TI-84 Plus quick reference

See also the generic guide on graphing calculators in AA.

This is an overview of essential features for the IB Analysis and Approaches course on the TI-84 Plus (CE) family of calculators, so that you are aware of general capabilities. It is assumed that you already know the very basics of your TI-84 Plus. For detailed instructions, refer to the official manual for your model.

This is text on calculator screen. This is a TI-84 BUTTON

General
Mode
PolySmlt
Functions and graphing
Draw
Lists
- grouped data and discrete random variables
- regression
Distributions
Calculus
Finance

General

action	buttons
home screen	2ND QUIT MODE
reset gdc	2ND MEM " +
get function name	A‑LOCK ALPHA CALC F4 TRACE or DISTR VARS `Y-VARS`
get list 1	2ND L1 Y 1
equation solver	TEST A MATH [UP]
solve	A‑LOCK ALPHA ENTRY SOLVE ENTER
save value to `A`	RCL X STO> A‑LOCK ALPHA TEST A MATH
use value in `A`	A‑LOCK ALPHA TEST A MATH
copy/paste expression	2ND ENTRY SOLVE ENTER
change to insert	2ND INS DEL
many commands per line	A‑LOCK ALPHA 𝑖 ︰ •
$\times 10^{n}$	2ND EE J ❟
$\binom nr, n!,$ etc.	TEST A MATH `PROB`
complex numbers (HL)	TEST A MATH `CPX`

Expressions are by default in overwrite mode (blinking box). Insert mode (blinking underscore) means add before the blinking character.

The pasted expression is evaluated using the latest values. It is for the entire line, so it does not work in conjunction with the colon-separated multiple commands in a single line.

Mode

After each calculator reset, use QUIT MODE to make the following changes.

Switch from RADIAN TO DEGREE and first solve all questions involving degrees, before switching back to RADIAN for rest of the questions.
Switch from CONNECTED to DOT for faster graphing. In addition, or alternatively, in TBLSET F2 WINDOW, set Xres=3 to triple the graphing speed. Unfortunately Xres may revert back to 1 when the zoom is changed.

On the second page of MODE

Switch from MATHPRINT to CLASSIC to get expressions to wrap. MATHPRINT involves fewer parentheses but for longer expressions it can be more difficult to debug.
Turn on STAT DIAGNOSTICS.

The rest of the guide assumes these settings.

PolySmlt

This polynomial root finder and simultaneous (linear) equation solver is allowed on IB exams. You can download it from Texas Instrument website . An alternative version is available from this other TI download link. .

Functions and graphing

Reminder that in many circumstances, vertical asymptotes appear as though the graph is connected. Though in such cases, the calculator often draws the vertical asymptote as well.

show/hide functions

In STAT PLOT F1 Y=, use arrow keys to highlight the = and ENTRY SOLVE ENTER to toggle showing and hiding the graph.

change function line style or graph inequality

In STAT PLOT F1 Y=, use arrow keys to highlight the line left of Y1 and ENTRY SOLVE ENTER to rotate through available line styles including solid, thick solid, dotted, shade above, shade below, among others.

zooms

When plotting, it is best to hide the irrelevant functions and only graph a single function at once. Either enter the given domain or an estimate as Xmin and Xmax in TBLSET F2 WINDOW. Then select FORMAT F3 ZOOM 0:ZoomFit. It works by including the max/min of the current Xmin and Xmax. When you have no idea what to set for the domain, it is useful to first see the table of values via 2ND TABLE F5 GRAPH.

2:Zoom In and 3:Zoom Out uses the zoom factors set in Memory tab under 4:SetFactors. Default is 4 for both directions.

curve calculations

Zeros of polynomials are best solved using the PolySmlt app.

Otherwise, 2ND CALC F4 TRACE can find value, zero, min/max, intersections of two functions, numerical derivative, and definite integrals.

Instead of solving intersections of Y1(X) and Y2(X) it is often easier to find the zeros of Y1(X)-Y2(X). ZoomFit works better for zeros than intersections.

