Chapter 1
Contents
1. Adds a fast processor and more Flash memory to the TI 83 Plus series Only cal culators that can run Math Introduced in 2013 First color screen TI 84 Plus model Introduced in 1993 2002 Similar in features to the TI 83 Plus but lacking Flash applications and an upgradeable operating Flash applications Print operating systems system which runs under Windows or jsTIfied http www cemetech net projects jstified an online emulator We ll soon start scrutinizing your calculator and you ll learn the basics of it for sim ple arithmetic and math Before we do I want to teach you the difference between MathPrint MP and non MathPrint operating systems and how that difference will affect how you use this book MathPrint vs non MathPrint calculators From the 1990s until 2010 entering math on TI graphing calculators like the TI 82 TI 83 TI 83 Plus and TI 84 Plus stayed basically the same All these calculators have a home screen 16 characters wide and 8 characters tall On each one you entered math expres sions at the left side of the screen and the results of your calculations appeared on the right side of the screen More important you entered every expression as a straight line of numbers and symbols regardless of whether it included fractions square roots integrals or matrices You needed to carefully count opening and closing parentheses to make sure you didn t make a mistake OP2. 550 Figure 1 13 A table and graph of data points for estimating the speed of a car Five students stood along a road and each recorded both the time in seconds when the car passed them and how far in meters they stood from where the car started They didn t do a perfect job so the points aren t exactly in a straight line Five examples of what your calculator can do 15 Figure 1 14 Clearing old lists and using the SetUpEditor command to set up the List Editor left and entering the List Editor right These are the first three steps to fitting a line to some data In case you ve used the List Editor before you press to enter the Statistics menu and in the Edit tab that is the first screen you see choose 5 SetUpEditor You ll see SetUpEditor pasted to the homescreen press to run it When it completes it will have re created Li and Lz as empty lists and printed Done on the screen Your screen will look a lot like the left in figure 1 14 The next step is to enter the lists of times and distances Go back to the Statistics menu by pressing stat this time choosing 1 Edit You ll end up at the blank List Editor like the right side in figure 1 14 Using the arrow and number keys type in the five times and five distances shown in figure 1 13 Make sure your numbers match When you have the same table press to return to the homescreen PLOTTING THE DATA Before you analyze this data you probably want to plot it
3. Follow these steps 1 Press to go to the Y menu As in the previous examples use the key to erase any existing equations 2 Move the flashing cursor up to the Plot1 text and press ENTER It should turn from black text on a white background to white text on a black background 3 Press Y the Stat Plot menu and choose option 1 Make sure Plot1 is set On by moving the cursor over On and pressing ENTER Set Plot1 to the Scatter first type use L for the Xlist and use Lz for the Ylist Figure 1 15 shows what that should look like on a TI 83 Plus TI 83 Plus Silver Edition TI 84 Plus or TI 84 Plus Silver Edition 4 Press GRaPH But wait Where is everything The problem is that the edges of the graph are way too small and all the points are far off the right and top edges of the screen 5 Solution press zoom and scroll down to 9 ZoomStat When you press on it you re brought back to the graph screen There are your points As you might have expected from figure 1 13 which shows roughly what you should be seeing now they don t exactly line up The right side in figure 1 15 is what you ll see once you fit a line to the data But what is the best way to fit that line to the data Let s perform the final step FINDING A LINE OF BEST FIT Your calculator can fit all kinds of lines from straight linear lines to polynomial curves to logarithmic and exponential curves It s up to you to give the calculator a hint about w
4. You can also cube 9 by reg 799 raising it to the third power which means a multiplying the number by itself three times right Depending on what calculator type 729 and version you have your results will look like either the top or bottom section 1 3 will explain more the result of the arithmetic you typed by pressing ENTER You ll see the result of the cal culation printed at the right side of the screen 729 cubic inches SCREENSHOTS Throughout this book I use TI 83 Plus TI 84 Plus screenshots to demonstrate most problems interspersed with occasional TI 84 Plus C Sil ver Edition screenshots No matter which calculator you re using all the examples and skills in this book will work on any TI 83 Plus or TI 84 Plus fam ily calculator even if what you see on the screen is a bit different Another way you can find the volume of a 9 inch cube is to take the length of one side 9 and cube it Cubing a number is raising it to the third power written 9 On your calculator you type this as 9 3 and then press Enter As you might expect and as the right side in figure 1 3 confirms the result is still 729 Note that depending on whether you have a MathPrint operating system on your calculator the key sequence 9 4 3 might display different but equivalent math on your screen As a final exercise imagine slicing the top 3 inches off the box Perhaps you needed to open it or perhaps the cube was actually a 6 inch ta
5. area under a curve Two of the most important skills you ll learn in calculus are taking the derivative and integral of functions These might at first seem like abstract confusing concepts but they have some important real world purposes When you take the derivative of a function you can choose any point along the function and calculate how steep the function is at that point as the left side in figure 1 10 demonstrates An integral lets you calculate the area in any area bounded by two x values the x axis and any function as the right side in figure 1 10 and figure 1 11 show In this example you ll see how your calculator can find the area under a curve using an integral curve at x 2 found with the derivative Shaded area found using integral FFCE Ide 19 1 ee79 Figure 1 10 Using calculus skills to find information from graphs On the left the derivative lets you calculate the slope of a line that exactly touches a function at a given point On the right the integral helps you calculate the area of an oddly shaped region Your calculator is capable of doing both In this example you Il get the area of the region on the right Five examples of what your calculator can do 13 NORMAL FLOAT AUTO REAL RADIAN MP CALC INTEGRAL OVER INTERVAL Figure 1 11 Calculating the area of a bounded area under a curve also called a definite integral using a TI 84 Plus C Silver Edition As you can S 0x0dx 19 213379 see you
