 
FAQs FOR TI
AND CASIO GRAPHING
CALCULATORS
CONTENT: Answers to a variety of problems with TI82,
TI83 Plus, TI89, and Casio graphing calculators.
There are several FAQs on scientific calculators.
How to search for an answer on this sheet:
In order to make maintenance of this sheet easier, I designed it so that you can
use your browser to locate an answer. After you've located the FAQ number
that you want, just use the Find and enter the index number.
Be sure to enclose the number in parentheses or you'll not find the answer
quickly. The start point for the search should be below the listing in the index.
Index: (There are more FAQs on page 2.
Click "More Difficult Page 2" under TI FAQs in the navigation panel to go there.)
(1) How do I graph both branches of the hyperbola √(4x^2+16) on a TI83?
(2) If I do i^{12} on a TI83, I get 1+2E13i. How do I get the right answer?
(3) How do I raise a number to the onehalf power on a TI83.
(4) How do I graph piecewise functions?
(5) Please help. I have no idea how to use the regression capabilities of my
TI83+ calculator. My problem is: I have the number of bankruptcies (in thousands) for 18 years.
(6) What's the best graphing calculator, and where's the best place to buy
one?
(7) How do I do the rref and ref on my TI82 calculator as the other
people in my class do on their TI83?
(8) How do I graph a circle on the TI83?
(9) How do I draw a circle on the TI83?
(10) How do I put text on a graph?
(11) When I draw text on a graph and use the coordinates that I use for
OUTPUT, the text overlaps. Why?
(12) How do I find the inverse of a matrix on the TI83?
(13) When I enter an equation with large coefficients, I often can't find
the graph on my TI83Plus. How do I find it?
(14) Is there a way to solve quadratics on a TI83Plus?
(15) Can I enter fractions and get answers in mixed numbers?
(16) How do I find Sin, Cos, and other trig functions? I keep
getting answers that don't make sense.
(17) Can I store pictures/graphs that I have made/drawn on my screen?
(18) Is there a way to solve an equation on the TI83Plus without
graphing?
(19) How do I enter a matrix in a TI83?
(20) How do I solve a system of equations on the TI83Plus?
(21) How do I do matrix row operations with the TI83Plus?
(22) How do I find the angle whose cos is
0.5?
(23) How do I transfer a program from one TI83 Plus to another TI83
Plus?
(24) Can I find the fractional equivalent for values such as Intersection
and Zero?
(25) Can I graph inequalities on the TI83Plus?
(26) How do I set up the domain for a function on a TI83?
(27) How do I graph
the residuals after I do a linear regression on the TI83Plus?
(28) How do I generate random numbers on a TI83/TI83Plus?
(29) How do I store random numbers in a list and arrange them in order?
(30) How do I calculate IRR on a possible investment?
(31) How do I do a quartic regression and graph the scatter plot and the
regression equation on the same axis?
(32) The TI83+ selects the number of classes when I do a histogram. Is there
any way I can choose my own?
(33) Do I really need to change the batteries on my TI83+ when I upgrade the
operating system?
(34) Does the conics application for the TI83+ provide the same graphing
capability as the graphing functions that are built into the calculator?
(35) I've read various places on the Internet that there's not much difference
between the TI83+ and the TI82. Is that correct?
(36) Is it possible to do a stemandleaf chart on the TI83 Plus?
(37) How do I find the critical numbers for y = x^{3} x^{2}
3x +1 on my TI83 Plus?
(38) On my TI82, when I enter (32)^(1/5); then (2)^3 I get a correct
answer, 8, but when I enter ( 32)^(3/5) I get Ma ERROR. Why?
(39) My teacher says the TI83Plus is useless for finding the derivative.
Why is that?
(40) Can I draw points on the graph screen on my TI83Plus?
DISCLAIMER:
The FAQs
on this web site, and especially FAQ #6 here, reflect the writer's subjective
opinion and observations. The FAQs should be considered only as another source
of information. The writer is not endorsing any particular brand or model of
the calculators mentioned or any particular store or shop. The writer does not
warrant the accuracy of any FAQ. Any calculator mentioned may not be a
representative sample of what is on the market, and the manufacturers may change
their products or specifications without my knowing about it.
Answers:

(1) How do I graph both branches of the hyperbola √(4x^2+16) on a TI83?
Enter the following into Y1:
{1, 1} √(4x^{2} +16) Or you can enter Y1 into Y2 to get the second branch.

(2) If I do i^12 on a TI83, I get 1+2E13i. How do I get the right answer?
Actually that is the correct answer from the calculator's perspective.
That's the answer written in rectangular form, a +bi. The calculator
considers 2E13 to be zero, so the answer would be 1 + 0i in rectangular format.
Here's a somewhat more detailed discussion of doing powers of "i" with the TI83
Plus.
1. One simple way to raise "i" to a power, as you probably know, is to divide the exponent by 4 and
raise i to the remainder.
Ex: I^14 = 1^12 * i² = 1*(1)= 1.
If you want to get a little trickier, you can use the fact that you can raise "i"
up to powers where the units or tens digit is up to and including 6 without the
2E13 or some such number..
Ex: i^66 = i^60 * i^6, and i^68 = i*60*i^6*i²
You can also do this:
i^12 = (i^3)^4, or i^14 = (i^6)^2*i² so long as the SUM of ALL the exponents is
<12.
Actually though, all of this seems a little excessively tedious when all you
need do is throw away the 2E13 or whatever very small number you get.