$x$ value of the zero, intersection, min/max is stored in X, which can be accessed either from link X,T,θ,n or A‑LOCK ALPHA RCL X STO>. Similarly the $y$ value is stored in A‑LOCK ALPHA L1 Y 1.

reciprocal function

The reciprocal function of Y1 is Y1(X)⁻¹.

not inverses and not squares

For this calculator only: Y1⁻¹(X) means $\displaystyle\frac{x}{y_1(x)}$ ; Y1²(X) means ${x\cdot y_1^2(x)}$ .

For graphing inverse relations, see Draw below.

evaluate a function over many values

Define the function in Y1. List the values in L1. Go over to L2, up arrow, to define L2 as Y1(L1).

Alternatively, 2ND TABLE F5 GRAPH can generate a table over integer values of X.

table of values / solve over integers

Solver is useless when solving over integers (eg when involving the factorial). Instead, use 2ND TABLE F5 GRAPH to generate a table of values.

Example In the expansion of

\left(2x + \frac{3}{10}\right)^{40}

find the lowest degree term whose coefficient exceeds $10^5$ .

Using binomial expansion, we want to find the lowest integer $k$ such that

\binom{40}k 2^k \left(\frac{3}{10}\right)^{40-k} \geq 10^5

Using TEST A MATH PRB tab 3:nCr, define

Y1=40 nCr X2^X0.3^(40−X)

(same as Y1=40 nCr X*2^X*0.3^(40−X))

2ND TABLE F5 GRAPH

to see that when X=19, Y1=719984 which is the first value to exceed $10^5$ .

The desired term is $719984x^{19}\qed$

piecewise functions

Graphing piecewise functions require inequality comparison operators under 2ND TEST A MATH. For a finite interval, use the and operator in the LOGIC tab.

Example: Graph

f(x) = \begin{cases} \sin x & \text{if } x < 0 \\ x & \text{if } 0 \leq x < 2 \\ e^{x-2} + 1 & \text{if } x \geq 2 \end{cases}

Y1=sin(X)(X<0)+X(0≤X and X<2)+(e^(X-2)+1)(X≥2)

The graph should be continuous and look like three pieces of sinusoidal, linear, and exponential functions respectively.

Each piece is multiplied by some inequality in parentheses. Surround each piece in parentheses as well if necessary (due to order of operations). 0≤X<2 is not accepted.

Draw

The draw menu constructs non-interactive sketches using 2ND DRAW C PRGM. In other words, calculations are not possible with drawings. Useful features include drawing lines including vertical lines, tangent lines, inverse relations; and shading areas between curves.

Example Sketch $y^3 - 3y^2 + y + 1 = 2x,\, -4\leq x\leq4$ .

Define Y1=0.5*(X^3-3X^2+X+1). Hide this function (for faster graphing). Go to TBLSET F2 WINDOW and set Xmin and Ymin to -4 and Xmax and Ymax to 4.

Under the draw menu, use the eighth option and enter DrawInv Y1.

Note that drawings are often erased after some zoom or window changes. Drawings can be persisted using the STO tab in the draw menu.

Lists

A list is a column of values. They are typically used in statistics, but can also be used for sequences with an explicit formula (as opposed to recursive formulas).

Lists are defined using LIST STAT 1:EDIT. Use 2ND alongside numbers 1 through 6 for L1 to L6.

grouped data and discrete random variables

Both grouped data and discrete random variables are analyzed using 1-Var Stats.

Here is an example using discrete random variable. For grouped data, L1 has the mid-interval values, and L2 has the frequencies.

Example: (Adapted from 2021 IB SPEC papers HL P2 Q6 to suit SL) Given some discrete random variable

$x$	$\mathrm P(X=x)$
1	0.60
2	0.30
3	0.03
4	0.05
5	0.02

Find $\mathrm E(X)$ and $\mathrm{Var}(X)$ .

Store $x$ values in L1, and the corresponding probabilities L2.

Using LIST STAT CALC then 1:1-Var Stats.

Set List:L1 and FreqList:L2. Calculate.

The expected value is ̅x, and the variance is the square of σx, the standard deviation.