6. get the same answer as a TI 83 Plus 4 58 or TI 84 Plus see figure 1 10 As with the previous example you ll start by clearing any functions you already have defined in the Y menu Press _Y _ move the cursor to any functions that are filled in and press to erase them If you followed the instructions for the previous example you should have already set the graph window to the calculator s defaults If not press 6 to select the 6 ZStandard option in the Zoom menu Returning to the Y menu with the key enter the following sequence of keys with the cursor next to Yi Geen cos J 0 L 5 ten _ _ This should type the expression you see on the left side in figure 1 12 Xcos 0 5X You can now press to see the result which will resemble the center in figure 1 12 but without the extra text Where you will get that extra text is by pressing to access to the Calculate menu and choosing 7 f x dx You can move the cur sor left and right along the curve with the arrow keys but I ll ask you to type 4 C 5 to enter the exact lower limit x 4 5 Press ENTER and the calculator will ask for the upper right limit You can again move the cursor side to side but you should type the exact value 8 shown on the right side in figure 1 12 and press Enter The calculator will silently divide the area into lots of tiny trapezoids sum their individual areas and present the result about 19 21 as figure 1 10 and figu
7. one to use MathPrint If you want to disable MathPrint press ModE move the cursor down to CLASSIC on the second page of the menu and press ENTER How do I upgrade to a MathPrint OS If you have a TI 84 Plus or TI 84 Plus Silver Edition install TIl Connect from http education ti com on your computer plug your calculator into your computer with a mini USB cable and then run the TI OS Downloader application It will provide you with further instructions Other calculator models can t be upgraded to run MathPrint TI 84 Plus C Silver Edition calculators always come with MathPrint operating systems TI 84 PLUS C SILVER EDITION CHECK MATHPRINT MODE If you have a TI 84 Plus C Silver Edition check the status bar the gray area at the top of the screen MP means you re in MathPrint mode and CL means you re in Classic MathPrint disabled mode Chapter 12 explains more about what the status bar shows The upshot of all this is that you can choose to enter equations the newer fancier way or you can use the older established way You may want to try both and choose for yourself or your teacher may tell you which mode to use Throughout this book Pll occasionally point back to this section to refresh your memory about how to turn MathPrint on and off Now that you ve learned about what your calculator can do and how this book can help Pll leave you with a few final thoughts before we dive into the first complete steps in using you
8. so if you typed 1 1 2 2 3 3 and pressed ENTER the result would be 6 Why bother using colons instead of putting each store com mand on a different line Because as you ll learn in chapter 2 you can go back to lines 1 0 236 140 1 0 236 140 i i B ICB 4ACp ee p Je aac eco SA3 i 1 Without MathPri l aratta an nee Figure 1 6 On the left storing values a 1 b 2 and c 1 These values can be used in the Quadratic Formula as shown in the center and right The center screenshot applies to TI 84 Plus TI 84 Plus Silver Edition and TI 84 Plus C Silver Edition calculators running one of the MathPrint operating systems The right screenshot shows the same equation entered on a calculator without MathPrint In section 1 3 lII explain more about the MathPrint operating systems Throughout this book lIl show you how to do things both with and without MathPrint Five examples of what your calculator can do 9 you already entered and run them again and if you set A B and C on the same line you can change them all by modifying one line instead of three Now that you have values in A B and C it s time to calculate the two solutions to the Quadratic Formula This is going to get a bit tricky because depending on whether you have a calculator with a MathPrint operating system newer TI 84 Plus Silver Edition calculators or a non MathPrint operating system TI 82 TI 83 TI 83 Plus Silver Edition and some TI 84 Plus S
9. yet Solving the Quadratic Formula The Quadratic Formula is used to figure out values of the variable x that make a qua dratic equation 0 ax bx c true once you pick three constant numbers a b and c If you re not familiar with the notation you can read it as O equals a times x squared plus b times x plus c You square x multiply the result by a add that to b times x and add c If you use a value of x that is a correct solution for the given a b and c you ll get 0 For an x value that isn t a solution the result of that multiplication and division will be a number other than 0 Even if you haven t worked with this type of math before fear not Follow along and in later chapters and math classes you ll learn more about the Quadratic Formula MEET THE QUADRATIC FORMULA You don t need to guess values for x and plug them in The Quadratic Formula is a tool to find the 0 1 or 2 values of x that satisfy solve 0 ax bx cfor a given set of three constants a b and c The Quadratic Formula is shown and demonstrated in action in figure 1 5 We ll try solving for the roots of 0 2x 8x 2 where the roots are values of x that make the right side of the equation equal to 0 In this case a 2 b 8 and c 2 The top of figure 1 5 shows the Quadratic Formula into which you ll plug values for a b and c Your calculator can handle named variables so you can store 2 into A 8 into B and 2 into C your ca
10. ERATING SYSTEM The operating system OS is the built in software on your calculator that makes it do math plot graphs and even show text on the screen Without the OS your calculator would be just a hunk of plastic and circuits In February 2010 TI introduced something new called MathPrint An operating sys tem upgrade for the TI 84 Plus TI 84 Plus Silver Edition and TI 84 Plus C Silver Edi tion calculators and only those calculators MathPrint makes the equations that you MathPrint vs non MathPrint calculators 21 a 1 73stles Echen uth fasors sch 2 5 6568542494Without MP be 656854249 k4 Ta line roots and Me MathPrint does not simplif tet ii With MP M ia ioe 4 2 diii Figure 1 17 Working with fractions square roots and powers exponents The left side shows the same operations without MathPrint that the right side shows with MathPrint enter look more like what you might see in your math textbook For example as you can see on the right side in figure 1 17 now square root symbols extend over the entire contents of the radical On older calculator operating systems you enclosed the con tents in parentheses Figure 1 17 also shows how exponents got fancier appearing above and to the side of the expression Fractions now look more like fractions as illustrated in figure 1 17 and especially on the right in figure 1 18 It s easier to see what you re doing while entering matrices demonstrated i