(3) How do I raise a number to the onehalf power on a TI83.
Probably the easiest way, using 4 as an example, is this: 4^(1/2)

(4) How do I graph a piecewise function on a TI83?
This is going to be a rather long answer. I assume you know that when you want to limit the domain of a function you use the inequalities obtained by pressing [2nd], [TEST] and selecting one of those. Yet there are a couple nuances that you need to know.
Students typically enter a problem as follows: (x>3)2x +1. Now, the problem with that is that the test is only applied to
2x and the unwanted graph of y =1 appears on the screen. That's easily fixed by doing this: (x>3)(2x+1).
Still, some students complain that there's an extraneous vertical line where the graph goes from zero to the function. There are a couple of ways to fix that:
A) Press [MODE] and change from <Connected> to <Dot>. That's probably the best general method for eliminating extraneous lines on a TI83
or TI83 Plus..
So, let's take this problem, and see how we'd do it:
{x+5 ; x< 2
f(x) {2x1 : 2 <x< 2
{ 2x9 ; x > 2
One way to do this perfectly is as follows:
Y1= (x< 2)(x+5)
Y2= (2<x)(x<2)(2x1)
Y2= (x>2)(2x9)
The press [MODE], change the display from [Connected] to [Dot].
Then press [GRAPH]
B) Here's the method I prefer:
I don't like switching back and forth between <Connected> and <Dot>. So, I prefer simply to divide the function by the test. Like this, for example:
Let's take the same problem and enter it like this:
Y1= (x+5)/(x< 2)
Y2= (2x1)/((2<x)(x<2)
Y3= (2x9)/(x>2)
(Actually, you won't need some of the parentheses enclosing the functions, but I sometimes use parentheses just so I won't have to figure out if I need them.)
Using that method, in the region where the
test is false, i.e., zero, the function is divided by zero and, so is undefined.
So the calculator displays nothing. In the region where the test is true, the
function is divided by 1. Notice in the Y2= , entry, that you must enclose each
test in parentheses; then enclose the whole two tests in parentheses. Otherwise
the calculator will divide by the first test, (2<x), and multiply by the
second, (x<2), and you'll get an extraneous returntozero line.
So, all you need to remember with this method is to divide by the tests, and be sure to use grouping symbols as the calculator needs them.

(5) Please help I have no idea how to use the regression capabilities of my TI83Plus calculator. My problem is: I have the number of
bankruptcies (in thousands) for 18 years.
First
you need to get your data in lists.
You can do it from the home screen, but with that much data I prefer to enter it
directly into the list tables. Here's how to do it:
[STAT], [ENTER]
Then enter the numbers 1 through 18 in L1 and the corresponding values in L2.
[2nd], [QUIT]
[STAT], Cursor to CALC, <7>, [ENTER] (Where <7> is just the number 7 from the keyboard.)
QuartReg will appear on the screen. Immediately after that enter the following:
[2nd], [L1] [,], [2nd], [L2], [, ] Note that the commas outside the brackets are just separators so you can tell what I'm doing. They do not appear in the syntax. Now, you want to store this as a Yvariable, say, Y1. So, do it this way:
[VARS], Cursor to YVARS, [ENTER], [ENTER]
You should now have this on your screen. QuartReg L1, L2, Y1
Press [ENTER]
After a few seconds a long equation with coefficients having several decimal places will appear on the screen.
To graph that, you could just press GRAPH, but you probably won't get anything on the screen because of the WINDOW setting. So, do this:
[WINDOW]; Xmin = 3; Xmax = 20; Ymin = 3;Ymax = 2000; Yscl = 100; press [GRAPH]
That should do it.

