Introductory to TI-84 Plus Graphing Calculator

Transcription

1 Introductory to TI-84 Plus Graphing Calculator Training Module

2 Table of Contents INTRODUCTION: WORKING WITH TI-84 PLUS...1 TI-84 PLUS KEYBOARD...2 SWITCHING ON/OFF THE TI-84 PLUS...3 HOME SCREEN...4 SCREEN CONTRAST...4 CURSOR...4 IMPORTANT KEYS...4 SUCCESSIVE COMMANDS...5 STORING NUMBERS...6 USING MENUS...6 STANDARD SETTINGS...7 INTRODUCTION: CALCULATIONS...9 EQUATION OPERATING SYSTEM (EOS) ORDER OF EVALUATION...9 Practice Examples:...10 EDITING...12 USING THE DEL KEY...12 INSERTING A NUMBER...13 POWER AND ROOTS...13 MATH MENU...14 Example:...14 REPEAT CALCULATIONS...15 REPEATING SIMILAR CALCULATIONS...15 INTRODUCTION : GRAPHING...17 MAIN GRAPHING KEYS...17 HOW TO CREATE A GRAPH...18 Defining Functions to be Graphed...18 Defining Windows STATWORKS (M) SDN BHD i

3 Graphing the Function...19 Tracing the Function...20 Graphing a Second Function...20 Zooming...21 Evaluating at a specific x values...21 SOLVING EQUATIONS...22 Graphical Solutions...22 GRAPH VIEWS...25 Practice Example...25 INTRODUCTION...27 RELEVANT KEYS FOR STATISTICS...27 UNIVARIATE STATISTICS...27 Entering Data as a List...27 Clear a List...29 Build A Histogram...29 Naming A List...30 BIVARIATE STATISTICS...31 Practice Example...31 INTRODUCTION : SPECIAL FEATURES...33 FLASH TECHNOLOGY...33 DATA COLLECTION DEVICES WITH THE TI-84 PLUS...33 TI-84 PLUS AND THE TI-GRAPHLINK CABLE WITH TI-CONNECT...34 TI-Connect Homescreen...36 Connecting A device...37 Updating device software...37 TI DeviceExplorer Overview...38 Transferring device files using drag and drop...39 Backing up device files...40 Restoring backed-up device files...40 TI ScreenCapture overview...41 Capturing device screens STATWORKS (M) SDN BHD ii

4 Saving captured screens...42 Sending images to a device...43 Deleting device applications...44 TI-INTERACTIVE WITH THE TI-84 PLUS...44 Features...45 The Math Box...45 The Math Palette...46 Graphing Function...47 Data Analysis...48 Connecting a Graphing Calculator...51 ACKNOWLEDGEMENTS STATWORKS (M) SDN BHD iii

5 1 Working with TI-84 PLUS Introduction: Working with TI-84 PLUS This introduction training manual is to help educators to understand the operations of a TI-84 PLUS graphing calculator and its application for computation purposes. Mathematics and Science are visual subjects, and graphics calculators can provide the picture in a number of important areas of mathematics. They are also useful in allowing students to explore mathematics numerically and graphically. Graphics calculators are portable, powerful and, for what they do, relatively cheap. These notes are specifically designed for use with the TI-84 Plus, a graphic calculator manufactured by Texas Instruments. It is suitable for those who already have some knowledge about graphics calculators, but are looking for directions with specific operations those who have only just found the ON button. What can do the TI-84 Plus do? all the features of a scientific calculator plus matrices and complex numbers multi-line screen, which displays input and output of calculations simultaneously ability to graph Cartesian, parametric, polar and sequence graphs statistical functions for organising, analysing and displaying data programmable, with a large number of programs available for downloading can be linked to other calculators, computers and printers for electronic transfer of programs, data, etc and downloading programs from a computer or the web can be used in conjunction with a data logger and its probes (Calculator based laboratory (CBL 2)): these enable easy collection of real data, which can be organised, displayed and analysed an overhead-projector view screen is available (only for the Teacher s set) STATWORKS (M) SDN BHD 1

6 1 Working with TI-84 PLUS TI-84 PLUS Keyboard Generally, the keyboard is divided into these zones: Graphing Graphing keys access the interactive graphing features. Editing Editing keys allow you to edit expressions and values. Advanced Advanced function keys display menus that access the advanced functions. Scientific Scientific calculator keys access the capabilities of a standard scientific calculator STATWORKS (M) SDN BHD 2

7 1 Working with TI-84 PLUS The keys on the TI-84 Plus are color-coded to help you easily locate the key you need. The light gray keys are the number keys. The blue keys along the right side of the keyboard are the common math functions. The blue keys across the top, set up and display graphs. The blue Œ key provides access to applications such as the Finance application. The primary function of each key is printed on the keys. For example, when you press, the MATH menu is displayed. The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then, the TEST menu is displayed. This guidebook describes this keystroke combination as y :. The alpha function of each key is printed in green above the key. When you press the green ƒ key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press ƒ and then, the letter A is entered. This keystroke combination as ƒ [A]. Switching on/off the TI-84 Plus The calculator is turned on by pressing the É button; press y É (i.e. OFF) when you have finished. The calculator will turn itself off if not used for a short time, but nothing is lost when this happens. Just turn it back on and you will return to your work where you last left it. Notice that the y key is yellow. When you need to use any function or value which is printed in yellow above a particular key, first press y and then the corresponding key STATWORKS (M) SDN BHD 3

8 1 Working with TI-84 PLUS Home Screen The Home screen is the main screen which is used to display operations and to enter expressions and instructions. It is the first screen you will see when the calculator is first turned on. Screen Contrast If the screen is difficult to read then adjust the contrast. To make the screen display darker press y and then hold down the } key. Pressing y and then will lighten the display. You will see a number in the top right hand corner of the screen at this stage. The numbers range from 1 (for lightest) to 9. If the screen is showing the number 9 and the contrast is only adequate, you should replace the AAA batteries soon. (Refer to the manual for instructions.) Cursor A flashing square appears in the position where the next entry is to be made. You can access previous entries by using the cursor keys (they are the four keys with little triangle arrows found at the top right of the keyboard) to move about the screen. Important Keys Í There is no = key on a graphics calculator. When you want to carry out a calculation, enter the complete expression and then press Í These are the cursor keys. In these notes they are referred to using the symbols } ~ and These keys will enable you to move around the screen. { This key is used to correct a little mistake. Using the cursor keys, place the cursor over the item to be deleted and then press { 2006 STATWORKS (M) SDN BHD 4

