutes 1 What is the Point of Intersection POI and what is the meaning of the POI in relation to the cell phone plans 2 Under what conditions is it best to use the Talk More cell phone plan 3 Under what conditions is it best to use the We Talk cell phone plan 4 How does the graph help you to determine which cell phone plan is the most appropriate at any given time TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 16 4 2 2 Music is My Best Friend iTones and Music Mine are two online music providers Each company charges a monthly membership fee and then a per song download rate iTones charges 10 per month and 1 per song C n 10 Music Mine charges 7 per month and 1 50 per song C 1 5n 7 Where C represents the total cost for one month and n represents the number of songs purchased Create a table of values showing the total charges for up to 8 songs purchased Graph the lines on the same graph below iTones Music Mine Online Music Purchasing Cost Number of Songs 1 If Lulu plans to purchase 7 songs this month which is the best plan for her Explain 2 Which plan
105. ilizer will be required to cover the lawn Project B The Hedge To determine the total amount of hedging needed we need to calculate the total perimeter of the park Recall that the small hedges are to be planted along the inside of the path TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 15 7 4 3 Proposing the Park Continued 1 In the spaces below draw the basic shapes that were found in Part A Basic Shape 1 Basic Shape 2 Basic Shape 3 Basic Shape 4 2 Using a different colour pencil highlight the sides of each shape that will receive hedging 3 Inthe spaces below calculate the length of each coloured side you found in the previous question Question 2 above Perimeter Basic Shape 1 Perimeter Basic Shape 2 Perimeter Basic Shape 3 Perimeter Basic Shape 4 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 16 7 4 3 Proposing the Park Continued 4 Find the total perimeter of the park that is to receive hedging State your solution using the following units i feet ii meters 5 If each hedge plant takes up 1 5 feet how many hedge plants are needed to surround the park Part C The Cost The local nursery is selling the exact hedge you have chosen for the park The sale price for the hedge is 12 per linear meter Also the sod price is 2 50 for a roll If you have to pay 13 tax what would be the total cost for the s
106. ing questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future E Always G Sometimes S Need Improvement N Never Organization e EGSN came prepared for class with all materials e EGSN My work is submitted on time e EGSN keep my notebook organized S N attempt all of my homework N use my class time efficiently N limit my talking to the math topic on hand N am on time N If am away ask someone what missed N complete the work from the day that missed am an active participant in pairs group work co operate with others within my group respect the opinions of others nnne lt QNOAS oooooQooQo Z Z Z 5 e Im m m mne MMM TI TI TI TI TI e participate in class discussion lessons When I have difficulty seek extra help After resolve my difficulties reattempt the problem review the daily lesson ideas concepts G 6 o ndependently attempt the work on my own try before seeking help If have difficulties ask others but stay on task am committed to tasks at hand Tl TI Tl ITI G 0 0 NNNNA NNNM 22229 c 4 e e e Yes No know all the different ways available in my school where can seek extra help Yes No tried my best What will do differently in the next unit to improve TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c
107. interprets part of the information but carries on to make some otherwise reasonable statements Usually uses mathematical symbols labels and conventions correctly Usually uses mathematical vocabulary correctly when expected Explanations and justifications are clear for a range of audiences Justification of the answer presented has a direct connection to the problem solving process and models presented Makes appropriate connections Makes appropriate connections Correctly interprets the information and makes reasonable statements Consistently uses mathematical symbols labels and conventions correctly Consistently uses mathematical vocabulary correctly when expected TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 Explanations and justifications are particularly clear and detailed Justification of the answer has a direct connection to the problem solving process and models presented with evidence of reflection Makes strong connections Makes strong connections Correctly interprets the information and makes subtle or insightful statements Consistently and meticulously uses mathematical symbols labels and conventions recognizing novel opportunities for their use Consistently uses mathematical vocabulary correctly recognizing novel opportunities for its use 7 18 7 5 1 Job Opportunity Your proposal for the memorial park in
108. ious to check by pencil and paper but it is quick to check with the handheld Here is how to do it First be certain that you are on a Calculator page If you need help with this see the Getting Started section from earlier in this manual Here is how to do it l 1 1 DEG AUTO REAL First type in the equation but do not press Gis The Bn screen looks like Next continue typing by pressing the grey key with the DEG AUTO REAL vertical line in the top row This symbol means such that Continue typing x 13 6 The screen looks like D A D Al When you press ci the handheld says true to indicate that the solution is correct If the solution is not correct the handheld will return false DEG AUTO REAL LI Now check your solutions to the three equations you solved on the previous page If there are any notes you want to make to help you remember how to solve and check equations use the box below TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 50 3 5 2 Temperature Conversions Investigation Goal With a partner you will investigate how to solve one variable equations that have fractional coefficients using CAS and pencil and paper Nethead is planning to go to visit Wingman in Detroit Wingman says that the temperature is 23 Fahrenheit Nethead wants to know if he needs to packs warm clothing for his trip How many degrees Celsius is 23 Fahrenheit We fir
109. ire 2 8 Using the graphs what is the area of the fires at 6 hours a Area of Fire 1 b Area of Fire 2 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 56 3 6 2 Can You Stop The Fire Continued 9 Using the values of the slopes and y intercepts write an equation of both fires in the form of y mx b a Equation of Fire 1 b Equation of Fire 2 10 Using the regression function of the graphing calculator check to see if your equations are correct See 3 6 3 for details 11 Using the graphing calculator check to see if your graphs are correct by graphing both equations See 3 6 3 for details 12 Using the equations find the areas of both fires at 6 hours Compare your answers to the answers from question 9 Show work for Fire 1 Area of Fire 1 at 6 hours Show work for Fire 2 Area of Fire 1 at 6 hours 13 Looking at both graphs do the lines ever meet Circle one Yes or No 14 If the lines meet at what time and area does it occur a Time b Area of Fire 15 Explain the significance of this point in this context TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 57 3 6 3 Can The Graphing Calculator Stop the Fire Determining the Equation of a Line 1 Prepare your calculator by either running a get ready program or resetting the graphing calculator 1 Enter the time Once all the data has been entered the calculator will per
110. irs group work co operate with others within my group respect the opinions of others e 9 4 Q oocoSg ZZZ 0002 ooooQ00 Init IT ITI ITI IH amp ITI ITI TI S TI ITI TI ITI ITI ITI e N participate in class discussion lessons N When have difficulty seek extra help N After resolve my difficulties reattempt the problem N p G C C G review the daily lesson ideas concepts O TI TI T T lt 5 ndependently attempt the work on my own try before seeking help If have difficulties ask others but stay on task am committed to tasks at hand know all the different ways available in my school where can seek extra NDANNNDAa ooo0 G C C G N N N N 2 O oO 0 Zz O Yes No tried my best What will do differently in the next unit to improve TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 54 Targeted implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MFM2P Unit 5 Introduction to Quadratic Relations Dufferin Peel Catholic District School Board REVISED D Stunfent August 2008 Unit 5 Introduction to Quadratic Relations Secion Acivty Page 5 14 Going Around the Curve ExpermenD 6 53 2 Key Features of Quadratic Relations 8 533 Key Terminology 9 12 Quadratic Power M
111. irst what will be the first step you take to create the conditions necessary for elimination 2 Solve the linear system now You may use CAS to help find the answer and check the solution Use the space below for rough work 3 Does it matter which variable is eliminated first That is does it change the final answer 4 Think back to when you solved this problem by graphing Do you find the method of elimination easier or harder Explain TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 39 4 6 4 Two for You Try solving the following questions using the method of elimination You may use CAS on the handhelds to help solve the questions and check your solutions 1 A fitness club charges an annual fee and an hourly fee In a single year member A worked out for 76 hours and paid 277 in total Member B worked out for 49 hours and paid 223 in total What is the annual fee What is the hourly fee HINT Start by writing let statements to define the variables you will use For example Let a represent the amount of the annual fee Let h represent the amount of the hourly fee 2 This past summer you ran a food booth at a local festival You sold hotdogs for 1 each and samosas for 2 50 each From 205 purchases you made 400 in total To help plan purchases for next year s festival you d like to know how many hotdogs and samosas were sold Unfortunately you forgot to keep track of this when selling the food Can
