Adjust Your Screen & Understand the Keys

Turn on your machine; the ON key is at the bottom left of the keyboard. A new calculator or one whose batteries are run down needs to have the brightness adjusted.

• To darken --- Press the yellow key (labeled 2^nd) and depress the blue ­ arrow key
• To lighten --- Press the yellow key and depress the blue ¯ arrow key

The Home Screen & Menus

Our tour begins at the home screen. Press QUIT (2^nd state next to yellow button) to open the home screen. The home screen is where calculations are made. The calculations on the next page involve symbols stored in the MATH menus. Before we get started with these examples, take a look at the MATH menus: press the MATH key (left side, under the green key).

Top Math menu

The MATH commands are organized into the 4 subsets listed across the top of this screen: MATH, NUM, CPX, and PRB. The MATH submenu is highlighted so its items appear. It contains more commands than we see so the last item includes the ¯ symbol. Press the ¯ key to scroll down to see three more commands. Press the ® arrow key to open a new submenu.
 
 

Sample Calculations

Make sure you start each calculation from the home screen.

• Evaluate (-3)^3: type (-3) using the negatives symbol (-), open the MATH menu, arrow down to the third option, and press ENTER.

• Write .3875 into a fraction: type .3875, open the Math menu, highlight the command Þ Frac, press ENTER.

• Clean the screen: press the CLEAR key.

There's always the chance that someone has left your calculator in a strange operating state, so when you begin, check the mode screen, shown above.

Line 1 refers to how numbers are presented. There's no need to switch from NORMAL mode. It engages scientific mode for large numbers and small numbers, and engineering mode is like scientific mode:
 

Line 2 refers to the number of digits used. FLOAT is the default mode; in it the calculator decides how many decimals to use in the display.
 

Line 3 refers to angle measurements. In angle mode, sin(60) equals 1/2 but in radian mode it won't. In radian mode you can put in a degree symbol, e.g., sin(60° ).

Line 4 refers to the type of formulas one wants to graph/table:

SEQ --- u, v or w is a recursive function of n

Graph & Table Basics

The top row of keys has the graphics and table options. Our tour continues with a demonstration of how to use them to solve the following problem:

We'll enter length L as a function of width w and use its graph and table to get the L corresponding to w=9. Since 2L+2w=25, L=(25-2w)/2. To use the TI-83 we'll have to rename the variables: w becomes x and L becomes y1, y2, y3, or anyone of the default function names.

3 steps create our graph of L versus w as illustrated in the screens that follow:

1. Open the Y= screen (left side, under the screen) and enter this formula as shown on the left. Use the "hot key" (right of green key) to type x; this is easier than typing the 2-key ALPHA sequence for the letter X.
2. Open the WINDOW screen (next to Y=) and put in the values shown below in the middle screen.
3. Open the GRAPH screen (right key) to obtain the line shown at the right. X is between 0 and 13 with tick marks every 2 units because of the first three inputs in the WINDOW screen. Y is between -1 and 13 with tick marks every 5 units.

To capture a couple of points from the line, open TRACE mode by pressing the TRACE key in the top row. This places a blinking cursor on the line, at horizontal midpoint. The left and right arrows move the cursor along the line. In this example, the cursor starts at (6.5,6) and these coordinates appear at the bottom of the screen.

It's hard to get the cursor on the point where x=9 because that point isn't at one of the light pixels used in making this graph. Many texts, in such cases, suggest that students adjust the window or zoom-in on the point. A less frustrating option used the CALC commands (2^nd state on the TRACE key):

1. Open the CALC menu, highlight VALUE (left screen below)
2. Press ENTER to get the graph and type 9 (middle screen).
3. Press ENTER to see the coordinate corresponding to x=9 (left screen).

Another way to get function values is to make a table. We start with AUTO mode:

1. Open the 2^nd state screen TBLSET (above WINDOW).
2. Change its settings to match the screen on the left below.
3. Open the TABLE screen (above GRAPH) to see the same table shown below.

In AUTO mode, a table is "scrollable": we see entries for smaller x values by depressing the up arrow and larger ones by depressing the down arrow. ASK mode allows more control. Once the mode is changed in TBLSET (left figure below), open the TABLE screen (middle) and type 9 to get Y1=3.5 (right).

Tables have more columns when more functions are active on the Y= screen.