9 1 Working with TI-84 PLUS This key clears bigger mistakes. It will clear all of the line that you are currently working on. But if you have already pressed Í then pressing clears the whole screen. 5 To access this feature you need to press y z. These keystrokes will always return you to the Home Screen. If necessary use these when you are stuck and can't see how to recover. y This key has already been mentioned. It is used to access any feature which is printed in yellow at the top left of most keys. For example, to use the value of B in a calculation, press y z This key fixes the way the calculator operates. For example you can choose to display answers with a fixed or floating number of decimal places, you can have a graph which is joined or just a series of points and so on. Successive Commands You can construct lengthy commands on the screen if you want before pressing Í, but you can also do chain calculations. The result of the most recent calculation is stored in Z. This is used in chain calculations, and can be recalled using y. As an example, try the following key sequence. Watch where Z is automatically recalled. À Â Ã À Ã À Í Í Í Í C Z Í note that you have to key in Ans here 2006 STATWORKS (M) SDN BHD 5

10 1 Working with TI-84 PLUS What is the affect of the following? À Í Á Í Í Í Pressing Í repeats the previous entry. Storing Numbers Memories are named alphabetically, as if variables are being given values. To store a specific value in a variable (or memory), first type the value onto your screen, then press, type a variable name ƒ followed by a single letter A, and press Í. The value stored in the variable will not change unless you store something else in that variable name. Let s store 3 in variable/memory P and 4 in variable/memory Q: Â ƒ P Í. ƒ Q Í. Now try the following (don t forget the ALPHA key before each letter): P Í 2 P Í P Q Í 3 P Q Í C P + Q Í Using Menus The TI-84 is menu-driven, which explains why the keyboard is relatively uncluttered. For example, many functions are located in the MATH menu. To access this, press 2006 STATWORKS (M) SDN BHD 6

11 1 Working with TI-84 PLUS and you will see the four sub-menus displayed, with headings [MATH], [NUM], [CPX] and [PRB]. The arrow keys allow you to move between these. To access a menu function, press its number (or use the up- and down-arrow keys and Í ). Generally you construct an expression just as you would on paper. To leave a menu without selecting a function, press, which returns you to the home screen. Try the following examples: Â Í for 7 3 ~ À Á ¹ Í ~ Â À Í for 2-9 : absolute-value function for [3.1], greatest-integer function À Â Í for 15 C 4 À Í Í for successive random numbers on (0: 1) À Á Í for 12! Á Ã Â À Í for 2/7 + 3/5 as a fraction Standard Settings When you first turn on a new calculator (or when you have reset to clear all the memories) it is already set to display certain features and to be used in a predetermined way. We can change these to suit the type of calculations that are to be performed. What are the standard settings and what other options are there anyway? Press z - the screen looks a bit daunting doesn't it! Notice that there are a number of words already 'blacked out' - this means that these settings have already been selected. The first line determines the how the calculation results are displayed o Normal means that numbers are written in the normal way. But on the same row, we could choose Sci or Eng. Sci means that the answers would 2006 STATWORKS (M) SDN BHD 7

12 1 Working with TI-84 PLUS be given in scientific notation. If we wanted to have answers given in scientific notation, we would use the cursor keys to move the cursor so that it is blinking on Sci, however because Normal is still blacked out this is still the selected option. To change to Sci, when the cursor is flashing on Sci, press Í. Notice that Sci becomes the selected choice. The second line determines how many decimal places you may want in the answers. The third line determines whether angles are expressed in radians or degrees. The fourth line indicates the different types of graphs that are possible. o Func for function graphs, y = f(x), and this is the graph mode we will use most of the time. o The other modes are parametric, polar and sequence. Line 5 in Mode controls whether the plotted dots in a function (or other) plot are connected or not. Change the mode to Dot, and graph again using ZOOM Standard. Set line 5 back to Connected, and change line 6 from Sequential to Simul(taneous) Graph again, and figure out what this setting does. Line 7 allows you to enter Complex mode, with complex numbers in either Cartesian or polar form. Change line 8 from Full screen to G T. Graph again. o Press 0 to move to the table and s to go back to the graph. Then try r. You need to use the arrow keys appropriate to the graph to move around both the table and the graph. o If you choose Horiz on line 8, the top half of the screen shows the graph, while the home screen, 0, oand p all use the bottom half of the screen. o Full-screen menus (e.g. MODE) will temporarily use the whole screen and then restore the split screen (if it is still selected) when you exit from them STATWORKS (M) SDN BHD 8

13 3 Graphing with the TI-84 PLUS Introduction: Calculations Calculations are performed by entering the numbers in the usual manner, keeping in mind that rule of order is obeyed. You can make use of the brackets on the keypad to enter quite complex computations. Try this simple addition: When you press Í the addition remains on the screen and the answer appears on the right hand side of the next line. It is not necessary to press before the next calculation. Equation Operating System (EOS) Order of Evaluation The Equation Operating System (EOS) defines the order in which functions in expressions are entered and evaluated on the TI-84 Plus. EOS lets you enter numbers and functions in a simple, straightforward sequence. EOS evaluates the functions in an expression in this order. Order Number Function 1 Functions that precede the argument, such as (, sin(, or log( 2 Functions that are entered after the argument, such as 2, -1,!,, r, and conversions 3 Powers and roots, such as 2^5 or 5 x 32 4 Permutations (npr) and combinations (ncr) 5 Multiplication, implied multiplication, and division 6 Addition and subtraction 7 elational functions, such as > or 8 Logic operator and 9 Logic operators or and xor 2006 STATWORKS (M) SDN BHD 9

