Brief Users Guide for the TI-83 Plus & TI-84

Content:
This document covers basic math, special expression, graphing, complex numbers,
list arithmetic, tables, special
functions, calculus, matrices,

sequences, transferring programs and all basic operations as performed on the
TI-83 Plus calculator.

**INDEX:
**

To facilitate lookup, the instructions are divided into the following categories:

I.
**Basic Information** - What's my operating system version?, how much RAM do my
programs

take,
is my calc upgradeable?, adjusting brightness of display, friendly values using
TRACE.

II. **Basic Math** – Math operations, how to change
settings, and how to obtain certain symbols.

III. **Special Expressions** – Absolute Value, Greatest
Integer, logs of different bases, etc.

IV. **Graphing and Evaluating Functions** – Graphing, finding
roots, graphing inequalities with and without the

Inequalz App., finding intersections of graphs, graphing inequalities, marking points on a graph,
using [TABLE]

to find points for graphing a parabola by
hand, using the Solver, CALC, or TABLE to find roots or evaluate a

function etc, using TABLE to graph an equation by hand,
solving equations with roots >2 with Solver,

V. **Special Functions** – Greatest Integer, Absolute Value, Piecewise
Functions, Trig Functions, hyperbolic

functions, graphing parametric equations, etc. .

VI. **Calculus** –
Finding the derivative at a certain point, finding the integral,

VII. **Matrices** – Determinant, Transpose, Row Operations,
system of equations, source for
program for rref and ref.

VIII. **Sequences** - Finding several terms of
a sequence, finding a specific term of a sequence,

summing sequences,
cumulative sum of sequence.

IX. **Complex Numbers - **
Solving a polynomial with complex coefficients, program for finding
complex coefficients,

X. **Combining and
Connecting Operations** - Doing expressions with several terms,

XI. **Arithmetic and other
operations with lists **- clearing lists, arithmetic with lists, logic with lists,

XII. ** ****Special Techniques - **Graphing equations of the form
x=y² +3x +2, **
** XIII.

another, entering TI-84 programs on a computer, transferring a program from a computer to a TI-84 calculator, transferring a

program from a TI-84 to a computer,

XIV.

XV.

Navigation: Home of website. Index page for mobile devices.

*RELEASE DATE: 10/5/03 DATE LAST REVISED:
3/17/11*

© 2003 Frank Kizer
NOTE: See copy restrictions and printing
hints at the end of this document.

**
General Operating Instructions: ** 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 yellow print (gray or blue on some later models) on the panel
immediately above

the key. When ALPHA is pressed, the function is the white
(green on TI-84)
label immediately above the key and, in most cases, near the right

end of the
key. When APPS is pressed, the names of applications that are installed on your calculator
displayed.

**
Things the TI-83 Plus and TI-84 will not do: **
Students should be aware that TI-83 Plus, and TI-84
calculators 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, they will not do indefinite
integrals or find the anti-derivative of an expression with variables.

They will, however, find the area under a curve between limits that the user
specifies and they will find the value of the derivative of a function

at a specific point.

** I. BASIC
INFORMATION
**

a) To turn on: Press the ON key.

b) To turn off: Press 2

**2. Adjusting the contrast of the screen.
**

a) To make the screen display darker: Press the 2nd key; then press the
up arrow

key.

b) To make the screen display lighter: Press the 2nd key; then press
the down

arrow key.

**3. Finding your operating system version number.**

a) Press 2nd; then MEM.
The memory management screen will be displayed at the top of the screen.

b) Press ENTER and a screen
will be displayed with the version number of the OS. It may be

anything from 1.12 to 1.19.

**4. Finding our how much free RAM I have.**

a) Press 2nd; then MEM. Scroll
to 2: Mem Mgmt/Del...and press ENTER.

b) The FREE RAM and ARC MEM
(archive memory) will be displayed.

c) To find out how your memory
is used, for example how much memory a program uses,

from
the above screen, highlight 1:All and press ENTER.

** 5. Is my calculator upgradeable?** TI-83 Plus and later
are upgradeable. The TI-82 and TI-83 (not

Plus) are not upgradeable.

**6)
Friendly Values on Graphs Using TRACE:
** Many times
when you use the TRACE function, you will get an x-value such as 2.784532. If
you change the x-min and x-max in the WINDOW function to be multiples of 4.7 and
the y-min and y-max to multiples of 3.1, the displayed values will be
"friendlier." That is, they will be integers or numbers with one or two decimal
places. You can always set the values by hand, but the easiest method is to use
the ZDecimal function of ZOOM. Just press ZOOM; then 4, for ZDecimal.