The Equation Solver

The previous example was really just an exercise in solving the equation 2L+2w=25 when w=9. This we can do using the SOLVE option, and we can do this without changing the variable names:

1. Open the MATH menu and highlight the 10^th option, Solver
2. Press ENTER to open the Solver screen and then press the ­ arrow to open the equation screen.
3. Type the equation so that all the terms are on one side and then press ENTER. In this case 0=25-(2L+2w) works.
4. All the variables used in your equation appear listed and set equal to 0. You must specify values for all of them; the value assigned to the unknown is an "initial guess" for its value. In this case, enter w=9 and L=0 works fine.
5. Place the cursor on the unknown and press ALPHA ENTER. After a few seconds the TI-83 updates the unknown with its (true) approximate value.

In general, an equation may have multiple solutions. Your choice of an initial guess influences which solution the TI-83 produces. Another way to limit the search is to alter the last line; it specifies the interval in which you seek a solution.
 
 

More Graph & Table Features

One of the most frustrating aspects of producing a graph is choosing a window. The TI-83 helps by picking the vertical parameters (YMIN and YMAX) that fit an x-interval we select:

1. Enter your function(s).
2. Put the XMIN/XMAX values you wish to use in the WINDOW screen.
3. Open the ZOOM screen (top row) and select the ZOOMFIT option.

Suppose you wish to graph or make a table of a composition of functions. For example, one might wish to check whether x^2+4 is the same as f(x+2) for f(x)=x^2. Fortunately, the TI-83 "understands" functional notation so one can compare their graphs using this feature. Unfortunately, the TI-83 does not recognize the "word" Y1 as the function with this name. It requires that we use a command that is stored in the Y-VARS submenu from the VARS screen shown below:

The submenu VARS contains screen parameters and quantities that are computed "behind the scene". They are divided into the categories shown in the figure above, e.g. Window, and each option opens its own submenu. For example, selecting Window opens a list of screen parameters that includes Xmin and Xmax. The Statistics option opens a screen displaying the names of five lists and the contents of the XY list: single-variable statistics about the last data set (x,y) that was active. These VARS symbols are typically used in writing programs.

The Y-VARS submenu is also divided into categories shown in the left figure below. Its submenu FUNCTION (right figure) contains the symbols for the functions: Y1, Y2, etc. When typing an expression involving a function, open this screen to highlight and copy its name just as one copies a symbol like Ö into an expression.

The following steps creates the composite function f(x+2) for f(x)=x^2 and sets up the graphical comparison with the function x^2+4:

1. Open the Y= screen, clear the Y1 and Y2 lines, and type in the formula X^2 as Y1.
2. Deactivate this curve (we won't want its graph confusing our comparison) by placing the cursor on its = and pressing ENTER.
3. Move the cursor to the Y2 line.
4. Open the VARS menu, arrow over to Y-VARS, and open the FUNCTION menu.
5. Highlight Y1 and press ENTER. This places the symbol Y1 on the Y2 line.
6. Type the rest of the composition expression as shown in the figure below.

7. Move the cursor to the Y3 line and type the formula X^2 + 4.
8. 8. Open WINDOW and make your parameter selections.

Another TI-83 feature makes viewing two or more graphs easier. Open the Y= screen. At the left side of each line there's an icon that symbolizes how the curve will be drawn. Arrow left of the Y and the icon blinks: strike ENTER to see the next choice of seven possible choices. The figure at the top of the next page displays the ``shade under'' option.

Look again at the Y= screen. Notice that the = sign of the function you used is quite dark. This denotes an "activated" function. The next table or graph constructed will include all the activated functions from the list. The = symbol is like a light switch: it turns off and on in the same way. In this case, placing the cursor an = symbol and striking ENTER changes it from OFF to ON or ON to OFF.

Other CALC Options

Option 2 finds the zero of a function in an x-interval you select. Options 3 and 4 optimize a function over an x-interval you select. Option 5 finds the intersection of two graphed functions over an x-interval you select. Option 6 finds the slope at a point you select. Option 7 integrates under a function between endpoints you select.

Each option requires you to input one or more x-values. You may do this in two ways:

1. Type the x-value from the keyboard as we did to find a value OR
2. Trace the curve to a point with that x-coordinate. Press ENTER to input its value.

The TI-83 limits the number of matrices that can be stored in memory to 10. The symbols for these matrices consist of square brackets around a letter, A-J: [A], [B], etc. These symbols don't appear on the key board, and they can't be typed The MATRIX screen shows three submenus . Like the FUNCTION submenu of Y-VARS, the NAMES submenu contains the matrix symbols. Its second submenu MATH contains operations such as ref( which converts a matrix to its reduced echelon form and rref( which gives the row-reduced echelon form. For example, if there's a matrix called [A] in memory, then creating the expression ref([A]) on the home screen is the first step to finding its reduced echelon form.