11. SAMPLE CHAPTER Using the TI 83 Plus TI 84 Plus LETTY ss Sa ss ALTIS Full coverage of the Tl 84 Plus C amet Edition zF 4 Christopher R Mitchell EE MANNING Using the TI 83 Plus TI 84 Plus by Christopher R Mitchell Chapter 1 Copyright 2013 Manning Publications brief contents PART 1 PART 2 PART 3 PART 4 BASICS AND ALGEBRA ON THE TI 83 PLUS TI 84 PLUS 1 1 m Whatcan your calculator do 3 2 a Get started with your calculator 25 3 m Basic graphing 57 4 a Variables matrices and lists 83 PRECALCULUS AND CALCULUS cccccccccccccccccccccccecs 111 5 m Expanding your graphing skills 113 6 m Precalculus and your calculator 141 7 m Calculus on the TI 83 Plus TI 84 Plus 158 STATISTICS PROBABILITY AND FINANCE cccccsccsceees 171 8 m Calculating and plotting statistics 173 9 m Working with probability and distributions 202 10 a Financial tools 223 GOING FURTHER WITH THE TI 83 PLUS TI 84 PLUS 235 11 wm Turbocharging math with programming 237 12 a The TI 84 Plus C Silver Edition 260 13 m Nowwhat 282 iil What can y calculator A graphing calculator is one of the most powerful tools you can use in school or at work From the name you can guess that it s great at math from the simplest arith metic like 2 2 to calculating statistics and multiplying matrices It s also a pro at graphing and helping you understand its graphs You can use your grap
12. both versions and you ll see the MP symbol in the margin The sidebars that succinctly explain the steps for each new skill always clarify differences between MathPrint and non MathPrint instructions The only remaining task for you is to decide whether you want to use MathPrint m Can I use MathPrint If you have a TI 84 Plus TI 84 Plus Silver Edition or TI 84 Plus C Silver Edition you can use MathPrint If you have any other calculator model you can t Am using MathPrint now If you don t have a TI 84 Plus TI 84 Plus Silver Edition or TI 84 Plus C Silver Edition you re not If you have one of those three models though you might be Press to quit to the homescreen and then press to get to the About section of the Memory menu If your OS TI S4 1 4 Summary 23 version has an MP suffix like 2 53MP or 2 55MP or it s version 4 0 or higher then you re running a MathPrint operating system But even if you have a Math Print operating system you might not have MathPrint enabled Press and scroll down until you see MATHPRINT CLASSIC If MATHPRINT is highlighted white text inside a black box you have it enabled If CLASSIC is highlighted Math Print is disabled How can I enable MathPrint If you have a MathPrint operating system installed see previous entry you can press MODE scroll down or up to MATHPRINT and press ENTER If you don t have a MathPrint operating system installed you need to install
13. calculator as well as gener ate random numbers and work with combinatorics Chapter 9 explains it all with plenty of examples Finance An often overlooked function of your calculator the financial tools can be used to calculate interest depreciation and much more The tools and illustrative problems are introduced in chapter 10 Programming Your calculator is such a powerful programming tool that I ve written a whole book about it You can write little math programs to help you check homework answers test answers and SAT questions Although one chap ter is only enough for a brief introduction chapter 11 will give you a good framework for exploring programming on your own Physics Depending on what level of physics you re learning you may need alge bra and graphing to study kinematics and projectile motion and you can use cal culus to simplify solutions Chapters 3 4 7 and others will help you there 1 2 2 This book and your calculator 19 Once again although this book will succinctly teach you the menus and keystrokes to use for each of your calculator s features it also provides tons of illustrated examples to drive the skills home and make you feel more comfortable using your TI 83 Plus TI 84 Plus Now that you know what this book can offer you Pll tell you what you need to bring with you to use this book to its full potential What you ll need What do you need to use this book The shorter answer is that y
14. d variables something you saw in the Quadratic Formula example in section 1 1 2 Precalculus First you ll see how to use lists and matrices in chapter 4 Next are different types of graphing including Polar and Parametric modes in chapter 5 Chapter 6 fills in the remaining precalculus odds and ends you might want to know how to work with from complex numbers and trigonom etry to limits and logarithms Calculus The TI 83 Plus TI 84 Plus can t do symbolic differentiation and inte gration but as you saw in the example in section 1 1 4 your calculator can do numeric differentiation and integration Chapter 7 is a methodical introduc tion to how to use these features and how they can help you find things like the slope minima maxima and inflection points of functions Statistics One of the biggest differences between the TI 83 Plus TI 84 Plus cal culators and earlier graphing calculators is that the newer ones can manipulate statistics The example in section 1 1 5 showed you how to enter lists of data fit a line and graph it chapter 8 will show you lots more You ll learn how to calcu late properties of data like the average mean median and maximum on your calculator and how to draw all different kinds of plots using data and you ll see the types of regression line fitting the calculator can do Probability You can calculate probability distribution functions PDFs and cumulative distribution functions CDFs with your