14 3 Graphing with the TI-84 PLUS Practice Examples: Example Keystrokes Answer 1 2(5 2 1) Á ¹ À Í œ Í Í (-2) + (-5) Ì Á Ã Ì Í -7 Ì Á ¹ Ì Í 5 (-2) (-5) Notice the difference between a negative sign associated with a number and the abstract operation π y Í Notice that you do not need to enter a multiplication sign between π and a constant π X 10 2 y À Ê Í STATWORKS (M) SDN BHD 10

15 3 Graphing with the TI-84 PLUS Example Answer X / / x ( ) (6 4.5) X x (-4.8) /(123 * 456) / ( ) ( ) / ( ) / ( ) ( ) /(-2.4) STATWORKS (M) SDN BHD 11

16 3 Graphing with the TI-84 PLUS Editing Editing is how you correct your mistakes, or change your mind about a calculation. Suppose you have entered the calculation The answer given on the right hand side of the screen is But perhaps you have now realized that instead of 25 (in the numerator) you should have entered 35. Since you can see what you have done on the screen, these kinds of mistakes are easy to spot! Press y Í and you will see the calculation repeated (you have recalled the previous entry) - but there is no answer this time. Use the key repeatedly (or } ~ ) so that the cursor is blinking on top of the 2. Then press 3 (which changes 25 to 35) and Í The corrected answer is given Using the DEL key Suppose that the calculation above should have been i.e. the 1 63 should have been simply 1.3 Press y Í until you reach , place the cursor over the 6 and then press { followed by Í - the answer is now STATWORKS (M) SDN BHD 12

17 3 Graphing with the TI-84 PLUS Inserting a Number If you need to insert a number, move the cursor until it is to the immediate right of where you need to insert, press y { (this is equivalent to INS), followed by the number (or numbers) to be inserted. Complete the calculation by pressing Í Power and Roots You may have noticed that the key is used to indicate that something is raised to a power. However, if you wish to square a number then is an option which uses one less keystroke. Example can be found by either of these methods. 7 6 Í or 7 6 ^ 2 ÍThe answer is The square root key is accessed by y but these must be pressed before the number is entered. Example 64 is entered as y 64 ( ) is entered using brackets like this Í (Answer = 13) The final bracket is optional here, though there may be times when it is essential. You need to think about the calculation and the rule of order to decide when the closing bracket is essential STATWORKS (M) SDN BHD 13

18 3 Graphing with the TI-84 PLUS Math Menu Evaluate and give the answer as a fraction. 3 5 There is no fraction key on the TI-84, however this is not a problem. The sum is entered in conventional manner using the 'divide' symbol. Here are the keystrokes: 2 3 Ã 4 5 Í The answer is given as We can change this to fraction form by using the following keystrokes: À You will be returned to the Home screen and see that the calculator has been instructed to change the answer to a fraction. Í The answer is given as 22/15 If you want to change this back to a decimal form, press Á If a calculation involves a mixed numeral (for example 6 2/5 ) then you can change it to an improper fraction ( 32/5 ) or recognize that 6 2/5 means (6 + 2/5 ) Example: 6 50 can be found by: You will be immediately returned to the Home screen with the symbol x shown. This gives the instruction to find the sixth root of the number which is entered next. 50 Í The answer is displayed. There are many other operations that can be done from the MATH menu, but we will only consider some of them here STATWORKS (M) SDN BHD 14

19 3 Graphing with the TI-84 PLUS Repeat Calculations Most calculators have the ability to repeat an operation over and over. Let's see how the TI-84 Plus does this. Suppose we need to fill in a table of values like this. What we are doing is starting with 100 then multiplying it and each successive answer by 1.2, ie repeatedly increasing by 20%. Here are the keystrokes that we would use. 100 Í The starting number of 100 is shown. 1.2 Í 100 multiplied by 1.2 = 120 Í = 144 Í = 17.8 and so on. Every time Í is pressed the previous answer is multiplied by 1.2. Complete the table above. The next results that you should see are: , , Repeating Similar Calculations Suppose we want to find the height of a cylinder which has a radius of 5 cm and has a volume of 500 cm3. A guess and check method could be to use the formula V = πr 2 h, giving h different values until the answer is 500. Use these keystrokes to try an initial value as h = 3 cm STATWORKS (M) SDN BHD 15

20 3 Graphing with the TI-84 PLUS π Í The value for V is , obviously then h = 3 cm is too little. So we could next try h = 4 cm. Instead of entering the complete calculation again, simply press y Í You will now see the previous expression on the screen. Use the cursor keys to replace 3 with 4, and again press Í. The key combination of y Í recalls the previous expression. This can then be edited and an answer recalculated. If you continue this process of recalling the previous expression and trying other values for h you should find that h = 6 37 cm (2 d.p.) STATWORKS (M) SDN BHD 16

21 3 Graphing with the TI-84 PLUS Introduction : Graphing Main Graphing Keys The keys which are located just under the screen are the main ones used to create and investigate graphs. o This is the key used to enter the expression, or function, which you want to graph. p This key allows you to specify the scale for the x- and y-axes. This is where you set the maximum values for x and for y that you wish to see on the screen. q You can zoom in on a graph to show more detail - just like using a magnifying glass. Or you can zoom out to see more of the graph if you need to see the 'big picture'. Other options will be described as they are needed later. r When you need to investigate how x and y values are changing, we use the trace facility. It allows you to follow the path of a graph with a cursor, and to read the coordinates of the point where the cursor is located s Once you have told the calculator what you want to graph, pressing this key then actually draws the graph. There are other options printed in yellow above each of these keys. These are accessed by first pressing y - their use will be explained later STATWORKS (M) SDN BHD 17

