TI-84

General Use

Home Screen Use

Scroll Previous Values

  • left and right arrows
  • ENTRY (repeat for earlier value)

Use colon for multiple statements:

8\rightarrowR : \pi R^2
  • Last answer is stored in ANS
  • Use X,T,\theta,n for a shortcut to X etc. depending on context

Searching for Functions and Instructions

  1. CATALOG
  2. scroll or use A-LOCK then <first letter of the function>
  3. ENTER

Variables

  • VARS to access different variables and settings

Types of Variables

  • Real, complex, numbers: $A, B, \dots, Z, \theta$
  • Matrices: $[A], [B], [C], \dots, [J]$
  • Lists: $L1, L2, L3, L4, L5, L6, \text{ and user-defined names}$
  • Functions: $Y1, Y2, \dots, Y9, Y0$
  • Parametric equations: $X1T$ and $Y1T$, $\dots$, $X6T$ and $Y6T$
  • Polar equations: $r1$, $\dots$, $r6$

Store (assign) value to a Variable

  1. Enter context appropriate expression or value
  2. STO
  3. <variable identifier>
  4. ENTER
  • List expression: {1, 2, ..., n}
  • Matrix expression (3 x 2): [[1,2][3,4][5,6]]
  • Function: "<expression>" (note it must be in double quotes e.g "x^2")

Load Variable with RCL

  • <letter of variable>
  • LIST or L_n
  • MATRIX
  • VARS

Graphing a Function

Graph a Function

  1. Set MODE to FUNC
  2. Y=
  3. Enter the function
  4. GRAPH

Graph Parametric Functions

  1. MODE
  2. Select PAR
  3. Select RADIAN
  4. Y=
  5. Enter the functions
  6. GRAPH

Graph Polar Equations

  1. MODE
  2. Select POLAR
  3. Select RADIAN
  4. Y=
  5. Enter the function
  6. GRAPH

Toggle Visibility

  1. Y=
  2. A = with solid background means the function is graphed

Compose functions

  1. Y=
  2. F4 select the desired function(s)

Menus

F1

  • Fraction Templates

F2

  • Function Shortcuts

F3

  • Edit Matrices

F4

  • Insert Y-Vars

ANGLE

  • for angle problems

Convert to degrees, minutes, seconds

  1. DMS
  • Convert degrees to radians with ^\circ<n> in radian mode
  • Convert radians to degrees with r in degree mode

CALC

  • Solve problems related to a function

Solve for $x$

  1. value

Find a zero (x-intercept)

  1. zero
  2. Select the left boundary
  3. Select the right boundary
  4. Provide a guess to speed things up

Find a maximum

  1. maximum
  2. Select the left boundary
  3. Select the right boundary
  4. Provide a guess to speed things up

Find a maximum

  1. minimum
  2. Select the left boundary
  3. Select the right boundary
  4. Provide a guess to speed things up

DRAW

Draw inverse of a graph

  1. DrawInv
  2. F4
  3. Insert the appropriate function

Draw Horizontal Line

  1. Horizontal

Draw Vertical Line

  1. Vertical

Draw Tangent Line

  1. Tangent(<Y-function>, <x-value>)

Draw a Line Segment

  1. Line(<x1>, <y1>, <x2>, <y2>)

When on the current graph you can draw a tangent

FORMAT

Change the graph format

MATH

MATH

  • Frac - input a fraction
  • Dec - to convert to decimal
  • input roots other than $2$
  • logBase - input logarithm with different base

Compute the Derivative

The interface is different on the calculator, but the order of the arguments is the same.

  • nDeriv(<var to use>, <equation>, <x-value>)
  • nDeriv(X, Y1, X) - computes $\frac{d}{dx}(Y_1(X))$, use in Y= to graph the derivative
  • nDeriv(X, Y1, 2) - computes $\frac{d}{dx}(Y_1(2))$

Compute an Integral

The interface is different on the calculator, but the order of the arguments is the same.

  • fnInt(<lower limit>, <upper limit>, <function>, <variable of integration>)
  • fnInt(0, 5, Y1, X) compute $\int_0^5 Y_1 dx$

Compute an Indefinite Integral

  • Setup the equation such that X is the upper bound, 0 is the lower bound, the function is in terms of X, and differentiate in terms of X

For example, f(x) = x^2:

$$ \int_0^x (x^2) dx $$
  • This should be equivalent to derivative, in this case X^3/3

NUM

  • abs( - absolute value
  • round( - with (x, n) round x to n places
  • lcm( - with (a, b) find least common multiple
  • gcd( - with (a, b) find greatest common denominator
  • remainder( - with (x, y) get remainder of x/y
  • n/d Un/d - convert from improper fraction/mixed number to the other
  • F D - convert from decimal/fraction to the other
  • n/d - input a fraction
  • Un/d - input an improper fraction

PRB

Probability operations

  • nPr - permutations, with 52 nPr 2 find 2-permutations from set of 52 (e.g. different ways of pairing 2 cards from a deck of cards)
  • nCr - combinations, with 52 nCr 2 find 2-combinations from set of 52 (e.g. combinations of 2 cards from a deck of cards)
  • ! - factorial operator n! find “n factorial”

MEM

Reset RAM (resets all variables):

  1. MEM
  2. RESET
  3. ALL RAM

MODE

  • change Radians v. Degrees

SOLVER

Solve for unknown variables with SOLVER:

  1. SOLVER
  2. Enter the equation such that the equation equals $0$ e.g. $0=mx + b - y$ for $y = mx + b$ or for a stored function $Y_1 - Y$
  3. Enter desired values for variables.
  4. Provide a range to guess in by setting BOUND.
  5. Select the variable to solve for
  6. SOLVE.

