Brief User Guide for TI-82
Calculators
INDEX:
To facilitate lookup, the instructions are divided into
the following categories:
I. Basic Math –
Capabilities, Math operations, how to change
settings, and how to obtain certain symbols.
II. Special Expressions – Absolute Value, Greatest
Integer, etc.
III. Graphing and Evaluating Functions – Graphing, finding
roots, finding intersections of graphs,
graphing
inequalities, etc.
IV. Special Functions – Greatest Integer, Piecewise
Functions, Trig Functions, Logic & Truth
Tables, Sequences, Recursion Formulas, arithmetic of lists, etc.
V. Calculus – Finding the derivative at a certain point, finding the
integral.
VI. Matrices – Determinant, Transpose, Row Operations,
solving systems of equations, source for
program for
rref and ref.
VII. Transferring Programs and Data – Transferring data or programs from
one calculator to
another.
VIII. Problems with the
calculator.
IX. Appendices -
Instructions for using my programs REFRREF2 and INEQGRAF.
RELEASE DATE: 10/5/03 DATE LAST REVISED:
5/7/09
Printer friendly page here.
NOTE: Copy limitations and
printing hints are listed at the end of this document.
GENERAL: All
keys have at least two functions and some have three. The default function for
a key is the white
print on the key. When 2^{nd} is pressed, the key
function is as indicated in blue print (gray on some later models) on
the panel
immediately above the key. When ALPHA is pressed, the function is the white
label immediately above
and, in most cases, near the right end of the
key.
I. BASIC MATH
General Capabilities:
Students should be aware that the TI-82, TI-83 Plus, and TI-84
will not manipulate variables. That is,
they will not simplify expressions, factor expression such as
quadratic equations, and they will not do multiplications of variables
such as in the FOIL method. Furthermore, the TI-82
will not do the row-echelon or reduced row-echelon method of solving a
system
of equations without a separate program.
The TI-82 will generally evaluate expressions using a particular
value for an expression,
it will find roots of equations, intersections of graphs, do
arithmetic on matrices, and many other operations which are listed in
the index above.
1. Turning the calculator ON and OFF.
a) To turn on: Press the ON key.
b) To turn off: Press 2^{nd}; then OFF (the second function
for the ON key.)
2. Adjusting the contrast of the screen.
a) To make the screen display
darker: Press the 2nd key; then hold down the
UP arrow
key
until the contrast is satisfactory.
b) To make the screen display lighter: Press the 2nd key; then hold down the DOWN arrow
key
until the contrast is satisfactory.
3. Clearing the Calculator Screen.
a) To clear the calculator screen: Press the CLEAR key.
b) Note that CLEAR may also take you to another screen if you are
using one of
the screens that does not permit data entry.
4. To move to another screen:
a) Press 2^{nd}, QUIT.
b) You can also use CLEAR
if you are not using a screen such as Y=, List, or
PRGM where entries can be
made.
5. Correcting errors or changing characters.
a) To replace a character at
the cursor position, just press the new
character.
b) To insert a character in the
position of the cursor, press 2^{nd}, press
the INS key, and then press the key for
the desired character.
c) To delete a character in the
position of the cursor, press the
DEL key.
6. Changing the MODE:
(Use the MODE for such things as changing from degrees to radians, displaying numbers as powers of ten,
using split screen, and other similar things.)
a) Press the MODE key.
b) Use the arrow keys to move the cursor to the desired item.
c) Press ENTER to highlight the selected item.
d) Press CLEAR or 2^{nd}, QUIT to return to the home screen,
7. Performing numerical calculations:
a) On the graphing calculator screen, the multiplication symbol will
appear
as * and the division symbol will appear as /.
b) Parentheses can be used to denote multiplication or as grouping symbols
to
clarify the order of
operations.
c) To enter an exponent use the ^ key for any exponent. You can also use
the x^{2}
to raise a number
to the second power.
d) Use the (-) key for negative numbers and the - key for subtraction.
8. Raising a number to a power:
a) Enter the number.
b) Press the ^ key
c) Enter the number for the power. Enclose
fractional exponents in parentheses.
d) Press ENTER.
e) For an exponent of 2 only, you can use the x^{2}
key after entering the
number that you want to raise to the second power.
f) Alternate method for raising to the third power
only: Enter your number,
press MATH; then 3; then ENTER. (Note that using ^
is more efficient.)