22 3 Graphing with the TI-84 PLUS How to create a Graph Defining Functions to be Graphed In order to graph a function, it must first be entered on the function list. Press o to go to the function list. If there are any functions already defined, you can clear these by moving the flashing cursor (using the ~ etc. keys) to any position of the expression itself (but not on the = sign), and press. You can define up to 10 different functions (labelled as Y1, Y2, Y3, etc.) and all or some of these can be graphed simultaneously. If you wish to leave a function defined but do not want it graphed, then move the flashing cursor to be over the = of that expression, and press Í. The = sign will no longer be highlighted. To reselect a function to be graphed, move the cursor to the = sign and press Í. Defining Windows Unless you specify otherwise, a graph will be displayed on the standard screen. For this the x-axis is from 10 to +10 in steps of 1 unit, and the same for the y-axis. You need to be aware of the settings for the axes so that you can interpret the graph, as no scale is written on the axes. You can design the x and y axes for a graph by specifying maximum and minimum values that you wish. Press p. You will see the current information about the axes. You can change any of these settings by overwriting them. The setting Xscl means the scale for the marks along the x-axis; that is, the size of the 'jumps' between the maximum and minimum values. Similarly for Yscl. Xres sets the pixel resolution. If Xres = 1, the function is graphed at every pixel on the x-axis. If Xres = 8, the function is graphed at every 8th pixel on the x-axis. Generally we leave Xres = STATWORKS (M) SDN BHD 18

23 3 Graphing with the TI-84 PLUS Graphing the Function Press o At Y1, press This enters the variable x. Press Now we have the variable squared. For the graph of y = x 2, let's choose the x-axis to be from 4 to +4, going up in steps of 1; and for the y-axis, set Ymin to be 1 (since we know that the curve will be above the x-axis), and Ymax to be 20, again going up in steps of 1. Press p and enter these settings. Xmin = 4 Make sure you enter this using the keys ( ) 4 Xmax = 4 Xscl = 1 Ymin = 1 Enter using ( ) 1 Ymax = 20 Yscl = 1 Press s The graph of y = x 2 will now be displayed on the setting you have chosen for the axes STATWORKS (M) SDN BHD 19

24 3 Graphing with the TI-84 PLUS Tracing the Function A graph can be traced by pressing the r key. A flashing cursor ('star') appears on the graph, the coordinates of that point are given at the bottom of the screen. The equation on which the cursor is currently located is shown at the top left of the screen. Use the ~ key to move the cursor to the right along the graph. Notice how the coordinates given at the base of the screen of this point change. To move to the left, use the key. These coordinates are given to the number of decimal places specified using the z key. To remove the tracing cursor (and its coordinates) press. The starting position of the cursor is always at the central value for x on the screen. Since the window is set for 4 x 4, the central position is at x = 0. Graphing a Second Function 1. Press o. At Y 2, press This enters the variable x. 2. Press Press s The graphs of y = x 2 and y = x + 2 are both displayed. If we wish to investigate where these two graphs intersect it will be more convenient to view over a smaller range of x and y values. 4. Change these values using p ( 4 x 4 and 1 y 5 is a good window to use.) 5. Press s to return to the graph screen, and then press TRACE. The flashing cursor will be on the curve of y = x 2 - as indicated by the equation at the top of the screen. Use the } (or ) keys to move the cursor to the graph of Y2 (i.e. y = x + 2), and the equation Y 2 = x + 2 is now shown at the top of the screen STATWORKS (M) SDN BHD 20

25 3 Graphing with the TI-84 PLUS To determine the coordinates of the points of intersection, move the cursor (either ~ or ), until it appears to be at the point of intersection and then read the coordinates. (One point should be very close to x = 2, y = 4) Zooming In trying to locate the point of intersection of y = x 2 and y = x + 2 when x is positive (above) you may have noticed that the cursor 'jumps' and you may not be sure of its position. This is when we need to 'zoom in' to magnify the graph. With the cursor located as close as you can to the point of intersection, which we know will be at (2,4), Press q 2 The number 2 is pressed so that you zoom in. At this stage you will be returned back to the graph, but nothing seems to have changed - yet! Press Í Now you will see a close up of the point of intersection! Press r and use the cursor keys to locate the point of intersection more accurately, and then zoom in again if you wish. The keystrokes q 3 Í will undo the zooming process. Alternatively, q 6 Í will return you to the standard graph window, i.e. 10 x 10 and 10 y 10. Evaluating at a specific x values A very convenient feature is the ability to find the y-value for any graph at any particular value for x. Whilst you have the graphs on the screen, press y r and then choose the option value. You will be returned to the graph screen and notice that the cursor is positioned at the bottom of the screen and waiting for you to prompt it with an x value STATWORKS (M) SDN BHD 21

26 3 Graphing with the TI-84 PLUS Enter 1, say - this means find the y-value of Y1 when x = 1. After pressing Í the value of y is also shown at the bottom of the screen; in this case, y = 1. If you press } you will notice that the cursor moves to Y2, and you can also evaluate Y 2 at x = 1. Since this will show you that Y2 also is 1 when x = 1, you have confirmed that the point ( 1, 1) is a point of intersection of the graph. If you look at the graph, it appears that the other point of intersection is at x = 2. Try evaluating Y 1 and Y 2 at x = 2 to confirm that this is the other point of intersection. You will have probably realised by now that finding these points of intersection has actually given you the solution of the equation x 2 = x + 2 or x 2 x 2 = 0 Solving Equations Algebraic equations can be solved graphically by finding where the equation intersects with the x-axis, or by using an algebraic method. For a quadratic equation, an algebraic method could be by factorizing or using the quadratic formula. Using a graphics calculator any equation can be solved by either graphical or algebraic means. Graphical Solutions There are two alternatives to use here: 1. You can graph the function and then use the Trace facility to zoom in on the coordinates of the x-intercepts. Enlarge the region around the intercept until you have the desired level of accuracy. 2. You can use the Calc facility and ask the calculator to find the roots of any graph. We will use the function f(x) = x 3 3x to demonstrate both of these methods: 2006 STATWORKS (M) SDN BHD 22

27 3 Graphing with the TI-84 PLUS The 'trace' method Plot the function f(x) = x 3 3x Suggested window settings: Xmin = 2 Ymin = 3 Xmax = 4 Ymax = 3 Xscl = 0 5 Yscl = Press s The graph appears to have one root at x = 1, and the other two are in the intervals 1< x < 0.5 and 2.5 < x < Press r You will notice that the cursor is at the point (1,0),because x = 1 is the centre of the screen. This confirms that there is one root at x = Use the ~ key to put the cursor as close as possible to the root which is at x 2.7. You will notice that you only need to use the ~ and keys to move the cursor along the path of the curve. 5. Press q 2 Í r Using TRACE ensures that the cursor Stays on the curve when either or are pressed. Position it as close as possible to the intersection of the curve and the x-axis. 6. Continue to press q 2 Í r until you have a value for the xintercept which is to the required level of accuracy. (To 2 d.p., x = 2.73) 2006 STATWORKS (M) SDN BHD 23