(6) What's the best graphing calculator, and where's the best place to buy
one?
Caveat:
The following is an attempt to give some help to those who are unfamiliar
with the capabilities of graphing calculators and how their capabilities relate
to courses of study. It is not intended as definitive advice on what
a particular student should buy. I
would appreciate knowing of any disagreements you have with me. Send me an
email at the address listed elsewhere.
Bottom Line: Talk with the teachers of the classes
you're going to be taking. Buy the calculator that they're going to be
using in their instructions if you can afford it and don't already have another
type.
Guidelines: If the
teachers don't use calculators, or if you're enrolled in a distance course or
some other situation prevents your consulting the teachers, here are some
guidelines. Please realize that it's ultimately up to you to make the
decision based on what information you collect. This is only one source of
information. So, the following is a set of guidelines based on the level
of math you might be taking.
General Discussion: If you're a real math and calculator geek and money is not a
problem, you'd probably be happier with the TI89. If you are mainly interested
in a tool to do your math in the most efficient way, then a TI83 Silver
addition would be entirely sufficient for courses that don't include functions
of more than one variable. That unusually comes in second semester calculus. The
TI83 Plus is simple to use and fairly versatile.
I would point out that it is possible to graph functions of more
than one variable on a TI83, but you have to hold all but one variable
constant. For example, if you want to graph e^(x² +y²), you could replace y²
with A, and supply constant values of A from the home screen to get a family of
curves. I understand that TI is developing a set of applications that will give
the TI83 Plus some of the capability of the TI89. If you buy the TI83 Plus, you get the GraphLink
or Connect software that allows you to download applications
from the Internet to your calculator.
For taking derivatives and integrals of functions of more than one
variable, the TI86 would be suitable and, in my opinion, it's somewhat simpler
to use than the TI89. The last time I checked it was also cheaper.
If you want the ultimate in graphing calculators, then go with the TI89. As I
previously said, if you're not really into calculators, it's going to take quite
a lot of studying of the manual to learn to use it.
And Now: The following is an attempt to give some
idea of what calculator might be needed for a particular set of courses of
study.
High School: I don't have
contact with high school students, so I don't have a good feel for their needs.
Generally, I would think that if you're not planning to take Precalculus
or AP Calculus, a good scientific calculator would be entirely satisfactory.
(FAQ 1 on the Scientific Calculator FAQs is about buying a scientific
calculator.) But be sure to check with some of the teachers to see if they
might use graphing calculators for doing graphs is Algebra II.
Incidentally, scientific calculators are sometimes more efficient and easier to
use than graphing calculators.
If you plan to take Precalculus or AP Calculus,
and especially if you're planning to major in engineering, science, or math in
college; then you probably should buy a graphing calculator if the cost is not a
problem with you. A TI83Plus or a Casio Cfx9850GB would be sufficient,
but I would be remiss if I didn't say that the TI83Plus is more often the
choice among college students. Be cautious about buying a TI86 or TI89.
Although these are excellent for those who have a more than average interest in
math, many students never really learn to use these calculators with anything
like their potential.
Developmental Math: For
Basic Math and Beginning Algebra, Elementary Algebra, or whatever your school
calls it, you can get by with a good scientific calculator. Don't buy one
of those sixor eightfunction calculators. They're not worth carrying
around. Don't pay more than $14.95 if you're on a tight budget. See
my Scientific Calculator FAQs, FAQ #1, for more information on buying a scientific
calculator.
For Intermediate Algebra, you may need a graphing
calculator depending on whether your school uses one. In any case, it
would be nice to have one to check your answers. Make your decision based on your
major as listed in the categories below.
Elementary School Teacher, Nursing, Liberal Arts,
Communications: I'm assuming you're going to take
College Algebra and either Elementary Calculus or something like Foundations of
Mathematics. Unless you're some kind of calculator guru, don't buy one of
the heavy hitters like a TI89. Chances are you'll never understand how to
use all its power. Instead, buy a TI83 Plus or a Casio CFX9850GB Plus.
You can get by with a TI82 if you'll enter my program for doing rref and ref on
augmented matrices and, for finite math, the program for doing the simplex
method. Otherwise you're going to be left out when you get to
doing augmented matrices or simplex. The Casio has a program that you'll need to
activate for doing rref, or you could use my program for rrefref for the Casio.
That'll give you both ref and rref. If your teacher is one of those who
gives you a lot of augmented matrix work to do by hand, you might find my matrix
row operations program helpful for both the TI and the Casio.
Suppose you absolutely can't afford any graphing calculator.
Hang in there and get you a good scientific for no more than $14.95. Go to
the Tutoring Lab, Learning Center, Academic Assistance Center or whatever your
school (community colleges) calls it and use their calculator to do your
homework. They may even have one you can check out and take to do tests.
You might also ask your professor about one of the cheaper Casios:
FX7400G Plus or FX9750 Plus. I have an older FX9750, and I worked some
with an older FX7400, but I am not familiar enough with the newer versions of
these calculator to give advice on them. Read my notesbelow on the
Durabrand that has recently appeared at WalMart for $1995.
Economics and Heavy Business Courses:
I'm assuming you'll take Calculus I and Finite Mathematics with some other
financial courses. The finite math may be heavy in linear
programming and the Simplex method. Be sure to find out if your teacher
uses one of those special financial calculators in your class. Otherwise,
you can use a TI83 Plus or a Casio CFX9850GB Plus. The Casio has a
program called LINPROG that needs to be activated for doing simplex. You can use my program
called LINPRG2 for the TI83 Plus to do the Simplex method. Both of these
calculators have functions for doing amortization, different types of interest,
and other financial functions.
Chemistry: You guys probably know what
you need. If you're going to take Calc I and II and no differential
equations you probably could get by with a TI83 Plus or a Casio CFX9850GB Plus.
If you're going to take higher math, buy one of the heavy hitters like a TI86
or TI89.
Electrical Engineers & Physicists: You
guys know what you need. If you don't, talk with your professors. My
inclination: Don't buy one of the simpler graphing calculators. Buy
one of the heavy hitters. You need the best tools you can get.
Where to buy: I'm not going to tell you
where to buy; I'm going to tell you some places they're available.
WalMart, Best Buys, Home Depot, Office Depot, Target (I believe Target still
has them.), and others that may be specific to your area. If you want to
save money, watch the advertising inserts to your local newspaper about the time
the fall semester starts. Many stores have significant savings at that
time. Call around and see who has the best price.
Now, here's something that may seem a little weird to you,
but it works for many of the students who come to me and are pressed for money.
I send them to pawn shops. Many pawn shops in this area have used TI83
Plus calculators for $35 to $45 dollars. I tell the students to make
the pawn shop dealer agree to take the calculator back for a couple days or so,
until they come in and have me check it out. You might also try to bargain
a little by telling the dealer that the TI83 Plus is now two versions out of
date. Now, let me give you a little
hint on getting a calculator from the pawn shop: Turn the calculator on;
press 2nd, MEM, ENTER. In the middle of the screen, right below the
TI83Plus will be an entry such as 1.19. This is the version of the
operating system and may tell you indirectly how old the calculator is.
(I say may because someone, like me, may have upgraded the operating system.) The
higher the number, the newer, with 1.19 being the highest as of 6/1/06.
If the pawn shop has several calculators, try them all and get the one with the
latest version unless you have to pay considerably more. Try to get one with
1.14 or higher. If you must settle for a lower number, tell the dealer
that it's old and he should give you a price break on it. If you have a
friend with Connect or GraphLink installed, you can upgrade the operating
system.
Now, how about the Durabrand calculator that has recently
appeared at WalMart for $19.95? Here's what little preliminary
information I have on it. (Please read the DISCLAIMER at the start of
these FAQs)
PROS:
* Has a 50key keyboard that appears to
be fairly well arranged except, possibly for the SHIFT key.
* Has fraction and Ans keys.
* Has sufficient memories for most any purpose 
26.
* Has about any of the standard algebraic and
trig functions that you would want  including one and twovariable
statistics.
* Algebraic entry of formulas.
* Easily obtained battery  CR2032. This is the
same as the battery used for the memory in the TI83 Plus.
* Has some limited programming ability.
CONS:
* The display for the graph is very small, 35 x
23 pixels. The fullscreen display on the TI83 Plus is 62 x 94 and
the split
screen GT display is 50 x 46.
* As far as I can see, there is no equivalent of the ENTRY
function on the TI83 Plus. This is very useful when you need to use
a long expression and only edit a number or
maybe two.
* Programming is limited to 400 steps divided among ten
predesignated programs. Gamers, forget about it.
SUMMARY OF DURABRAND CALC:
Don't let the small number of
cons lead you to believe this is equivalent to the TI83 Plus or the Casion
CFX9850 series. This is more on the order of the old Casio 7000G Graphic
calculator. This is merely my opinion, but I'd try to come up with 15 to
20 dollars more money and look hard for a used TI83 Plus or equivalent.

(7) How do I do the rref and ref on a TI82 calculator as
the other people in my class do on their TI83.
There's no quick method for doing Gauss and GaussJordan
elimination on the older TI82 calculators. At some point TI may include
that as a program, but as far as I know, it's not there yet. Best
thing to do, of course :), is to use my program for doing that. You'll
find it listed in the program descriptions. It'll take you about 20 to 30
minutes to load it, depending on how familiar you are with programming of TI
calculators.

(8) How do I graph a circle on the TI83?
There are a couple ways to do this, but
in any case you must first solve the equation for y.
Example:
x^{2} +y^{2} =5
y =± √(x^{2}
+5)
Now, enter the equation, without a leading sign, into the Y1= position.
Now, cursor down to Y2= and enter a negative sign. That's the () sign.
Press VARS, cursor over to YVARS, press ENTER, ENTER. You'll now have Y1
in the Y2 position. Press GRAPH.
Your graph won't look like a circle unless you're in ZSquare screen mode.
To get that, press ZOOM, 5.

