The TI-86 Tutorial

When you first get your calculator, make sure the batteries are installed correctly, and turn it on. You should see a blinking cursor in the upper left corner of the screen (there may be a message on the screen; if so, press CLEAR to clear it). To turn your calculator off, press [2nd OFF] (it's on the same key as ON). If you leave the calculator idle for a while, it will automatically turn itself off; if this happens, just turn it back on--whatever you were working on will still be there.

Adjusting the Contrast

If the display is too dim or too dark, adjust the contrast by pressing [2nd] and then the up or down arrow (the gray keys in the upper right corner of the calculator). Over time, your batteries will run down a bit, causing the display to become dimmer. To compensate for this, you will from time to time need to set the contrast to a higher level. (The contrast level, on a scale of 1 to 9, is indicated by the number in the upper right corner of the screen when you press 2nd and the up or down arrow. As long as you don't have to set it all the way up to 8 or 9, your batteries are still okay.)

Try a few calculations.

  1. Find 25 - 7 ÷ 17.3
    [Type 2^5 for 25. Press ENTER after the 17.3.]
    The answer should be 31.5953757225.

  2. Find (25 - 7) ÷ 17.3
    You should get 1.4450867052.
    (Why is this different than the previous example?)

  3. Multiply your previous answer by 72. You don't have to retype the number; just press the multiply key, type in 72, and Enter. The display should say Ans*72, with an answer of 104.046242775. ("Ans" stands for "most recent answer".)

  4. Find the square root of your last answer (the 104.046...). Press 2nd then the key with the square root sign above it in yellow, then press 2nd ANS, then Enter. (ANS is in yellow, above the (-) key.)

    Note that to access anything printed above a key in yellow, you first press the 2nd key. Also note that in this example, since the square root comes before the number you are taking the square root of, the calculator does not automatically insert "Ans" the way it did in the multiplication example.

  5. Clear the screen, then find the following. Round your answer to 4 decimal places.

    36*17.2 - 15
    __________
    34 + .03

    Be sure to use parentheses where needed. You should get 7.4565.

  6. Repeat the previous example, but this time change the 36 to -.005. You can save a lot of typing by retrieving your previous entry. Press [2nd Entry] to do this (it's above Enter). Then use the arrow keys to move the cursor to the part you want to edit (the 36), use DEL (to the left of the arrow keys) to delete the 36, and 2nd INS (same key as DEL) to insert the -.005. Be careful to use the negative sign (-) to the left of the Enter key, which is different from the the subtraction key. When everything looks right, hit Enter. You should get -.1862 (rounded to 4 decimal places).

    You can use [2nd Entry] to retrieve earlier entries, not just the most recent one. To do this, press [2nd Entry] more than once (once gets the most recent entry, twice gets the one before that, etc.) Try pressing it several times, and see what previous entries come up.

Using Memory

 If you do a calculation in more than one step, you should always use all of the decimal places as you go along, so you don't accumulate a lot of round-off error. The easiest way to do this is to make use of your calculator's memory. Don't forget that you can always use [2nd Ans] to retrieve the most recent answer, or [2nd Entry] to retrieve the most recent entry (press it more than once to get entries before that). You can also store a value to a variable so that you can refer to it by name.

To store a value to a variable, you need to give it a name, like "x" or "Helen" or "K3". To type letters, which are printed above the keys in blue, use the blue ALPHA key. For example, try typing a "W" by pressing the ALPHA key then the key with the blue W above it. Pressing ALPHA twice puts you in alpha-lock mode (kind of like caps lock on a keyboard); press it again to get out of alpha mode. Use [2nd alpha] to get lower case letters; you can lock that too. Try typing your name, using upper and lower case letters. Clear the screen when you are done [if you hit enter, you will get an error message because your variable is undefined; if that happens, just press the menu key F5 ("quit").]

To store a number to a variable, type in the number, press "STO>" (store), then type in a name for your variable (and Enter). Pressing the store button automatically puts you into alpha-lock mode; you don't have to press ALPHA. For example, store the number 39/7 to a variable called M: type in the 39, the divide key, the 7, then press the store button, then M, then ENTER. To retrieve this value, use the alpha key to type an M, and hit Enter (try it). Find 4M2 by typing 4*M^2.