15. e arithmetic and algebra skills in chapter 2 If you want to see some examples of what your calculator can do here s what this section will cover 1 Calculating the volume of a cube and then cutting off the top of the cube and finding the new volume 2 Finding solutions to the Quadratic Formula a method for solving ax bx c 0 1 1 1 Five examples of what your calculator can do 5 3 Graphing the sine and cosine functions 4 Graphing a curve and then figuring out the area under a portion of the curve 5 Fitting a line of best fit to a series of data points These examples are arranged in order from easiest to hardest and are taken respec tively from algebra geometry precalculus trigonometry and statistics BEFORE YOU BEGIN All five of these examples should work well on your calcu lator without any special setup If you re getting different answers for some of the examples consider resetting your calculator to its default settings Section 2 1 explains how to do that Let s get started with the first example finding the volume of a cube Besides being a nifty demonstration that might come in handy during a geometry class it s a great way to begin doing useful arithmetic on your graphing calculator Calculating the volume of a cube Your calculator is a pro at arithmetic like addition subtraction multiplication and divi sion It can also raise numbers to powers and perform lots of mathematical operations like logarith
16. e in timidating This book turns the tables and puts you in control In it you ll find terrific tutorials that guide you through the most important techniques dozens of examples and exercises that let you learn by doing and well designed reference materials so you can find the answers to your ques tions fast Using the TI 83 Plus TI 84 Plus starts by making you com fortable with these powerful calculators screens buttons and special vocabulary Then you ll explore key features while you tackle problems just like the ones you ll see in your math and sciences classes What s Inside e Get up and running with your calculator fast e Lots of examples e Special tips for SAT and ACT math e Covers the color screen TI 84 Plus C Silver Edition Written for anyone who wants to use the TI 83 Plus TI 84 Plus No advanced knowledge of math and science required Christopher Mitchell is a teacher PhD candidate and recog nized leader in the calculator enthusiast community You ll find Christopher aka Kerm Martian and his cadre of calculator experts answering questions and sharing advice on his website cemetech net To download their free eBook in PDF ePub and Kindle formats owners of this book should visit manning com UsingtheTl 83Plus Tl 84Plus MANNING US 24 99 Can 26 99 The user manual but shorter clearer and much more entertaining Louis Becquey Joseph Fourier University Grenoble Exper
17. e work with the next example in which you ll graph the sine and cosine functions Graphing sine and cosine Sine and cosine are two trigonometric functions They re periodic which means that they repeat over and over again Both look like a wave repeatedly curving between y 1 and y l as you go left to right along the x axis On your calculator sine is abbrevi ated sin and cosine is abbreviated cos The parentheses mean you re taking the sine or cosine of whatever number or variable is inside the parentheses Individually the two equations y sin x and y cos x look something like the left and right sides of figure 1 7 respectively In this example you ll be superimposing one sine graph and one cosine graph Both sine and cosine only alternate between y 1 and y l1 This looks tiny with the calcula tor s standard graphing window so you ll multiply both functions by a coefficient of 5 to make the functions taller You ll be graphing these two functions together Y Sein x Y beos x Before you can graph these you should make sure all your graph settings are set to reasonable defaults First press _Y _ use the Y and A keys to move the cursor to any of the Y equa tions that are filled in and press to erase them Next to make sure the graph Figure 1 7 Graphs of sin x left and cos x right These are both graphed from x 10 to x 10 with limits of y 3 at the bottom and y 3 a
18. eady speed down a highway Along the road you add stu dents standing with stopwatches and notebooks Each student looks at their stopwatch when the car passes and writes down the time Later they compare notes to compute how fast the car was going But they re only human so their measurements aren t perfect The data points they collected are shown on the left side in figure 1 13 and a graph of those points with time on the x axis and distance on the y axis is on the right side In the table L is a list containing items representing numbers of seconds since the experiment began Lz is a list holding the number of meters between where the car started and where that student was standing 1 meter is a little over 3 feet You can see by glancing at figure 1 13 that the points don t form a perfectly straight line You might be able to start at the table and see that the time measure ments are spaced about 30 seconds apart while the distances are about 600 meters apart But you can get a much more accurate estimate than that ENTERING THE DATA First just in case you ve worked with the lists on your calculator before you ll want to start with fresh clean lists You ll use the ClrList command Press 4 to paste ClrList to the homescreen then type gt 2 You ll have ClrList Li L2 on the screen so press to clear Li and Lo Time seconds Distance meters 147 3100 o 113 2350 g 5 92 740 65 1270 n 30
19. figure 1 5 where a 1 b 2 and c 1 From the figure you can see that you should get two identical solutions x 1 and x l1 First make sure you re at the homescreen You may have to press to get there or to start with a blank line The first thing you ll do is assign store values to the variables A B and c The key prints the symbol which takes whatever is on its left side and stores it into whatever is on its right side For example 3 A stores the number 3 into the A variable whereas 4 5 X stores 4 5 negative 4 5 into the X variable You can then use those variables in expressions so if you calculated A 4 after storing 3 into A it would be like 3 4 and you would get 7 as the answer With that in mind try these steps 1 Type Don t press yet You should see 1A on the screen as in figure 1 6 2 Continue by typing 2 REN You should now have 1 gt A 2 B 1 gt C on the screen 3 Press to store values to A B and C Although the calculator will just print 1 at the right edge of the screen as you can see on the left side in figure 1 6 you executed three commands at once You simultane ously put values in the three variables A B and C On your calculator you can separate multiple commands or calculations with a colon and when you press ENTER all the commands or calculations will be performed from left to right The calculator only shows the result for the last operation