(9) How do I draw a circle on the TI83?
I want to emphasize that drawing is
different from graphing. Drawn graphs cannot be analyzed by any of the
CALC functions. Anyway, to draw a circle with center at (2,4) and radius
7, do the following:
Preferably deselect the entries in the Y=
positions.
Press 2ND, DRAW, 9. You'll now have Circle(
on your home screen.
Complete the entry like this: Circle(2,4,7).
Then press ENTER.
To clear the screen of a Draw or Text entry,
select item 1, ClrDraw, from the DRAW menu.
I would just add that TI has a very nice conics
application for the TI83 Plus that can be
downloaded for free if you have with the proper
software and electronic device.

(10) How do I put text on a graph?
You can do it either
from the home screen by specifying the pixels where you want the text placed or
you can do it directly on the graph.. The home screen method is the method to use in a program,
or, if for some reason, you want to enter text from the home screen. FAQ 11 will show you how to
do that. The easiest way outside a program, I think, is just to enter text on your graph. Here's
how to do that:
a) Graph the function that you want the label to appear on.
b) Press 2nd, DRAW, and scroll down to item 0 and press ENTER.
c) Using the cursor arrows, move the cursor to the point where you want to
start the text.
d) Press 2nd, ALPHA to lock the ALPHA function in, and start typing in the
letters that appear in green on your keyboard.
e) Remember, if you type number, commas, and other such
characters, you'll need to press
the ALPHA key to get the keyboard out of the alphabetic mode.

(11) When I draw text on a graph and use the coordinates that I use for
OUTPUT, the text overlaps. Why?
You want to remember that
the home screen is different from the graphing screen. The home screen has
8 horizontal rows and 16 vertical columns. The graphing screen has 62
horizontal rows (pixels) and 94 vertical columns. I normally use about 7
vertical spaces and 4 horizontal for each letter.
Example: Let's say I wanted to write SOME TEXT on the screen. Here's how
I'd specify it.
Of course, to get to Text(, you press 2nd, DRAW and select item 0.
Text(1,1,"SOME"
Text(1,21, "TEXT"
If I wanted to write TEXT below SOME, I'd do this:
Text(1,1,"SOME"
Text(1,8,"TEXT"
You can play with the formatting and see what spacing pleases you.

(12) How do I find the inverse of a matrix on the TI83?
1) First enter the matrix in one of the positions, say matrix [A].
2) Press 2nd, QUIT to go to the home screen
3) Press 2nd, MATRIX, 1 (1 selects the matrix A. If you put
the matrix in another location press that number.)
4) Press x^{1} . That's the key on the left side; four keys down.
5) Press ENTER. Your matrix will be displayed if it has an inverse.
If it has no inverse, you'll get a SINGULAR MAT error.
_________________
(13) When I enter an equation with large coefficients, I often can't
find the graph on my TI83Plus. How do I find it?
The TI83 makes it very simple: Press ZOOM; then the number 0 to
select ZoomFit.
For TI82 or older TI83 calculators that might not have the ZoomFit capability,
there are different ways you can find the values to set your window. You
could use TRACE and see where the max and min occur. Another perhaps
simpler way is as follows: Press <2nd>, <CALC>,<ENTER>; then enter a negative
number for "x" where you'd like to see the graph; then do the same for a
positive number. Set the yvalues of your window at approximately these
numbers. Example: Graph 300x^{3} 50x^{ }+50.
If you follow the steps above and enter 4, you'll get 21070. For 4,
you'll get 17330. Now, set your window at, say Ymin = 25000 and Ymax =
20000.

(14) Is there a way to solve quadratics on a TI83Plus?
Well, yes there are at least four different ways. I'll give each a
brief description.
Method I: (Using graph and CALC for real values only.)
a) Press Y=, and enter your quadratic in the Y1= position.
b) Press 2nd, [CALC], cursor down to item 2 (zero); then press ENTER.
c) A screen will appear with "Left Bound," which means for you to move the
cursor to the left of the first zero. Do that, and then press ENTER.
(Rather than use the cursor, you can just enter a number that's slightly to the
left of the zero and press ENTER.)
d) "Right Bound" will appear. Do the same thing as above for
the right bound of the first zero.
e) When "Guess" appears, move the cursor to about where you think the zero
is and press ENTER. (You could also enter a number for this, but I prefer
to use the cursor for this value.)
f) The values for x and y will appear.
Method II: (Using Table. For real values only.)
a) Press Y=, and enter your quadratic in the Y1= position.
b) Press 2nd, [TABLE].
c) Look for the xvalues that correspond to the values for 0 in the Y
column.
d) You may need to change the difference between xvalues. To do
that, press 2nd, [WINDOWSET] and change the delta to whatever you want.
Method III: (Equations Solver. For real values only.)
a) Press MATH; 0; ENTER. ( Item 0 is Solver.)
b) If the solver is empty, just start entering your equation. If
there's already an equation at the top of the screen, press the up arrow key and
enter your equation.
c) Press ALPHA, SOLVE. Your solution should appear after X=.
d) You can enter a guess for the unknown if you want, but I've found that
this sometimes causes the calculator to miss a solution, even if your guess is
within four or five units. Actually, I find solution of quadratics much
easier if I first graph them and get a fairly good guess as to what their roots
are. Then I can paste the YVar into the equation on the solver and guess
the roots fairly accurately. To past a Yvars, say Y1, do this:
(You need to be in the equation entry position as indicated above.)
a) Press VARS; cursor over to YVARS; press ENTER.
b) Select the yvariable where you have the equation entered for the
graph and press ENTER.
c) The variable you selected will be pasted into the equation position.
Method IV: (Using the quadratic equation. For either real or
imaginary.)
Actually the best thing for this is to download and enter my little program
QUAD, but if you're not into programming, do the following.
a) Press Y= and enter the part of the quadratic equation with the positive
radical into Y9=. (Actually, you can enter the equations in any yvariable, but
I like to get them out of the mostfrequentlyused variables.)
Do that with the following keystrokes: (, (), ALPHA, B, +√,
(,B,^,2,,4,^{,} ALPHA, A,
ALPHA, C,) )/(, 2,ALPHA, A). Don't enter the commas. They're for
separation only. When you finish, your entry should look like this:
(B+4AC)/(2A)
b) Enter the part of the quadratic equation with the negative
radical into Y_{0}=.
NOTE: If you want to solve a quadratic with imaginary numbers, be sure to
go to MODE and highlight a+bi in the seventh line down.
c) Now, when you want to solve a quadratic, first store the coefficients
as follows:
1) From the home screen, press the number
for the first coefficient; then press STO; then ALPHA, A.
2) Follow that same procedure for each
variable separating the variables with a colon. A colon is entered by
pressing ALPHA, :.
d) Now press VARS, cursor over to YVARS; press ENTER, then 9; and finally
ENTER.
e) After you have that answer, follow the same procedure as in d), except
press 0 instead of 9 in the next to last step.