9. Finding the root of a number:
For square root only, press 2nd, the square root
key, enter the number whose square root you
want and press ENTER. For other roots, do the
following:
a) Enter the number for the root index.
b) Press the MATH key.
c) Press 5 to paste the unspecified root symbol to
the screen.
d) Enter the number you want to find the root of.
e) Press ENTER.
f) As an alternate method for cube root only, you
can also choose to press
MATH, enter 4 to select item 4, and enter your
number. Finally, press ENTER.
10. Operations with fractions:
a) Use the divide symbol between the numerator
and denominator. Ex: ¼ is
entered as 1÷4.
b) Use the correct operator symbol (divide,
multiply, add, subtract) between
fractions.
c) Pressing ENTER will give you the answer in
decimal format. To get the answer
as a fraction, skip step c) and continue as below.
d) Press MATH to select Frac;
then ENTER. Press ENTER again to display the answer.
NOTE: You can convert decimals to
fractions using step d), but the decimal
must have 12 decimal places. Example: To convert
the decimal equivalent of
1/3 to a fraction, you must enter this number, .333333333333.
Otherwise the
calculator will just return the decimal you entered.
II. SPECIAL
EXPRESSIONS:
1. To enter the symbols, =,
≠, >, <, ≥, or ≤:
a) Press the 2^{nd} ; then the TEST key.
b) Enter the item number for the desired symbol.
2. To find the absolute value of a number:
a) Press the, 2^{nd}, ABS (blue print
above the x^{-1} key).
b) Enter your number.
c) Press ENTER.
3. Finding the greatest integer function of a number.
a) Press the MATH key.
b) Use right arrow to move the
highlight to NUM.
c) Press 4 to select lnt.
d) Enter your number.
e) Press ENTER.
III. GRAPHING &
EVALUATING FUNCTIONS:
1. Graphing a function: (Note that all
equations must be in the Y= form before entry.)
a) Press the Y= key.
b) Enter the function(s) using the [X,T,Θ] key to enter the
variable X.
c) Press GRAPH to graph the function. (If you don’t see your
graph, press
TRACE and use the arrows to find the maximum or minimum value of your
function. Press ENTER.)
d) To leave the screen without graphing: press 2^{nd},
QUIT.
e) Press CLEAR while the cursor is on the same line as the
function to erase the
function.
f) To deselect a function, move the cursor to the equal sign
and press ENTER.
2. To obtain the standard size viewing window:
a) Press the ZOOM key.
b) Press 6 to execute Z Standard.
3. To change the viewing window to a custom size:
a) Press the Window key.
b) Use the arrow keys to move the cursor to the value to be
changed.
c) Enter the new value.
d) Press Graph to see the new graph, or press,
2nd, QUIT to return to
the calculations
screen.
e) ZSquare keeps the y-scale the same and adjusts the x-scale so
that one unit
on the x-axis equals one unit on the y-axis.
f) ZDecimal makes each movement of the cursor equivalent to
one-tenth of a
unit.
g) ZInteger makes each movement of the cursor equivalent to one
unit.
4. Evaluating a function
without going to the Graph screen: (Note that the function must be entered
in the Y= screen.)
a) Press 2^{nd}, Y-VARS.
b) Press ENTER.
c) Select the name of a
function, e.g., Y1, and press ENTER.
d) Enter an x-value such as YI (3) or a list of x-values in the format
Y1 ({2,3,4,5}). (In the
last format, make sure the interior grouping symbols are braces rather than
parentheses.)
e) Press ENTER.
5. To change or erase a function:
a) Press the Y= key.
b) Use the arrow keys to move the cursor to the desired location
and make
changes by inserting, deleting, or changing the desired characters.
c) To erase a function, with the cursor on the same line as the
function, press the
CLEAR key.
6. To use the trace function:
a) Press the TRACE key.
b) Use the right and left arrow keys to move the cursor along
the graph. The
coordinates of the cursor location are shown.
c) If more than one graph is on the screen, you can press the up
or down arrows
to jump
between graphs.
