Use your own TI-86 and follow the instructions in each Do Now, read the comments between the Do Nows, and if you start exploring on your own, you may have to backtrack in order to follow the next Do Now instructions.

Adjust Your Screen & Understand the Keys

Do Now --- Turn on your machine and adjust the screen brightness. Note: 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 gray ­ arrow key
• To lighten --- Press the yellow key and depress the gray ¯ arrow key

The TI-86, permits "common" operations like ln, sin, and tan to be entered letter-by-letter, in either uppercase (ALPHA mode) or lowercase letters (alpha mode). To engage an ALPHA state on a key, press the blue key first. To lock the calculator in ALPHA mode (to type more than one letter consecutively), press ALPHA twice. To cancel ALPHA mode, press ALPHA again. Lowercase alpha is activated by the 2^nd state on the ALPHA key. Lock into lowercase alpha by first pressing the 3-key sequence 2^nd ALPHA ALPHA.

The Home Screen & Menus

Our tour begins at the home screen. This is where calculations are made.

Do Now -- Press QUIT (2^nd state next to yellow button) to open the home screen. Press the CLEAR key once or twice to erase everything on this screen.

Do Now --- Compute log (10^4) in two ways: (1) use the log key to create the expression thenpress ENTER to get the value (4); (2) lock into ALPHA mode to type the word log letter by letter, cancel ALPHA mode, finish typing the expression log (10^4), then press ENTER. The ^ symbol is above the division key ¸ . Most commands are not on the TI-86 keys; they are accessed through menus. The figure below shows the first page of the MATH menu line. It runs across the bottom of the homescreen. The arrow ® after MISC indicates that there is more to see on the menu list. The MORE key pages through menu lists, wrapping back to the start from the last page.

The MATH menu line: 1^st page

Do Now --- Open the second page of the MATH menu line: press the MATH key (2^nd state on times key X) to get the first page, and then press the MORE key (next to arrow keys) to move to the second page.

Do Now --- Open the MISC submenu: press MORE to return to page 1 of the MATH menu,press F5 because MISC is menu item displayed just above the F5 key. Note: with each menu the F-keys change. Each F-key turns on or opens the menu item displayed on the screen above it. Press the MORE key to display the second page of MISC items.

The 1^st page of the MISC line menu

Any time you select a menu item that displays another menu, the first menu line moves up to make room for the second. The item selected from the top line displays as black on white. The MORE key pages through the bottom menu line, and the F-keys (just under the screen) access its items.

The following Do Nows walk you through two calculations using commands copied from menus. The description of the second calculation is less detailed but involves almost the same steps as the first. Good luck.

Do Now --- Create the expression .3875Þ Frac on the home screen using the steps that follow. Once that's done, you can press ENTER to obtain the fraction equal to .3875, 31/80.

Start on the homescreen (press QUIT) and type .3875. Now you need to copy the command Þ Frac from the menu where it's stored. Since it's in the MISC submenu of the MATH menu, press the MATH key (2^nd state on the times key), locate the MISC option on the line menu, and press the corresponding F-key, F5 in this case. This choice opened a second line menu at the bottom of the screen. Look for the command Þ Frac on this bottom line menu. It isn't on the first page of options so press MORE to see the second page. Since it's now the first displayed option, press F1.

Look at the screen above the menu lines. You should see the expression we set out to create: .3875Þ Frac . Now you can press ENTER to finish the conversion to a fraction.

Do Now --- On the home screen, type the expression

Do Now --- Close all menus.
 

The CATLG-VARS Menus

The contents of all the TI-86 menus are displayed on pages 380-392 of the Guidebook that came with your calculator. However, there's an easier way to find things: the catalogue and the variables menus. All the stored commands, symbols and (temporary) variable values are found on the CATLG-VARS menu.