It may be that the display is now partially off the screen. If you want the entire graph on the screen, use the Zoom Out function. To do that, press ZOOM, 3, ENTER. Incidentally, 4 seems to be the default setting for the zoom factors. So, if your graph is now too small, set the factors to 2 if they’re not already set at 2. To do that press ZOOM, cursor to MEMORY, press 4, and set both factors to 2.

If you’re trying to find the value at a specific point, a zero for example, and the cursor still does not fall on the x-axis, you could try different strategies such as ZBox, but I usually prefer to use the zero function. To do that, press 2

**II.
BASIC MATH
1**

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.

**2****. To move to another screen:**

a) Press 2^{nd}, QUIT.

b) You can also use CLEAR if you’re not using a screen
on which entries are made. Some

examples of screens where entries are made are the following: Y=,
List, or PRGM.

**3****. 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.

**4. Changing the MODE:**

(Use the MODE for such things as changing from degrees to radians, displaying numbers as

powers of ten, using split screen, enabling
complex number calculations 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,

**5. 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. Other functions are available by pressing MATH.

d) Use the (-) key for negative numbers and the - key for subtraction.

**6. Raising a number to a power: **

a) Enter the number.

b) Press the ^ key

c) Enter the number for the power.

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.)

**7. Finding the root of a number:**

a) For square root, press 2nd; then the
square root symbol (x^{2} key).

b) For other roots, enter the number for the root index.

c) Press the MATH key.

d) Press 5 to paste the unspecified root symbol to
the screen.

e) Enter the number you want to find the root of.

f) Press ENTER.

g) 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.

** 8. 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.

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.

**III. SPECIAL
EXPRESSIONS:
** 1.

a) Press the 2

b) Enter the item number for the desired symbol.

**2. To find the absolute value of a number:**

a) Press MATH and move the
cursor to NUM.

b) Press 1 to paste Abs( to the home
screen.

c) Enter your number.

d) 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 5 to select int(.

d) Enter your number.

e) Press ENTER. (Note that
this also works for negative numbers.)

**4. Logs to different bases:
**Of course, logs to base 10, LOG, and to
base e, LN, are functions on the keyboard. But what about the most

common log with computers, often designated as lg? What we must do is divide the available logarithm by the

logarithm of the base wanted. The algebraic expression in general terms is as follows: the equation is as follows:

log

Using the natural log, ln, and lg for log to base 2, we have the following:

lg x =ln x/ln 2

Since 0.69314 is a good approximation to ln 2, we can change that to the following:

lg x =ln x/0.69314 and truncate any numbers greater than zero.

**IV. GRAPHING &
EVALUATING FUNCTIONS:
** (NOTE: Always make sure that the Plot
functions are not highlighted before graphing anything other

than statistical information.)

a) Press the Y= key. All equations must be in the slope-intercept form, y=mx+b, before entry.

b) Enter the function(s) using the [X,T,Θ,n] key to enter the variable, for example 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

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 cursor 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 adjust 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
using the graph screen. **

a) Press 2^{nd}, Y-VARS.

b) Press ENTER.

c) Select the name of a function, e.g., Y1.

d) Enter an x-value as YI (3) or a list of x-values in the form
Y1 ({2,3,4,5}). (In the

last form, make sure the interior grouping symbols are braces rather than

parentheses.)

e) Press Enter.

f) As an alternative to
this, see "Finding the value of a function at a given value of x," below.

**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
at the bottom of the screen.

c) If more than one graph is on the screen, you can press the up
or down arrows

to jump from
one graph to another.

**7. Finding the maximum and minimum points.**

a) Enter the function and graph.

b) Press the 2nd, CALC.

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) Move the cursor
slightly between those two points and press ENTER again.

g) The 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 the Calc key.

c) Press 1 to select value.

d) Enter the x-value and press
ENTER. The y-value will appear at the bottom of the screen

** 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) Enter two functions on
separate "Y=" lines and press GRAPH. Equations must be in

slope-intercept form.

b) Press 2^{nd}, CALC.

c) Press 5 to select intersect.

d) Move the cursor to a little away from the intersection and
press ENTER to mark the first graph

line and move the cursor to the next graph line.

e) Move the cursor to a little away from the intersection and
press ENTER to mark the second graph

line and set the cursor to guess the intersection.

e) Move the cursor approximately to the intersection and press
ENTER.

f) The coordinates for
the point of intersection will appear at the bottom of the
screen.

**11. Solving an equation in one variable. (Also
known as finding the roots or x-axis intercepts.)**

a) Enter the function and graph.

b) Press 2^{nd}, CALC.

c) Press 2 to select
zero.