7. Finding the maximum and minimum points.
a) Enter the function and graph.
b) Press 2nd; then the CALC key.
c) Press 3 for minimum or 4 for maximum.
d) Move the cursor to the left of the point and press ENTER.
e) Move the cursor to the right
of the point and press ENTER
f) Press Enter again.
g) The values for maxima or minima will appear at the bottom of the screen.
8. Finding the value of a function at a given value of x.
a) Enter the function and the graph.
b) Press 2nd; then the CALC key.
c) Press 1 to select "1: value."
d) Enter the x-value and press
ENTER.
9. To zoom in using a box.
a) Enter the function and graph.
b) Press the ZOOM key.
c) Press 1 to select ZBox.
d) Move the cursor above and to the left of the location you
want enlarged and
press ENTER.
e) Move the cursor below and to the right of the location you
want enlarged and
press ENTER.
f) The box is then enlarged to fill the screen.
10. Finding the intersection point of two graphs.
a) Press "Y=" and enter
two equations whose intersection you want to find.
b) Press 2^{nd}, CALC.
c) Press 5 to select Intersect.
d) Using the left or
right cursor, move the cursor near the point of intersection if it's not already
there. If it's on the intersection, you might want to move it away
slightly.
e) The
prompt "First curve" should appear on the screen.
f) Press ENTER and
the prompt "Second curve," will appear and the cursor will have moved
to
to the second curve.
g) The prompt "Guess,"
should now be displayed. Move the cursor near the intersection and
press ENTER.
f) The values for the
coordinates of the point of intersection will appear at the bottom of the
screen.
11. Solving an equation in one variable. (Also
know as finding the roots.)
a) Press "Y=" and enter
the equation you want to solve.
b) Press 2^{nd}, CALC.
c) Press 2 to select
root.
d) Move the cursor to the left of the intercept and press ENTER.
e) Move the cursor to the right of the intercept and press
ENTER.
f) Move the cursor
between the above two points and press ENTER again.
g) The "x" and "y"
coordinates of the root will appear at the bottom of the screen.
12.
Graphing inequalities:
Graphing inequalities with the standard TI-82 is tedious. Use my
program, INEQGRAF. The
instructions for using this program are in
Appendix IA of this manual.
IV. SPECIAL
FUNCTIONS:
1. Changing from radian measure to the degree mode.
a) Press the MODE key.
b) Move the cursor to either
Radian or Degree to match the units
of your angle.
c) Press ENTER.
d) Press CLEAR or 2^{nd}, QUIT to return to the
calculator screen.
2. Graphing piecewise functions or functions on an interval.
a) To graph a function on the interval x < a, enter the function
in parentheses, followed by
(x<a).
For example, to graph x² -2 on the interval x<1, enter this: (x²-2)(x<1)
b) To graph a function on
the interval x > a, enter the function in parentheses, followed by (x>a).
c) To graph a function of the interval a<x<b, enter the function
in parentheses, followed by
(x>a)(x<b).
3.
Graphing trigonometric functions:
a) You must have
the calculator set to radians to graph a trig function. See the MODE
section if
you don't know how to do that.
b) Press "Y=" and
then press the button for the function you want to graph.
c) Enter the
argument of the function, e.g., X, and press GRAPH.
4. Using the LOGIC functions:
NOTE: You can use the logic functions
such as "and", "or," "xor," or "not," to do things such as
Boolean algebra and truth tables. Note that you must use "1" for true and
"0" for false. As
a simple example, suppose you wanted to do p ^ q. (Unfortunately, the
TI-82 will not get
data from a list and perform operations on it, so we'll have to work around
that.)
a) Press STAT,
ENTER and enter the proper combination of 1s and 0s in for p in the table under
L_{1.
}
b) Enter the proper combination of 1s and 0s for q in L_{2}.
c) Enter an
equivalent number of 0s in L_{3} to dimension it, otherwise you will get
a dimension error
message.
d) Press 2nd, QUIT to go
to the home screen.
e) Press 1, STO, x:
(Make sure you have the colon.
f) Now enter L_{1}(x)
and L_{2}(x), STO, L_{3}(x) and press ENTER. The first row in
the tables will be
evaluated and stored in L_{3}. The "and" statement is obtained by
pressing 2nd, TEST, selecting
LOGIC, and pressing number 1 for "and."
g) Press 2nd,
ENTER and the expression 1→x:L_{1}(x)
and L_{2}(x)→
L_{3}(x) will be redisplayed.
h) Change the
expression "1→x"
to "2→x"
and press ENTER.
i)
Continue this until all entries in the lists have been evaluated.