\mathrm E(X) = 1.59 \qed

\mathrm{Var}(X) = (0.91755\dots)^2 \approx 0.842 \qed

regression

Example: (Adapted from 2021 IB SPEC papers HL P2 Q4, SL P2 Q5) Given a table of values

x	y
15	20
23	26
25	27
30	32
34	35
34	37
40	35

a) Write down

i. the regression line of y on x;

ii. the regression line of x on y.

b) Find the intersection of these two regression lines.

c) Estimate $x$ when $y = 29$ .

a) In L1 input the x values, and the y values in L2.

i. LIST STAT CALC > 4:LinReg(ax+b). Set Store RegEQ to Y1 using DISTR VARS Y-VARS > Y1. Calculate.

STAT PLOT F1 Y= should show

Y1=.6999... X + 10.1876...

$y = 0.700x + 10.2 \qed$

ii. For $x$ on $y$ regression, enter L2 as XList and L1 as YList. Save to Y2. Calculate. You should obtain

Y2=1.2908... X + - 10.379 ...

$x = 1.29y - 10.4 \qed$

b) The intersection of these two regression lines is $(\bar x, \bar y)$ , ie the components are the arithmetic means.

Using LIST STAT CALC then 2:2-Var Stats with XList:L1 and YList:L2, we obtain

(\bar{x},\bar{y}) \approx (28.7, 30.3)\qed

If you instead solved the system of equations, you would need to keep 5 sig figs to obtain the correct point to 3 sig figs.

c) To estimate $x$ , we use the $x$ on $y$ regression line stored in Y2.

Y2(29) returns 27.0546... or $27.1\qed$ .

It was not necessary to store the $y$ on $x$ regression line. But it’s a good habit in case we needed it.

Distributions

Normal and binomial distributions are in 2ND DISTR VARS. Assume N is a normally distributed random variable, and B is a binomially distributed random variable. Here are common built in functions

command	returns
`2:normalcdf(`	$\mathrm P(a < N < b)$
`3:invNorm(`	$n$ such that $\mathrm P(N < n) = p$
`A:binompdf(`	$\mathrm P(B = b)$
`B:binomcdf(`	$\mathrm P(0 \leq B \leq b)$

In particular, TI-84 Plus does not allow for calculating sum of binomial probabilities over an interval that does not include $B=0$ .

Calculus

Derivatives and definite integrals are more easily inputted using MATHPRINT mode.

Use TEST A MATH options 8:nDeriv( and 9:fnInt( provide numerical derivatives and definite integrals. Functions are returned when you use X=X for the numerical derivative, or set a limit of integration to X when integrating.

Example Solve for $a$ .

\int_e^a \frac{e^x}{\ln x}\d x = 100,\, a > 0

Define Y1= $\displaystyle \int_e^X \frac{e^X}{\ln X}\d X$

Using Y1, solve Y1(X)=100 using solver or functions.

Note: Do not in your IA or exams write an integral with same variable in both the integrand the the limits of integration.

Because indefinite integrals are expensive to graph, it is better to use solver. If you have to graph a definite integral, best to manually set Xmax to be within 2 or 3 of Xmin.

Solving 0=Y1(X)−100 using solver with initial guess 4 yields

$a \approx 4.26\qed$

Finance

The Finance app is available via ANGLE B APPS

The TVM Solver can be used for compound interest, appreciation, depreciation and/or inflation problems. However, it is intended for annuities, eg mortgage payments, so some care is needed to adapt it for compound interest purposes.

In particular in the TVM Solver, use negative amounts for deposits, and positive amounts for withdrawals. This makes more sense in annuities which are beyond the scope of AA.

variable	description
`N`	number of payments
`I%`	annual interest rate
`PV`	present value (typically negative)
`PMT`	recurring deposit or withdraw (`0` in AA)
`FV`	future value (typically positive)
`P/Y`	payments per year
`C/Y`	compounding periods per year

Due to the sign differences, PV and FV are not fully interchangeable with the counterparts in the formula booklet.

Also, N depends on P/Y. For example

`P/Y`	`N`
`1`	number of years
`2`	number of half-years
`4`	number of quarters
`12`	number of months

Usually you want P/Y=1 for N in number of years.

To solve for an unknown, first enter all known values in 1:TVM Solver..., leaving 0 for the unknown. Then highlight the unknown field and A‑LOCK ALPHA ENTRY SOLVE ENTER to solve.