20. hPrint right on a TI 84 Plus or TI 84 Plus Silver Edition Although the non MathPrint version is slightly faster to type you need to remember the correct order for the arguments to the and fnInt functions With the MathPrint version entering summations and integrals is more like writing them on paper You don t have to memorize the order of arguments or parameters to summations and integrals as shown in figure 1 20 The goal of MathPrint operating systems is to make entering equations and matri ces easier and more intuitive By making what you see on your calculator screen closer to what you see in your textbook and what your teacher writes on the board TI hoped to make your calculator easier to use But MathPrint has a few caveats It has more options to configure all found in the Mode menu It can only run on TI 84 Plus TI 84 Plus Silver Edition and TI 84 Plus C Silver Edition calculators It was slightly rushed and if you get into graphing calculator programming you ll discover several annoying bugs and quirks in the MathPrint operating sys tems If you just use MathPrint for math and science class you won t run across these bugs This book will cover both the MathPrint and non MathPrint ways to do things When you re learning something new and your screen looks different depending on whether you have a MathPrint operating system I m always careful to point out the differences and show you screenshots of
21. hat sort of fit it should try Here because it looks like the data almost 16 CHAPTER 1 What can your calculator do Figure 1 15 On the left setting up a Stat Plot for display on your calculator s graph screen The result of turning this feature on was shown on the right in figure 1 13 In the center the numbers calculated from linear regression fitting a straight line to a data set on a MathPrint calculator On the right that line Y 21 5X 141 7 graphed over the five data points it was fit to Pretty close defines a straight line we ll try linear regression which means to try to fit a straight line to the data Press to return once more to the homescreen Press for the Statis tics menu but this time press the gt key to get to the Calc tab Choose 4 Lin Reg ax b m On some calculators the non MathPrint ones you ll see LinReg ax b pasted to the homescreen just press ENTER Your calculator will assume that you mean to perform regression with x values in L and y values in L2 unless you tell it oth erwise You should get a 21 5 and b 141 7 meaning the best fit line is y 21 5x 141 7 Want to graph it Press and then 550 to paste the RegEQ the regression equation into Yi Finally press GRAPH and you ll see the best fit line graphed over the points The right screenshot in figure 1 15 is the result you ll be looking at If you have a TI 84 Plus C Silver Edition you ll see the result shown in figure 1 16 ins
22. hing calcu lator for algebra trigonometry precalculus and calculus you can even use it to write programs and games If you re a student or teacher a graphing calculator can be used in every math subject from middle school to college as well as in science and computer classes Many graphing calculators are available from Texas Instru ments HP and Casio this book focuses on the TI 83 Plus TI 84 Plus TI 83 Plus Sil ver Edition TI 84 Plus Silver Edition and TI 84 Plus C Silver Edition but it can help you use all the calculators shown in figure 1 1 Your calculator can also be an intimidating device with so many functions and buttons It certainly looks harder to use than other familiar gadgets like a cell phone or a handheld game console Instead of a mouse or touchscreen you use 1 1 CHAPTER 1 What can your calculator do Figure 1 1 Calculators covered in this book from left TI 82 TI 83 TI 83 Plus TI 83 Plus Silver Edition TI 84 Plus TI 84 Plus Silver Edition and TI 84 Plus C Silver Edition The focus is on the TI 83 Plus and TI 84 Plus models although most of the skills and examples also apply to the TI 82 TI 83 and TI 82 Stats fr the keyboard to navigate through its features Fear not complicated though it might look you can easily become a calculator expert and this book will hold your hand every step of the way Whether you use this guide as a quick reference to do something specific or do a thorough read
23. ilver Edition calculators you ll have to enter a different series of commands SOLVING THE QUADRATIC FORMULA Before we can continue you need to figure out whether you have a MathPrint operat ing system and moreover whether the MathPrint mode is enabled If you just stored values to A B and C you should still be at the homescreen Press the key right under the key If the cursor is a dark square blinking inside a dotted square next to and slightly above the word Ans you have MathPrint installed and enabled Ifthe cursor is a dark rectangle blinking normally next to the text Ans with no dotted line around the cursor you either don t have MathPrint installed or have it disabled Without MathPrint Type in the plus version of the Quadratic Formula remember the symbol with the following key sequence _ _ LPH apps C_x C C4 ALPHA marh ara prom _ JC C 2 tpHa mar _ Your screen should look like the right side in figure 1 6 If you made any mis takes you can press to clear the line and start over or you can use the 4 and gt arrow keys to move the cursor through the line press to delete extra symbols or numbers and press to switch into Insert mode When you ve finished and your screen matches the right side in figure 1 6 press ENTER You should see the answer l NEGATION AND IMPLICIT MULTIPLICATION Notice that to type the negative sym bol you don t pre
24. in figure 1 15 which shows the same result on any other TI 83 Plus or TI 84 Plus family calculator The only differences are color and higher resolution things it can do applicable to your classes and to life in general Before we dive into the material let me tell you more about what exactly this book will teach you and why you need it to accompany you on your journey with your calculator This book and your calculator Your calculator is a powerful and versatile tool It s basically a pocket computer that you can use for many math and science classes for financial calculations and else where in your life But if you don t have the time or the experience to experiment and discover all of its features on your own you might be missing out on a lot of the stuff it can do I d like to step in as your guide showing you the many things your calculator can do In this section ll tell you about how your calculator can help make your math and science classes simpler and more understandable I ll mention how this book will guide you toward using each of those features I ll also explain that I don t assume you know anything about graphing calculators when you start reading I ll talk about which calculators this book covers and if you don t yet have one which one you should get Let s take a look at what your calculator can do for your classes Your calculator a multipurpose tool As you go through school you ll encounter