Obviously, you can also use the other logic operations in place of "and."
All of this is much
easier done with a program, but for those of you not into programming, this will
work.
5. Finding terms of
sequences.
a) Press 2^{nd},
LIST, 5 to paste Seq( to the home screen.
b) Enter the
sequence information in the following format.
Seq(formula, variable, beginning, end, step).
Example: Find the first five terms of : a_{n} = 3n +4.
1) Convert the variables in the formula to ‘x’; then enter: Seq(3x+4, x,1, 5, 1). Press ENTER to
get the answers.
c) If you
want the answer in fractions rather than decimals do this:
1) After you’ve entered the information for the sequence, press MATH, ENTER.
That will
paste ►Frac to the end of the sequence information.
2) Press ENTER to get the answer in fractions.
6. Recursion formula:
Let’s take this recursion formula:
a_{n} = 3a_{n-1} +2, when a_{1} = 5.
a) From the
home screen, Press 5; then
ENTER to place the value for
a_{1 }to the variable Ans.
b) Enter the formula as follows: Press 3, 2^{nd}, Ans, +, 2.
c) You will now get a new term each time you press ENTER.
7. Arithmetic of Lists:
Arithmetic of lists, multiplication,
squaring, addition, subtraction, etc., can always be done from the
home screen, but sometimes it's much easier to do
it from the lists. Let's take a look at how to multiply
the corresponding elements of list L_{1 }
times those in list L_{2 }and store the data in L_{3}.
a) Press STAT, ENTER to go to the list
tables.
b) Enter the data in L_{1} and L_{2}.
c) Place the cursor on the title, L_{3},
and press CLEAR, ENTER to clear the list if necessary.
d) Place the cursor on the title, L_{3},
and press 2nd, L_{1}, x (the multiply symbol), 2nd, L_{3}. You
should have
L_{1}*L_{2}
opposite L_{3}= at the bottom of the screen.
e) Press ENTER and the products of corresponding
elements will be stored in L_{3}.
V. CALCULUS
1. Finding the numerical derivative from a function:
(Note that the function must be
entered on the Y= screen before using this method. Also set the
Window to ZDecimal before using
this method by pressing ZOOM, 4.)
a) Press the MATH key.
b) Press 8 to select nDeriv(.
c) Press 2^{nd}, Y-VARS,
ENTER; select the variable you want
and press ENTER.
d) Enter the name of the independent variable, probably X.
e) Enter the value
of the point where you want the derivative evaluated. For example if you want
the derivative for Y1 evaluated at 3, you would have this: nDeriv(Y1, x,3).
f) Press ENTER
and the value will be displayed.
2. Determining the value of the derivative from points on a graph.
a) Enter the function and graph.
b) Press 2^{nd}, CALC.
c) Press 6 to choose dy/dx.
d) Move the cursor to the desired point and press ENTER. The
value of the
numerical derivative
at the point you selected will appear at the bottom of the screen.
3. Drawing a tangent line at a point:
a) Enter the function and graph.
b) Press 2^{nd}, DRAW.
c) Press 5 to select Tangent(.
d) Move the cursor to the point of tangency desired and press
ENTER.
e) To clear the tangent line, press 2^{nd}, DRAW and
then ENTER.
4. Calculating the value of a definite integral:
a) Press the MATH key.
b) Press 9 to select fnInt(.
c) You will now enter an expression in the form Y,X,a,b inside
the parentheses.
In that
expression, Y is the expression you’re integrating; for example Y1, X is the
variable of integration, usually X; a is lower limit and b is the upper limit.
d) For the expression to be integrated, you can either choose a
variable entered
into the Y= screen, or you can enter the expression itself. As an example,
you
might have fnInt(Y1,X,1,2 with your expression entered into Y1, or you
might have fnInt( x^{2},x,1,2
where you have entered the expression x^{2} yourself.