The third submenu EDIT is similar to the STAT EDIT submenu: one creates the matrix here. The following steps illustrate using MATRIX EDIT to make a 2x2 matrix [B]:

1. Open the EDIT screen (shown below on the left).
2. Place the cursor on the second option [B] and press Enter.
3. The cursor is in position to type the dimension of [B]: type 2, press ENTER, type 2, and then press Enter again. Notice that a matrix with 4 entries appears below.
4. Place the appropriate entries into the matrix. You may arrow from position to position or press ENTER after each change. In the latter case, the cursor moves down each row, going to the next row after reaching the row's rightmost entry.

Working with Data

The TI-83 data lists resemble spreadsheet lists. Six list names are fixed in the memory, and their names appear on the key board: L1 is the 2^nd state of the 1 key, L2 is the 2^nd state of the 2 key, etc. To restore your spreadsheet display to show L1-L6, open the STAT screen, highlight the 5^th option SetUpEditor and press ENTER.

There are 2 common data entry procedures: (1) enter the values one by one or (2) to download them from another calculator. The following steps create two lists L1 and L2 from the four data pairs (1,20), (2,37), (3,71) and (4,139).

1. Open the STAT menu (left figure below).
2. Select the Edit option to open the spreadsheet.
3. Clear the lists L1 and L2. To clear a list, place the cursor its name, press the CLEAR key, and then press ENTER.
4. Enter the four values in each list as shown below at the right.

STAT menu and the spreadsheet screen

The TI-83 was designed for statistics applications, and it has commands that none of the other TI calculators have. Those commands are in the STAT submenu TESTS. The CALC submenu contains many options for curve fitting. To plot data points (and the fitting curves) we use the STAT PLOTS menu (2^nd state on Y=).

The following steps produce a plot of the data you just entered:

1. Do some "housekeeping": check that you're in FUNC mode and deactivate all of the functions on the Y= list.
2. Open the STAT PLOTS screen (2^nd state of Y=), highlight a plot window, say Plot1, and press ENTER to open that screen.
3. Use the arrow keys to scroll down the screen and make the choices indicated in the middle screen below. This will produce a scatterplot of (unconnected) data points with L1 data on the horizontal axis, L2 data on the vertical.
4. To set the window so that the data points ``fit perfectly'', open the ZOOM screen (middle of the top row) and select option 9: ZOOMSTAT. Zoom options automatically create the graph.

The last stop on out tour will be the TI-83 regression or curve-fitting options. The data just entered will be our data, and since its graph seems parabolic we'll try a QUADRATIC fit (y=ax^2+bx+c). The formula will be computed and placed in y6.

1. CLEAR the homescreen, and open the Y= screen to clear the formula for Y6.
2. Return to the homescreen.
3. Press STAT and the arrow over to the CALC submenu.
4. Highlight the 5th option QuadReg and press ENTER.
5. Create the expression

QuadReg L1, L2, Y6

with the following steps: press L1 (2^nd on 1 key), press the comma (2^nd on 7 key), press L2 key, press the comma, and then paste the Y1 symbol from the Y-VARS submenu by opening the VARS menu, arrowing over to Y-VARS, selecting the FUNCTION option, and then selecting Y6.

6. Press ENTER and you'll see the regression formula. Press GRAPH to see its graph.

Regression result and plotted with data

Linking is a great way to share data sets with your students. Using the linking cables, you and your students can transfer lists in just a few minutes. To link, start by connecting 2 calculators, plugging each end of a linking chord into the circular opening at the front edge.

PRESS FIRMLY. Virtually all linking failure result from poorly connected cables.

The person receiving data has less to do:

1. Open the STAT submenu EDIT and clear the lists about to be received.
2. Open the LINK menu (2^nd on the variable key) shown below on the left.
3. Arrow over to RECEIVE, press ENTER and wait (screen is below on the right).

Sending a list is almost as easy. The following screens show the steps to send the contents of L3 and L4. We start by opening the LINK screen and then selecting the List option. This opens a screen with a list of the sender's lists in memory.

In the middle screen L3 and L4 have been activated for transmission. To activate a list and leave a bullet marking the its active status, arrow down to it and press ENTER. To make the transfer, arrow over to TRANSMIT (at the top) to open the transmission window. Press ENTER when the receiving calculator is ready.

The middle screen above shows a list named JOE. The following steps will create such a list and display it as the 7^th list on the EDIT screen. (One can insert a new list between any two displayed in the EDIT screen.) Our list JOE will contain the square roots of the values in L2:

1. Open STAT and press ENTER to enter the EDIT spreadsheet.
2. Place the cursor on the top row and arrow to the right of L6. This opens a new list.
3. Type the name JOE using the ALPHA keys and then press ENTER.
4. With JOE highlighted, type Ö (L2), and press ENTER.