(15) Can I enter fractions and get answers in mixed numbers?
No, the results of multiplication of fractions on the TI82/83 only gives
results in fractions, either proper or improper depending on the answer.
There are some methods, probably considered cumbersome by most students, to
enter fractions and get mixed numbers. Here are a couple examples:
Let's say we want to add 4⅞ + 3⅝.
a) Enter that as 4 +7/8 +3 + 5/8.
b) Press ENTER and the answer will be 8.25.
c) Take 8 as the whole part of the mixed number.
d) Now to find the fractional part press MATH, cursor to NUM, press 4 (fPart(),
2nd, Ans.
e) Now press MATH, ENTER. You should now have this: fPart(Ans►Frac.
f) Press ENTER and you'll get the fractional part, 1/4.
Multiplication of fractions is much the same. If the
above problem were multiplication, you'd enter it like this:
(4 +7/8) (3 + 5/8).
That would give you 17.671875 and you'd find the fractional part the same was as
above. Division of that problem would, of course, be entered like this:
(4 +7/8)
/(3 + 5/8).

(16) How do I find Sin, Cos, and other trig functions?
I keep getting answers that don't make sense.
The most common problem that students have is having the
Radian/Degree mode set in Radian when they're entering degrees. To change
that press MODE, press the down arrow to move to Radian; then the right arrow to Degree;
then press ENTER and CLEAR.
After you're all set up on the MODE, just press the function you
want and enter the degrees.
Example: Find Cos 45
Press COS; then enter 45. At that point you'll have cos(45; then
press ENTER, and you'll get .707106.... There's no need to close
parentheses unless you have something following that might be mistaken for part
of the argument of the trig function.

(17) Can I store pictures/graphs that I have made/drawn on my screen?
Yes, you can store up to 10 graph/pictures by using StorePic. Assume
you want to store the "picture" in Pic 1.
a) With the graph displayed press 2nd, [DRAW] and cursor over to STO and
select item 1, StorePic. Press ENTER, and StorePic will be pasted to the
home screen.
b) Enter the number for the storage location where you want the picture
stored. If you enter 1 it will be stored in location Pic 1; 2 for Pic 2,
etc. Press ENTER.
c) Remember, that to store another picture or to recall a picture, you
must clear the screen. You do that by pressing 2nd, [DRAW] and selecting
item 1, ClrDraw; then pressing ENTER.
I would suggest that, to keep your memory usage to a minimum,
you clear the drawings from the Pic locations after you're finished with them.
Here's how to do that:
a) Press2nd, [MEM], select item 2 and press [ENTER]
b) Select item 8, Pic, and press [ENTER]. Delete the items you want
to delete with the [DEL] key. Press 2nd, [QUIT] where you're finished.

(18) Is there a way to solve an equation on the TI83Plus
without graphing?
Yes, you can use the Solver to solve equations with real
solutions.. Here's how to do it:
a) Press MATH; 0; ENTER. ( Item 0 is Solver.)
b) If the solver is empty, just start entering your equation. If
there's already an equation at the top of the screen, press the up arrow key and
enter your equation.
c) Press ALPHA, SOLVE. Your solution should appear after X=.
d) You can enter a guess for the unknown if you want, but I've found that
this sometimes causes the calculator to miss a solution, even if your guess is
within four or five units. Actually, I find solution of quadratics much
easier if I first graph them and get a fairly good guess as to what their roots
are. Then I can paste the YVar into the equation on the solver and guess
the roots fairly accurately. To past a Yvars, say Y1, do this:
(You need to be in the equation entry position as indicated above.)
a) Press VARS; cursor over to YVARS; press ENTER.
b) Select the yvariable where you have the equation entered for the
graph and press ENTER.
c) The variable you selected will be pasted into the equation position.

(19) How do I enter a matrix in a TI83?
a) Press 2nd, MATIX, and cursor over to EDIT and press ENTER.
b) Enter the number of rows; press ENTER; enter the number of columns and
press ENTER.
c) Now enter the numbers in the matrix, pressing ENTER after each
entry. Do this until you have all of the numbers entered. (Note:
Do not just skip over a number that's already in the matrix. It may be a
calculated number and may be just a bit less accurate than an entered number.) To
get out of matrix edit, press 2nd, QUIT.

(20) How do I solve a system of equations on the TI83Plus?
a) First enter the augmented matrix in one of the matrix positions,
say [A], as described in item (19) above.
b) After you have the matrix entered, press 2nd, QUIT to get out of matrix
edit.
c) Press 2nd, MATRIX, cursor over to MATH, and cursor down to item B,:rref(.
d) Press ENTER. You will now have rref( pasted to the home screen.
Now you want to paste matrix A to the home screen. So, press 2nd,
MATRIX, and press ENTER.
e) You will now have rref([A] pasted to your home screen. If you
want the answer in fractions, skip to the next item, item f).
If you want the answer in deciamals, press
ENTER and the solution will appear.
f) To obtain the answer in fractions press MATH, ENTER, ENTER and the
answer will be displayed.