TABLE

Adjust characteristics of a table

  1. TBLSET
  2. use TblStart to adjust starting value for $x$
  3. use Tbl to adjust the increment/decrement from each $x$ to the next
  4. Setting Indpnt: to Ask allows the $x$ value to be provided by user.
  5. Setting Depend: to Ask requires the user to press ENTER to populate a field.

TRACE

  1. use \leftarrow and \rightarrow to move cursor along the graph
  2. ENTER to center graph on trace cursor

WINDOW

adjust graph characteristics

  • Xmin - left-most $x$ value
  • Xmax - right-most $x$ value
  • Xscl - distance between $x$ tick marks
  • Ymin - left-most $y$ value
  • Ymax - right-most $y$ value
  • Yscl - distance between $y$ tick marks

ZOOM

Make zoom adjustments to the graph

  • ZBox - draw box to zoom in on
  • ZStandard - Sets standard window variables
  • ZTrig - Sets trig window variables
  • ZoomFit - fits YMin and YMax between XMin and XMax

TRACE

  • Type in a value to trace from that value

MATRIX

Assign a matrix

Solve a system of linear Equations

  • uses reduced rho echelon form

Given the system of equations:

$$ A + C = 5\\ -6A + B = -7\\ -6B + 3C = 9 $$

First, we make this more matrix-like (note that the ordering is consistent for each):

$$ A + B(0) + C = 5\\ -6A + B + C(0) = -7\\ A(0) + (-6B) + 3C = 9 $$

Now, create a matrix in which the number of rows is equal to the number of equations, and the number of columns is equal to the number of terms in a given equation e.g. a $3 \times 4$ matrix. The first three columns are the coefficients on each of the left-hand side terms. Tha last column is the term on the right side.

$$ \begin{bmatrix} 1 & 0 & 1 & 5\\ -6 & 1 & 0 -7\\ 0 & -6 & 3 & 9 \end{bmatrix} $$

Now, we can solve with

  1. MATRIX
  2. MATH
  3. rref(

If the matrix is in A, setup the expression so that it is rref([A]) and press enter.

The result contains the answers in the fourth column. If these are decimals, use Frac get them as fractions.

Find the Inverse

Take your matrix $n \times n$ $\mathbf{A}$ and make a new $n \times 2n$ matrix such that the left side is $\mathbf{A}$ and the right side is $\mathbf{I}_n$.

Use RREF( to reduce the matrix. This will cause the inverse to show up on the right side. of the matrix.

STAT

Statistical analysis and list editing

CALC

1-VAR Stats

  • gives some stats

EDIT

  • edit lists with Edit

DISTR

normalcdf()

Normal cumulative distribution function

normalcdf(lower_bound, upper_bound, mean, standard_deviation) gives you P(lower_bound < X < upper_bound) for normal distribution with the mean and standard deviation provided.

binompdf()

Binomial probability distribution function

binompdf(t, p, x) give probability of x successes in t trials where probability of success is p

binomcdf()

Binomial cumulative distribution function

binomcdf(b, p, t) gives you probability <= b successes given a probability of success of p and t trials

geometcdf()

geometcdf(p, t) gives you probability of success in <= t trials given a probability of success p

LIST

Insert lists and perform operations on lists.

Create a list of elements from the range of a function (i.e. results of a function):

  1. OPS
  2. seq(
  • Expr is the function
  • Variable is independent variable e.g. X
  • start: is start value from domain
  • end: is end value from domain
  • step: distance between $x_1$ to $x_2$
  • Paste will paste command which can then be executed
  1. At the homescreen STO, then L1 or the desired list to store the list

MATH

Statistical functions and more…

  • min(
  • max(
  • mean(
  • median(
  • sum(
  • stDdev(
  • variance

Misc

Newton’s Method

  1. Type in $f(x)$ in Y1
  2. Type in $f'(x)$ in Y2
  3. Type in $x_0$ and press ENTER to store in ANS
  4. Type in ANS,STO, :, X-Y1/Y3
  5. Press ENTER to perform the next iteration

Riemann Sums

  1. Create the function with Y=
  2. MATH
  3. summation...

Programming

Program with PRGM

  1. NEW to create new program

Prompt for input

  1. PRGM
  2. I/O
  3. Prompt
  4. `

Create a Menu

Menu("Title", "Option1", LABEL1)
LABEL1
"Do something"
Stop

Use LIST to access list variables and list functions.

  • the L operator with variable name is required in some contexts

Combine lists:

  1. OPS
  2. `augment(L1, L2)

Add number to end of list:

  1. 1->L1(1+dim(L1))

If and Then

Simple single line

If (<condition>)
<command>

Multiple statements

If (<condition>)
Then
<commands>
End

If (<condition>)
Then
<commands>
Else
<commands>
End

Pause the program with Pause

  • Pause 1 - displays 1

Wait until user presses any key.

Repeat getKey
End
  • TblInput - a 7-element list of the values of a variable in the table.