112. irths vs Year scatter plot on your graphing calculator 1956 450739 2 Perform a Linear Regression on your graphing calculator 1957 469093 Write the equation of the line 1958 470118 3 How well does the Linear Regression fit the data 1959 479275 5 Perform a Quadratic Regression on your graphing calculator 1960 478551 Write the equation of the line 1961 475700 5 How well does the Quadratic Regression fit the data 1962 469693 6 Which regression best describes the data 1963 465767 Source http www keypress com fathom pages community exchange activities and documents activities php TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 12 5 4 3 Modelling Canada s Baby Boom You examined Baby Boom births in Canada between 1950 1967 Sketch what you think the graph of the number of births in Canada between 1950 2005 might look like Explain your reasoning and any assumptions you made Births in Canada 1950 2005 Number of Births Year TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 13 5 9 1 Ball Bouncing Instructions Record your hypothesis on the Ball Bouncing Record Sheet Use the CBR and the graphing calculator to examine the relationship between the bounce heights of your ball versus time after it is dropped from 1 m Instructions to Use Technology ot OK ey INC x Press the APPS button on your calculator and select CBR CBL Foll
113. is cheaper if you only plan to buy 4 songs per month How do you know from the graph 3 Which cell phone plan would you choose and why Relate your answer back to the POI TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 17 4 2 3 Where Do We Meet For each of the following situations find the point of intersection and describe the meaning of this point Describe which company or service you would choose under what circumstances A template has been provided for the first situations Lawn Service U sessed FW LL Point of intersection Interpretation of the point If the job lasts less than hours choose __ If the job lasts more than hours choose If the job lasts hours choose either company and the cost is Time hours Car Rental Companies AUTTT TTTLTTT TT T Point of intersection Interpretation of the point If the kilometers driven is less than choose If the kilometers driven is more than choose If the kilometers driven is choose either company and the cost is 10 20 30 40 50 BU S0 100 Kilometers Driven TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 18 4 2 3 Where Do We Meet Continued For each of the following situations find the point of intersection and describe the meaning of this point Refer back to the template provided for the first situations Snowboard Rental Talking Time hours TIPSARM Grade 10 Applied Unit 4 Linear
114. is submitted on time e EGSN keep my notebook organized o a L Q ZZZzzz z o9 attempt all of my homework use my class time efficiently limit my talking to the math topic on hand am on time If am away ask someone what missed complete the work from the day that missed e o oe oe eO oooooooSg am an active participant in pairs group work co operate with others within my group respect the opinions of others e ee j 4 Q lt DODE AHNOADOD nnn Zzz e N participate in class discussion lessons N When have difficulty seek extra help N After resolve my difficulties reattempt the problem N p wow 2 et mrmmrmgo mrnms rrr rmn rn rn rm G C C G review the daily lesson ideas concepts o ndependently attempt the work on my own try before seeking help If have difficulties ask others but stay on task am committed to tasks at hand 2 2 5S O TI TI T T gt lt G C CO NNNNA oooo N N N N Yes No know all the different ways available in my school where can seek extra help Yes No tried my best What will do differently in the next unit to improve TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 20 Ip Targeted Implementation and Planning Supports for Revised Mathematics Grades 7 8 9 Applied 10 Applied Course Grade 10 Applied Mathematics MF
115. itt ititiea 1111111 4 37 TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 6 2 Elimination Preparation 1 Consider the following linear system 3k 15m 15 k masi If you add or subtract the equations will a variable be eliminated Explain 2 What could be done to create the conditions necessary for elimination TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 38 4 6 3 Algebra the Musical Redux Recall that in the first lesson of this unit you solved the following problem by graphing The school is putting on the play Algebra The Musical Adult tickets were sold at a cost of 8 and student tickets were sold at a cost of 5 A total of 220 tickets were sold to the premiere and a total of 1460 was collected from ticket sales How many adult and student tickets were sold to the premiere of the musical If x represents the number of student tickets sold and y represents the number of adult tickets sold then the equations that model this problem are from cost of tickets 5x 8y 1460 from number of tickets sold x y 220 You probably remember that this problem took a while to solve by graphing and the answer you found was not necessarily very accurate since you read the point of intersection off of the graph You will work with a partner now to solve this problem using the method of elimination 1 Since you have been asked to eliminate the x or y variable circle one f
116. l chosen Make connections among mathematical concepts and procedures Relate mathematical ideas to situations drawn from other contexts Makes weak connections Makes weak connections Makes simple connections Makes simple connections Makes appropriate connections Makes appropriate connections TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 Makes strong connections Makes strong connections 1 42 7 11 1 Count on Frank One of the facts shared in the book Counting on Frank is that only ten humpback whales would fit in his house When answering the questions below use either metric or imperial units humpback whale EX F GRE ur E 3 metres 9 feet 2002 Encyclop dia Britannica Inc 1 How big is the average humpback whale estimate 2 What type of box can we fit the whale in e g rectangular triangular cylindrical or other 3 What size of box would you need to fit one whale 4 Determine the dimensions of the box 5 Imagine ten of these boxes how much space would that fill 6 How big is the house TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 43 7 11 2 Formulas to Know Vets or V area of hase height V huh V a area of baseX height Vetblh or Va m TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 44 7 11 3 Shapes to Go
117. lass with all materials e EGSN My work is submitted on time e EGSN Keep my notebook organized Work Habits e EGSN attempt all of my homework e EGSN use my class time efficiently e EGSN limit my talking to the math topic on hand e EGSN am on time e EGSN If am away ask someone what missed e EGSN complete the work from the day that missed Team Work e EGSN am an active participant in pairs group work e EGSN co operate with others within my group e EGSN respect the opinions of others Initiative e EGSN participate in class discussion lessons e EGSN When I have difficulty seek extra help e EGSN After resolve my difficulties reattempt the problem e EGSN review the daily lesson ideas concepts Works Independently e EGSN attempt the work on my own e EGSN try before seeking help e EGSN If have difficulties ask others but stay on task e EGSN am committed to tasks at hand Yes No know all the different ways available in my school where can seek extra help Yes No tried my best What will do differently in the next unit to improve TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 61 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 62
118. left column in a table and on the vertical axis ina graph EMEN A relation in which one variable is a multiple of the other TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 4 3 1 1 Definition Match continued In a relation the variable whose values you choose usually placed in the right column in a table of values and on the horizontal in a graph A line that best describes the relationship between two variables in a scatter plot A symbol used to represent an unspecified number For example x and y are variables in the expression x 2y A relation whose graph is not a straight line TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 5 3 1 1 Definition Match continued Equation OR Table of Values Number of Weeks 0 20 L 30 40 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 15 85 95 105 3 1 4 Reminiscing Old Relationships There are 4 different envelopes that match the relationships below Partner A will work on ENVELOPES A and C Partner B will work on ENVELOPES B and D Your job is to glue the appropriate values from your envelope onto the space provided Another Banquet Hall Earning Money A banquet hall charges a flat rate of 300 plus Lindsay earns 10 per hour 20 per person Initial Value Initial Value Money Money Internet Fees Ayda receives a base salary of
119. length and width 3 If the area of a rectangle is given by X 8x 15 what expression will represent the length and the width TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 10 6 4 3 Factoring Using Algebra Tiles and Making Connections to the Graph Name Part A For each of the following shade in the appropriate rectangular area Then shade in the tiles that represent the length and width for each of those areas Use the length and width to represent and state the factors State the x intercepts Check using a graphing calculator 1 yx 3x 2 X 2 y xX 5xt 4 Y x intercepts x intercepts Check with calculator Check with calculator x intercepts x intercepts Check with calculator Check with calculator TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 11 6 4 3 Factoring Using Algebra Tiles and Making Connections to the Graph continued Part B Using the diagrams in Part A find the x and y intercepts for each quadratic relation Use the information to make the sketch on the grid provided 1 standard form y2xX 3x 2 factored form 3 y intercept first x intercept second x intercept 2 standard form y x 5x 4 factored form 3 y intercept first x intercept second x intercept TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of th
120. lied Unit 1 Similar Triangles August 2008 1 5 1 2 2 Review of Metric Length Units Complete the following 1 Fill in the blanks below with the correct number a 1 m mm b 1m cm c 1 cm mm d 1 km m 2 Convert each given measurement to the unit specified a 4 5 m mm b 5 3 m cm c 25 8 cm mm d 36 8 km m e 5694 m km f 2 5 mm cm 3 The diameter of a golf ball is about 4 cm What is the radius of the ball in millimetres 4 Fill in the blanks with the correct units a 8 m 8000 b 500 mm 50 c 85 8500 cm TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 6 Complete the following conversion worksheets 1 10 13 16 19 22 25 28 31 1000 mL 2cm 12000 m 3 L 900 cm 7000 mL 1 kg 1100 cL 7000 L 9 cL 6 g L cL kL mL g 1 2 3 Metric Funsheet 2 T3 14 17 20 23 26 29 32 120 mm 11000 L 8g 2000 L 11 cg 5 kg 4000 mL 10000 g 70 ml TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 cm 3 kL 6 cg 9 mg 15 g 18 cL 2f cg 30 kL 12 kg 24 1200 mL 10 cL 80 ml 5 cm 9000 m 60 mm 1 cL 2000 mL Dg 8 kg 30 mg mL cl mm km cm mL Cg g 1 2 3 Metric Funsheet Continued 1 3metres centim