28 3 Graphing with the TI-84 PLUS 7. To leave this enlarged screen, you can return directly to the standard screen by pressing q 6 Í. Then reset the window to the settings as given at the beginning. You can 'unzoom' by progressively pressing q 3 Í. However this will not take you back to the original window, so the method above is probably the easier one. Finding the Roots of the Function Method Plot the function f(x) = x 3 3x Suggested window settings: Xmin = 2 Ymin = 3 Xmax = 4 Ymax = 3 Xscl = 0.5 Yscl = Press s The graph appears to have one root at x = 1, and the other two are in the intervals 1< x < 0.5 and 2.5 < x < Press y r This accesses the Calc key. 4. Press 2 This chooses to calculate a zero (or root) of the equation. 5. The graph is displayed with a prompt at the bottom of the screen to enter Left Bound. This is a value for x which is less than the actual root. Use the cursor ~ or to move along the curve to locate an x value less than the required zero. Then press Í. You will notice that a little black triangle appears at the top of the screen - this is to let you know where you have selected the lower estimate for the root. 6. You will now be prompted for an Right Bound, so use the cursor to move along the curve to locate an x value greater than the required zero. Press Í, another little triangle will appear to show you the interval that you have selected and from which the zero will be determined STATWORKS (M) SDN BHD 24

29 3 Graphing with the TI-84 PLUS 7. The calculator now asks you for a Guess. In other words, guess a value where you think the zero is, but it must be between the Left Bound and the Right Bound. Select this guess by moving the cursor back to the left and pressing Í 8. The coordinates of this root will now be displayed. The y coordinate will be 0 or very close to it. The x coordinate is the value of the zero to an accuracy of as many decimal places set using the z key. For this example, you should find x = (to 7 d.p.) is the zero of the equation in the interval 2 5 < x < 3. Repeat the procedure to find the zero which is in the interval 0 5 < x < 1. You should find that this zero is at x = (to 7 d.p.) Graph Views On the TI-84, there are different ways that you can view a graph. Practice Example Graph Y1 = x 2 + 4x using a window of 2 x 6, 2 y 6 and both Xscl = Yscl = 1. After pressing s you will see the graph with the standard view: 1. Press o then use the cursor keys to select the \ mark to the left of Y1. 2. Press Í. You will notice that the \ mark changes to a thick oblique line. This changes the graph to one with a thick line. 3. Press s to have a peek. 4. Go back to o and again select the mark to the left of Y1. 5. Successively pressing Í changes the mark to the following options. Try them, and then look at the resulting graph STATWORKS (M) SDN BHD 25

30 3 Graphing with the TI-84 PLUS Here's what each option does STATWORKS (M) SDN BHD 26

31 4 Lists and Statistics with TI-84 Plus Introduction There are a few keys which are used frequently when analysing statistics. A brief description of the relevant ones is given. Relevant Keys for Statistics This key allows you to enter data as lists (when EDIT is chosen) and the / option enables you to specify which calculations or analysis you wish to carry out. y o This key combination accesses STAT PLOTS, and allows you to define and view three different statistical graphs. y You can access lists of data in this way. Up to 6 different lists can be entered using the TI-84 Plus lists which are labelled L1 to L6, however you can generate more giving them your own names. These can then be sorted into order, filled with a constant or a sequence created and stored as a list. Univariate Statistics Entering Data as a List Press Í This chooses the 'Edit' feature. You will now see a table on the screen - it is actually just 3 columns of the 6 standard lists. For the time being we will only enter one list. The cursor should already be in L1 column, and you will see L1(1) at the base of the screen. You are ready to enter a number into position 1 of list L1. Enter this list of 13 numbers into L1 as follows: 12 Í 13 Í 6 Í 26 Í 20 Í 2006 STATWORKS (M) SDN BHD 27

32 4 Lists and Statistics with TI-84 Plus 40 Í 15 Í 30 Í 16 Í 21 Í 31 Í 29 Í 18 Í You can check the list at this stage to make sure you have not made any mistakes if you have, simply use the - key to select the incorrect entry and re-enter the correct value by 'overwriting'. If you wish you can sort the list into either ascending or descending order. To sort into ascending order press Á y À Í To check that this has been done, press Í. Since there is only one list entered, calculation of statistical measures can only be found for 1 variable. Press ~ À This returns you to the Home Screen and shows that 1- Var Stats will be generated, but you have to tell the calculator that data is in L1. Press y À Í The 1-Var Stats will be calculated and displayed. You will need to use the to see all the summary statistics. Unless you specify otherwise, the calculator assumes that the data is in L1 and that the frequency of each score is 1. So for this situation, simply pressing Í will calculate the required one variable statistics. You should find that the mean is and the median is 20. Note: Sx means the sample standard deviation σx means the population standard deviation Q1 is the lower quartile and Q3 is the upper quartile 2006 STATWORKS (M) SDN BHD 28

33 4 Lists and Statistics with TI-84 Plus Clear a List There are a few ways that this can be done: 1. After choosing Í you can manually delete (by pressing {), each list value individually - pretty tedious eh? 2. Press ; you then need to specify which lists are to be cleared. Press y 1 to clear L1, 2nd 2 to clear L2 and so on. Each of these must be separated by a comma. 3. After choosing Í if you use the arrow keys to place the cursor over the heading for L1, then just press Í and the whole list will be deleted. 4. Pressing y à takes you to the Memory menu. Press Á to select Delete, and to ask for a List to be deleted. Use the cursor keys to move the small triangle to the list you want to delete, then press Í. Build A Histogram A frequency table of data such as the following is entered with the scores in one list (perhaps L1) and the frequencies in another list (say, L2), or vice versa - it doesn't matter, as long as you know which list represents what. Alternatively, you can choose to name these lists, perhaps as SCORE and FREQ. Instructions to name list is given later STATWORKS (M) SDN BHD 29