25. lators this book can help you use Table 1 1 and its accompanying calculator pictures show all the graphing calculators you can use with this book Every example in this book and every calculator feature taught will work on the TI 83 Plus TI 83 Plus Silver Edition TI 84 Plus TI 84 Plus Silver Edition and TI 84 Plus C Silver Edition Almost everything will also work on the TI 83 and the TI 82 Stats fr calculators and most even apply to the TI 82 If you don t already have a calculator you should really buy one before continu ing with this book If you can afford it the TI 84 Plus Silver Edition black and white screen or TI 84 Plus C Silver Edition color screen is your best choice but any of the calculators in the TI 83 Plus and TI 84 Plus series can perform all the functions discussed in this book If you prefer the MathPrint features which Ill tell you more about in section 1 3 you need a TI 84 Plus TI 84 Plus Silver Edition or TI 84 Plus C Silver Edition calculator There are also many emulators that let you use a virtual calculator on your computer but they all legally require a ROM image from your real calculator to function I prefer Wabbitemu http wabbit codeplex com 20 1 3 CHAPTER 1 What can your calculator do Table 1 1 Calculators you can use with this book Introduced in 1999 Graphing math statistics probability finance calcu lus features Upgradeable operating system and Introduced in 2004
26. lculator only has uppercase variables like A B X and M You ve seen the squared symbol as in b in the previous example finding the volume of a box But there are two new symbols that you might be unfamiliar with The symbol means you can put either a plus sign or a minus sign at that position In other words the Quadratic Formula is actually two different equations one with a plus and one with a minus When you plug in a b and c you get two solutions one for the equation with a plus and one for it with a minus The other symbol that might be _ btv b 4ac SOLUTION WITH DOUBLE ROOT SOLUTION WITH REAL ROOTS a 1 b 2 c 1 a 2 b 8 c 2 0 2 4 22 4 1 _ 2 v0 0 8 82 4 2 2 _ 8 v48 7 2 1 2 d 2 2 4 x 1 x 24V3 Figure 1 5 The Quadratic Formula top solved for two sets of a b and c constants On the left we set a 1 b 2 and c 1 and get the double root 1 1 On the right setting a 2 b 8 and c 2 yields two difference roots 2 plus and minus the square root of 3 CHAPTER 1 What can your calculator do new but hopefully not is the radical or square root symbol y It indicates that you should take the square root of everything inside STORING VALUES FOR A B AND C Let s set up your a b and c values into the A B and C variables on your calculator first and then type the two different forms of the Quadratic Formula to find the solu tions We ll try solving the case on the left in
27. ll box with a 3 inch lid that you just took off Either way as the right side in figure 1 2 shows you now have a 9 inch by 9 inch by 6 inch box and you want to calculate the new volume This time you must multiply 9 x 9 x 6 which is very similar to your previous experience multiply ing 9 x 9 x 9 Figure 1 4 shows what the equation will look like when you type 9 x 9 x 6 as before the key acts like an key to make the volume of the shorter box appear 486 Because 9 x 9 is 9 squared you could even be clever and type 9 x 9x 6 as 9 x 6 which once again as the right side in figure 1 4 demonstrates pro duces the correct volume of the shorter box 486 To type the squared symbol you could type 2 but it s faster to use the key Thus to calculate 9 x 6 press 9 Go 6 ENTER That s a quick introduction to using your calculator for math You type in the expression to calculate with the number keys and operators like x and Figure 1 4 Calculating the volume of the 9 inch cube with the top 3 inches sliced off The last line shows the same calculation using the key instead of typing 9 x 9 1 1 2 Five examples of what your calculator can do 7 You then ask your calculator to produce the result with ENTER Section 2 2 will teach you more about basic arithmetic and your calculator A more complicated math example is solving the Quadratic Formula which will require using a few tools you haven t seen
28. many classes that require math skills Math classes are the obvious ones but there are also science classes finance and eco nomics classes computer classes and more Your calculator can help you learn more and learn faster in each of these types of courses I ll take you through each of them and what your calculator and this book can do together to help you This book is nota math book and isn t an adequate substitute for a class or textbook in each subject But it s a complete calculator reference that can help you understand subjects better as you explore them on your calculator Math classes range from the simplest arithmetic up through complex college cal culus and further Your graphing calculator can do arithmetic from 2 2 to advanced matrix math as well as algebra trigonometry statistics calculus and more This book is the perfect accompaniment to each subject 18 CHAPTER 1 What can your calculator do Arithmettc Chapter 2 will teach you how to do basic calculations on your cal culator including arithmetic exponents using functions and changing the modes that control how you enter expressions and how your calculator dis plays answers Algebra Your calculator can solve algebraic expressions chapter 2 shows you how Graphing is one of the things graphing calculators do best and chapter 3 details creating and examining graphs with plenty of examples Chapter 4 intro duces how your calculator can store and use name
29. me equations We re ready to graph now press the key You should see the two lines shown on the right side in figure 1 8 appear If you have a TI 84 Plus C Silver Edition your graph will look like figure 1 9 instead You ve graphed your first equations If you want to be adventurous you can press the key to examine points along each line or to see the table view of x and y values What just happened Your calculator graphed sine and cosine on the graph screen It can graph up to 10 different functions at the same time so 2 is a breeze When you choose ZStandard you set the top of the screen to y 10 and the bottom to y 10 You multiplied both the sine and cosine functions by 5 so that the resulting NORMAL FLOAT AUTO REAL RADIAN MP NORMAL FLOAT AUTO REAL RADIAN MP Ploti Plot2 Plot3 BNYi18S5Ssin Xx BNY 28Scos X Figure 1 9 The same graphing operation as in figure 1 8 but on a TI 84 Plus C Silver Edition The left side shows entering two trigonometric functions for graphing the right side shows the result 12 1 1 4 CHAPTER 1 What can your calculator do lines would alternate between y 5 and y 5 instead of l1 and 1 This makes them much easier to see For our fourth example we ll move from precalculus to calculus to find the area under a simple curve This will build on the graphing example you just worked with so make sure you understand the basics of graphing before you continue Calculating the