The CATLG submenu of CATLG-VARS displays all the TI functions and instructions in alphanumeric order; commands that don't begin with a letter are listed after the z. You can scroll through the list with the arrow keys ­ and ¯ . To speed up the process, type the first letter in the command name to move closer and then scroll. Note: when you enter the catalogue, the TI-86 goes into ALPHA mode anticipating that you'll want to type a letter.

Do Now --- Create the factorial expression 10! on the home screen and press ENTER tocompute its value, 3,628,8000. To do this, return to the home screen and type 10. To find the factorial symbol to put after 10, use to the catalogue. That is, press the CATLG-VARS key, open the CATLG menu, find and highlight the factorial symbol (!) and press ENTER.
 

MODE SCREEN

There's always the chance that someone has left your calculator in a strange operating state, so when you begin, check the MODE screen (2^nd state on the MORE key).

Do Now --- Open the MODE screen and check that all options match the defaults shown below. To make a change, use the arrow keys to highlight a new choice and press ENTER.

Line 1 refers to how numbers are presented. NORMAL is a good choice: it engages scientific mode for large numbers and small numbers. 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 may put in a degree symbol if needed, e.g., sin (60° ).

Line 4 refers to type of coordinates to use on your graphs: rectangular coordinates or polar coordinates.

Line 5 refers to the type of formulas one wants to graph/table:

  Graph & Table Basics

The GRAPH menu line has the graphics options, and the TABLE menu line has the 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. We'll have to rename the variables: w becomes x and L becomes y1, y2, y3, or any one of the default function names.

Do Now --- Press GRAPH (below ALPHA key) and open the y(x) = screen ( F1). Press the CLEAR key to erase any previous formula and then type the formula (25-2x)/2 in the first line so it becomes the function y1. Note: y(x)= opens a second menu line containing an x: use this x instead of the ALPHA x. Look at the top row of this screen. If any of the words PLOT1, PLOT2 or PLOT3 appears in boldface, someone has left a data plot on. It must be turned off or it will interfere with our tracing: arrow the cursor up to its name and press SELCT (F5).

Do Now --- Open the WINDOW screen from the top menu line (M2). Use the arrow keys to put in the values shown in the WINDOW screen below. Note: The bottom menu line closed because you're no longer typing formulas.

Do Now --- Open the GRAPH screen (F5) and press CLEAR to remove the menu line and uncover the x-axis. Note: Because of the first three WINDOW inputs, the graph shows X between 0 and 13 with tick marks every 2 units. Y is between -1 and 13 with ticks every 5 units.

The point of having this graph was to capture points from it, including the pair with x=9.

Do Now --- Press the GRAPH key to bring back the Graph menu line and select the TRACE Option (F4). This places a blinking cursor on the graph at the horizontal midpoint, (6.5,6) in this case. Depress the right arrow ® to move the cursor close to the horizontal position x=9. The left arrow ¬ moves it backwards.

You can't place the cursor on the point exactly 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 we adjust the window or zoom-in on the point. A less frustrating option when the x-value is within the dimensions of the displayed window is to type it from the keyboard while in trace mode.

Do Now --- Select the TRACE option, type 9, and press ENTER. The tracing cursor moves to the position where x=9 and the y-value (3.5) is displayed at the bottom of the screen.

Another way to get function values is to make a table. Tables can be created in two modes; we start with AUTO mode.

Do Now --- Press the TABLE key and open the TBLST (table set) editor (F2). Change the settings to match the TBLST screen below and then select TABLE to open the table screen. Note: To get the correct setting on the last line of TBLST, highlight AUTO and then press ENTER.

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 table mode allows more control.

Do Now --- Press F1 and adjust the TBLST to the options shown below. Note: remember to press ENTER after you highlight ASK. Now open the TABLE (shown in middle screen below). Type 9 in the x-column. Press ENTER to get Y1=3.5.

The Equation Solver

The fencing example started on page 5 is really about solving the equation 2L+2w=25 when w=9. This we can do using the SOLVER, and we can do it without changing the variable names:

Do Now --- Press the SOLVER key (2^nd state on GRAPH) to open the equation-entry editor.Press CLEAR to erase any previous equation. Type the equation, in this case 25=2L+2w. Note: Use ALPHA for L,w, and the = symbol (ALPHA state on the key above ON).