34 4 Lists and Statistics with TI-84 Plus Press p to set the axes for the histogram as you want them. Perhaps going from 0-11 along the horizontal axis, and 0-15 for the vertical axis. Both the x scale and the y scale should be 1. Use PLOTS to ensure that only one graph is ON - otherwise you may find it confusing if two or more graphs are superimposed. Choose whichever plot is convenient, though we will choose Plot 1. Press y o À Make sure that Plot 1 is ON by pressing ENTER when the cursor is flashing here ~ ~ Ò Í You should now have the flashing cursor over the histogram icon. y À To select L1 for the Xlist, and y Á For L2 as the frequency. s The histogram should now be displayed. Naming A List As with many of the functions and operations of the calculator there is more than one way to name a list. We'll use the frequency data above and enter these under the names SCORE and FREQ. Press Í. This takes you to the screen showing lists and the cursor is already in L STATWORKS (M) SDN BHD 30

35 4 Lists and Statistics with TI-84 Plus Move the cursor over the heading for L1 and then press 2nd DEL (i.e. INS ) This creates a new list, and moves all the other lists, L1 to L6, to the right. You will be prompted for a name at the bottom of the screen and alpha lock is on, so you use the keys to spell the name SCORE. Then press Í The name is transferred to the top of the list. Move the cursor over the heading for L1 and go through the same process to enter the name FREQ. Bivariate Statistics When we are dealing with two data lists, usually we need to calculate statistical information about the two separate lists, and also about how the two lists are related. That is, we are interested in the bi-variate statistics. To illustrate the use of the TI-84 for the calculation of bi-variate statistics, work through the following example. Practice Example The following data shows IQ and corresponding results of a Scholastic Aptitude Test (AST) for 10 people. For this data (a) determine the summary statistics (b) plot a scatter diagram Solution: Enter the x data into L1 and the y data into L STATWORKS (M) SDN BHD 31

36 4 Lists and Statistics with TI-84 Plus Press ~ Á This returns you to the Home Screen and indicates that 2-Var Stats will be calculated. The cursor will be prompting you to enter the Xlist and Ylist, separated by a comma. Press y À, y Á then Í The statistics are now displayed. You will need to use the key to see all the summary statistics. First set the range for x and y values using WINDOW. ( To predict for a SAT score of 145 Xmax should be >145.) Suggested: Xmin = 90 Xmax = 150 Xscl = 5 Ymin = 40 Ymin = 90 Yscl = 5 Press y o Í You have chosen Plot 1, Ensure that it is ON, and use the cursor arrows to choose the 'scatter plot' icon. At this stage also check that x and y data are being read from the correct lists. Press s The scatter diagram is now displayed STATWORKS (M) SDN BHD 32

37 5 Special Features Introduction : Special Features Flash Technology The TI-84 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new calculator. As new functionality becomes available, you can electronically upgrade your TI-84 Plus from the Internet. Future software versions include maintenance upgrades that will be released free of charge, as well as new applications and major software upgrades that will be available for purchase from the TI web site: education.ti.com The TI84 Plus has 160K of available memory whereas the TI-84 Plus Silver Edition has 1.56 M. About 24 kilobytes (K) of RAM (random access memory) are available for to compute and store functions, programs, and data. About 1.54 M of user data archive allow you to store data, programs, applications, or any other variables to a safe location where they cannot be edited or deleted inadvertently. You can also free up RAM by archiving variables to user data Applications can be installed to customize the TI-84 Plus to your classroom needs. The big 1.54 M archive space lets you store up to 94 applications at one time. Applications can also be stored on a computer for later use or linked unit-to-unit. Press Πto see the complete list of applications that came with your calculator. Data Collection Devices with the TI-84 Plus The TI-84 Plus comes with the CBL/CBR application already installed. When coupled with the CBL 2 or CBR accessories, you can use the TI-84 Plus to analyze real world data. CBL 2 and CBR with the available probes let you explore mathematical and scientific relationships among distance, velocity, acceleration, and time using data collected from activities you perform. CBL 2 and CBR differ in that CBL 2 allows you to collect data using several different probes analyzing temperature, ph, light, voltage, or sonic (motion) data. CBR collects data using a built-in Sonic probe. CBL 2 and CBR accessories can be linked together to collect more than one type of data at the same time. These handheld data collection devices together with the TI-84 Plus will be explained further in the Science sessions STATWORKS (M) SDN BHD 33

38 5 Special Features TI-84 Plus and the TI-Graphlink cable with TI-Connect The TI Connect software is the next-generation link software taking TI handheld technology to a new level of TI device, computer, and Internet connectivity. The TI Connect software makes downloading and transferring data, operating systems, and handheld software applications (Apps) easier than ever before. The TI Connect software and the TI-Graphlink cable let you attach the TI-84 Plus graphing calculator to a personal computer (PC) running Windows (95/98/Me/2000/XP or NT 4.x). The main features of the TI-Connect software is: TI DeviceExplorer. Transfer files between your computer and the connected device STATWORKS (M) SDN BHD 34

39 5 Special Features TI GroupExplorer. Combine device files into groups and then move those grouped files back and forth between the device and your computer. TI ScreenCapture. Capture screens from the attached device. Paste the captured screens into another application or save them to a file on your computer. TI DataEditor. Create, display, and modify List, Number, or Matrix files. TI DeviceInformation. Find information about your device, including general information, installed applications, and ID Lists. Shop. The TI Connect software provides limited World Wide Web access that lets you browse the TI Online Store, locate and download operating system upgrades, purchase applications, and receive product support. Backup. Backup device files (except Flash applications) onto your computer. Restore. Restore backed-up files to your device. Options. Specify the type of device that is connected to your computer, select the start-up screen to display, select your default directories, enable or disable the check for an upgraded operating system, or change your communication settings. Updates. Scan the TI Online Store automatically to locate a new device operating system or application upgrades. Choose to upgrade now, save the upgrades to your computer so you can upgrade later, or cancel. Utilities. Start other TI applications from your computer, including TI CellSheet Converter, TI StudyCards Creator, TI InterActive! software, and TI NoteFolio Creator STATWORKS (M) SDN BHD 35