30. ms and trigonometry For our first example of what your calculator can do imagine a cube of which every side is 9 inches like the one on the left in figure 1 2 VOLUME OF A BOX To calculate the volume of a box multiply its width length and height together If it s a cube then the width length and height are all the same To calculate the volume of the 9 inch cube you need to multiply 9 x 9 x 9 Turn on your calculator and you should be at the homescreen the area of your calculator s software where you do math If you re not press to quit to the home screen which should have a blinking cursor and either be blank or show the previous calculations you performed Next type 9 x 9 9 to get 9 9 9 on the screen Your screen should match the left side in figure 1 3 There s no key on your calculator instead you calculate 9 width Nu leagth qeenneenee ig A SON s IS Figure 1 2 Measuring the volume of a cube On the left a cube with 9 inch sides You can calculate its volume by multiplying width x length x height On the right the top 3 inches of the cube are cut off and you want to find the volume of the new box that is 6 inches high instead of 9 inches qu theight leagth A height CHAPTER 1 What can your calculator do Figure 1 3 Two different ways to calculate the volume of a cube with 9 inch edges On the left multiply width x length x height to ok get the volume 729
31. n fig ure 1 19 Floti Filete Filoks tt In tnd CHEE Jax Figure 1 18 Several screenshots of MathPrint only features On the left pressing through to access context menus In the center one of the new statistics wizards for regression On the right some of the most complex stuff you can do with MathPrint including fancy fractions absolute values integrals square roots exponents and fancy equation entry You can still enter the same equations on non MathPrint operating systems and graph them but they won t look as fancy PTE 1 2713 425 Without MP igen t Type matrices EE 1 With MP visually like equations E 4 Matrix answers are Similar Figure 1 19 Entering matrices without MathPrint left and with MathPrint right The display of the matrix answer is similar with and without the MathPrint features except for slightly cleaner square brackets in the MathPrint version It s easier but slightly slower to keep track of the row and column for which you re entering a number when using the MathPrint version 22 Hath Print CHAPTER 1 What can your calculator do E J J l eeeeti Hal tO m vty Print lode hs Lawson A lextbook like l 1g Summations ad integrals N 6 891349663 Wih MP Clog hd In line summations and A313496673 integrals Figure 1 20 The differences between summations and integrals when performed without MathPrint left and with Mat
32. ou need almost noth ing other than your brain this book and a graphing calculator The slightly longer answer is that you shouldn t try to use this book as a math textbook because it isn t one I do my best to refresh your memory about details of the math you re applying as you Saw in the five examples in section 1 1 But we ll be covering such a broad swath of math science and other subjects that it would be impossible to teach them all from scratch in one or even two or three books Therefore I strongly recommend that you use this book while you take the relevant courses and ideally pair it with the textbooks that are teaching you the particular math or science material That s not to say you can t use this book as an independent reference If you re already well into high school or college or no matter where you are in life a graphing calculator is still an important tool As long as you have a vague recollection of your schooling you should be able to follow most of the lessons and examples in this book Even if you aren t that far into your classes all the examples in this book are laid out in detail from start to finish and don t require that you have to solve anything on your own to get the same answers I get The other important prerequisite is a graphing calculator The TI 84 Plus Silver Edition TI 83 Plus and TI 84 Plus C Silver Edition all appear on the front page of this book and they re three of the many calcu
33. r calculator Summary In this chapter you got a cross sectional view of your calculator s power and how this book can unlock it You saw five examples from geometry algebra trigonometry cal culus and statistics that covered a range of things you might want to use your calcula tor for I discussed the many different calculators this book will help you use and you learned how to use this book To prevent confusion as you venture into the next chapter you now also know what MathPrint is and you should be clear whether your calculator has it If you don t yet have a calculator I recommend that you get one or an emula tor with a legal ROM image as discussed in section 1 2 2 before you continue 24 CHAPTER 1 What can your calculator do Remember that you can use this book as an instant reference finding what you need in the index or table of contents and jumping to that section or you can read it chapter by chapter In chapter 2 you ll officially meet your calculator including learning how to use the keyboard how to care for the device how to do basic math on it and how to solve simple algebraic equations I look forward to taking this journey with you so let s get started MATHEMATICS GENERAL Using the TI 83 Plus TI 84 Plus Full Coverage of the TI 84 Plus C Silver Edition Christopher R Mitchell ith so many features and functions the TI 83 Plus TI 84 Plus graphing calculators can be a littl
34. re 1 11 show The method the calculator uses to perform integration called the Trapezoid Rule is something you might even learn to do by hand in your calculus class Another skill your calculator can automate is the painstaking process of finding a Floti Fiekte Flats T1 Heo EA i Aco EA Figure 1 12 Calculating the area under a curve On the left entering the equation for the curve in Y In the center graphing the equation and choosing the left side of the area to be measured On the right choosing the right side of the area to measure Once you choose both sides the calculator returns the total area in that region as shown on the right side in figure 1 10 14 1 1 5 CHAPTER 1 What can your calculator do line that fits a collection of data points The fifth and final example in this chapter shows you how Fitting a line to data In math and especially science you can make predictions For example you can fig ure out the equation for the acceleration of a wooden car as it rolls down a ramp or the arc of a cannonball fired across a field You can even model more complicated sit uations such as the number of people infected by a disease as it spreads or the popu lation of the human race at specific points in the future For these sorts of problems you start with a bunch of data points called observations or samples and try to fit a line to the data to find trends or predict other data Consider a car driving at a st