(21) How do I do matrix row operations with the TI83Plus?
Let's say that you have this set of equations:
x +2y +3z = 4
2x  y  2z = 0
x 3y  3z = 2
So that, you have this augmented matrix:
[ 1 2 3 4
2 1 2 0
1 3 3 2]
Now, you want to multiply row 1 by 2 and add it to row 2. I'll use
"shorthand" such as 2R1 + R2=>R2, to indicate this type of operation.
a) So, enter the matrix as in Item (19) above; then press 2nd, QUIT to go
to the home screen.
b) From the home screen, press 2nd, MATRIX; scroll over to MATH; scroll
down to item F, and press ENTER. You should now have *row+( on your home
screen.
c) Now you want to enter the multiplier, letter of the matrix, row number
multiplied by, row number to replace in that order. Do this: Enter
2, press the comma button, press 2nd, MATRIX, ENTER. You should now have
*row+(2, [A] on your screen. DO NOT enter [A] with the brackets and the
letter A.
d) Now press the comma button, enter 1; press the comma button and
enter 2. You should now have *row+(2,[A],1,2 on your screen.
e) Press STO, 2nd, MATRIX, ENTER.
f) You should now have *row+(2,[A], 1,2►[A]
on your screen. DO NOT enter [A] with the brackets and the letter
A. (Note carefully that if you don't add the STO, [A], then matrix A will
not be changed in your calculator. Also notice that you can either
close the parentheses after the last row number or leave them open.)
g) To get a zero in column 1 of the 3rd row, enter this:
*row+(1,[A],1,3►[A].
h) You now have this matrix:
[ 1 2 3 4
0 5 7 8
0 5 6 6
i) Now enter this: *row+(1,[A], 2,3►[A].
Note that instead of reentering all of these, you can just press 2nd, ENTER,
and then edit the entry that appears for the proper multiplier and row numbers.
j) Now, multiply row 2 by 1/5 as follows: *row(1/5,[A],2►[A].
k) If you want to add two rows; then the syntax is this: row+(matrix
letter, row to be added, row to be replaced)►[A]
l) To swap rows, use this syntax: rowSwap(matrix letter, first row,
second row►[A]

(22) How do I find the angle whose cos is
0.5?
First make sure that your calculator is set
for radians or degrees, whichever you want the answer in. (Usually you'll want
it in degrees.) To change the mode, do this:
a) Press MODE; then cursor down to the line with Radian and
Degree. Select the one you want and press ENTER. Press CLEAR
to get back to the home screen. Now to find COS^{1} 0.5,
just press 2nd, press the COS button; then enter the argument 0.5 and
press ENTER.

(23) How do I transfer a program from one TI83 Plus to another TI83
Plus?
I'll assume both are TI83 Plus.
1) Turn both calculators off and plug in the unittounit cable in both
calculators.
2) Turn on both calculators and Press 2nd, LINK on both. Cursor over to RECEIVE
on the RECEIVE calculator, the calculator that you're transferring the program
to.
3) Press ENTER on the Receive calculator. The word "Waiting" should appear.
4) On the sending calculator, cursor down to Prgm and press ENTER.
5) Cursor down to the program you want to transfer and press ENTER. The program
that you selected will be marked with a square "dot."
6) Cursor over to TRANSMIT press ENTER.
If everything is connected satisfactorily, transmission of the program should
start. Otherwise, you'll get a transmit error after a few seconds.

(24) Can I find the fractional equivalent for values such as
Intersection and Zero?
You can if the decimals are rational numbers. As an example, suppose
we've graphed y = x+5 and y = 4x + 10 and found the intersection at x=1.666667,
y = 3.3333333. Here's how to find the fractional equivalent. (The answer
is obvious, but this is a simple example.)
a) Press 2nd, [QUIT] to go to the home screen.
b) Press [x,T,0,n]; then MATH; ENTER; ENTER. The fractional
equivalent of x, 5/3, will
be displayed.
c) Press [ALPHA], Y, MATH, ENTER, ENTER. The fractional equivalent
of y, 10/3, will be
displayed.

