TI 83 and Equivalent Philippe B. Laval Kennesaw State University

Abstract This handout is an overview of the TI 83 and the features most needed for this class. It does not replace the manual which came with the calculator.

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Introduction

The main differences between the TI 81/82/83 family of calculators and simpler and less expensive calculators are: • It can evaluate expressions containing variables. • It has graphing capabilities. • It can handle matrices. • It is programmable. Of all these differences, we are only interested in the first three.

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Entering information in the calculator • The user communicates with the calculator by pressing the keys which correspond to the operation to perform. Certain operations are accessible only by using a combination of keys (2nd plus a key, or ALPHA plus a key). Other operations are available simply by pressing a key, then selecting options from a menu. The shape of the cursor helps you determine which mode you are in. — A blinking square means normal (overstrike) mode. — A square with an up arrow means the 2nd key has been pressed. — A square with an A means ALPHA has been pressed. — An underscore means insert mode. 1

• As you type, if you make a mistake, you can correct it by using the arrow keys to position the cursor where the error is. Then, the correction can be made by using keys such as INS (to put the calculator in insert mode), DEL (to delete the entry where the cursor is), or CLEAR (to clear the entire line). If you do not press INS, the calculator is in overstrike mode. • You can recall the last expression typed by pressing ”2nd ENTER” • No matter which operation you have asked the calculator to do, it will not perform it until you press the ENTER key.

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Operations

In this section, we study the various operations we will perform the most.

3.1

Basic operations

• addition: + • Subtraction: −, not to be confused with the negation key • Negation: (−) • multiplication: × • Division: ÷ • Exponents: ^ • Square: x2 . For example, to compute 42 , you will press 4 x2 ENTER √ • Square roots: √ . For example, to compute 2, you will press 2nd x2 2 ENTER

3.2

Precedence of operations

When several operations are present on the same line, the calculator does not execute them in the order in which they appear. Some operations have higher precedence, and are done first. The table below shows some of the operations and their precedence. Operations on the same row have the same precedence, and are evaluated from left to right. Operations on the first row have higher precedence than those on the second row, and so on. To change the order in which the calculator does operations, you will have to use parentheses.

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Order 1 2 3 4 5 6

3.3

Operation or function Functions entered after the argument such as x2 , x−1 Powers and roots Implied multiplication (-), √ , sin or log Multiplication and division Addition and subtraction

Practice

Evaluate each of the expressions below using the calculator.
7772.884 − 2(9.67)3 Exercise 1 (answer: −16.609) −4.65 Exercise 2

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4 1 − 3.141592 (answer: −1.0749) + 2 × 4.123 3 × 12.21343

Other Important Keys

4.1

Editing Keys

•
   are used to move the cursor on the display as well as in menus to make selections. • DEL key. Used to delete the character under the cursor. • INS key. You access it by pressing 2nd DEL. It toggles the calculator between insert and overstrike modes. The shape of the cursor will tell you which mode you are in. The default is overstrike. • CLEAR key. If pressed when the cursor is at the beginning of a line, the whole display will be cleared. If the cursor is somewhere on a line, only that line will be cleared.

4.2

Other Keys

• Letter Keys (A through Z). They are accessed by using the ALPHA key. Each letter of the alphabet can be a variable for the TI81/82/83. • STO key. Used to store a value into a variable. To set A = 2, you will press 2 STO ALPHA MATH ENTER (with a TI 82/83) 2 STO A ENTER (with a TI 81) • MODE Key. Used to set certain parameters on your calculator. Some of the parameters you can set with it are: 3

— Units — Number of digits after the decimal point • QUIT Key. Will bring you back to the main screen from wherever you are.

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Evaluating Expressions

5.1

Variables

There are different variable types depending on the data they represent. • A variable used to store a number can be any letter of the alphabet. • Functions are stored in Y1 .. Y4 for the TI 81, and Y0 .. Y9 for the TI 82/83 • Matrices are stored as [A], [B], [C]. The TI 82 can also store matrices as [E] or [F]

5.2

Accessing a variable

• Variables used to store numbers can be accessed directly by pressing a combination of keys (ALPHA plus a key). The calculator will then display the variable name. Since X is used a lot, there is a special key for X so that the ALPHA key does not have to be used. • Variables used to store a function do not have a direct access. On the TI 81, press 2nd VARS then select the desired variable from the menu. On the TI 82, press 2nd VARS then 1 (to select Function), then select the desired variable from the list. On the TI 83, press VARS then select YVARS then 1 (to select Function), then select the desired variable from the list.