Try the following examples:

  1. Suppose a rectangular lawn is 347.6 feet long and 178.2 feet wide. Store these values in the variables L and W, then use L and W to find the area and perimeter of the lawn. (You should get an area of 61942.32 square feet, and a perimeter of 1051.6 feet.)

  2. Find f(13.6) for the function
    f(x)=x3 + 2.1x - 4x2 + 6/x
    Start by storing 13.6 in the variable x, then just type in x3 + 2.1x - 4x2 + 6/x. You can use [2nd alpha] to get a lower case x, but it's easier to just hit the button next to the alpha key that says "x-VAR" (x-variable). You don't need the alpha key with the x-VAR button. We'll use the x-VAR button a lot.

Using the Menu Keys

 When using your calculator, you will often have a menu of options along the bottom of the screen. To access the menu items, use the 5 menu keys (labeled F1 through F5) along the top of the calculator. If you have two layers of menus, use F1 through F5 to access the bottom row, and [2nd] M1 through M5 to access the top row. To get rid of a menu, press EXIT (next to the [2nd] key).

For example, let's use the unit conversion menu. Press [2nd CONV] (it's above the 5 key) to call up this menu. The little triangle pointing to the right indicates that there are more items on the menu. Press the MORE key (next to the arrow keys) to see additional items. Let's convert a speed of 15 feet per second into miles per hour. Find "SPEED" on the menu, and select it by pressing the menu key immediately beneath it. Type in the 15, then select the unit it is in, ft/s, from the menu. Then select the unit we want to convert to, mi/hr, and Enter. This converts 15 ft/s to (about) 10.2 mi/hr. When you're through, hit the EXIT key to get out of the SPEED menu (and EXIT again to get out altogether).

Try using the CONV menu to find your age in seconds.

By the way, another handy menu to know about is 2nd CONS (constant), which has built-in values of physical constants you might need in a science class. (See pages 58-59 of the calculator manual for details.)

Graphing

 First, get out some paper and draw a graph of the function y=x2 by plotting a few points and connecting them in a smooth curve.

Now try graphing it on your calculator. Press the GRAPH key (just below the Alpha key). From the menu, select "y(x)=". This is where you go to enter functions you want to graph. Near the top of the screen, it should say "\y1=". Type in your function, x2, on this line, so that it says y1=x^2. Be sure to use a lower case x for the variable (use the x-VAR button or select "x" off the menu). To display the graph, we need to select "Graph" from the menu; it's on the top row, so use [2nd M5] to do this (alternatively, you can hit the EXIT key to get rid of the bottom row, then press F5). Try it; hopefully the graph looks something like the one you drew on paper.

Try tracing along your graph. To do this, select "Trace" from the menu, then use the left and right arrow keys to move along the graph. Watch how the x and y coordinates change as you move along the curve. Often we will trace to find the coordinates of a specific point on the graph (for instance, the point where x=2.5). If you trace with the arrow keys, though, chances are you will not hit exactly this point (it might skip from something like x=2.38 to x=2.53). To trace to the point where x is equal to exactly 2.5, type in the number 2.5 and press Enter (try it). You can then continue tracing with the right/left arrows, or enter another x-value to jump to. When you're through tracing, press EXIT to get the menu back.

If your calculator is brand new, it probably graphed your function using the default graphing window (domain and range settings). Normally you will need to set the window yourself. To do this, select "Wind" (window) from the menu. It will say something like xMin=-10, xMax=10, xScl=1, yMin=-10, yMax=10, yScl=1, and (if you go down to the bottom with the down arrow), xRes=1. This means that the graph is displayed from -10 (xMin) to 10 (xMax) along the x-axis, and -10 (yMin) to 10 (yMax) along the y-axis. xScl=1 and yScl=1 set the tick marks one unit apart on each axis. Try changing these values. Try, say, -5 and 5 for xMin and xMax, -5 and 40 for yMin and yMax. Select "Graph" from the menu to display the graph with these new settings.

Experiment with different window settings to see how they affect the appearance of the curve. See if you can make the parabola tall and skinny, or short and wide. Try changing the tickmarks (xScl and yScl) to see what that does (what happens if they are set to 0?). xRes (down at the very bottom), controls the resolution. xRes can have an integer value from 1 to 8. A low xRes graphs more accurately; a high xRes will graph more quickly, but less accurately. Try changing xRes to 8 to see what it does, and see how this affects "Trace". Most of the time you will probably want to leave xRes set to 1, the most accurate.