121. line joining the two given points a 2 1 3 4 c 4 5 5 0 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 103 Unit 3 Equations of Lines Review continued 1 Babysitting Earnings 2 Bank Account 3 Car Rental Costs A family pays the Balance Rent A Ride charges babysitter 4 00 hr plus A bank account is a flat fee of 55 plus a tip of 5 00 opened with a balance 0 25 km to rent a of 900 Each week Car 150 is withdrawn from the account Introduce Variables Equation in the form of y mx b In real life terms what is the y intercept What would be the real life implication of a greater y intercept What would be the real life implication of a smaller y intercept In real life terms what is the rate of change m What would be the real life implication of a greater steeper rate of change What would be the real life implication of a smaller flatter rate of change TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 104 3 W Definition Page Dependent Variable Independent Variable Direct Variation Partial Variation First Differences Slope TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 105 3 W Definition Page Continued X intercept Y intercept Algebraic Model Vertical Line Horizontal Line Standard Form of a Line Slope Y intercept Form of a Line TIPS4R
122. mplete the following questions Feel free to consult your notebook if you cannot remember 1 Whatis a y intercept What is an x intercept 2 Give an example of an equation in Standard Form 3 If you graph the line using the Standard Form how many intercepts do you have 4 s it possible to graph a line so that it will have no intercepts Explain Give an example of each in coordinate form How does the Standard Form make graphing easier for you Can you graph a line any other way so that it will only have 1 intercept If so sketch an example below Is it possible to have more than 2 intercepts Explain TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 83 3 10 2 So You Think You Know Everything About Lines Horizontal Lines Investigation With your partner complete the investigation below You will be asked to coach someone later 1 For the graph below write the coordinates of each point on the graph in the table below A B C D E F G 2 What do all the points have in common 3 There is only one point that has a coordinate of zero What is another name for this point TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 84 3 10 2 So You Think You Know Everything About Lines Horizontal Lines Investigation continued 4 What is the equation of the line joining all the points Hint The slope of the line is
123. n and profession and profession profession Communication No Report amp poster Report amp poster Report amp poster Report amp poster evidence shows limited shows some shows clarity shows a high clarity clarity degree of clarity Comments TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 11 2 6 1 Constructing a Clinometer A clinometer is used to find the angle of elevation of an object Read all directions carefully before you begin 1 Cut along the dotted line above and glue the protractor onto a piece of cardboard Carefully cut around the edge of the protractor 2 Take a 20 cm piece of string and tie a washer or paperclip to one end The other end should be taped to the flat edge of the protractor so that the end touches the vertical line in the center and the string can swing freely This can best be done by taping the string to the back of the protractor and wrapping it around the bottom 3 Glue a straw to the flat edge of the clinometer The finished product should look like figure 1 below l Paper Clip Figure 1 You can now use your clinometer To find an angle of elevation look through the straw to line up the top of an object The string hanging down will then be touching the angle of elevation Note The angle you measure will always be less than 90 when you are reading the clinometer TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 12 2 6 2 A
124. n 1 E Option 3 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 35 7 9 2 Constructing Cylinders Use the following table to keep track of different cylinders you attempt to construct using Geometer s Sketchpad Once you get one that works circle it cut it out and see if it makes a cylinder Describe any strategies that you used TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 36 7 9 3 Cylinder Surfaces Below you will find two cylinders You need to calculate their total surface areas d 22 inches en TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 37 7 9 4 GSP Instructions for Students File Edit Display Construct Transform Measure Graph File Edit Display Construct Transform Measure Graph Instructions gsp Instructions gsp This tool selects an object If you want How do I I to measure the area of a shape you must first select the shape by clicking on it Geometer s This tool will create a circle If you Sketch pad click on this button then you can create Version 4 a circle This tool will draw a line You must use this four times to create a Instruction Booklet rectangle Created by File Edit Display Construct Transform Measure Graph File Edit Display Construct Transform Measure Graph Instructions gsp Instructions gsp Once you have constructed a rectangle or a circle You can SELECT it with
125. n both sides Again just start 3 y 16 6 x y 3 x B typing the operation you want to perform Press p OAH The handheld will insert Ans for you Press to calculate the result As you can see the handheld reports that y 3x 8 TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 3 Nspire CAS Handheld Manual Continued How to Solve for a Variable Example Two Say that you wish to solve the equation 6x 2y 18 for the variable y To do this first be certain that you are on a Calculator page If you need help with this see the Getting Started section above First type in the equation that you want to solve Use the number pad and the green letter keys the operations x are located on the right and the equals sign is in the top left corner of the keypad When you have typed in the equation press the key found in the bottom right corner RAD AUTO REAL m The top of your screen will look something like this e orama Now decide how you would start solving for y Perhaps you ve decided that subtracting 6x from both RAD AUTO REAL L sides of the equation is a good start Wonderful To aE aao do this immediately press lt S 65 Notice that the Ww 4 handheld automatically inserts Ans What is this nsx Ans stands for the last answer you found If you now PAD AUTO REAL press the key the handheld will subtract 6x from E ERE the left side and the right side of 6x 2y 18
126. n explain Hint Use a ruler and a protractor to make measurements Similar Explain Similar Explain Similar Explain Similar O5 Explain Similar Explain Similar Explain TIPS4RM Grade 10 Applied Unit 1 Similar Triangles August 2008 1413 Grade 10 Applied Unit 1 Similar Triangles August 2008 1 4 2 What Is Similarity Anticipation Guide In a triangle can calculate the length of the third side if know the length of the other two sides All triangles are similar When I enlarge a geometric shape the number of degrees in each angle will become larger K W L Chart Pythagorean relationship If two triangles are similar then TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 14 1 4 3 What Is Similarity 1 a On your geoboard create a right angled triangle with the two perpendicular sides having lengths 1 and 2 units b Create two more triangles on your geoboard that are enlargements of the triangle created in a Draw the three triangles using different colours on the grid and label the vertices as indicated triangle one label vertices ABC triangle two label vertices DEF triangle three label vertices GHJ a Determine the lengths of the hypotenuse of each of the Hint Pythagorean Theorem b Indicate the length of each side of each triangle on the diagram TIPSARM Grade 10 A
127. ng bike ride You rush to the kitchen and open the cupboard to see only two glasses remaining One is tall and thin and the other is short and wide You are so relieved because thanks to your math classes you are confident that you can choose the glass that holds the most amount of juice 1 Take a look at the glasses at your station Which glass would you choose to quench your thirst Using what you have learned about the volume of 3 D objects justify your choice LETS EXPERIMENT i Fill the taller glass to the top with water li Transfer the water from the taller glass to the shorter glass Are you surprised at what you see 2 Using the measurement device provided calculate the volume of both the tall and short glasses 3 Compare your height and radius measurements of the glasses a What do you notice b Does height or radius have a greater effect on the volume of a cylinder Why HINT Refer to the volume formula for a cylinder 4 Most people would say that the volume of the taller glass exceeds the volume of the shorter glass Why might they have this perception TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 48 7 11 4 Two Shapes Are Better Than One Solve two of the following three problems Please show all of your work Problem 1 Determine the volume of ice cream if the diameter of the scoop is 10 cm and the height of the cone is 20 cm What possible assumptions are made when s
128. ng depositing that is positive negative correlation Circle correct answers b Rule in words Balance starts at and increase decrease by per week rate c Algebraic Rule B d After 12 weeks 2 This person is withdrawing depositing that is positive negative correlation Circle correct answers b Rule in words Balance starts at and increase decrease by per week rate c Algebraic Rule B d After 12 weeks TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 12 3 1 8 Variables and Equations with Graphs Continued 3 This person is withdrawing depositing that is positive negative correlation Circle correct answers b Rule in words Balance starts at and increase decrease by per week rate c Algebraic Rule B d After 12 weeks On a graph the initial value is shown as the On a graph the rate is shown as 4 This person is withdrawing depositing that is positive negative correlation Circle correct answers b Rule in words Balance starts at and increase decrease by per week rate c Algebraic Rule B d After 12 weeks TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 13 3 1 8 Variables and Equations with Graphs Continued 5 This person is withdrawing depositing that is positive negative correlation Circle correct answers b Rule in words Balance starts at and by per week c Algebraic Rule B d Afte