Press ENTER to open the interactive-solver editor where all the variables in your equation are listed. Enter a value for each letter except the unknown variable, and move the cursor to the unknown's line. In this case, make w=9 and place the cursor behind the L. Note: some variables may already have assigned values because these letters were used in some earlier calculation. Select the SOLVE option to engage the TI-86's numerical solver. The TI-86 updates the unknown value when it's done solving. In this case, L becomes 3.5.

In general, an equation may have multiple solutions. Your choice of the endpoints on the last line of the interactive-solver screen can be changed to pinpoint the interval in which you want the calculator to solve. The default endpoints (-1E 99 and 1E 99) describe an enormous interval.

More Graph & Table Features

One of the most frustrating aspects of producing a graph is choosing a window. The TI-86 helps by picking the vertical parameters (YMIN and YMAX) that fit an x-interval we select. In general, one first enters the function(s) on the y(x)= screen and the Xmin/Xmax values in the WINDOW screen. Since you have these entered already, go directly to the ZOOM menu to engage ZFIT:

Do Now --- Press GRAPH and select ZOOM. ZFIT is on the 2^nd page of the ZOOM line menu options, so use MORE find ZFIT. Select this option and the TI-86 makes a graph whose Ymin/Ymax values make the graph fit the screen with no extra space above or below.

Another TI-86 feature makes viewing two or more graphs easier: different curves can be drawn in different ways with dashes or heavy lines, etc.

Do Now --- Return to the y(x)= screen. In front of each formula there's an icon that symbolizes how its graph will be drawn. The icon is controlled by the STYLE option on the 2^nd page of the y(x)= menu. Each time you select STYLE the icon will change. Note: there are seven possible styles, including thin, thick and dashed lines.

Suppose you wish to store a function on the y(x)= list but you don't want it displayed in the next graph. Deactivate it. A formula is deactivated with the SELCT command on the y(x)=menu:

Do Now - Return to the y(x)= screen and deactivate y1: with the blinking cursor on the y1 line, press SELCT. Note: SELCT changed the = symbol's appearance. Press SELCT again to see the = in a black box, denoting an active state. Press SELCT again to deactivate.

Suppose you wish to check a composition formula graphically. The following steps create the composite function f(x+2) for f(x)=x^2 and set up the graphical comparison with x^2+4 :

Do Now --- Return to the y(x)= screen . If y2 already exists, place the cursor on its formula,Press CLEAR, and then type x^2 as its (new) formula. If y1 is the only function displayed, then press ENTER to create y2 and type x^2 as its formula. Deactivate y1 and y2. Now create y3, using the y from the bottom menu to type its formula as y2(x+2). Note: y3 is the composite expression f(x+2) and f is y2.

Create the y4 line and type x^2+4 as its formula. Change the STYLE icon on y4 and then select GRAPH to see y3 and y4, the only activated functions. Note: since their graphs don't coincide, f(x+2) isn't the same (algebraically) as x^2+4.
 
 

Making Data Lists

The TI-86 data lists resemble spreadsheet lists. Three list names are fixed in the memory: xStat, yStat and fStat. To restore your spreadsheet display to show them, use the command SetLEdit:

Do Now --- Return to the homescreen and CLEAR it. Select the command SetLEdit from the catalogue and press ENTER. The TI-86 responds with the word Done to indicate that the list editor screen is in default state. Press STAT (2^nd on the + key) and then EDIT to open the list editor. Note: depending on whether your lists have been used before, they may contain values.

The STAT EDIT screen

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

Do Now --- Clear the list xStat: place the cursor on its name, press the CLEAR key, and then press ENTER. Create the new list by placing the cursor on the names line and arrowing past fStat: this opens a blank list and locks the TI-86 in ALPHA mode. Type the word MYOWN, press ENTER, and then using the arrow keys, enter the four values in each list as shown below.