Using a graph to find x and y values

Go to "y(x)=" (from the GRAPH menu), clear out whatever functions you have in there, and enter the function f(x) = 25 - 30*(x+15)^(1/2) in y1 (recall that the 1/2 power is the same as taking the squareroot). Display the graph with the default window settings, -10 to 10 for x, and -10 to 10 for y. [To set this automatically, you can select "Zoom" then "ZSTD", for "zoom standard".] With the default window settings, you won't see the graph at all; it is entirely outside this window. You will need to change the window. You can often get a rough idea of how to set yMin and yMax by finding (or even estimating) the y-intercept. You can also try tracing; the coordinates will be displayed even if the graph is completely off the screen. Experiment until you find a suitable viewing window. You should be able to see where the graph crosses the x and y axes, and have a good picture of the overall shape of the curve.

Once you have a good viewing window, use your graph to do the following exercises. By the way, if the menu is obscuring part of the graph, you can press the CLEAR key to erase the menu (and EXIT to get it back).

  1. Find f(17) and f(-3) for our function. (Select "TRACE", then type in the x-value, for example 17, then Enter.) You should get f(17)=-144.7056275 and f(-3)=-102.2792206. (If you get "Error 04 Domain" when you do this, it means that the x-value is outside the viewing window. Adjust your window and try again.)

    Another way to find f(17) and f(-3) is to EXIT from your graph (press EXIT twice if there are two layers of menus on your screen), then simply type in y1(17) or y1(-3) or whatever.

  2. Find the value of x for which f(x)=-75. You can get a rough idea of where this is by tracing, but this is not very accurate. To get an accurate answer, do the following. Go back to the "y(x)=" list, and in y2 enter the function y=-75 (if the cursor is on y1, just hit the down arrow to go down to y2, and type in -75). Display the graph. You should see both the original curve and the horizontal line y=-75 (adjust your window if necessary). To find where f(x)=-75, we need to find the interesection of the line with the curve. To do this, look around on the graph menu for "MATH" (use MORE), and select it. Then look around for "ISECT" (intersect), and select it. The cursor will be on y1 (our curve), and you will be prompted "First curve?"; hit enter to accept y1 as your first curve (if you had several curves graphed, you would use the down arrow to skip to the one you want). Next you will be prompted "Second curve?"; hit Enter to accept y2 (our line). Then you will be prompted "Guess?", which means you should take a guess where the functions intersect; to do this, either use the left or right arrow to move the cursor close to the intersection point, or type in an estimate of the x-value of the point of intersection, and hit Enter. The intersection point should be x=-3.888888889, y=-75. This means that f(x)=-75 when x is (approximately) -3.888888889.

    For practise, use this same procedure to find where f(x)=-100 (you should get x=2.3611111111).

  3. Our function has one root, i.e., one place where f(x)=0. Let's find the value of this root. First go back to the y(x) list and turn off y2 by putting the cursor on y2 and selecting "SELCT" (select) from the menu. SELCT selects functions, i.e., turns them on or off (a function is turned on if there is a dark box around the equal sign; otherwise it is off). Now display the graph of y1 (our original function), and find the x-intercept (root). To do this, look around for "MATH" (use MORE), and select it, then select "ROOT". You will be prompted "Left Bound?"; use the left or right arrow to move the cursor slightly to the left of the root, then hit Enter. Do the same thing for the "Right Bound", by moving the cursor a bit to the right of the root, then Enter. Then "Guess", i.e., move the cursor near the root, then hit Enter, and wait a moment for the calculator to compute the root. (You can also type in numerical values for the left and right bounds and the guess.) You should get x=-14.30555556, y=8E-12. This means that the root (value where f(x)=0) is located at (about) x=-14.30555556. The y=8E-12 is scientific notation: it means y=8*10-12, i.e., .000000000008 (in other words, just about zero.)
In short, if you know the x-value and need to find y, you can TRACE (and type in the specific x-value); if you know y and need to find x, graph the horizontal line (y=constant) and find the intersection (MORE MATH MORE ISECT); to find where y=0, find the root(s) (MORE MATH ROOT).

Working with Data

Page written and maintained by Helen Read.

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