129. nit 1 Similar Triangles August 2008 1 36 1 RLS Reflecting on Learning Skills Students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the following questions Be honest with yourself Good Learning Skills will help you now in other courses and in the future e E Always e G Sometimes e S Need Improvement e N Never Organization e EGSN came prepared for class with all materials e EGSN My work is submitted on time e EGSN keep my notebook organized Work Habits EGSN attempt all of my homework use my class time efficiently limit my talking to the math topic on hand am on time If am away ask someone what missed complete the work from the day that missed ZZZzZzZ am an active participant in pairs group work co operate with others within my group respect the opinions of others e 9 e e e o eo Q oocdoS9 onnon 000zoo000 Ic Initiati em TI TI ITI TI j ITI TI ITI S ITI ITI ITI ITI ITI e participate in class discussion lessons When have difficulty seek extra help After resolve my difficulties reattempt the problem review the daily lesson ideas concepts ndently attempt the work on my own try before seeking help If have difficulties ask others but stay on task am committed to tasks at hand G C C C o nae NDANNNANANnNDNN
130. ns If you decide to present a skit it should be 5 minutes and could involve 3 people maximum If you select to write a newspaper story it should 350 400 words one graphic proper newspaper format and includes one interview quote A presentation done as a brochure should be 4 or 6 sided and has 2 graphics If you want to do an e presentation it should include 12 14 slides and make use of different transitions A verbal presentation would be 2 3 minutes and have interaction with the audience A visual poster would be bristle board size TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 10 2 5 3 Who Uses Trigonometry Research Assignment continued A Word on Plagiarism Copying and pasting something from the internet is plagiarism You are submitting someone else s work as your own If suspect that your voice is not coming through when read the paper will question you on your sources Evaluation Rubric Your report will be evaluated using the following rubric Knowledge No Shows a limited Shows some Shows an Shows a high Understanding evidence understanding understanding understanding degree of of the concepts of the concepts of the concepts understanding of the concepts Application No Shows a limited Shows some Shows a Shows more than evidence connection connection connection one connection between between between between trigonometry trigonometry trigonometry trigonometry and and professio
131. od and hedge TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 4 4 Degree of clarity in explanations and justifications in reporting Making inferences conclusions and justifications Application Connecting Make connections among mathematical concepts and procedures Relate mathematical ideas to situations drawn from other contexts Communication Communicating Ability to read and interpret mathematical language charts and graphs Correct use of mathematical symbols labels units and conventions Appropriate use of mathematical vocabulary Explanations and justifications are partially understandable Justification of the answer presented has a limited connection to the problem solving process and models presented Makes weak connections Makes weak connections Misinterprets a major part of the information but carries on to make some otherwise reasonable statements Sometimes uses mathematical symbols labels and conventions correctly Sometimes uses mathematical vocabulary correctly when expected Proposing the Park Rubric Thinking Reasoning and Proving Explanations and justifications are understandable by me but would likely be unclear to others Justification of the answer presented has some connection to the problem solving process and models presented Makes simple connections Makes simple connections Mis
132. odelling Canada s Baby Boom TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 1 1 Going Around the Curve Experiment A A particular mould grows in the following way If there is one blob of mould today then there will be 4 tomorrow 9 the next day 16 the next day and so on Model this relationship using linking cubes Purpose Find the relationship between the side length and the number of cubes Hypothesis What type of relationship do you think exists between the side length and the number of cubes Procedure 1 Build the following sequence of models using the cubes 2 Build the next model in the sequence Mathematical Models Complete the table including first and second differences T Make a scatter plot and a line of best fit 24 22 20 TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 3 5 1 2 Going Around the Curve Experiment B Jenny wants to build a square pool for her pet iguana She plans to buy tiles to place around the edge to make a full play area for her pet Model the relationship comparing total play area pool combined within the edging to the side length of the pool using linking cubes Purpose Find the relationship between the side length of the pool shaded inside square and the total play area Hypothesis What type of relationship do you think exists between the side length and the play area Proce
133. olution to someone else in the class TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 24 4 3 4 The Sub Way e In groups of three have each person in the group solve one of the systems below e Use your CAS handheld to help you solve and check your system e Share your solutions with each person in the group y 4x 24and y 5x 12 13x y 4and 5x y 4 0 Challenge y X 8and y 5x CHALLENGE Plot each of the POI s from Systems A B and C and find the equation of the line that connects the three points Equation of Line TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 25 4 3 5 What s My Equation Part 2 Problem A Yasser is renting a car Zeno Car Rental charges 45 for the rental equations of the car and 0 15 per kilometre driven Erdos Car Rental charges 45 0 15x 35 for the rental of the same car and 0 25 per kilometre driven y For what distance do the two rental companies charge the same amount i j y 35 0 25x Problem B Equations The school council is trying to determine where to hold the athletic banquet The Algebra Ballroom charges an 800 flat fee and 60 60x 800 per person The Geometry Hall charges a 1000 flat fee and 55 y per person For what amount of guests do the two banquet halls charge the same amount y 55x 1000 Problem C The yearbook club is considering two different companies to print Equations the yearbook
134. olving this problem Problem 2 Determine the volume of medicine that will fill the following capsule What possible assumptions are made when solving this problem Problem 3 Determine the volume of cake that is surrounding the cream filling TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 49 7 11 5 Mega Mind Map Comparing Concepts Volume amp Area Concept 1 Volume Concept 2 Area TIPS4RM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 50 7 12 1 Pumping Up the Volume Solving problems dealing with three dimensional objects is similar to pulling a puzzle apart pieces need to be thought of separately The following swimming pool problem illustrates this Part A Pool Volume Determine the volume of water in cubic feet needed to fill the above municipal swimming pool Steps 1 Break up your three dimensional object into the basic objects such as cylinders rectangular and triangular prisms etc This will make determining the volume of these objects much simpler N One method of breaking up the object is shown above The pool has been broken into seven objects How many other ways could you break up the pool ad Label each section of the pool shown in step 1 above with the letters A B C D E F and G and identify the geometric shapes A B C D E F G 4 The problem asks you to determine the volume in cu
135. ons Say that you are considering the following linear system 3X 2y 16 5x 2y 9 You probably agree that if we add these two equations the y variable will be eliminated Here is how to do this on a handheld First be certain that you are on a Calculator page If you need help with this see the Getting Started section from earlier in this manual When you type in the equations be certain to enclose them in brackets Remember that we decided to add the equations Here are the keys you should press DBPOPPOUOVOW OD POPP OOE GP It will look like this on your handheld PAD AUTO REAL T Press the amp key The handheld will display the result RAD AUTO REAL 0 You have eliminated the y variable Sack 2y 16 4 5 x 2 y 8 8x24 i Subtracting two equations works the same way as adding two equations The key is to remember that you must enclose each equation in brackets when you type it into the handheld How to Multiply to Find an Equivalent Equation Consider the following linear system 2X by 7 6x 3y 3 lf we immediately add or subtract the equations neither the x or the y variable is eliminated Instead we must multiply one of the equations by an integer so that the coefficients match Then if we subtract the equations a variable will be eliminated Let s multiply the first equation by 3 Remember that all terms on both sides of the equation must be multiplied by 3 so that the equation stays balanced Her
136. or Down Continued Part B The Folding Up of the Net 1 Now we are going to fold the net to create a square based pyramid Follow the stages below Stage 4 The Folding Up Stage 1 The NET Stage 2 Tilt Back Stage 3 Tilt Further back Begins Stage 8 Complete 2 Take the stage 8 diagram and locate the measurements from part A on the pyramid ft This is called the slant height of the pyramid hs which bisects the base ft This is the base of the pyramid b 3 Create a formula to find the surface area of any square based pyramid using b for the length of the base and h for the length of the slant height Use the equation format below as a guide S Asquare based pyramid y 4 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 23 7 6 2 Rectangular Based Pyramids Part A Rectangular Base Formula e dentify the slant heights length and width of the rectangular base e Create a formula to calculate the surface area of a rectangular based pyramid e Sketch the net of this rectangular based pyramid Part B Rectangular Base Surface Area e Determine the slant heights of each triangle with the help of the Pythagorean Theorem e Calculate the total surface area of the object TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 24 7 7 1 Which Net Take a look at the rectangular prism 5 cm a Which one