Notice that you must enter Y1 from the Y-VARS
menu if you use that
method.
e) Press the ENTER key to see the value of the definite
integral.
5. Alternate procedure for finding the
value of a definite integral:
a) Press the ZOOM key.
b) Press 4 to select ZDecimal. (You don’t have to do this step,
but it probably will be
easier to set your limits if you do.)
c) Press the Y= key.
d) Enter the function you are integrating.
e) Press the GRAPH key.
f) Press 2^{nd}, CALC.
g) Press 7 to select Integral.
h) Move the cursor to the
lower limit of integration and press the ENTER key.
i) Move the cursor to the upper limit of
integration and press the ENTER key.
j) The integrated region will be shaded, and the value of the
definite integral will
appear at the bottom of the screen.
k) To clear the
shading from the screen, Press 2nd, DRAW, ENTER.
VI. MATRICES:
1) Entering a matrix:
a) Press MATRIX, move the cursor to EDIT.
b) Move the cursor to the matrix number you want to edit or
enter numbers in,
and press ENTER.
c) Enter the number of rows and press ENTER;
then enter the number of
columns and press ENTER.
d) Enter each value of the matrix and press ENTER after
each value.
e) Press 2^{nd}, QUIT to go to the home screen.
2) Multiplying two matrices [A] * [B]:
a) Enter the data into matrices [A] and [B] and press 2^{nd},
QUIT to go to the
home screen.
b) Press MATRIX, select the matrix you want as the first
in the product, [A],
and press ENTER.
c) Press the multiply symbol.
d) Press MATRIX, select the matrix you want as the second
in the product,
[B], and press ENTER.
e) Press ENTER to perform the multiplication step.
f) Remember that the numbers of columns in [A] must equal
the number of
rows in [B] or you will get a dimension error.
3) Doing other matrix math:
a) Press MATRIX and cursor over to MATH. There you
will see a list of
operations that you can do. To find the determinant, use Det. To find
the transpose, use T.
b) After you select the operation you want, press ENTER.
c) Press MATRIX, select the matrix you want to operate
on, and press
ENTER.
d) Press ENTER again to get your answer.
4) Solving systems of equations:
The TI-82 does not
have the ref and rref functions as the TI-83 Plus and TI-84 do. You can
use my program,
see item 5)
below. Perhaps the easiest way is to make use of this equation:
[A][X]
=[K] where [A] is the matrix of coefficients, [X] is the variables, and
[K] is the matrix of coefficeints.
Now, we solve that equation for this:
[X] =[A]^{-1} [K]
To perform
the math for this, do the following:
a) Enter the
coefficients in matrix [A] or whatever matrix you choose.
b) Enter the
constants in matrix [B] or whatever matrix you choose other than the one you
have the
coefficients in.
c) From the home screen,
press 2nd, MATRIX, and press 1 for matrix [A].
d) Press the inverse
button, x-1.
e) Press the multiply
button.
f) Press 2nd,
MATRIX, 2 for matrix [B]. You should now have [A]^{-1} *[B] on the home
screen.
g) Press ENTER and the
answer will be displayed
NOTE: You can do any of the elementary row
operations. They are very useful for doing the arithmetic for Gauss or
Gauss-Jordan elimination, but a little time is required to get the hang of
solving a matrix a row at a time. So, since most students don’t take the time to use those
functions, I’m not going to include them. Instead, I’ll give you my
Website as a reference for finding out how to do those operations if you want
to do them. First go to my Website:
http://www.anglefire.com/pro/fkizer
Go to the listing “TI FAQs” in the navigation bar on the left. Click on
the link “More Detailed Page 1”. That will take you to a long page of 40 FAQs. Cursor down to the answers
and then down to answer (21). That will give you the procedure for doing the row operations.
Alternately, to find item 21, you can use Find under the Edit menu and enter (21) in the dialog
box. Then click Next to find the answer.
5) Doing rref and ref:
a) You cannot do these
operations on the TI-82 without a program. There
is a program on
my Website for doing this. Go to my Website at the URL listed above.
The program takes about 25 minutes to enter by hand. For STCC students,
as time permits,
I will transfer this
program electronically from a TI-82 that I have the program stored in to
the
student's calculator. To set up a time to have this done, email me at
dkizer@southwest.tn.edu . The instructions for this program are
in Appendix IB of this
manual.
