1.    Turn [ON]. Off: [2^nd] [OFF] or just wait about 4 minutes. It turns itself off!

       Darken/lighten screen: [2^nd] [↑] [↓].

2.    When calculator is turned on, press [CLEAR] and/or [EXIT] to clear the screen of whatever may be on the screen when you turn it on.

3.    a) Direct functions—on the buttons in white letters.

       b) Indirect functions—above the button in yellow letters. Use [2^nd] to access.

       c) [ALPHA]—blue button, allows you to type words in upper case letters,

            [2^nd] [alpha] type words in lower case letters,

            [ALPHA] [ALPHA] allows you to stay in alpha mode for more than one letter.

       d) Menu functions—some functions have entire menus that are accessed using

F1, F2, F3, F4, and F5. Use [GRAPH] as an example, but save this for later.

Also, notice after pressing [GRAPH], the arrow on the right side above F5.

This indicates that there are "more" functions. Press [MORE] three times.  Now you can press [EXIT] to get out of this and back to a blank calculator screen.

4.    a) Raising to a power. 2⁵ : [2] [^] [5] [ENTER] Ans = 32.

       b) Squaring numbers. 5² : [5] [^] [2] [ENTER] Ans = 25.

            or  you can press:           [5] [x²] [ENTER] Ans = 25.

5.    Square root.

       a) : [2^nd] [√ ] [25] [ENTER] Ans = 5.

       b) : [2^nd] [√ ] [1000000] [ENTER] Ans = 1000.

6.    Difference between negative [(-)] and minus [—].

       Negative [(-)] is like an adjective. Minus [—] is like a verb.

      Calculate: 6 — 3 and compare to 6 (-) 3. The first answer is 3 (subtraction!).  The second answer is –18, since you actually multiplied times –3.

7.    Differences between TI-85 and TI-86:

       1)    More memory in TI-86,

       2)    [TABLE] in TI-86,

       3)    [STAT] button is moved

       4)    A few glitches in TI-85 corrected in 86

       5)    [GRAPH] [F2 WIND] or [F2 RANGE]

       6)    Method of finding [ROOTS]—later!

8.    Setting the [CUSTOM] menu.  

TI 85: Press [CUSTOM] The calculator opens 5 slots above the F1, F2, F3, F4, F5 keys. There will be blank spaces above these keys, unless someone has previously stored functions in these locations.

Press [2^nd] [CATALOG], and the calculator displays a list of all functions in the calculator, probably beginning with [abs]. If the cursor is not next to [abs], then press [ALPHA] [A], and it will take you there. Next press [F3 (CUSTOM)]. With the cursor next to [abs], press [F3], and [abs] will be installed in the space above [F3].  Now skip to the paragraph below with the heading "TI 85 and 86."

TI 86: Press [CUSTOM] The calculator opens 5 slots above the F1, F2, F3, F4, F5 keys. There will be blank spaces above these keys, unless you or someone has previously stored functions in these locations.

Press [2^nd] [CATALOG] then [F1 (CATLG)], and the calculator displays a list of all functions in the calculator, probably beginning with [abs]. If the cursor is not next to [abs], then press [ALPHA] [A], and it will take you there. Next press [F3 (CUSTOM)]. With the cursor next to [abs], press [F3], and [abs] will be installed in the space above [F3].  Continue to the next paragraph for additional steps.

TI 85 and 86:

Next press the up arrow [↑] repeatedly until the cursor is next to [FRAC]. Press [F5] and [FRAC] is stored in the [F5] position.

Continue to press the up arrow [↑] until you reach []. With the cursor next to [], press [F1] and the [] is installed in the [F1] position.

Finally, to install [det], press [ALPHA] [D], followed by [↓] repeatedly until the cursor is next to [det]. Press [F2] and [det] is installed above [F2].

Notice there is an arrow to the right of the [F5] position, indicating that there are [MORE] spaces available in this custom menu. If you press [MORE] you probably will see five blank spaces above the F-keys. Press [MORE] again, and you should see five more blank spaces. Press [MORE] again, and you return to the functions that you just installed. In other words, you can install a total of 15 functions in the custom menu.