137. ources used e Your final submission can include some of the following for a career type of education training required potential average salary employability example of job posting newspaper Internet etc ii for a topic or activity historical background related issues TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 5 2 4 1 What s My Triangle 1 Decide whether to use sine cosine tangent or the Pythagorean relationship to find x Solve for x 24 cm Hypotenuse 2 Decide whether to use sine cosine tangent or the Pythagorean relationship to find ZC Solve for ZC 3 Decide whether to use sine cosine tangent or the Pythagorean relationship to find b Solve for b C b S cm B 12 cm A 4 Decide whether to use sine cosine tangent or the Pythagorean relationship to find x Solve for x C 30 mm TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 6 2 4 1 What s My Triangle continued 5 Decide whether to use sine cosine tangent or the Pythagorean relationship to find x Solve for x 20 cm B 16cm A 6 Decide whether to use sine cosine tangent or the Pythagorean relationship to find ZB Solve forZ B C 54 mm 30 mm B A 7 Decide whether to use sine cosine tangent or the Pythagorean relationship to find a Solve for a 8 Decide whether to use sine cosine tangent or Pythagorean relationship to
138. ow the instructions on the calculator screen and press ENTER Run the Ranger program on your calculator From the main menu of the Ranger Program select 3 APPLICATIONS Select 1 METERS and then select 3 BALL BOUNCE Follow the directions on the screen of your calculator Release the ball so that the bottom of the ball is 1 m above the floor The CBR should be at the same height as the bottom of the ball Drop the ball and then press the trigger key on the CBR just before the ball strikes the ground Try to keep the CBR steady as it collects the data This may take a little practice Your graph should have a minimum of 3 bounces If you are not satisfied with the results of your experiment press ENTER select 5 REPEAT SAMPLE and try again Repeat it until you get a nice graph of the ball bouncing Data Collection The goal is to capture the motion of the ball that represents the period from the first bounce to the second bounce 1 Press ENTER to return to the PLOT MENU Select 7 QUIT to exit the Ranger Program The data that you will work with will be in L1 and L2 Use the built in Select feature of the calculator to select the data you want Follow the keystrokes below a Press 2 STAT scroll over to OPS menu and then scroll down to 8 SELECT and press ENTER b After the bracket enter where you want to store the selected data To use L3 and L4 press 2 L3 2 L4 and ENTER c To actually select a part of the graph
139. own below Ye 3 To enter an equation for graphing press the 4 Enter your equation in Y1 For example to graph y 3x 4 enter Os BS 4 You will see the following on your screen Floki Flotz Floks B 5 To view your graph press the button You will see the graph as shown below TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 39 3 4 3 Can Graphing Get Any Easier 1 x 4 3 10 6 B 4 2 21 4 B g iyll 1 Start at the y intercept 2 Only moving up or down how many units do you need to reach the same level as point B 3 Only moving right how many units do you have to move your pencil to connect to point B 4 Qiven the equation for the graph state the slope and the y intercept Slope y intercept TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 40 3 4 3 Can Graphing Get Any Easier Continued 1 Start at the y intercept 2 Only moving up or down how many units do you need to reach the same level as point B 3 Only moving right how many units do you have to move your pencil to connect to point B 4 Given the equation for the graph state the slope and the y intercept Slope y intercept TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 41 3 4 3 Can Graphing Get Any Easier Continued y 2x 5 I A A 4 2 1 Start at the y intercept 2 Only moving up
140. pplications of Trigonometry Assignment Introduction How would you find the height of a tree You could climb to the top to measure it but that would not be either safe or practical How can we measure the height of clouds airplanes or other highly inaccessible objects Airports measure the clouds for pilots to let them know at what altitude they should fly In this activity you will measure the heights of various objects using a single clinometer and trigonometric ratios You will measure the following heights 1 2 3 You must hand in the following details gt Show a table of data gt Show ALL calculations gt Table of results gt Sources of error Building Clinometer First you will need to make clinometer You will be using the protractor template using the instructions on handout 2 6 1 given to you by your teacher Glue the template onto a piece of cardboard el ile iu dons rd dd Sts 3 ae Cae di Ares r Hole tor string krot lay F Jar mE TIPSARM Grade 10 Applied Unit 2 Trigonometry August 2008 2 13 2 6 2 Applications of Trigonometry Assignment continued Measuring Distances Use a tape measure to find an appropriate distance back from the object you are finding the height of Hold the clinometer level along the horizon line and adjust the angle of the straw to sight the top of the object through the straw METHOD for finding inaccessible heights TIPS4RM Grade
141. pplied Unit 1 Similar Triangles August 2008 1 15 1 4 3 What Is Similarity continued 4 a Place AABC ADEF and AGHJ on the geoboard JM LA E EUNDEM X so that one vertex of each triangle is on the same oe o gt o o o peg and two of the sides are overlapping e 9 o b Copy your model on the grid oe Bee tee ee ag 5 a What do you notice about the corresponding angles of AABC ADEF and AGHJ b What do you notice about the corresponding sides of AABC ADEF and AGHJ Summary know the following about similar triangles TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 16 1 4 3 What Is Similarity continued 6 Use the geoboards to explore whether the following triangles are similar Explain your reasoning Explain your reasoning Explain your reasoning TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 i7 1 4 4 Exploring Similarity 1 Which of the following four houses are similar Explain why Label the diagrams 2 Onthe grid draw a house that is similar to one of the figures Complete the following statement The house drew is similar to house know this because TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 18 1 5 1 Similar Triangles Definition Properties Characteristics Similar Non examples Triangles TIPSARM Grade 10 Applied Unit 1 Similar Triangles
142. pplied Unit 3 Equation of Lines November 2008 3 2 Section Activity Practising Modelling Y the X Are You Intercepting Me Y the X Are You Intercepting Me Practice Jack and Jill Go up a Hill Slopes A way So You Think You Know Everything 83 About Lines Review of Concepts So You Think You Know Everything 84 About Lines Review of Concepts Horizontal Lines Investigation So You Think You Know Everything About Lines Review of Concepts Vertical Lines Investigation olope Y intercept Form Practice Ulli MEN Instructions 105 105 Unit 3 Equations of Lines Review TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 3 3 1 1 Definition Match Definitions An orderly arrangement of facts set out for easy reference e g an arrangement of numerical values in vertical and horizontal columns The difference between two consecutive y values in a table in which the difference between the x values is constant The vertical distance between two points The horizontal distance between two points A relation in which the graph forms a straight line A relation in which one variable is a multiple of the other plus a constant amount The change in one variable relative to the change in another The starting numerical worth or starting amount A description of how two variables are connected In a relation the variable whose values you calculate usually placed in the
143. pt Then graph the equations on the grid below Use a different colour for each line and label each line a 3x y 120 b 3x 4y 12 20 Practice 5 For each equation gt Calculate the x intercept and the y intercept gt Graph on the grid provided Use a different colour for each line and label each line a 2x y 4 0 b 4x 2y 6 0 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 69 3 8 2 Jack and Jill Go up a Hill For each of the following questions a Plot the points on the given grid b Draw a line connecting the points Calculate the rise by counting squares Calculate the rise again by using the coordinates of the points Show your work to confirm your answers The first one is done for you Calculate the run by counting squares Calculate the run again by using the coordinates of the points Show your work to confirm your answers Calculate the slope rate of change Rise 3 023 Run 0 22 2 Rise Slope E Run TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 70 3 8 2 Jack and Jill go up a Hill continued slope is undefined SRR eee BRR eee LL tT tT LL ET EA ET EE dL LL LL LL LLLI LE LA eee ERR REE Eee LL LLL Ld LL ee ett LLL tT tT LL LLLA LL LL LL d ll LL LLL k A a LL dL LL d LL Lal LL S LL LLL LLL ff Reminder d EL d d d d d LL Lad LL LL LL LL LL LL Vertical lines Jeet tt LL EL al LL LL LLL Ll Ll l denothavea LLL Ld Ll LLLA
144. quation 5x 93y 1520 Graph this equation on the grid with your other two graphs Using the graph does this equation ever cross one of the other lines What do these points mean in the context of this problem c Basedon the graph and the equation is your friends bridge better worse or the same as the Beam bridge Offer mathematical proof d Based on the graph and the equation is your friends bridge better worse or the same as the Arch bridge Explain using mathematics TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 97 Unit 3 Equations of Lines Review 1 Ona Cartesian coordinate system plot and label the following points A 2 1 B 4 10 C 1 7 D 2 3 a Draw the following lines AB AC BC CD b Calculate the slope for each line using a rate triangle Slope AB Slope AC c Calculate the following slopes algebraically Verify with the graph Slope BC Slope CD 2 Comparison of Slopes a If a line slants upward from left to right it has a slope b If a line slants downward from left to right it has a slope TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 98 Unit 3 Equations of Lines Review continued 3 Draw two examples of lines with a positive slope and two examples of lines with a negative slope in the corresponding grids below Lines With Positive Slopes Lines With Negative Slopes HH H 4 Circle the equations of the lines that