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.

e) Move the cursor
approximately the intercept and press
ENTER.

f) The coordinates for
the root wilI appear at the bottom of the screen.

NOTE: This
can also be done using the Solver. See the last item in this section for
that procedure.

**12.
Finding coordinates to graph a parabola by hand.**

a) Enter the graph
in your calculator as described above.

b) Next locate the
vertex by pressing [2nd],[CALC], and pressing either 3 or 4, depending on

whether the vertex is a minimum or maximum for the parabola.

c) Move the cursor
slightly to the left of the vertex and press [ENTER].

d) Move the cursor
slightly to the right of the vertex and press [ENTER].

e) Finally, move
the cursor approximately to the vertex and press [ENTER]. The x- and
y-values

for the vertex will appear at the bottom of the screen.

f) Press
[2nd],[TABLE]. (Be sure that your independent variable is set for
Ask. If not press

[2nd], [TBLSET] and highlight "Ask" (opposite Indpnt.)

g) Enter two
more values for "x" in the table and the corresponding values for "y" will
appear.

h) Use these
coordinates and the symmetry property of a parabola to graph the parabola on a

sheet of paper. (NOTE: If the vertex is at an integer value, you can find
the vertex from the

table.)

**13.
Graphing Inequalities.
**I will
first describe the method for TI-83 Plus calculators that don't have the
Inequalz application and

the method for the TI-84 and TI-83 plus calculators that have the application.

a) Write each equation in the y =mx + b format and enter them into the "Y=" positions.

(Remember that you may need to change the direction of the inequality sign if you have to

multiply or divide by -1 during the rearranging of the equation.)

b) Shading of the graph is determined by the symbol to the left of the "Y=" entry. Using the left

arrow, move the cursor all the way to the left of the Y= symbol.

c) Pressing ENTER in that position will display different symbols. For < or

until the upright triangle is displayed. For > or

triangle is displayed.

d) After you have the correct symbol displayed, press ENTER to graph the inequality.

ENTER. When the Inequality Graphing screen appears, press ENTER to go to the graphing screen.

b) If the cursor isn’t already on the = sign, move it there and press ALPHA, F3 ( the ZOOM key) to enter

the ≤ symbol.

c) Now move the cursor off the symbol and enter –x +6, the right side of the inequality. Press GRAPH

and the graph with the applicable area shaded will be displayed.

If you want to solve a system of linear equations, click on the line TI-83 Plus Lin Prog and you will find

the complete method in that document. You can use the index to make finding the procedure easier.

**14.
Marking points on a graph.**

A few students who
capture screens like to have marks on graphs. Although some would

consider this more
trouble than it's worth, I'll include it for those brave souls who feel they must

have them. Although
marks can be put directly
on the graphing screen, that method uses the

dot as a mark and it cannot be seen when imposed on the
line of a graph. So, I will describe the

method of entering
marks from the home screen where you can select a + or a box..

a)
First, if you are a little picky about having the marks line up exactly on the
graph, you

should press ZOOM, 4 to select ZDECIMAL. Then graph your function and see
if it the x-

and y-values that you are interested in appear on the screen. If not,
press ZOOM, cursor

over to MEMORY and press 4. Then make the X- and Y-Fact integers larger
than 1. Then

press ZOOM, 3 to change the x- and y-scales.

b) Go
to the home screen to start the procedure. The syntax is Pt-On(x,y,mark.
So, press

2nd, DRAW and cursor over to POINTS.

c)
Press ENTER and Pt-On( will appear on the home screen.

d)
Enter the x-coordinate, y-coordinate, and the mark number. For the mark, 1=a
dot, 2 = a

box and 3 = a cross. I will use 3. Let's say we graph X^{2}
and we want to mark coordinates

(2,4). Then your entry will be Pt-On(2,4,3. (The mark will be a +.)

e) To
mark additional points, press 2nd, ENTRY and change the x-, y-coordinates to
those for

the next point. Continue this for additional points.

f) To
erase all points, press 2nd, DRAW, ENTER.

**15.
Finding roots of equations by several methods:
**There are three commonly used methods
for finding roots: Using the CALC function of the grapher,

other methods, I will describe all three. Since this is a brief guide, I will not cover every single detail of

all methods.

b) Press 2ND, CALC, 2 and the graph will be displayed with the prompt to set the Left Bound.

c) Move the cursor to slightly to the left of the point where the graph crosses the x-axis and press

ENTER.

d) Move the cursor to slightly beyond the x-intercept and press ENTER.

e) At the "Guess?" prompt move the cursor to approximately where the graph crosses the x-axis

and press ENTER. (Actually you don't really have to move it this last step.) The answer 3 will

appear for the first root. Go through the same steps for the second root.

f) Suppose you get a decimal answer that you think might be a fraction, and you want to convert

it to a fraction. Press 2ND, QUIT to leave the grapher, press X (on the X, T, 0, n button.). Now,

press MATH, 1, ENTER and the fractional equivalent will be displayed if the answer is a rational

number.

b) Press 2ND< TABLE and scroll down the list of y-values in the tables to see if there is a zero.