The xStat & MYOWN lists

Using the linking cables, you can transfer lists (or anything else) in just a few seconds.

Do Now --- Connect 2 calculators, plugging each end of a linking chord into the circular opening at the front edge of one of the two. PRESS FIRMLY.

Decide which is the receiver and which is the sender, and each follows the appropriate set of steps that follow.

Do Now --- The person receiving data has less to do: clear out the lists about to be tranferred (in case they're not empty), open the Link menu (below EXIT) and select RECV. The TI-86 responds with the message that it's waiting.

The receiver does more when he/she didn't clear lists. In this case, a dialogue box will eventually appear offering options to overwrite, ignore (skip this transfer) or rename the transmitted list(s).
 

Sending a list is almost as easy. Start by opening the Link menu (below EXIT) and selecting SEND. This opens the SEND menu showing the categories of stored items. Press MORE to get the second page and select LIST from this page. A list with the names of all the sender's lists appears. Using the arrow keys, scroll to each list to be sent and press F2 to SELCT it. A bullet appears in front of each list selected.

To make the transfer, the sender selects the XMIT option on this same menu line.
 
 

Plotting Data Lists

The STAT menu line contains the CALC and PLOT submenus. CALC contains many options for curve fitting and PLOT deals with plotting data points. The following steps produce a scatterplot of the data you just entered. Before you make a data plot, it's a good idea to make sure other things are turned off and that the calculator is in the correct modes.

Do Now --- Check that you're in FUNC mode and deactivate all of the functions on the y(x)=list. Open the STAT menu, select PLOT (F3), and from its menu, select PLOT1. Note: The TI-86 can store set-up information for three different statistical plots called Plot1, Plot2 and Plot3. There are four lines of information to set-up PLOT1 as shown below. The first is set-up by moving the cursor to ON and pressing ENTER. Note: when the cursor moves to the second line, a new menu with different graph types open.

Press F1 to select SCAT from the type menu and press ENTER. Note: the Type menu closes and another menu with list names opens. The values selected for the Xlist are plotted along the horizontal axis and the data for Ylist is plotted on the vertical axis. Press F1 to select xStat for the Xlist Name, press ENTER, and select MYOWN for the Ylist Name and press ENTER.

The data points are marked by one of three symbols now showing on the newest bottom menu. The dots are barely visible so select either the squares or the circles.
  The final part of the data plotting process is shorter. We set up the WINDOW from the GRAPH menu:

Do Now --- Press the GRAPH key and select the ZOOM option. Use MORE to get to the second page and then select the ZDATA option. It works like the ZFIT you saw before, setting the window so that the data points ``fit perfectly''. Press CLEAR to remove the menu and see the x-axis. Curve Fitting to Data
 

The last stop on out tour will be the TI-86 curve-fitting options. The data in the lists xStat and MYOWN will be our data, and since its graph seems parabolic we'll try a 2^nd degree polynomial fit, P2Reg (y(x)=ax^2+bx+c). The following steps set up this fit, store the fitting formula as y5, and plot it and the data.

Do Now --- CLEAR the homescreen, and open the y(x)= screen to clear the formula for y5. Return to the homescreen because we'll create a fitting expression on the screen: open the STAT menu, select the CALC option, and then select P2Reg from the second page of its options. This puts the fit command on the homescreen. Finish typing the fitting expression: P2Reg xStat, MYOWN, y5. Note: You may type the names xStat, MYOWN, and y5 letter by letter or copy them from various the VARS submenus on the CATLG-VARS menu. The fitting expression consists of the fit type, followed by the Xlist name, the Ylist name, and the function name where the formula will be stored. Once it's been typed, press ENTER to obtain the result: (1) the coefficients are listed in alphabetic order shown on the homescreen below:

and (2) in this case, the formula 12.75x^2-24.65x+32.75 is stored as y5. To see the data and the fitting curve plotted together, open the GRAPH menu and select GRAPH.