145. r 12 weeks 6 This person is withdrawing depositing that is positive negative correlation Circle correct answers b Rule in words Balance starts at and by per week c Algebraic Rule B d After 12 weeks TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 14 3 2 1 Agree to Disagree a Point A has coordinates 3 2 b Point B has coordinates 3 4 c Point C has coordinates 1 1 d Point A is in Quadrant 4 e The origin is located at 0 0 a The rate of change is 25 week b The initial value is 200 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 15 3 2 1 Agree to Disagree Continued A family meal deal at Chicken Deluxe costs 26 plus 1 50 for every extra piece of chicken added to the bucket a The rate of change is 26 b The initial value is 426 c The independent variable is number of pieces of chicken A Chinese food restaurant has a special price for groups Dinner for two costs 24 plus 11 for each additional person a The rate of change is 11 b The initial value is 11 Number of Cost ofa Toppings Large Pizza oO J 940 a The initial value is 9 40 b The rate of change is 1 10 c Dependent variable is the Cost of a Large Pizza c The dependent variable is the number of people TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 16 3 2 2 Exploring an MB Eh Y in
146. r on Point B you can now click and drag the line Look at the slope number Answer questions 1 6 on the worksheet amp Now that you have looked at the slope let s look at the y intercept Select New Sketch from the File menu Let s show some grid first see instructions above Now click on the Point Tool on the left hand side and create a point anywhere on the y axis Select Translate from the Transform menu On the pop up menu click on Rectangular on the top Enter 3 for Horizontal and 2 for Vertical or any one digit number that you want Click Translate Select the Arrow Tool on the left hand side menu and click on any white space Click on the point on the y axis to highlight it and select Ordinate y from the Measure menu Click on any white space TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 31 3 3 4 Slopes and Stuff on GSP Optional continued Create a line with those two points see instructions above After you have created the line click on any white space and then highlight the line Select Slope from the Measure menu Click on any white space and then highlight the line again Now as you move the line look at the y ordinate number and look at the slope value Answer questions 7 10 on the worksheet Ok a little bit more and the activity is done But first we need to create another line Click on the Point Tool on the left hand side again and create a point anywhere on the y
147. rm y ax bx c August 2008 6 30 6 11 2 Review of Quadratics continued 4 Forms of A Quadratic Factored Form y z x r x s a There are two methods of factoring algebra tiles and algebra b Example factor y x 3x 2 using tiles Product Sum Form Factor y ax bx c In this caserxs candr s b Find the x intercepts of the following Common Factoring y ax bx Let us factor y x 3x This can be written as Based on this r x s r s The factored form is y or 1 Factor as state the x and y intercepts of y 2x 2x 60 Difference of Squares y ax b 2 y 2 x 4 can be written as y rxs r s factored form TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 31 6 S Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit Summary TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 32 6 R Reflecting on My Learning 3 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 33 6 RLS Reflecting on Learning Skills Students should be aware of the importance that these skills have on your performance After receiving your marked assessment answer the follow
148. rmine e The zeros x intercepts e The y intercept With the information you find and using symmetry graph each parabola b y x 7x 10 TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 23 6 10 1 Problem Solving with Quadratic Graphs Interpreting Parabolas 1 The graph below shows the height in meters of a diver jumping off a springboard versus time in seconds a What is the initial height of the jumper What is this called in math terminology b Label and write the ordered pair of the vertex What does this mean in real life C Label and write the ordered pairs of the roots zeros What do these points mean in real life 2 The graph below shows the height of a toy rocket after it is launched a How many seconds is the rocket in the air b What math concept did you use to determine this a 180 c What is the maximum height of the rocket 120 d At what time does the maximum height occur 60 e At what times is the rocket 120 meters above the earth g What pattern did you observe in the second differences from the table How does this prove that the relationship is quadratic TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 24 6 10 2 Applying Quadratic Relationships There are many relationships that turn out to be quadratic One of the most common is the relationship betw
149. rs R Us charges 60 00 per weekend for a midsize car plus 0 20 per km Travel With Us charges 0 50 per km Renting a Car a Graph both options on the grid and determine the number of kilometres where both companies will cost the same amount 200 b Explain what this means for your weekend trip 190 Cost 100 90 100 200 300 400 Number of kms 2 Anthony and Anne are bicycling at a Provincial Park Anthony travels at the rate of 10 km hr and begins 2 km from the park entrance Anne begins at the park entrance and travels at a rate of 15 km hr They both travel at a constant rate towards the Outdoor Education Centre Bicycling in the Park Graph both routes on the grid and determine the meaning of the point of intersection Distance From Park Entrance km Time hours TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 14 4 1 3 Meaning of the Point of Intersection continued 3 Foracar wash fundraiser Team A washes 2 cars per hour starting a 7 00 a m Team B begins washing cars at 9 00 a m and washes 3 cars per hour Graph the car washing progress of each team on the grid and determine the meaning of the point of intersection as well as the meaning of the points before and after the point of intersection Fund Raiser Number of Cars Hours Elapsed TIPS4RM Grade 10 Applied Unit 4 Linear Systems August 2008 4 15 4 2 1 A Visual Cell Phone Problem Two cell phone compan
150. rsor to the left of one X intercept or just enter an x value that is to the left of the x intercept Press ENTER T1 Cn sitnt d k Right Bound f 2 555191 J 2 72 02QQ05 6 Repeat for the right bound being sure that you are to the right of the same x intercept 7 The next screen will say guess You can guess if you want but it is not necessary Press ENTER You will get one x intercept 8 Repeat steps 3 through 7 to get the other x intercept TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 8 6 4 1 Finding the x Intercepts of a Quadratic Equation continued 1 Use the graphing calculator to find the x intercepts for each of the following 2 Can you determine the x intercepts by looking at a quadratic equation Explain 3 Which form of the quadratic equation did you find the easiest to use when determining the x intercepts Explain the connection between the factors and the x intercepts TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 9 6 4 2 Area with Algebra Tiles Name Using algebra tiles create the rectangles for the following areas Complete the following chart X6 7x 12 1 Find a relationship between the number of x tiles and the numbers in the expressions for the length and width 2 Find a relationship between the number of unit tiles and the numbers in the expressions for the
151. s hurricane in km Photo taken with a 90mm camera lens on a Linhof camera at an altitude of 267 km Draw a diagram to help TIPS4RM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 31 1 8 3 Practice 1 A tower casts a shadow that is 750 m long At the same time a metre stick casts a shadow 1 4 m long Label the diagram Find the height of the tower A 2 Sam places a mirror on the ground 5 m from the base of a tree He then walks backwards until he can see the top of the tree in the mirror He is now standing 0 75 m from the mirror Sam s eye level is 1 75 m high Label the diagram Find the height of the tree TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 32 1 W Definition Page Acute Triangle Obtuse Triangles Right Triangle TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 33 1 W Definition Page Continued ocalene Triangle Equilateral Triangle Isosceles Triangle Similarity Corresponding Sides Ratio of Sides TIPSARM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 34 1 S Unit Summary Page Unit Name Using a graphic organizer of your choice create a unit Summary TIPS4RM Grade 10 Applied Unit 1 Similar Triangles August 2008 1 35 1 R Reflecting on My Learning 8 2 1 3 Things know well from this unit 2 Things need explained more 1 Question still have TIPSARM Grade 10 Applied U
152. s the independent variable 10 What is the dependent variable TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 10 3 1 6 A Mathematical Spelling Bee Continued 11 Create a scatter plot from your data on the grid provided Label the axis with the independent variable on the x axis and dependent variable on the y axis 12 Draw a line of best fit from the scatter plot above Extend your line to both the x axis and y axis 13 Using a rate triangle calculate the rate of change of your line of best fit 14 Interpret the meaning of the rate of change as it relates to this activity 15 At what value does the line cross the y axis 16 Interpret this value in the context of this activity 17 At what value does the line cross the x axis 18 Interpret this value in the context of this activity TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 11 3 1 8 Variables and Equations with Graphs For each of the following graphs determine a The rate and the initial value from the graph Show your work on the graph b Arule in words that relates the balance B the number n of weekly withdrawals or deposits and the initial amount in the account and c An algebraic rule relating Balance B the number of weekly withdrawals deposits n and the initial value in the account d Determine how much will be in the account after 12 weeks using the formula 1 This person is withdrawi
153. solving process and models presented Level 4 Explanations and justifications are particularly clear and detailed Justification of the answer has a direct connection to the problem solving process and models presented with evidence of reflection Application Connecting Make connections among mathematical concepts and procedures Relate mathematical ideas to situations drawn from other contexts Makes weak connections Makes weak connections Makes simple connections Makes simple connections Makes appropriate connections Makes appropriate connections Makes strong connections Makes strong connections Communication Communicating Ability to read and interpret mathematical language charts and graphs Correct use of mathematical symbols labels units and conventions Appropriate use of mathematical vocabulary Misinterprets a major part of the information but carries on to make some otherwise reasonable statements Sometimes uses mathematical symbols labels and conventions correctly Sometimes uses mathematical vocabulary correctly when expected Misinterprets part of the information but carries on to make some otherwise reasonable statements Usually uses mathematical symbols labels and conventions correctly Usually uses mathematical vocabulary correctly when expected Correctly interprets the information and makes reasonable statem