Press [EXIT] two times to exit the TI 85 or three times to exit the TI 86, and you are out of this menu. To return to the custom menu, just press [CUSTOM].

9.    Cube root, fourth root, fifth root, etc. If you have not already installed [] in the custom menu, then complete step 8 above. If you have installed [], then press [CUSTOM] to open the custom menu. Once it is opened, it remains open until you close it by pressing the [EXIT] button. To take a cube root, begin with [3] for cube root, [F1 ()], followed by the radicand to be calculated. To take a fourth root, begin with [4] for fourth root, [F1 ()], followed by the radicand to be calculated. Likewise, to take a fifth root, enter [5] for cube root, [F1 ()], followed by the radicand to be calculated.

    a)   Press [CUSTOM] if you have not already done so.

          Then, [3] [F1 ()] 125. Ans: 5

    b)   [3] [F1 ()] 1000000. Ans: 100

    c)   : [4] [F1 ()] 81. Ans: 3

    d)   : [4] [F1 ()] 4096. Ans: 8

    e)   : [5] [F1 ()] 32. Ans: 2

    f)   : [5] [F1 ()] 1024. Ans: 4

10.   Decimals to fractions: [CUSTOM] [F5 (FRAC)] [decimal number] [ENTER].

Again, this assumes you have placed [FRAC] in the [CUSTOM] menu.

    a)   Convert 0 .25 to a fraction: [.25] [CUSTOM—if it is not already opened]

           [F5 (FRAC)] [ENTER].   Ans:

    b)   Convert 0.1666 to a fraction: [.1666] [F5 (FRAC)] [ENTER].

           Ans:

     c)   Convert 0.166666666666 to a fraction. Note: Be sure to give the calculator enough 6s (in this case, at least 11 digits of [6]) to establish the pattern as an infinite, repeating decimal.

            [.166666666666] [F5 (FRAC)] [ENTER].    Ans:

     d)   Convert 0.16666 to a fraction: [.16666] [F5 (FRAC)] [ENTER].

If a decimal results in a denominator of 5 or more digits, the calculator cannot express the result as a fraction, and the calculator gives the answer as the decimal value. Ans: 0.16666

     e)   Convert 0.181818181818 to a fraction. Note: In this case, at least 6 repetitions [18] pattern establishes the repeating decimal.

            [.181818181818] [F5 (FRAC)] [ENTER]. Ans:

     f)   Convert 0.1818181818 to a fraction: Note: In this case, since there are not enough repetitions to establish the repeating decimal, the calculator cannot convert to a fraction, and it gives Ans: 0.1818181818

11.   Need for parentheses. There are many occasions in which parentheses are needed in order to establish the correct order of operations. 

For example, find the value of .   The answer is obviously , which is 10. 

However, if you use the calculator entering 12 times 5 divided by 3 times 2, the result is 40.  Obviously, this is not what you really meant to do! The intended order of operations can be established by placing parentheses around the numerator and denominator.

      [(]  [12]  [x]  [5]  [ )]  [÷]  [(]  [3]  [x]  [2]  [ )]  [ENTER]      Ans: 10

12. Scientific notation.

     a)   Multiply 4,000,000 times 2,000,000.         Ans: 8E12

Interpretation: The answer 8,000,000,000,000 is too large to display on the calculator screen. Therefore, the calculator automatically converts to scientific notation which the calculator prints as 8E12. Notice that, in words, this is 4 million times 2 million. The answer is 8 trillion. Be sure to give the final answer in the form , not in the form 8E12.

     b)   Convert 4,000,000 to scientific notation.

Locate the [MODE] function (above the [MORE] key!), but don't press it yet!

Type [4000000] into the calculator. Press [2^nd] [MODE]. (The calculator displays a screen full of options, most of which are irrelevant at this time.)

In the top row, you should see the words [Normal] [Sci] [Eng].

The word [Normal] should be surrounded by a dark, flashing box.

Press the right arrow key once, and the dark flashing box moves to [Sci].

Press [ENTER] to lock it into scientific notation mode.

Press [EXIT] to return the calculator to the previous calculation.