The corresponding x-value is a root.

c) If the answer is not an integer you may not find zeros, depending on the answer and how you

have the TABLSET configured. You can get fractional values by pressing 2ND TBLSET

and changing the ΔTbl to a decimal. Generally, if this happens I would change to one of the

other methods.

b) Enter your equation opposite eqn:0=. If that is not displayed, press the up-arrow; then enter

the equation.

c) Press ENTER and the present value of x and the bounds will be displayed. Change the bound

if you wish; then position the cursor opposite x=.

d) Press ALPHA, SOLVE (the ENTER button) and the smalller will be displayed after a short time.

e) Now, to find the other root, change the left bound to slightly above 3, say 3.001and enter 4.

f) Press ALPHA, SOLVE and the second root will be displayed.

**16.
Using TABLE to Graph an Equation by Hand:
**a) Press
Y= and clear all equations from the Y= positions, then enter an your equation,
say

x² -8x +15, opposite Y1=.

b) Press 2

numbers that are convenient for the size of your graph paper. X-values 1, 2, and 3

with corresponding y values 8, 3, and 0 would normally be satisfactory for this particular

equation.

c) Use the x- and y-values to locate points on your graph and draw the graph in the usual

manner.

d) If the numbers are too far apart in value, you can change their spacing by changing the

ΔTbl setting. To do that, press 2ND TBLSET and changing the ΔTbl to the

separation you want. Then press TBLSET to go back to the tables.

e) If you want to use specific values of “X,” press 2

“Ask” opposite “Indpnt” and press ENTER. Now press 2

tables. You can now enter the x-value(s) of your choice and the corresponding y-value

will be displayed in the y-column.

Easier Method: The following method is easier and just as good for linear equations:

First use a) and b) above to graph the equation.

c) Press Trace and move the cursor in the range of the values of "x" that you want to find values for.

d) Enter a value for "x" that you want to find a y-value for. The x- and y-values will appear on the screen.

f) Repeat this process starting with "Press Trace" for each set of values that you want.

**17.
Evaluating a Function at a specific variable value:
** There are four ways to do this:

a) From the home screen, enter -2; then press X (the X,T,0,n button), STO, ALPHA, :(the colon is made

with the decimal key.

b) Enter your equation, say x² -8x +15, immediately after the semicolon so that you have -2→X:x²+3x+2.

c) Press ENTER and the answer will be displayed.

d) If you want to do additional values, press 2ND, ENTRY. Change the -2 to whatever you want and press

ENTER.

e) If you want the answer in fractions, after step b), press MATH ENTER to get -2→X:x²+3x+2►Frac.

b) Press 2ND, CALC, ENTER and the graph will be displayed.

c) After the graph is drawn, enter -2 opposite the X= entry and press ENTER. The answer will be displayed.

to evaluate the function at several values such as doing a curve by hand.

a) Press 2ND, TABLESET, move the cursor to "ASK" opposite Indpnt and press ENTER.

b) Press 2ND, TABLE and enter whatever values you want in the x-column. The corresponding

values of y will appear in the Y-column.

b) Enter your equation opposite eqn:0=. If that is not displayed, press the up-arrow; then enter

the equation. After you have entered the equation above, you will need to enter a dummy variable,

say D, so that the entry looks like this: eqn:0=x²+3x +2 -D. Enter the "D" by pressing ALPHA,

D (the key for x

c) Press ENTER and the present value of x and the bounds will be displayed. Change the value of x to

x=-2. Change the bounds if you wish; then move the cursor to D, the variable you want to find the value for.

d) Press ALPHA, SOLVE and the answer will be displayed as the value for D after a short time. With this

problem, the answer will be D=35 for x=-2.

**18. Using the
Solver for Polynomials of degree >2:
**Let's take as
the example

b) Enter your equation opposite eqn:0=. If that is not displayed, press the up-arrow; then enter

the equation.

c) Press ENTER and the present value of x and the bounds will be displayed. Change the bound

if you wish. Let's use {-24,0}. Then position the cursor opposite x= and enter -24.

d) Press ALPHA, SOLVE (the ENTER button) and the smaller of the roots will be displayed after a short time.