154. st 72 unit for example if you are estimating the length of your arm you might guess 1 75 feet 2 feet or 2 75 feet sid ee yd ine LLL IR ine LL In Us wan o Length from your classroom door to the door next door yd yd TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 5 7 2 1 Imperial Decisions Fill in the following table by completing the ESTIMATE column first When you have finished filling in the middle column the actual conversions will be revealed Inches to Feet How many inches are in ONE foot Feet to Yards How many feet are in ONE yard Square inch to Square foot How many square inches are ina square foot Square foot to Square yard How many square feet are in ONE Square yard Cubic inch to Cubic foot How many cubic inches are in ONE cubic foot Cubic foot to Cubic yard How many cubic feet are in ONE cubic yard TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 1 6 7 3 1 Body Parts INCH FOOT YARD HAND CUBIT Originally was the length of three barley grains placed end to end Distance from tip of thumb to first knuckle or from first to second knuckle on index finger My INCH INCHES Length of foot from longest toe to heel My FOOT INCHES Distance from tip of nose to end of thumb with arm outstretched cloth merchants King Henry I My YARD INCHES Width of one hand including the thumb heig
155. st need a formula that converts Celsius to Fahrenheit Here s some info to help Lm 20 968 1 What is the y intercept 2 If we write the information as points 0 32 and 20 68 plot the two points and find the slope using a rate triangle E Slope lise _ 54 run Write the slope as a fraction in reduced form Fahrenheit iy E 2 4 6 8 10 12 14 16 18 20 Celsius x 3 Now that we know the y intercept and slope state the equation relating Celsius X to Fahrenheit y 4 Using your equation convert the following two temperatures in degrees Celsius to degrees Fahrenheit a 10 b 30 TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 51 3 5 2 Temperature Conversions Investigation Continued Lets help Nethead now How many degrees Celsius is it if its 23 Fahrenheit Hint Substitute 23 for y and solve the equation for x using the Nspire CAS handheld When you enter the equation it will look like First subtract 32 from both sides E Remember that means x multiplied by 9 and divided by 5 So you have to do the opposite of each of the two operations to solve for x Your screen will look like So 23 Fahrenheit is 5 Celsius DEG AUTO REAL If we could get rid of the fractions in the equation first you could solve the equation without using CAS Enter Qs jmd 5 the original equation 23 32 again and multiply by 2 115 95cF160 5 5 then s
156. t Slope Form yomx b What does the m and b represent Exploring the m We already know that ina table of values for a linear relationship a pattern will form his pattern is the e Pattern Equation TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 17 3 2 2 Exploring an MB Eh continued Exploring the m What is the pattern Pattern What is the equation Equation Exploring the m What is the slope TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 18 3 2 2 Exploring an MB Eh continued Exploring the m What is the slope Wh t de yoeu netice Es E Calculate the slope for each line What is the equation TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 19 3 2 2 Exploring an MB Eh continued What does the m represent What is the slope and what does the m represent TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 20 3 2 2 Exploring an MB Eh continued Exploring the b Look at the table and look at the equation What do you notice When x 0 Equation has Equation Look at the table and look at the equation What do you notice When x 0 Equation has Equation gt TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 2 2 Exploring an MB Eh continued Exploring the b Wh
157. t shows how much little Johnny will have over the first three weeks Fill in the picture of 4 shape b Create an equation in the form of y mx b Fill in the Total Area Column from the data above Create an equation in the form of y mx b He wants to buy a pet fish that he will name from the data above Ernie by Christmas that is in 9 weeks Will he have enough money to buy Ernie if he costs 23 Using your equation what will the area of 12 figure be Show your work How many shapes would you have to build to Little Johnny is also considering saving up for have 139 cubes Explain a new bike that costs 127 If he does not buy the fish how long will it take until he has saved up enough to buy the bike TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 60 3 6 4 Modelling Problems Algebraically continued The Mechanic Problem Patterns in Area A mechanic earns 25 per hour Consider the following patterns created with unit a The graph below illustrates hours worked versus earnings Build the first second third and fourth Sa shapes with the cubes Fill in the picture of Label the axis in the graph above the 4 shape Create an equation in the form of y mx b Fill in the Total Area Column from the data above Create an equation in the form of y mx b How much will the mechanic earn after 40 from the data above hours What will the area of 7 figure be Show your l l work
158. t that you want to undo press Ce If you undo something that you want back again press C How to Solve for a Variable Example One Say that you wish to solve the equation 6x 2y 16 for the variable y To do this first be certain that you are on a Calculator page If you need help with this see the Getting Started section above First type in the equation that you want to solve Use the number pad and the green letter keys the operations x are located on the right and the equals sign is in the top left corner of the keypad When you have typed in the equation press the key found in the bottom right corner RAD AUTO REAL The top of your screen will look something like this 6x 2 y 16 TE Now decide how you would start in solving for y RAD AUTO REAL Perhaps you ve decided that subtracting 6x from both sides of the equation is a good start Wonderful To 9x 2v 1 x7 aya lo do this immediately press lt S 6S Notice that the Ans 6x handheld automatically inserts Ans What is this Ans stands for the last answer you found If you now RAD AUTO REAL L press the amp key the handheld will subtract 6x from ay 6x ay 1e amp the left side and the right side of 6x 2y 16 You a s NN icu A will see this result 6 x 2 y 16 6 x 2 p 16 6 x Continue solving the equation You probably see that to finally isolate the y variable it is necessary to divide the equation by 2 o
159. the table including first and second differences 20 Make a scatter plot and a line of best fit TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 7 5 3 2 Key Features of Quadratic Relations The maximum or minimum point Vertex on the graph It is the point where x y the graph changes direction Minimum maximum value Axis of symmetry Label the graphs using the correct terminology Graph A NENNEN NL LI CCAR EEE LE LIE LLL LL LIN LI TIA S LL N LE LN LIA TT LL TT tT AT A ptt tt IN SE UN HH WII NL 3H44444 244 cH be bp IN TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 8 Cut out the following boxes and place them in the correct position on the two graphs on the previous page 5 3 3 Key Terminology Pe eB BB eB eB eB eB BE ES S hc eee e o e e e o m 1 e e e Le ee ee ee ee ee HL eee e e o e e Minimum y intercept Maximum Le e ee ee ee ee o ooo om ld 5 9 TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 TIPSARM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 10 5 4 1 Key Features of a Parabola Write the feature of a parabola that you were given in the centre of the graphic Complete the chart Include sketches and gr
160. the total area of the park Since you know how to find the areas of basic shapes e g circles rectangles and triangles you should try to break up the park into basic shapes and determine the areas of each 1 Examine the inside area that is to receive sod Draw line segments that will break up the field into basic shapes you may have duplicated shapes TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 13 7 4 3 Proposing the Park Continued 2 Draw the basic shapes in the space below Be sure to include the dimensions of each shape You may or may not use all of the space provided below Basic Shape 1 Basic Shape 2 Basic Shape 3 Basic Shape 4 3 Determine the area for each of your basic shapes drawn above to 1 decimal place Area Basic Shape 1 Area Basic Shape 2 Area Basic Shape 3 Area Basic Shape 4 TIPSARM Grade 10 Applied Unit 7 Surface Area and Volume August 2008 7 14 7 4 3 Proposing the Park Continued 4 Calculate the total area of the park that will receive sod to 1 decimal place State your solution using the following units i square feet ii square meters 5 If each roll of sod covers 16 square feet how many rolls of sod need to be ordered to complete the job 6 Sham City must use a special fertilizer for their grass to grow due to their northern climate This fertilizer comes in 15lb bags that cover 250 m of new laid sod How many bags of fert
161. to calculate how many hexagons you would have if you counted all the sides and got a number of sides equal to 1206 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 80 3 9 3 Fm on your side Continued TRIANGLE INVESTIGATION Start by placing triangles side by side as shown Note This arrangement of 3 triangles has 11 sides i ATX 3 1 Complete the following table relating the number of triangles and total number of sides Equation s n Remember You need the slope and y intercept Use your knowledge to calculate these values 2 Use your equation to calculate the number of sides that 76 triangles placed side by side would have 3 Use your equation to calculate how many triangles you would have if you counted all the sides and got a number of sides equal to 483 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 81 3 9 4 l m on your side Journal Your best friend has called you for help on writing equations of lines They have been given two points Explain to them two different ways to write the equation of the line You may use words numbers or graphs in your explanation TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 82 3 10 1 So You Think You Know Everything About Lines Review of Concepts You ve learned a lot up to this point in the unit and to ensure that you still remember it let s do a little review With your partner co