Press [ENTER], and the calculator gives the previous answer in scientific notation. Ans: 4E6 which means

     c)   Calculate 4 times 3. Ans: 1.2E1, which means 12.

You probably now realize that the calculator is still in scientific notation mode, and it will remain in this mode until you change it back to [Normal] mode. Obviously, for ordinary computations, you need to change it back!

     d)   To return to [Normal] mode, press [2^nd] [MODE] [Left arrow][ENTER] [EXIT]   (The calculator returns to previous calculation.)    [ENTER]    Ans: 12

     e)   Calculate using the [EE] button (located above the [7] button!).

Type [8] [EE] [15] [÷] [4] [EE] [3] [ENTER] Ans: 2E12 or .

Notice that parentheses were not needed, since the numerator and denominator were entered as single numbers 8E15 and 4E3 respectively.

Also notice that this one could easily have been done without a calculator: 8 ÷ 4 = 2 and subtract the exponents 15 - 3 = 12. Final answer: .

     f)   Calculate .

Notice that the denominator exponent is a "negative" (not a "minus") 8.

Again notice that parentheses are not needed.

Type [6.25] [EE] [12] [÷] [8.40] [EE] [(-)] [8] [ENTER]

Ans: 7.44047619048E19, which should be written .

     g)   Calculate .

In this example, the numerator and denominator contain more than one number, so play it safe and use parentheses around the entire numerator and parentheses around the entire denominator.

Type: [(]   [9.24]   [EE]   [9]   [x]   [2.03]   [EE]   [(-)]   [3]   [)]               [(]   [5.75]   [EE]   [(-)]   [8]   [x]   [6.42]   [EE]   [9]   [)]   [ENTER]

Ans: 50811.8650955.

However, the answer cannot be more accurate than the numbers that were used to compute that answer! Since the numbers used in the calculation are only accurate to three digits (three significant figures!), this means that the answer is only accurate to three digits. All the rest of the numbers in that answer represent false accuracy. The final answer should be rounded off using only the first three digits. Final Ans: 50,800.

13. Typing Shortcuts/Correcting Errors: [2^nd] [ANS]; [2^nd] [ENTRY]; [2^nd] [INS]

After a calculation has been made, sometimes it is convenient to use this answer in the next calculation. Sometimes it is helpful to be able to re-enter the previous calculator entry, make changes, and recalculate. These can be accomplished using [2^nd] [ANS] (above the [(-)] key) and [2^nd] [ENTRY] (above the [ENTER] key). The following examples illustrate these calculation shortcuts.

     a)   Calculate

Keystrokes: [(]   [6.3]   [+]   [3.2]   [)]   [^]   [7]   [ENTER]

Ans: 6983372.96094

Accurate ONLY to two significant figures: Final answer: 7,000,000

     b)   Suppose you discover that the previous problem should have been . Calculate this, without retyping the entire problem.

Begin with [2^nd] [ENTRY].

The calculator redisplays the previous problem, allowing you to use the left and right arrow keys to move the cursor. Using the left arrow key, move the cursor to the left, over the 6, and type the desired [8], which replaces the 6. Press [ENTER] . New Ans: 26600198.8047

Rounded to two significant figures: Final answer: 27,000,000

Perhaps you have noticed that the calculator makes corrections in a "strike-over" mode. That is, when you make a correction, it strikes over what was already there. Sometimes it is better to be able to insert characters instead of typing over them. This can be done using [2^nd] [INS] (below the [MORE] key). Consider the next example.

     c)   Suppose you wish to change the previous calculation from to . Calculate this, without retyping the entire problem.

Begin with [2^nd] [ENTRY], use the left arrow to move the cursor back to the 3. Now, since you need to insert an extra digit (instead of just replacing a digit), press [2^nd] [INS]. Notice that the cursor changes from a "black box" to an "underline." You are now prepared to "INSert" the digits 2 and 5. Then, with the cursor under the 3, press the [DEL] (delete) key. Next, press the right arrow until the cursor is over the 2 in the 3.2. Press [2^nd] [INS] [2], and the calculator inserts a 2 for you. Now, press [ENTER], and you should have this answer: Ans: 26118241.0239

Rounded to three significant figures: Final answer: 26,100,000

     d)   Calculate the two values of , and round to the nearest hundredth.