35. ss the subtract key On your calculator negative and sub tract are two different keys Notice also that your calculator does implicit multiplication 44C is like 4 A C With MathPrint Type in the plus version of the Quadratic Formula with the following key sequence _ _ arna apps 2na _x aena apps x 4 Grena BOIL __ _ Your screen should look like the right side in figure 1 6 The only difference from the non MathPrint instruc tions is that you need to press gt to get out of the square root radical symbol instead of pressing the _ _ key As with the non MathPrint instructions you can use the arrows DEL and to move the cursor around delete errors and insert missing numbers and symbols When your entry looks like the center screenshot in figure 1 6 press ENTER and you should get 1 10 1 1 3 CHAPTER 1 What can your calculator do GETTING THE OTHER ANSWER I told you the Quadratic Formula has two answers one for the case of the operator and one for the case To get the minus answer press ENTER which pastes the previous line again Use the 4 key to move the blinking cursor over the first sign and press to replace it with a subtraction symbol You can press to get the second solution without needing to move the cursor to the end of the line it should be 1 again This example was fairly simple but you had to press a lot of keys Let s save your fingers som
36. t the top If you know how to graph curves and you can t figure out why graphing sin x or cos x on your calculator doesn t look like these screenshots try pressing and setting Ymin to 3 and Ymax to 3 TI 4 _ Five examples of what your calculator can do 11 Floti Floke Flokts Figure 1 8 Screenshots of graphing sine and cosine from a TI 83 Plus or TI 84 Plus On the left the empty Y menu the same menu with the two functions you re graphing in this example filled in center and the result when you press right Read the section to learn how to enter the equations and graph them and read the sidebar Problems with graphing if anything goes wrong Take a look at figure 1 9 for the TI 84 Plus C Silver Edition versions of these screenshots window is set to useful values press 6 to select 6 ZStandard Zoom Standard in the Zoom menu Finally you can enter the equations for Y and Yz Press again to get back to the screen where you can enter equations to the graph which should look like the left side in figure 1 8 If it doesn t refer to the sidebar Problems with graphing for help Next enter the equations With the cursor flashing next to Yi press 5 Csin _ You should see 5sin X appear Press Y to move to Y2 and press 5 cos _ _ Now you should have 5cos X under the first equation If you want double check against the center in figure 1 8 to make sure you and I have the sa
37. tead On MathPrint calculators you ll see another menu when you choose 4 Lin Reg ax b Leave the defaults that is don t change any of the options the cal culator fills in for you move the cursor to Calculate and press ENTER You ll get a slightly fancier display of the resulting line of best fit than the non MathPrint folks as in the center in figure 1 15 but you should still get a 21 5 and b 141 7 To graph y 21 5x 141 7 quickly press and then 5 gt gt to paste the RegEQ into Y Press to see this best fit line graphed over the data points The right screenshot in figure 1 15 or figure 1 16 for a TI 84 Plus C Silver Edition is still the result you ll be looking at FIX YOUR GRAPH SETTINGS To prevent confusion when you go back to using your calculator for normal graphing be sure to turn off the Stat Plot Press again move the cursor up to Plotl and press to turn it back to black text on a white background Lists L and Lz are still in your calculator s memory but they take up little space You can delete them if you want to Now you ve seen five different examples of what your calculator can do ranging from arithmetic to calculus to statistics Throughout this book you ll learn many more cool 1 2 1 2 1 This book and your calculator 17 NORMAL FLOAT AUTO REAL RADIAN MP Figure 1 16 Fitting a line to a set of five points on the TI 84 Plus C Silver Edition Compare this to the right side
38. tly captivates readers at any level of study and provides practical examples that students will use in their academic years and beyond Samuel Gockel University of Illinois at Urbana Champaign The perfect complement to math and statistics courses of all levels Ryan Boyd University of Texas at Austin This is THE manual for your calculator Jonathan Walker computer science student NDSU ISBN 13 976 1 b617290 44 4 gt 1 617 84 X 290 290848 ISBN 10 781617
39. to learn how to use your calculator well you ll find les sons taught with simple steps and fun examples This chapter will immediately show you some calculator skills and demonstrate the variety of tasks a graphing calculator can help you do We ll start with five examples of what you can use your calculator for algebra geom etry graphing calculus and statistics You can go through them one by one trying them on your own calculator skip around or just peruse them You ll find a section describ ing more about this book and how it can help you use your calculator and then a discus sion of which calculators this book will teach You ll learn the difference between MathPrint and non MathPrint calculators this book covers both and end with a look forward at the basic calculator skills you ll discover in chapter 2 Let s get started with five fun examples and see how easy and powerful a graphing calculator can be Five examples of what your calculator can do Your calculator can solve countless different kinds of math and science problems and help you double check your work while doing homework or during tests even the SAT To help you jump right into using your calculator let s start with five complete examples picked from exactly the sort of problems you might encounter in class If you d prefer to start learning specific math skills immediately you might want to skip this section skim the rest of chapter 1 and then begin with th
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