VII. TRANSFERRING PROGRAMS AND DATA:
1) I will assume that both calculators are TI-82:
a) Turn both calculators off and plug in
the unit-to-unit cable for both calculators.
b) 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.
c) Press ENTER on the receive calculator. The word "Waiting"
should appear.
d) On the sending calculator, cursor down to Prgm and press ENTER.
e) Cursor down to the program you want to transfer and press ENTER.
The program that
you selected will be marked with a square
"dot."
f) Cursor over to TRANSMIT press ENTER.
g) If everything is connected satisfactorily, transmission of the
program should start.
Otherwise, you'll get a transmit error after a
few seconds.
h) If you get a transmit error, rotate the plugs on the cable slightly back and forth
and try again.
VIII. PROBLEMS:
a) Problems with trigonometric functions: The most common
problem with trig functions is not
having the MODE set to the to the dimension
of the number entered. For example, students may
have entered degrees, but have
their calculator MODE set to radians. To correct that, see
“Changing the MODE
in section I.
b) In the
graph function mode, you may get a strange graph or maybe even an error message.
If
that occurs, the first thing to check
is whether one or more of the Plot functions is turned on. To take
care of that, Press 2nd, STAT PLOT,
press 4, and press ENTER.
c) If your calculator hangs up and you are unable to correct
the problem, first try online or other
places that provide help. If you are
unable to get help, you can reset the calculator. Do that as follows:
1) Press 2^{nd}, MEM, press 3.
2) Decide if you really want to RESET.
Resetting will erase all of your programs.
IX. APPENDCES:
Appendix IA:
Graphing Inequalities:
This program, INEQGRAF, may be downloaded from my website
www.angelfire.com/pro.fkizer
in either text or .82P format. It will graph up to three inequalities on
the same screen. After the calculator has graphed the equation in Y1=, it then
moves on to the equation in Y2=. If you want to interrupt the graphing for some
reason, press the ON button.
Graphing is done as follows:
SETTING THE WINDOW:
For many Finite Math problems you will get the best display (the feasible
region) if you set Xmin and Ymin both at 0.
ENTERING EQUATIONS:
1) Put your inequalities in the slope-intercept form, y = ax+b, and enter
the part to the right of the equal
sign into the Y=
screen. Either clear or deselect all other equations on this screen.
2) Press 2nd, QUIT to leave the Y= screen.
RUNNING THE PROGRAM:
1) Press PRGM and select the program INEQGRAG by either pressing the number
before it on the
keyboard or highlighting its number and pressing ENTER.
2) Press ENTER. The menu will appear on the screen and wait for you to choose a
number. If you
press 1, the equation in Y1= will be selected for graphing.
3) Another menu will appear asking what type inequality you want to graph. Press the
appropriate number and press ENTER. All equations will be
graphed and the appropriate graph(s) will
be shaded. The menu will appear again and wait for you to
tell it what to do by selecting a number.
4) When you are done, press the number 3 for DONE, and the calculator will
display the shaded
inequalities. Notice that the calculator does not draw
the dashed line for < or >. It only draws a
solid line.
5) When you are finished with the graph for a particular problem, press ENTER.
The shading will be
erased and the graphs will be redrawn. Be sure to do
this last step because the program keeps
running until you do.
Appendix IB:
Doing ref and rref:
1) Enter the matrix data according to Item 1, in
section VI.
2) Press PRGM; then press the number before the program name
RREFREF2. The matrix that you
entered will be displayed for checking for accuracy.
Press ENTER.
3) When the menu appear, select the number for the operation that
you want to perform.
4) The solution will be displayed in decimal form. Note that
you can scroll to the right if the last
columns are not displayed on the screen.
5) Press ENTER to display the matrix in fractions.
6) Finally, press ENTER to quit the program.
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Printing Hint:
Most browsers will send both the navigation bar and the text to
the printer, and, as a result, will cut off the right edge of this document if it
the file is printed directly. To prevent this, highlight the instructions
portion only (not the navigation panel) and check "Selection" on the Print
dialog box; then click "Apply." This will eliminate the navigation panel
and get all of the instructions on the screen.
Revised: 12/12/07