This actually means two values and

Keystrokes: [4]   [+]   [2^nd]   []   [6]   [ENTER]   Ans: 6.45

[2^nd] [ENTRY], left arrow cursor over the +, press [—]  [ENTER]    Ans: 1.56

Sometimes when you make an error, the calculator catches it for you.

     e)   Suppose you are trying to calculate (see #12f) and in the process of entering the calculations, you enter a [—] instead of a [(-)].

When you press [ENTER], the calculator gives you an error message.

Try it as follows.

[6.25] [EE] [12] [÷] [8.40] [EE] [—] [8] [ENTER]

The calculator returns with the following message:

Now, you have two choices. You can [F5 QUIT]! Or, you can press

[F1 GOTO] to allow the calculator to show you where the error is.

Press [F1 GOTO], the calculator "goes to" the vicinity of the error, which is the [EE] [—]. To correct the error, move the cursor over the [—], replace it with a [(-)], press [ENTER], and the calculator gives the answer as before. Ans: 7.44047619048E19, which should be written .

14. Graphing.

Press the [GRAPH] button. If the calculator has been used before, the calculator will show the previous graph entered in the calculator and the basic graph menu above the F1, F2, F3, F4, and F5 keys. New or cleared calculators will show only the basic graph menu as shown below.

If you have a TI 85, in the F2 position, the word is [RANGE] instead of [WIND].

Whatever you have, TI 85 or TI 86, with previous graph or clear, the first button to press after [GRAPH] is [F1 y(x)= ]. The calculator gives you [y1=] and a flashing cursor. If the calculator had a previous graph, then you can press [CLEAR] to clear it, and then type the equation of your new graph. Clearing can also be done by pressing [F4 DELF], which means "DELete Function." It is possible to have several different equations to graph: y1, y2, y3, etc. In order to clear when you have multiple functions, the [CLEAR] does NOT work. You must use [F4 DELF].

a) Graph . To do this, you need to use [x-VAR], just below [EXIT].

If you have not already done so, type [GRAPH] [F1 y(x)=] and [CLEAR] if you need to clear a previous graph equation. Next, either press [x-VAR] [^] [2] or equivalently press [x-VAR] [].

Once you have entered the equation you wish to graph, press [ENTER] to lock it in, press [EXIT] to return the calculator to a single row in the graph menu, then [F5 GRAPH] usually works! You should get the graph below.

If you do NOT get this graph, then here are a few possible errors to look for.

1.   If you do NOT get the graph pictured above, perhaps your calculator is not in the standard window.

To standardize the window, press [F3 ZOOM] followed by [F4 ZSTD].

2.   If you have a TI 86 and get a [DIMENSION 13 ERROR], then press [2^nd ] [STAT (located above the + key)] [F3 PLOT] [F5 PlOff] [ENTER] [EXIT] .

3.   Recheck the equation and be sure y1= is typed correctly.

4.   If you wait and wait, and nothing happens, you may have accidentally

"deselected" the function for non-graphing. To check this, after pressing

[F1 y(x)=], there may or may not be a black box around the "=" sign in the y1=. If there IS a black box, then the calculator will graph this y1. If there is NOT a black box, then this equation will NOT be graphed. You will be waiting forever! Whatever it is, press [F5 SELCT], and watch what happens to the black box around the equal sign. When you press [F5] repeatedly, it selects or deselects the equation to be graphed. Of course, in order to graph any y1, you must make sure the black box surrounds the "=" sign.

b) Graph . Notice that this is "minus 4," and not a "negative 4."

Begin with [GRAPH], [F1 y(x)=], and [CLEAR] if you want a fresh start. Next, press [x-VAR] [] [— (minus)] [4]. Press [ENTER] to lock it in, [EXIT] to get a single row on the graphing menu, and [F5 GRAPH] to sketch the graph. The graph should be as the one below.

c) Graph . Notice that this is "negative ," and not a "minus."