5.3

Storing information in a number variable

The format is: value STO variable_name The variable name being a letter, to access it, in theory the ALPHA key should be used. This is true for the TI 82/83. But, the TI 81 is in alpha mode as soon as STO is pressed. So, to store 5 in the variable A, the user would press: 5 ST O A ENTER for the TI 81 5 ST O ALP HA A ENTER for the TI 82/83 The calculator will remember the values stored into the variables, even after the calculator is turned off. When your calculator was first purchased, all variables were initialized to 0. Variables which have never been assigned a value are still initialized to 0. 4

5.4

Storing an expression in a function variable

1. press Y= key 2. select the variable name to use 3. enter the expression 4. press Quit Once an expression has been stored into a function variable, this variable can be used in turn in other expressions. F or example, suppose you stored 2x − 4 2x − 4 . For Y2, you would simply have as Y1. Then, you want to define Y2 as 3x Y1 . to enter 3x

5.5

Displaying the content of a variable

1. Access the variable (see section above) 2. press ENTER

5.6

Evaluating an expression

To evaluate an expression, perform the following steps: 1. Store the expression in a function variable 2. Store the values of the number variables into those variables 3. Display the content of the function variable

5.7

Practice

1 − x2 4 + 3 for x = 3.12 and x = 4.521 (answer: 2x 3x -1.355842535 and -2.135476033) Exercise 3 Evaluate

6 3 x for x=6.29 (answer 7.484073621) Exercise 4 Evaluate 1 5 + x2 x3 √ −B + B 2 − 4AC Exercise 5 Let A = 11.2, B = 26.8, C = 9.1. Evaluate 2A √ −B − B 2 − 4AC and . Be as efficient as possible. (answer -0.4097003296 2A and -1.983156813) 1−

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Tables (TI 82/83 only)

Tables are useful when one has to evaluate one or more functions for several values of the independent variable as in the last problem of Practice Exercises II below. To use a table, you need to follow the steps below: 1. Enter all the functions you wish to use in the table. Turn off the functions you have defined that you do not wish to use. 2. Set the parameters of the table 3. Generate the table. You already know how to do the first step. We concentrate on the last two.

6.1

Setting the table.

• press 2nd WINDOW. You will see 4 items to set. 1. T blMin = Put the starting value of the independent variable. If you have to evaluate several functions for x = 0, x = 1, x = 2, ... you would put 0. 2. ∆T bl = Put the increment between the values of the independent variable. In the example above, you would put 1. If the values of the independent variable are not equally spaced, read below. 3. Indpnt : Here, you have a choice between Auto and Ask. Select Auto if the values of the independent variable are equally spaced. The calculator will then use what you entered in the previous two fields to generate these values. Otherwise, select Ask. When you generate the table, you will be able to specify which values you want to use for the independent variable. In this case, what you entered in the previous two fields is irrelevant. 4. Depend : Same as above, but deals with the independent variable.

6.2

Generating the table

• press 2nd GRAPH. • If you selected Auto for both the independent and the dependent variable, the table is generated. The only operations you may have to perform, is using the arrow keys to scroll the display. Note that as you scroll up or down, the table is updated with new values for the independent variable. • If you selected Ask for the independent variable, enter the values one at a time, pressing ENTER between each. The table will then be generated for the value you just entered.

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Graphing

7.1

Basic principles

For detailed explanations on how to graph a function, and all the features associated with graphing, see you manual. Graphing any function on the calculator involves three things 1. Enter the function to graph in the calculator (see above ) 2. Select which portion of the graph you wish to see. This is done by pressing the RANGE key (TI 81) or the WINDOW key (TI 82/83). You get to specify the four corners of the region you wish to see. These corners are called Xmin , Xmax , Ymin , and Ymax by your calculator. There is not a unique way of selecting this viewing window. Simply select value you think correspond to the region you wish to see. If you are not sure, experiment. 3. Then, press the graph key to display the graph. Remark 6 When you press the graph key, the calculator will actually display the graph of all the functions currently defined. If you want to graph only some of the functions, you need to turn the ones you do not want to graph off. To see if a function is ON or OFF, press the Y= key and look at the equal sign of each function. If it is highlighted, the function is ON, otherwise it is OFF. To change the status of a function, after you have pressed the Y= key, move the cursor to the equal sign of the function to change, and press ENTER. If the function was ON, it will be OFF, and vice-versa.