The answer we get will be -3.9999999... which is -4.

e) Now change the bounds to {-3.8, 0} and the number opposite x= to -3.8.

Press ALPHA SOLVE and you'll get -.99999999... which is 1.

f) You can either continue this process or use synthetic division to find the second degree equation and solve

that in the usual manner.

**V. SPECIAL FUNCTIONS
**

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

** ** **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.
Hyperbolic Functions:
** The hyperbolic functions are
available on the TI-84, but only from the catalog. Find cosh as follows:

a) Press 2ND, CATALOG and the catalog listing will appear.

b) Press C; then scroll down to cosh(, and press ENTER. Note that the catalog automatically selects

the ALPHA mode, so do not press ALPHA before pressing C.

c) Enter the value of the argument and press ENTER. You may either close the parentheses or not

as you choose.

d) You may enter more than one value for the argument by entering the values as a list. For example,

cosh({.5, .7, .9}); then ENTER. You must close the braces, but you have the option of closing the

parentheses.

Note that the other hyperbolic functions are listed in alphabetic order in the CATALOG.

e) The hyperbolic functions can also be graphed by pressing Y= and going through the steps above to

enter the desired function opposite Y1, for example. Enter "X" as the argument and press GRAPH to

display the graph of the function.

**5.
Graphing Parametric Equations:
**Suppose that an object has been launched with an
initial velocity of 50 m/s at an angle of 30 degrees. Graph the trajectory

and determine the maximum height and range.

a) Press MODE and highlight PAR in the fourth line and press ENTER.

b) Press Y= to go to the graphing screen and enter 50cos(30)T opposite X

c) Press WINDOW and set Tmin = 0, Tmax = 6, Tstep = .1, Xmin=0, Xmax=250, Ymin=-2, and Ymax=250. Set the scales at 10 or

whatever value you wish. Press Graph to graph the trajectory. The setting of Tmax is not critical, but if it is too long, the graph may

take a long time to complete, and if it is too short, the graph will not be extended to the x-axis.

d) Press TRACE and move the cursor to the maximum as indicated by the y-values at the bottom of the screen. Do the same for

the point where the graph crosses the x-axis to get the range.

f) You can find the velocity and the component velocities at any point as follows: Press 2ND, CALC, press the number for the component

( dy/dx, dy/dt, dx/dt) you want. Now, move the cursor to the point on graph where you want the value and press ENTER.

**VI. CALCULUS
**

a) Press the Math key.

b) Press 8 to select nDeriv(.

c) Press 2

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 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 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 the 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. (NOTE:
Be careful about curves that go below the x-axis.)

k) To clear the
shaded area, press 2ND, DRAW, ENTER.

**VII. MATRICES**:

**1) Entering a matrix:
** a) Press
2

b) Move the cursor to the matrix number you want to edit or enter numbers into

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

**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
2nd, MATRIX, select the matrix you want as the first
in the product, [A],

and press ENTER.

c) Press the multiply symbol.

d) Press
2nd, 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 2nd, MATRIX and cursor over to MATH. There you
will see a list of

operations that you can do. To do find the determinant, use Det. To find

the transpose, use T.

b) After you select the operation you want, press ENTER.

c) Press 2nd, MATRIX, select the matrix you want to operate
on, and press

ENTER.

d) Press ENTER again to get your answer.

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 doing row operations. 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 doing 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.

**4) Doing rref and ref:**

a) First enter your
matrix as in item 1 of this section and press 2nd, QUIT to go to the home

screen.

b) Press 2nd, MATRIX, and move the cursor to MATH.

c) Select item A for ref
or B for rref as you choose and press ENTER. Note that if you know you

want to use item B or A(for rref or ref) just press ALPHA; then the appropriate
letter.

d) Press 2nd, MATRIX and
press the number for the matrix you want to operate on. You should now

have displayed on the home screen rref(A, or the letter for whatever matrix you
have chosen.

e) If you want
non-integer answers to be displayed in fractions skip to the next step. If
you want them

displayed in decimals, press ENTER and the
answer will appear.

f) If you want the
answer in fractions, and press MATH, ENTER and rref([A]►Frac
will be displayed

on the home screen. Press ENTER to display the answer. .