162. ts What will your equation be now 6 What if all the points from the graph in question 1 shift left 4 units What will your equation be now 7 Write the equation of the vertical line that passes through a 3 4 b 2 4 c 0 1 8 Write a general equation for all vertical lines Hint Use a for the x intercept TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 87 3 10 6 Converting from Standard to Slope Y Intercept Form Practice 1 Convert the equations below into slope y intercept form a 3x y 1 0 b 3x 4y 1220 2 Now state the slope and y intercept for each equation a b 3 For each equation gt Convert to slope y intercept form gt State the slope and y intercept gt Graph on the grid provided Use a different colour for each line Label each a 2x y 4 0 b 4x 2y 6 0 Cc x y 520 d 3x 2y 8 0 MR a ea a a r e ae TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 88 3 11 2 London Bridge Is Falling Down Introduction Introduction to Bridge Building There are many different types of bridge designs which serve different purposes The factors that determine the bridge design includes the type of traffic i e more trucks or cars what is under the bridge the aesthetics and the cost Beam or Plank Bridge Arch Bridge Cable Stayed Bridge Suspension Bridge Source Images are taken from NOVA Online http www pbs org wgbh nova bridg
163. twear Fermat s Footwear VVages a P 0 01s 100 b P 0 10s 100 Py b gd gd py pp c P 21005 10 xL i Ll tt ft STT LIT d P 0 05s 200 Lam Provide a reason or justify why you selected the equation that you chose Refer back to the equation for Euclid s Electronics for hints Week s Pay 1000 X 1500 2000 2500 Total Value of Sales TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 7 4 1 1 Working on Commission Continued Which One ts Better Nahid needs help determining which job she should keep She decides to look at them as a system of equations when she creates a graph comparing the two equations at the same time Analyze the graph and complete the questions below Euclid s Electronics Fermat s Footwear St 1000 1500 2000 2500 Total Value of Sales 1 Where the two lines cross is called the point on intersection or the solution to the system At what coordinates do the two lines cross 2 What does this coordinate represent in terms of Nahid s sales and pay for the week 3 If Nahid usually makes 1500 worth of sales per week which job should she take Explain 4 How does the graph help Nahid determine which is the better job 5 What does the point 1000 250 represent in the graph TIPSARM Grade 10 Applied Unit 4 Linear Systems August 2008 4 8 4 1 2 What s My Equation You are given four problems below Each problem
164. ubtract and divide to solve Your solution 115 92 160 160 TEST looks like Drug MN Ld 45 9 x PEE Comparing the two solutions you can see the second one could be done without CAS 5 Convert the following two temperatures in degrees Fahrenheit to degrees Celsius by solving the equation by pencil and paper first and then checking your solution using CAS a 5 b 83 c 10 TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 52 3 5 3 Temperature Conversions Practice 1 Solve the following equations using pencil and paper C PT o 3 Hint Multiply each term by the common denominator 2 Typing Speed The formula for calculating typing speed is w 10e ges E where s is the speed w is the number of words t is the time in minutes e is the number of errors a Nethead types 250 words in 15 minutes with 9 errors Calculate his typing speed b Wingman types 500 words in 5 minutes and has a typing speed of 72 words per minute How many errors did he make TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 53 3 6 2 Can You Stop The Fire PROBLEM You work for the Ministry of Natural Resources as a Fire Fighting supervisor You arrive in Dryden Ontario where you find two fires burning e The first fire has just started along 3 km of shoreline beside a lake and is moving east at a rate of 1 km hr e he second fire is also rectangular in shape and is being extinguish
165. vity on Mars is less than half that on Earth A ball thrown upward can be modelled using h 2 15t 2 where his the height in m and fis the time in seconds a Graph the relationship using your graphing calculator Remember that you need to set your window settings Record the window settings you used You may need to play around with the settings until you see the full graph What is the initial height of the ball Explain what this means What is the maximum height of the ball When does the ball reach its maximum height When does the ball hit the ground When is the ball more 20 m above the ground You may need to give approximate answers If the same ball was thrown upward on the Earth how would you expect the relationship to change The force of gravity on Jupiter is much greater than on the Earth If the same ball was thrown upward on Jupiter how would you expect the relationship to change TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 26 6 11 1 FRAME Function Representation And Model Examples 9 919U07 Jeryedg JENSIA sjapow DJesqsebiy SonJ eA Jo s jqeL SDJOM Ady uondii seg en3xo1u05 C Q o A 3 O Q TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 27 6 11 2 Review of Quadratics 1 Linear vs Quadratic a A linear relation forms a graph with a b
166. x r x s How would you find the value of r and s TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 14 6 5 3 Match It Name Match each pair of numbers on the left with the correct product and sum on the right r 1 s 5 r 1 s 6 LI LE E E c E B s EN TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 6 1 Use Intercepts to Graph It Given the standard form of the quadratic relation identify the value of the sum and product needed to factor Express the relation in factored form identify the x intercepts and y intercept and use these results to make a sketch of each parabola y x x r s r s rrs Sketch of the relation TIPS4RM Grade 10 Applied Unit 6 Quadratic Relations of the Form y ax bx c August 2008 6 16 6 7 1 Investigate Relations of the Form y ax b Name 1 Obtain a graphing calculator and equation from your teacher 2 Type in the equation using the Y button on your calculator Key in zoom 6 to get the max and min from 10 to 10 on your window 3 Fill in the table y Coordinates of x intercepts and and the coordinate of the y intercept S 4 n your group sketch all four graphs 5 Identify what is the same and what is different in these four graphs TIPS4RM Grade 10 Applied Unit
167. you determine how many hotdogs and samosas were sold NOTE Assume one hotdog or one samosa per purchase TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 40 4 6 5 Help an Absent Friend Consider the following linear system 2x 3y 1 3x y 7 How would you solve it Write in words a description of the steps you would take To help you understand what to write pretend for a moment that you are writing the instructions for a friend who is not in class today What steps would you need to describe TIPSARM Grade 10 Applied Unit 4 Linear Systems July 2008 4 41 4 6 6 Here s To The Crazy Ones 1 Solve the following linear system by elimination 4x 2y 12 8x 4y 32 2 Did you encounter any results that are unusual Explain what is different compared to questions you have already solved 3 Re arrange each equation from the linear system into y mx b form then graph For example here is how the first equation can be re arranged Ax 2y 12 2y 4x 12 2 4x L2 Eun e S 2 2 2 y 2x 6 N N E N Ed IE E NE a a 0 W a E E IE N E N C 4 What do you notice about the slope in each equation that you re arranged What do you notice about how the two lines visually relate to each other Is there a solution to this linear system TIPS4RM Grade 10 Applied Unit 4 Linear Systems July 2008 4 42 4 6 6 Here s To The Crazy Ones Continued 5 Solv
168. you will use use the arrow keys to move to the left end of the parabola that you want to keep This should be the first bounce Press ENTER This sets the left bound Use the arrow keys to move to the right end of the parabola that you want This should be the second bounce Press ENTER The selected data will be placed in L3 L4 and then this data will be displayed d Sketch a graph of this single parabola using the instructions and grid provided on your Ball Bouncing Record Sheet 3 Repeat the experiment for each of the different balls TIPS4RM Grade 10 Applied Unit 5 Introduction to Quadratics August 2008 5 14 5 5 2 Ball Bouncing Record Sheet Hypothesis 1 We hypothesise the shape of the graph that represents the height of the ball over time will be Sketch the graph T HHH Explain your reasoning SEE coo 2 We hypothesise the time in the air between the first and the second bounce will be for each ball the same different Explain your reasoning Data Collection Follow the steps described on the Ball Bouncing Instructions sheet To make a graph of each ball bounce use the TRACE function or the LIST found using the STAT key EDIT from the graphing calculator to complete the table of values for 7 points starting at the first bounce and ending with the second bounce Include the maximum point Choose an appropriate scale to make an accurat
169. zero so the equation only depends on the value of the y intercept What if all the points from the graph in question 1 shift up 2 units What will your equation be now What if all the points from the graph in question 1 shift down 4 units What will your equation be now Write the equation of the horizontal line that passes through a 3 4 b 2 4 c 2 0 Write a general equation for all horizontal lines Hint Use b for the y intercept TIPS4RM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 85 3 10 3 So You Think You Know Everything About Lines Vertical Lines Investigation With your partner complete the investigation below You will be asked to coach someone later 1 For the graph below write the coordinates of each point on the graph in the table below E 5 K a o 3 z L 4 1 N P Ol 5 mA J K L M N O 2 What do all the points have in common 3 There is only one point that has a coordinate of zero Is there another name for this point TIPSARM Grade 10 Applied Unit 3 Equation of Lines November 2008 3 86 3 10 3 So You Think You Know Everything About Lines Vertical Lines Investigation Continued 4 What is the equation of the line joining all the points Hint The slope of the line is undefined so the equation only depends on the value of the x intercept 5 What if all the points from the graph in question 1 shift right 2 uni

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