40 5 Special Features The TI Connect software does not emulate the connected handheld device. The TI Connect software is designed for you to use in conjunction with the handheld device, not in place of it. The TI Connect software does not perform on-screen computations nor does it have graph functions. TI-Connect Homescreen You can launch software applications from the Home screen, Utilities screen, and Program Editors screen. Note: The software applications available under Utilities and Program Editors do not come with the TI Connect software. You must download or purchase these applications from the TI Connect Store. From the Home screen, you can launch TI DeviceExplorer, TI ScreenCapture, TI GroupExplorer, TI DataEditor, and TI DeviceInformation. 1. Click Home. 2. Click the desired application. From the Utilities screen, you can launch TI CellSheet Converter, TI StudyCards Creator, TI InterActive! software, and TI NoteFolio Creator. 1. Click Utilities. 2. Click the desired application. From Program Editors, you can launch the TI-GRAPH LINK application. To launch these application: 1. Click Program Editors. 2. Click the desired application STATWORKS (M) SDN BHD 36

41 5 Special Features Connecting A device You can connect a TI handheld device to your computer by using a TI-GRAPH LINK Serial cable for Windows (black), a TI-GRAPH LINK Serial cable for Windows/Mac (gray), or a TI-GRAPH LINK USB cable for Windows/Mac (silver). A 9-pin to 25-pin cable adapter is required only if you are connecting to a 9-pin serial port on the computer. To Connect Your Device with a TI-GRAPH LINK Serial Cable (Black or Gray) 1. Connect one end of the cable to the computer s serial port. 2. Connect the other end of the cable to the port on the device. To Connect Your Device with a TI-GRAPH LINK USB Cable (Silver) 1. Make sure you have installed the TI Connect software (see caution below). 2. Connect one end of the TI-GRAPH LINK USB cable to the computer s USB port. 3. Connect the other end of the cable to the port on the device. Caution: Always connect the TI-GRAPH LINK USB cable after you install the TI Connect software. If you connect the TI-GRAPH LINK USB cable before you install the TI Connect software and you are using Windows XP, Windows 2000, Windows Me, or Windows 98, the incorrect driver may be installed and you will have to re-install the USB driver. Updating device software Click Updates to update the operating system and/or Flash application software on the connected device. You must have an active connection to the Internet to update Flash applications, but you do not need an active connection to the Internet if you are updating the operating system. The TI Connect software includes the latest device operating systems STATWORKS (M) SDN BHD 37

42 5 Special Features The instructions below describe checking for updates and updating your device's operating system, free Flash applications, and purchased Flash applications. If Check for new software on every startup is your default setting, you do not need to check for updates. With this setting, the TI Connect software automatically checks for an updated operating system every time you start up. Caution: Do not disconnect a USB cable during the update. TI DeviceExplorer Overview Click TI DeviceExplorer to work with your device files. With TI DeviceExplorer and a TI device connected to your computer, you can Copy device files to your computer Copy computer files to a connected device Move device files to your computer Edit device files Delete device files 2006 STATWORKS (M) SDN BHD 38

43 5 Special Features Backup your device Restore backups to your device Manage device date and time Update the device's operating system Refresh device files in the TI DeviceExplorer window Transferring device files using drag and drop If you have device files located on your computer, you can drag a file and drop them onto the TI Connect desktop icon for a quick transfer to the device. Here are a couple of ways to transfer a file to your connected handheld device quickly without actually starting the TI Connect software. To transfer device files located on your hard drive: 1. Using Windows Explorer, locate the device file you want to transfer to the connected device. 2. Reduce the size of the Windows Explorer window so you can see the TI Connect desktop icon. 3. Click the device file you want to transfer. 4. Drag the device file out of Windows Explorer and drop it on the TI Connect desktop icon. To transfer device files located on your desktop: 1. Click the device file that you want to transfer. 2. Drag the device file and drop it on the TI Connect desktop icon. Cautions: Do not disconnect a USB cable during a transfer. You can accidentally overwrite a file located on the connected device. If the file name of the application variable (AppVar) or third-party data type you are transferring to the device begins with a digit, and that file exists on the connected device, TI DeviceExplorer does not ask if you want to replace it, it simply replaces it STATWORKS (M) SDN BHD 39

44 5 Special Features Notes: The total length of the full path and file name must be less than 128 characters when performing a drag-and-drop operation. You may receive an Out of Memory error message if you transfer a large file from your device to your computer and then try to send it back to your device. This happens because the device was at its memory limit when the large file was saved. Backing up device files Click Backup to back up your device to your computer. It s always a good idea to perform an occasional backup of your device files. Backup does not back up Flash applications. To backup the device to your computer 1. Make sure the device is properly connected to your computer and is turned on. 2. On the TI Connect home screen, click Backup. The TI Connect software displays the Save As window. 1. Navigate to the location on your computer where you want to put the backup file. 2. Enter a backup file name. 3. Click Save. Caution: Do not disconnect a USB cable during the backup. Restoring backed-up device files Click Restore to restore files backed up on your computer back to your device. To restore the backed up files to your device 1. Make sure your device is properly connected to your computer and is turned on STATWORKS (M) SDN BHD 40

45 5 Special Features 2. On the TI Connect home screen, click Restore. The TI Connect software displays the Open window. 1. Navigate to the location on your computer where you put the backup file. 2. Click the backup file to select it. 3. Click Open. Caution: Do not disconnect a USB cable during a transfer. TI ScreenCapture overview Click TI ScreenCapture to capture and edit device screens. You can then paste them into other applications, save them as a file on your computer, or send them to the device connected to your computer. TI ScreenCapture also gives you additional capabilities for customizing your captured screens, such as adding borders, changing image size, and rotating images. Use TI ScreenCapture to Capture screens 2006 STATWORKS (M) SDN BHD 41

46 5 Special Features Add borders to images Paste captured screens Flip images Resize images Rotate images Edit images Print images Save captured screens Send images to a device Capturing device screens To capture a device screen 1. Be sure the device is connected to your computer and is turned on. 2. On your device, display the screen you want to capture. 3. On the TI Connect home screen, click TI ScreenCapture. TI ScreenCapture starts, connects to the device, captures the screen, and displays it on your computer. 4. To capture another screen, click Actions > Get Screen. Notes: TI ScreenCapture cannot capture a device screen if the ComPort is busy. For example, you cannot capture a screen image while a transfer is in progress. You can display up to a maximum of 20 images at one time, from either new screen captures, saved image files, or any combination. Saving captured screens To save the captured screen as a file on your computer 2006 STATWORKS (M) SDN BHD 42

47 5 Special Features 1. In TI ScreenCapture, display the captured screen you want to save. 2. Click File > Save As. 3. Navigate to the location on your computer where you want to store the captured screen. 4. Select the file type (.jpg,.bmp, or a device-specific file type). 5. Click Save. Note: Saved screens are always slightly larger than the actual screen image captured from the device. Sending images to a device You can send an image to the connected device by using TI ScreenCapture, Windows Explorer, or TI DeviceExplorer. To send an image to the connected device using TI ScreenCapture 1. Capture a device screen or open an existing image file. 2. Click Actions > Send To Device. TI ScreenCapture displays the Send Picture window. 3. Depending on the type of device connected to your computer, either enter a name for the image or select a name from the list. 4. Click OK. To send an image file to the connected device using Windows Explorer 1. Start Windows Explorer. 2. Navigate to the directory that contains your image file. 3. Right-click the image file you want to send to the device. 4. Select Send To. 5. Select Connected TI Device. 6. Select Archive or RAM STATWORKS (M) SDN BHD 43

48 5 Special Features To send an image file to the connected device using TI DeviceExplorer Caution: Do not disconnect a USB cable during a transfer. Deleting device applications Your handheld device has only a limited amount of memory available. Therefore, in order to install additional applications, you may have to delete one of your other applications to free up more memory. To delete an application from the TI-84 Plus or TI-84 Plus Silver Edition 1. Press 2nd MEM to display the MEMORY menu. 2. Select 2:Mem Mgmt/Del. 3. Select A:Apps. 4. Select the application you want to delete 5. Press DEL. 6. Select 2:Yes. TI-Interactive with the TI-84 Plus TI InterActive! is a user-friendly, interactive computer software program that enables school and college teachers and students to easily investigate ideas in mathematics and science. Teachers can enhance students learning through interactive lessons that encourage exploration, visualization, data analysis, and writing. TI InterActive! can help students master math and science concepts and improve problem-solving skills STATWORKS (M) SDN BHD 44

49 5 Special Features Features Word processor with integrated math system TI graphing calculator functionality Symbolic Computer Algebra System Integrated Web browser Data editor with spreadsheet Calculator connectivity The Math Box 1. Click the Math Box Button on TI-InterActive toolbar. An empty Math Box is inserted, accompanied by the TI Math Palette. 2. Type your expression, for example, 2^8*43/12 into the Math Box. Press the Enter key or click enter on Math Palette to evaluate the expression. TI- InterActive creates another Math Box STATWORKS (M) SDN BHD 45

50 5 Special Features The Math Palette The TI Math Palette resembles a calculator keyboard. If you prefer to use the mouse instead of the keyboard, you can click the buttons on to the palette. 1. Click to the right and below the Math Box that you have already entered, and press Enter. This places the cursor at the end of the document. 2. Click the Math Box button. An empty Math Box is inserted beneath the previous one. 3. In the Math Palette, which opens automatically when you open a Math Box, you can type fraction, exponents and different roots, using the appropriate buttons. 4. The light blue and green keys have hidden menus, click on the box in TI-InterActive and hold mouse down to see the hidden operations STATWORKS (M) SDN BHD 46

51 5 Special Features Graphing Function Create a graph in a new document, or report in Ti-InterActive. 1. On the Ti-InterActive toolbar, locate the Graph button and click the down arrow nest to it. A group of buttons is displayed, representing the available graph types. 2. Click the Y= button. The Function editor is displayed along with the Graph Window. 3. Click the Save to Document button, to insert graph in document Changing the maximum and minimum values on graph. 1. Double clicking on the graph when it is in document will open the Function options, where you can use Zoom options or x and y axis field boxes to change size of the values STATWORKS (M) SDN BHD 47

52 5 Special Features Data Analysis Enter statistical data using the List Editor. 1. On the Ti-InterActive toolbar, click the List button. The List Editor is displayed, with the empty cell at the top of L1 already selected and ready for an entry. 2. Type in the data, and then press the down arrow key on the computer keyboard to move to the next cell. Key in all data using the arrow keys. 3. When all data is entered, click the close document button. The list will be inserted into a document. Viewing the plotted data STATWORKS (M) SDN BHD 48

53 5 Special Features 1. In the Graph window, select all the data to be included in your graph, then click the Zoom Statistics button adjusted automatically to show all the plotted points.. The viewing boundaries are 2. Click Save to Document button to close the Graph window and insert the graph in the document. Calculating a regression on the data. 1. Ti-InterActive allows you to calculate several types of regressions on data stored in lists. 2. Click the Stat Calculation button on the Ti-InterActive toolbar. The Statistics Regression Calculation tool is displayed. 3. Click the down arrow next to the Calculation Type, scroll down the through the list, and click on the type you would like. 4. In text box labeled X List: Type L1. 5. In test box labeled Y List: Type L2. 6. Click Calculate to calculate the regression equation and its variables. 7. Click the Save Results button. Ti-InterActive stores the results in variables, and displays the selected results tin your document STATWORKS (M) SDN BHD 49

54 5 Special Features Plotting the Regression 1. With cursor positioned at end of the regression results, press Enter on the computer keyboard, type the heading Graphed regression equation, (or a title to you graph) and press enter again. (Hint: it is a good idea to separate graphs vertically on page, with several spaces.) 2. On the TI-InterActive toolbar, click Graph button. 3. Click the Plots tab. 4. In the uppermost text box, type the name of your first set of data L1. 5. In the second text box, type the name of your second set of data, L2. 6. Press Enter on keyboard. (Check the check box at left if it not checked.) 7. Select the f(x) tab. 8. In the uppermost text box of the f(x), type regeq(x) and then press Enter on the computer keyboard. TI-InterActive graphs the regression equation. 9. Click the Zoom Statistics button in the Graph window to adjust the 2006 STATWORKS (M) SDN BHD 50