**5)
Solving a system of linear equations: **

Let's take the following set of simple equations:

3x -3y = -2

2x +y = 1

Entering the matrix:

a) Press
2^{nd}, MATRIX, move the cursor to EDIT.

b) Move the cursor to the
matrix (A, B, etc) that you want to edit or
enter numbers in,

and press ENTER.
(Alternatively, you can press the number opposite the matrix you choose.)

c) Enter 2 for the number of rows and press ENTER;
then enter 3 for the number of

columns and press ENTER again.

d) Enter each value of the matrix and press ENTER after
each value. Enter only the coefficients of the

variables and the constants. Do NOT enter variables, or plus signs, but do
enter a negative sign for either

a
negative or minus sign.

Enter the numbers 3, -3, -2, 2, 1, 1 and press ENTER after each number.

e) When you have finished, press 2^{nd},
QUIT to go to the home screen.

Solving the system of equations using the rref
operation:

f) From the home
screen, press 2nd, MATRIX, and move the cursor to MATH.

g) Select item B for rref
and press ENTER. Alternatively, you can press ALPHA; then B to paste
rref(

to
the home screen.

h) Press 2nd, MATRIX and
press the number for the matrix you want to solve, for example 1 for [A].

i) If you want the
answer in fractions, press MATH, ENTER, ENTER, otherwise, just press ENTER and

the
answer will appear.

**6)
Solving linear programming problems using the simplex method.**

You will need a program for this. You
can either copy one of my simplex programs from this

website and enter it by hand or copy
someone else's program. STCC students may call me at

333-5989 to arrange to have this program
transferred electronically to their calculator.

VIII. SEQUENCES:

**1) Find the first four terms of the sequence a _{n} =3n-2.**

a) Press 2nd, LIST, cursor over to OPS and press 5. seq( will be pasted to the home screen.

b) Enter 3; ALPHA; N; - ;2;, :ALPHA; N;, ; 1;, ;4 You now should have seq(3N-2, N, 1,4 on the

home screen. (It is not necessary to close the parentheses in this situation.) (Note that

the second "N" is just defining the variable that you want to use.)

c) Press ENTER and {1 4 7 10} will be displayed.

**
2) Find the sum of the sequence above.**

This type problem will
usually be written using the summation symbol, Σ.

a) Press 2nd, LIST; cursor over to MATH and press 5.

b) Press 2nd, LIST, cursor over to OPS and press 5. sum(seq(
will now appear on the

home screen.

c) Enter 3; ALPHA; N; -;2;, ;ALPHA; N;, ; 1;, ;4 You now should have
sum(seq(3N-2, N, 1,4

displayed on the home screen.

d) Press ENTER and 22 will be displayed.

**3) Find the cumulative sum of the above sequence.**

a) Press 2nd, LIST; cursor over to OPS and press 6.

b) Press 2nd, LIST, cursor over to OPS and press 5. cumSum(seq( will
now appear on the

home screen.

c) Enter 3; ALPHA; N; -;ALPHA; N;, ; 1;, ;4 You now should have
cumSum(seq(3N-2, N, 1,4.

d) Press ENTER and {1 5 12 22} will be displayed. Note that this method gives the
sum after each

increment of the variable N.

e) If you have a long list, you can store the results in list L_{1}
by closing the parentheses, pressing

STO, 2ND, L_{1}. You should now have cumSum(seq(3N-2, N, 1,4))→L_{1}.

f) Press ENTER and the list of numbers will be stored in list L_{1}.
You can access the list by pressing

STAT, ENTER

**4) Find the 5th term of
the above sequence.**

Although this is easily done by hand, some students like to check their results. So here's how to

do it with your
calculator.

a) Press 2nd, LIST, cursor over to OPS and press 5. seq( will be
pasted to the home screen.

b) Enter 3; ALPHA; N; -;2;ALPHA; N;, ; 5;, ;5 You now should have
seq(3N-2, N, 5,5 on the

home screen. (Note that the same number is entered for the beginning
and end.)

c) Press ENTER and {13} will be displayed.

**IX. Complex Numbers:**

**
1. Finding Solutions of a Polynomial with Complex
Coefficients:****
**Since the
solver will not handle complex numbers, we must resort to other methods. Let's
consider the equation

(2-3i)x² +(4+i)x +(1-3i) = 0.

a) Press MODE, cursor to FLOAT, move over to highlight 5, and press ENTER; then move down to the 7th line

and highlight a+bi and press ENTER. Press 2ND, QUIT to go back to the home screen.

b) Press 2, -, 3, 2ND, i (the second function of the decimal point), STO, ALPHA, A, ENTER. This stores the

coefficient of x² in variable "a."

c) Perform the same operation for the b, and c, the coefficient of x and the constant.

d) Now, press 2ND, √, ALPHA, B, x

in variable d. You can write this result down if you want it.

e) Press (, - (negative sign) , ALPHA, B, +, ALPHA, D, ), ÷, (, 2, ALPHA, A, ), ENTER. The first value for "x" will

be displayed.

f) Press 2ND, ENTRY (the ENTER key), and change the "+" sign between B and D to -.

g) Press ENTER and the second value for "x" will be displayed.