(25) Can I graph inequalities on the TI83Plus?
Well, yes, but it's not really just straight forward graphing. Let's
assume a couple of simple equations such as x + y
≤4 and xy ≤ 2.
a) First solve each equation
for "y," getting the following: y
≤ x +4 and y ≥x2. (Be sure you
don't just change the inequalities to equations and solve for y.)
Now, do the graphing as follows:
b) Press Y= and enter the first equation as Y1 and the second as Y2.
c) Now you want to set the shading. So, go to the Y1= and cursor over to the extreme left where you'll
see a flashing design. Press ENTER repeatedly until you see a filledin,
right triangle with it's right angle on the left bottom. That's the <
shading.
d) Now go to Y2= and do the same thing except that you want to select the
triangle that is flipped over from the one you selected above. .
e) Press GRAPH, and you'll see the shaded regions.
Remember to change the shading back to a regular line to graph equations.
A second method that I find somewhat less time
consuming.
Let's say we have this equation: x^{2 }x12 >3.
1) Enter the left side of the inequality in Y1= and the right side in Y2=.
2) In Y3 enter Y1 > Y2 as follows: Press VARS, cursor to YVARS,
ENTER, ENTER.
3) Press 2nd, TEST, 3.
4) Press VARS, cursor to YVARS, ENTER, 2.
5) Press GRAPH and your display will show both graphs and the graph of
where the inequality is true. You can disable the individual graphs if you
feel the display is too cluttered.
____________________
(26) How do I set up the domain for a function on a TI83?
This is pretty much like graphing piecewise functions. So, if you'll
read FAQ (4), that'll solve most of your problems. There's just one thing
I'd add to that: In the case of a function like cos(x) over the domain (
Π/2, Π/2)
you'll get a slightly nicer graph if you multiply by the limits rather than
divide by them. In other words, you would enter this: cos(x)(x≥Π/2)(x≤Π/2).
That way, the graph will return to zero at the end of the ranges.
____________________________
(27) How do I graph the residuals after I do a linear regression?
First you want to calculate the residuals. So, if you'll follow FAQ (5 )
above, that'll solve that problem for you. A few of the parameters such as the
window may be different, but it's basically the same. Now, you want to get the
residuals into L3 in the table.
a) Press [STAT], [1] and that'll take you to the List table. Cursor over and
up so that that the L3 over the L3 column is highlighted.
b) Press [2nd], [INS]. Names= is displayed at the bottom of the
screen.
c) Press[2nd], [LIST] and cursor down to RESID. Press [ENTER] and the values
are stored in column L3.
d) Press [Y=] and make sure that none of the Yvariables or Plot functions are
enabled (highlighted).
e) Press [2nd], [STAT PLOT] and select Plot 1. Highlight ON by cursoring there
and pressing [ENTER].
f) Leave L1 in XList, but change Ylist to RESID by entering those letters with
the ALPHA key.
g) Press ZOOM 9 and you should have a scatter plot of the residuals.
_________________________________
(28) How do I generate random numbers on a TI83/TI83 Plus?
1) Press [MATH]; cursor to PRB and press [ENTER]. rand will be pasted to
the home screen.
2) If you only want one number between 0 and 1, press [ENTER].
3) If you want more than one number between 0 and 1, add the number you want in
parentheses. Example: rand(5), for 5 random numbers.
4) If you want five numbers between 0 and 10, your entry will look like this:
rand(5)*10.
5) If you want five numbers between 0 and 50, your entry would look like this:
rand(5)*50.
6) If you want integers only, do this: Press [MATH], cursor to PRB, scroll to
rantInt( and press [ENTER].
7) randInt( will be posted to the screen. Now enter the numbers so your entry
looks like this: randInt(0, 50, 5).
_____________________
(29) How do I store random numbers in a list and arrange them in order?
1) To generate the numbers, follow the method in (28) above.
2) To store the numbers, follow your entry by [STO], and the list name, for
example, L1. If you want to store ten random numbers in list L1, your entry will
look like this: rand(10)>L1. The arrow is generated by pressing [STO].
3) To sort the numbers in L1, Press [STAT]; select item 2 or 3 depending on how
you want the numbers sorted; then press [ENTER]. SortA( will be pasted to the
home screen if you selected item 2.
4) Press [2nd], L1, [ENTER]. You'll get the "Done" response, indicating the
numbers are sorted.
=================
(30) How do I calculate IRR on an investment?
Let's say you invest $500 initially and your cash flows for years 1 through
4 are as follows: $150, $200, $250, and $250. Find IRR as follows:
1) From the home screen, press [STAT], [ENTER]; then enter the values
consecutively in list L_{1}.
2) Press [2nd], [QUIT] to go to the home screen.
3) Press [APPS]; then [ENTER]; then 8 to paste irr( to the home screen.
4) Enter items so that the entry on the home screen looks like this: irr(500,
L_{1}).
5) Press ENTER and after a couple seconds you'll get 22.77....
==========================
(31) How do I do a regression and graph the scatter plot and the
regression equation on the same axis?
First you need to get your data into lists.
Press
[STAT], [ENTER]
Then enter the datapoint numbers ( the xvalues) in L1 and the
corresponding values (yvalues) in L2.
Press
[2nd], [QUIT]
To do the scatter plot do this:
1) Press [2nd], [STAT PLOT] and press [ENTER] to turn Plot 1 on.
2) Cursor to the scatter diagram on Type and press [ENTER] to highlight the
scatter diagram.
3) Enter L_{1} in the Xlist, and L_{2} in the Ylist; the select
the type marker you prefer. (I like a + ).
4) Press [ZOOM], 9 and the scatter plot will
appear on the screen. (Alternatively, you could press GRAPH and set the
window as you choose.)
Now to set up the regression:
5)
Press
[STAT], cursor to CALC, and press the number to the left of the type regression
that you want. For example, press 4 for Linear.
6) LinReg(ax+b) will appear on the screen if you pressed 4 in item 5
above. If you have your data in the default lists, L_{1} and L_{2},
you can skip the rest of this step and go directly to step 7. Immediately after that enter the following:
[2nd], [L_{3}] [,], [2nd], [L_{4}], [, ] .Note that the commas outside the brackets
are just separators so you can tell what I'm doing. They do not appear in the
syntax.
7) Now, you want to store this as a Yvariable, say, Y1. So, do it this:
Press [VARS], cursor to YVARS, [ENTER], [ENTER]
8) If you pressed 4, you should now have this on your screen. LinReg(ax+b) L_{3}, L_{4}, Y1.
Note if you had your data in the default lists, you will have LinReg(ax+b) Y1.
Press [ENTER]. After a few seconds a long equation with coefficients having
several decimal places will appear on the screen.
9) Press [GRAPH] and both the scatter plot and the graph of the regression
equation will appear on your graph screen.
10) To predict the yvalue for an xvalue not in the data first press
VARS, cursor to YVARS, press 1, 1. Y1 will then be pasted to the home
screen.
11) Enter the xvalue of your choice in parentheses after Y1.
Example: Y1(12)
12 Press ENTER and the yvalue corresponding to the xvalue of 12
will appear.
13) (NOTE: After you've finished with the regression, cursor
to Plot1 on the graphing screen and press ENTER to remove the highlight.
Otherwise, you'll plot the scatter plot every time you do a function graph.)
===========================
(32) The TI83 Plus selects the number of classes when I do a histogram. Is
there any way I can choose my own?
Well, yes, but you'll need to do a little work. Here's how to do it.
1) Enter your data List L_{1}..
If your data is not in order, you can simplify the next steps by sorting the
data. Sort it by pressing STAT, selecting SortA(
or SortD( as appropriate, then entering the list name of the data
(often L_{1})
As an example, you might have this displayed on your screen: SortA(L_{1}.. Now, press ENTER, and your data will be sorted.
2) Now, from the sorted data, determine the class width and lower boundary of the
lowest class.
Now do this:
3) Press [2nd], [STAT PLOT], highlight 1, and press [ENTER].
4) Highlight ON on the next screen; then highlight the histogram symbol.
Make sure L_{1} is entered for the Xlist and use the default,1, for
Freq. (Note Freq would be the list name for the Freq list is you had "tabled"
data.)
5) Press [WINDOW], and enter the lower boundary of the lowest class
as Xmin and your chosen class width as Xscl.
6) Press [GRAPH]. You can use {TRACE] to display the value and boundaries of a
particular bar on the histogram.
===========================
(33) Do I really need to change the batteries on my TI83+ when I upgrade
the operating system?
Oh, absolutely. I would definitely do it. The OS is stored in flash
ROM. The way flash ROM works is that when you want to store a logic 1,
a voltage is applied that causes socalled hot electron to jump the band gap
between the semiconductor and gate insulator and get trapped as charge in the
gate insulator. I don't know what type circuit TI uses to do this,
but it stands to reason that the amount of charge stored in the insulator will
be proportional to the battery voltage. The greater the trapped charge the
"harder on" the transistor will be and, therefore, the the lower the
draintosource resistance. So, I some of the things you might expect form
fresh batteries are the following:
1) The upgrade will probably go faster because the higher voltage of a new
battery will charge the stray capacitances inside the circuitry faster.
2) Flash memory will have higher logic levels stored on their cells
providing a more definite logic level for the sense amplifier. That would
improve immunity
resulting in fewer transfer errors.
3) The charge on the cells might also last a little longer in case you
happen to have a slightly leaky cell.
That's probably more than you ever wanted to know on that subject, so enough. The way I do the upgrade is to keep a
set of new batteries on hand, and when I upgrade a student's calc, I put in the
new batteries. Then when the upgrade is finished, I reinstall the student's
older batteries.
===========================
(34) Does the conics application for the TI83 Plus provide the same graphing
capability as the graphing functions that are built into the calculator?
Not exactly. The conics application is more like a draw function than a graph function.
The [TABLE], [CALC], [WINDOW], and other functions will not work with the conics
app. The [TRACE] will work, however, and you can use that to get values off
your graph in case you're required to put it on paper. If you're wondering
about whether to get it, I recommend you get it. It's free, and it's better
than solving for "y" and entering two equations in most cases.
===========================
(35) I've read various places on the Internet that there's not much
difference between the TI83+ and the TI82. Is that correct?
Well, it depends on the perspective you have. From the perspective of the
student taking college algebra or precalculus, there are a couple important
differences. Here are a few differences that I'm aware of:
1) Probably the most important from the perspective I mentioned is the
inability of the TI82 to solve augmented matrices and display them in either
reduced rowechelon or rowechelon form. That's why I wrote my program REFRREF,
incidentally. That will give the TI82 that capability.
2) Next, I would say, is the inability of the TI82 to handle complex
numbers. That also prevents students from using certain programs that include
imaginary number solutions.
3) Next is the inability of the TI82 to handle the Conics application that
takes the hassle out of graphing conics.
4) I'll now list several items that are of various degrees of importance,
depending on how extensively your teacher uses the graphing calculator in
his/her teaching: Graph formats (solid line, dotted line, etc.); interactive
equation solver; and other things such as gcd, lcm.
If you already have a TI82, you can get by okay if you'll install programs,
mine or others of your choosing, for doing augmented matrices and imaginary
numbers. But if you have yet to buy a calc and have the money, I'd suggest
either the TI83+ or the TI83+ Silver Edition.
_____________________
(36) Is it possible to do a stemandleaf chart on the TI83 Plus?
Well, sort of. Let's say you have the numbers 41, 54, 67, 53, 46, 58, 63,
62, 71, 83, 74, and 86. Do the following:
1) Press [STAT], [ENTER]. Enter the data into L_{1}, and press [2nd],
[QUIT].
2) Press [STAT], cursor to item 2 and press [ENTER].
3) Press [2nd], [ENTER] and enter the stem data in L_{2 } and the leaf
data in L_{3.
}4) Press [2nd], [STAT Plot], [ENTER].
5) Turn Plot 1 ON, highlight the first type graph, enter L_{2} in the
Xlist and L_{3} in the Ylist. Select the type mark you prefer. ( I
like the + sign.)
6) Press [WINDOW] and set Xmin = 0, Xmax = 9, Ymin = 0, and ymax = 9.
7) Press [GRAPH].
If you want, you could press [2nd], [FORMAT], and highlight the GridOn. Then
press [GRAPH]. If you don't like the result, turn the resulting grid off.