Begin with [GRAPH], [F1 y(x)=], and [CLEAR]. Next, press [(-)]

[x-VAR] [] [+] [4]. Press [ENTER] to lock it in, [EXIT] to get a single row on the graphing menu, and [F5 GRAPH] to sketch the graph.

d) Graph . Notice that this graph involves absolute value, which is in your custom menu. Also, notice that it is the absolute value of a quantity, so it is necessary to place parentheses around the (x – 4). Finally, notice that the signs are both subtractions-- "minus" signs, not "negative" signs.

Begin with [GRAPH], [F1 y(x)=], and [CLEAR].

Next, press [CUSTOM] to access the absolute value, then [F3 abs]

[(] [x-var] [—] [4] [)] [—] [2] [ENTER]

Because you are in the custom menu, it will take two exits to get out of it. [EXIT] [EXIT] [F5 GRAPH]. You should get the V-shaped graph below.

e) Graph .

Begin with [GRAPH], [F1 y(x)=], and [CLEAR].

Next, press [x-VAR] [] [[— (minus)] [16]. Press [ENTER] to lock it in, [EXIT] to get a single row on the graphing menu, and [F5 GRAPH] to sketch the graph.

Notice that in the standard graph window, you can’t even see the bottom of the graph. Sometimes it helps to adjust the window. You may want to do this by pressing [F3 ZOOM] [F3 ZOUT] to zoom out. Or even better, you can adjust the window by pressing [F2].

Press [F2 WIND] for TI 86. Press [F2 RANGE] for TI 85.

As you can see, the "standard window" shows the graph with values of x from a minimum of –10 to a maximum of 10 with a scale of 1. The y values go from minimum of –10 to a maximum of 10 with a scale of 1. Of course, you can easily change that to set your window to whatever you want to see. Having seen that the previous graph is "cut off" at the bottom, maybe it would be a good idea to extend the graph down to –20 instead of –10. To do this, just press the down arrow three times, down to yMin = -10. With the cursor flashing on "yMin = -10", type [(-)20] [ENTER]. With the window set to your liking, press [F5 GRAPH], and the calculator gives the graph you can see. Notice in the graph below, the x units are much larger than the y units, and therefore, the graph is NOT drawn to scale.

If you want to see what the graph really looks like, drawn to scale, you can go to "zoom square." This simply means that the x and y axes have equal units (unlike in the window shown above!), and therefore the window is "square." To do this, press [F3 ZOOM] [MORE] [F2 ZSQR]. See next→

The graph really looks like this. This is the window.

MOST IMPORTANTLY, remember that this is now your "new" window for future graphs. The next time you draw a graph, after you enter the new equation, you should standardize the window: [F3 ZOOM] [F4 ZSTD].

f) Graph .

As always begin with [GRAPH] [F1 y(x)=].

Type the equation, using a minus sign: [x-VAR] [^] [3] [—] [4] [x-VAR] [ENTER] to lock it in;

[EXIT] to return to a single row of graph menu;

Remember that in the last graph you changed the window, so now you should return to a standard window: [F3 ZOOM] [F4 ZSTD].

g) Graph . Of course this is a straight line.

[GRAPH] [F1 y(x)=] [3] [÷] [4] [x-VAR] [+] [4] [ENTER] [EXIT] [F5 GRAPH]

At least that’s how it is supposed to look. Unfortunately, for users of the TI 85, there seems to be a glitch. For some reason, the TI 85 misinterprets what you have entered as y = 3/(4x) + 4, which is incorrect. To correct this, users of the TI85 must enter parentheses around the fraction (3/4).

TI 85: [(] [3] [÷] [4] [)] [x-VAR] [+] [4] [ENTER] [EXIT] [F5GRAPH]

1. Finding roots of graphs by the [ROOT] method.

2. Using the [ROOT] method of graphing to solve algebraic equations.

3. Complex numbers in the form a + bi.

4. Solving polynomial equations with [2^nd] [POLY].

5. Solving systems of equations using [2^nd] [SIMULT].

6. Finding maximum and minimum points of a graph.

7. Finding points of intersection of two graphs using [ISECT].

8. Matrices and determinants.

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