NOTE: You may want to change your number format back to Float.

:a + bi

:Fix 5

: Prompt A, B, C

: √(B² -4AC)→D

: ClrHome

:Disp "X1=", (-B+4AC)/(2A)

:Disp "X2=", (-B-4AC)/2A

: Float (This last step sets the calculator number format to Float. If you don't want that, leave it out.)

**X. Combining and Connecting Operations:**

**1) Doing expressions with several terms:
**One of the powerful tools for use
with a calculator is combining terms and connecting terms to perform

several operations sequentially. Let's take for example the index of Shannon which is used in ecological

assessments. This is the expression:

H' = -Σ(p

This table represents the equation as applied to four different types, i, of trees found in 100 m² of forest.

i | N_{i} |
p_{i} |
ln (p_{i}) |
p_{i}*ln(p_{i}) |

1 | 6 | .3 | -1.2034 | -.3612 |

2 | 4 | .2 | -1.6094 | -.3219 |

3 | 2 | .1 | -2.3026 | -.2303 |

4 | 8 | .4 | -0.9163 | -3.665 |

SUM | 20 | -1.27985 |

**Solving with lists:
NOTE: **If you get a dimension error in any of the following operations,
you will need to dimension the lists. You

can do that by just adding zeros of the same quantity as the numbers in List L

can use the dimension statement. Example: 10→dim(L

lists L

b) Place the cursor on the title for L

The expression L

c) Move the cursor to the L

d) Set the cursor on the L

numbers except SUM to make sure they are correct.

e) To get the final sum, press 2nd, QUIT to leave the lists, then press the (-) key.

f) Press 2nd, LIST, MATH, 5 ( for sum), 2nd, L

table above.

The values for N

as follows:

a) First clear the five lists by pressing STAT, 4 to paste ClrList to the home screen.

b) Then enter the five lists by pressing 2ND; then the key for the list number for each list to be cleared.

The list names should be separated by commas.

c) Enter the values for i in L

d) Now press 2ND, QUIT to go to the home screen.

e) Enter the following on the home screen: L

is entered by pressing 2ND, LIST, MATH, 5 and the colons are entered by pressing ALPHA, and the decimal

point button.

f) Press ENTER and all of the data in the table above will be entered in the lists except the sum and that will be

displayed on the home screen.

a) After clearing the lists and entering the data as in steps a through d above, enter this formula:

-sum((L

obtained by pressing 2ND, LIST, MATH, 5. Be careful that you have the parentheses correct.

XI. Operations with
List:

Arithmetic with lists is a very powerful tool
for saving time, especially when doing statistics. For a complete
treatment

of list arithmetic as applied to
statistics, see the statistics guide on this same website.

1) Clearing a list:

To clear a
list, place the cursor on the title of the list, for example L_{1}, and
press CLEAR, then

enter.

**2) Doing Arithmetic with Lists:
**The
normal arithmetic operations (-,+,x,÷,
√, and square), can be done by placing the cursor on the list title

and entering the desired arithmetic operation involving one or more lists. The columns in the reference

lists will be operated on item by item and stored in the list where the cursor is located. Note that you can do the sum of

of a list at the end of the items in a list if you wish.

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.

a) Press STAT, ENTER and enter the proper combination of 1s and 0s for p in list L

c) Clear L

d) Now press 2ND, L

e) Press ENTER. The entries in the first row in the tables will be evaluated and stored in L

Obviously, you can also use the other logic operations in place of "and." Also, you can do a longer

logic expression by using the results in one list with a set of truth values in another list.

XII. **Special Techniques:
1) Graphing equations of the form x=y² +3x
+2:
**

a) Press MODE, scroll down to highlight PAR in the fourth row and press ENTER. Press 2nd QUIT to exit

the MODE function.

b) Press Y= and enter T² + 3T +2 opposite X

c) Press ENTER and the parametric graph will be displayed.

Note that TRACE is operative in this move, but that Minimum, Maximum, Zero and other functions associated

with the function mode are not operative.

the function mode.

a) With the calculator in the normal function mode, re-write the equation as y=x²+3x +2.

b) Enter the right part of the equation opposite Y1= and graph as usual.

c) All of the functions are available as usual, but you must switch the values for x and y if you are going to do any

graphing by hand or use the values in any other way. .

d) If you want to see what the curve actually looks like, then draw the curve as follows:

1) Press 2nd, DRAW, scroll down to DrawInv, and press ENTER.