(37) How do I find the critical numbers for y = x^{3} x^{2}
3x +1 on my TI83 Plus?
1) First press [Y=] and enter the equation in the space opposite Y1=, and
press [GRAPH] to graph the equation.
2) Press [2nd], [CALC], press 4 (maximum).
3) Move the cursor slightly to the left of the peak of the curve at
approximately x = .7 and press [ENTER]; then move the cursor to the right of
that peak and press [ENTER]. Finally, move it to the center of the peak, and
press [ENTER] again.
4) The value at x = 0.7207 should appear for x.
5) For the minimum, repeat the above except select 3 (minimum) in step 2.
Incidentally, if you have places where the derivative does not exist, you can
approximate the value by using pressing [2nd], [TRACE], and moving the cursor
almost to the asymptote or discontinuity.

(38) On my TI82, when I enter (32)^(1/5); then (2)^3 I get a correct
answer, 8, but when I enter (32)^(3/5) I get Ma ERROR. Why?
It's probably because of the algorithm used in the last case. The way most
scientific calculators, the TI82, and the CFX9850 does x^^{m/n} is
with the identity e^{m/n*ln (x)} . As you can see, when you have 32,
you have the natural log of a negative number. That's a complex number and so
is listed as an error. Incidentally, the TI83 Plus handles all of these
exponentials with no problem. For more on this topic, see item 13 on the FAQs
for Scientific Calculators

(39) My teacher says the TI83Plus is useless for finding the
derivative. Why is that?
Well, I would be a little more charitable and say you need to
be aware of its limitations. First of all, you need to realize that the
TI83/Plus calculators will not give you an expression for the derivative.
That is, it won't give you 2x for the derivative of x^{2}.
What it will do is give you a number for the value of the derivative at a
particular point, say x = 2. But again, you need to be aware of it's
limitations. Because
the TI83/Plus uses the symmetric difference method of evaluating the
derivative, it will sometimes give you a value when the derivative does not
exist at a cusp or when the denominator is zero. Here are a couple
examples: derivatives of f(x)=x evaluated at zero; f(x) =x^{1/3}
evaluated at zero. If you're dealing with a suspicious derivative,
back off the evaluation point about .01 or so, and if you get a considerably
different value, then the first value is probably wrong. For example,
nDeriv of f(x) = x evaluated at .01 is 1 rather than zero for the value given
for x=0, and nDeriv of f(x) = x^{1/3} at .01 is 7.19 rather
than 100 at give for zero. It's not a bad idea to graph a function to alert
yourself to possible pitfalls.
_______________
(40) Can I draw points on the graph screen on my TI83Plus?
Yes, but I want to emphasize that drawing is different from plotting.
To draw a point from the graphing screen, do this:
1) It's probably best to set the window to ZDecimal.
2) Press 2nd, DRAW. That will take you to the graphing screen
with the cursor displayed.
3) Using the cursors arrows, move the cursors to the point you want as
indicated by X= and Y=; then press ENTER. Your point will be on the
screen.
___________________
There are more FAQs on page 2.
Click "More Difficult Page 2" under TI FAQs in the navigation panel to go there.
Last Revised: 2/20/07.
.