7.2

Extra Keys

while looking at a graph, the following keys are useful: • cursor keys. By pressing them, you can position the cursor wherever you want on the graph. The calculator will display the coordinates of the cursor. This can be useful to approximate the coordinates of special points such as intersection points, x and y-intercepts... • TRACE key. Similar to the cursor keys. But if you press TRACE before the cursor keys, the cursor will stay on the graph. In this case, to move along the graph, you simply press  or
. If you have more than one graph, to move from one to the other, you will use  or . • ZOOM key. You can zoom in, out, or specify a region to view. This has several applications. — If you do not know at all the shape of the graph you wish to view, it will be hard for you to know which window to specify. After you 7

have pressed the GRAPH key, if you see nothing, you can zoom out until you see a small portion of the graph. Then, you can zoom in to that portion. — When you use the cursor keys to approximate the coordinates of points, if you zoom closer to the point, you will get a better approximation of its coordinates.

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Practice Exercises I

Do all the computations below using your calculator. Have the calculator display 5 digits after the decimal point. 1. 23(52 − 27) = −46.0 2. 25 + 3(10 − 3.2) = 45.4 3.

23 = −11.5 4−6

4. π − 5. 6. 7. 8. 9.

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π2 = 2.7468 25

23 + π = 1.7278 25 − π 2 √ π 2 − 9 = .93253
√ π3 − 20 = 5.1511 √ π+5 = 4.6396 × 10−3 252 − 10  25 9 − 2 = 2.4944 3

Practice Exercises II

Do all the computations below using your calculator. Have the calculator display 4 digits after the decimal point. 1. evaluate

√ −B+ B 2 −4AC 2A

for the given values of A, B, and C

(a) A = 10, B = −30, C = −100 (Answer: 5) (b) A = 1, B = 4, C = −5 (Answer: 1) √ x2 + 5x + 3 for the given values of x 2. evaluate x − 1 3 x 8

(a) x = π (answer: 0.2881 ) √ (b) x = 10 (answer: 0.2834 ) √ (c) x = π + 10 (answer: 0.05336 ) 2

+1 . Compute f (0), f (1), f (10). (Answer: -1, does not 3. Let f (x) = xx−1 exist, 11.2222)  √ . Compute g(0), g(1) , g(3), g( 20). (Answer: 4. Let g(x) = (x−1)(x+3) 2x−5 .7746, 0, 3.4641, 2.5647)

5. With f and g defined above, compute the following: (a) f (2) + g(5). (Answer: 7.5298) (b) f (10)g(6). (Answer: 28.4535) (c)

f (3) g(4) .

(Answer: 1.8898)

x 2x -2 -1 6. Fill the table 0 1 2 3  x 2x  -2 .25    -1 .5  Answer : 0 1   1 2   2 4 3 8

10

3x−1 x+3

√ 2x + 5

√3x x+1

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3x−1 x+3

-7 -2 -.3333 .5 1 1.3333

√ 2x + 5 1 1.7321 2.2361 2.6458 3 3.3166

√3x x+1

ERROR ERROR 0 2.1213 3.4641 4.5

5 5 5 5 5 5 5

          

Practice Exercises III

1. Graph the function f (x) = (x + 1)2 − 3. Experiment by using different values for your viewing window. This will help you get a better feel for selecting the best viewing window. 2. Do the same as above with the function f (x) = 2x + 2 3. Using the TRACE key, get an approximation of the points of intersection between these two functions. Use the ZOOM key to improve the accuracy of your result. The exact coordinates of the points of intersection are (−2, −2) and (2, 6). 4. Try to graph f (x) = 2x + 1000. What do you see? why? how can you fix it?

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