2) Press VARS, move the cursor to Y-VARS and press ENTER, ENTER. You should have DrawInv Y1 on the home

Screen.

3) Press ENTER and the function will be drawn. Notice that none of the functions are operative. Then general

trace can be used, however.

XIII. TRANSFERRING PROGRAMS AND DATA:

**1)
Transferring programs between calculators for TI-83
Plus:**

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.

**2) Writing a program on a
computer for a TI-84 calculator:**

Well, there may be more
than one way to do it, but here's the way I do it. First you must have the
Graph Link software for

the TI-83 Plus calculator.
That can be downloaded free from the TI Website. Once you get that installed, just click on the icon

and the application will
open. It's pretty straightforward from that
point. I suggest you save the file to a folder that you will

use to
transfer the program to your calculator. I will deal
with that transfer in the next FAQ.

________________________

**3) Copying a program from my computer to my TI-84 calculator:
** Here's the way I do
it.

a. Open TI-Connect and connect the calculator to the computer with the USB cable.

b. Click on the TI-Device Explorer icon.

c. Open the folder where the program you want to copy to the calculator is stored.

d. Drag that file to the TI-Device Explorer folder.

e. Copying of the file will begin in a half minute or so.

_______________________________

a. Open TI-Connect and connect the calculator to the computer with the USB cable.

Make sure the calculator is on.

b. Click on the TI-Device Explorer icon.

c. After the connection to the calculator is established and the list is displayed, expand Program by

clicking on the + mark beside “Program.”

d. Highlight the program that you want to copy to the computer.

e. Click on the File menu and select Copy to PC.

f. The folder "My Documents" will appear with the folders listed. Select the folder where you want to store the program and

open it.

g. Copying the file will begin shortly.

**XIV. Applications:
1. Conversion Application:
**

go to the menu for the unit converter.

b) Press 2 for the UNIT CONVERTER. You will notice twelve items on the menu and a

CONSTANT function at the bottom of the screen. Pressing Y= or WINDOW toggles

between constants and conversions.

As an example, suppose you want to convert quarts to liters.

a) Select 3 for volume from the CONVERSION menu and move the cursor to highlight

qt. If you only want the conversion, press 1, but if you want to convert, say, 4 quarts

to liters, press 4. In this example, we’ll convert 4. So, press 4.

b) Press ENTER and the 4E0 qt► will be displayed on the screen.

c) Move the cursor to highlight “L “ and press ENTER. The conversion 3.785412E0 L

will be displayed on the screen.

a) If you want to export the conversion to the home screen for other calculations, press ZOOM for EXPT.

b) Now, you must press 2

be taken to the home screen.

Suppose we want to convert the gravitational constant from its normal dimensions of m/s² to ft/s²

a) If CONSTANT is not already selected, select it by pressing Y=.

b) Move the cursor to highlight “g” and the value in m/s² will be displayed.

c) Press TRACE for COPY to display the CONVERSION menu, then press 1 for

LENGTH.

d) Highlight “m” as the unit to convert from and press ENTER, then highlight “ft” and the unit to convert to.

Finally, press ENTER. The value 3.217405E1 will be displayed.

XV. PROBLEMS:

**1)
Problems with trigonometric functions: ** The most common problem with trig
functions is not having the MODE

set 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.

**2) Dim Mismatch: **This occurs when doing operations on lists
that do not have the same number of entries or when doing arithmetic on

matrices that do not have the same number of rows or columns. To correct
that, make sure you have the correct number of entries. It can

also occur when graphing if you have one of the plots highlighted and the number of data points
in the x-and y-lists do not match. To correct

that, just move the cursor
to the plot entry, Plot1, Plot 2, etc, and press ENTER to remove the highlight from
the plot entry.

**3) 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:

a) Press 2^{nd}, MEM, press 3.

b)
Press 7 to select RESET.

c) Press 2 to select Defaults. Your calculator should now be reset.

**
Copy Restrictions:
**You
may make single copies of this document for your own personal use and for the
use of other students, but inclusion in another document, publication or any use
for profit requires my permission. Teachers may make multiple copies of this
document for their students if they first get permission from me. Merely send
me an email (Just click on Webmaster in the navigation bar.) with a one-sentence
explanation of what you’re using the document for. I’ll give you permission in
a timely manner.

**
Making it Better****: **I
would be grateful if you would report any errors or suggestions for improvements
to me. Just click "E-mail Webmaster," site the item number, and tell me
your suggested change.

**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 printed pages.

Released: 3/15/11

Last Revised: