 Back That calculator you invested in for school and standardized tests is specifically designed to be really good at answering certain types of questions, if you know how to ask.

I wrote this to try to capture most of the useful TI-84 tools that I discuss with students frequently. It is not comprehensive and it is also a lot to digest. My hope is that if you find this article useful, you’ll pin it somewhere and look back at it as a reference or share it with a friend. If you learn better out loud, reach out and we can talk through these with more examples, focused on what you want to work on.

Before we get to the nitty gritty details of how to make your calculator work with you, there’s one more piece of advice I’d love for you to keep in mind:

Practice. I suggest that if you are taking a math class that doesn’t allow calculators on certain exams, still practice using your calculator on homework, not in place of doing the calculations by hand but to supplement what you’re learning. Really, do each question twice: first by hand and then on your graphing calculator. When you are allowed to use a calculator on an exam, you want that part of the process to be second nature. It also helps to connect functions with their graphs as you work with those functions symbolically. For equations, graph each side of the equation and see where the two intersect.

### Parentheses

Your calculator honors the PE(MD)(AS) order of operations.

#### Example

$$\frac{5+7}{14}$$ should be entered as

(5+7)/14

because 5+7/14 would evaluate the division before the addition and give you 5+2=7, not 0.85714286.

Sidenote: $$\frac{12}{14}=\frac{6}{7}$$ is a repeating decimal ($$0.\overline{857142}$$), and so your calculator will probably round after a few digits. If you want to see the fraction representation rather than this intimidating decimal, click [math] [enter] [enter]; the very first option under the first column under the [math] button is [>frac] which converts the output to a simplified fraction, if it can.

#### Example

$$\frac{6}{2*3}$$ should be entered as

6/(2*3)

because 6/2*3 would evaluate these equal precedent operations in order from left to right, so 6/2*3=3*3=9 instead of 6/(2*3)=6/6=1.

#### 3. Play it safe: “Erase and replace with parentheses!”

Any time you substitute in a value for a variable (especially a negative number), use parentheses as a habit to avoid common mixups.

#### Example

If you substitute x=-3 in for $$x^2$$, notice that $$-3^2=-3*3=-9$$ while $$(-3)^2=(-3)(-3)=9$$.

Sidenote: You can find the negative button near the bottom of your calculator. A negative is like an adjective while subtraction is like a verb that needs a subject and an object; if you use the subtraction button when you want a negative number, you’ll get a syntax error.

### Copy-Paste-Edit

In the homescreen, use the up arrow and highlight an expression that you want to copy and hit [enter] once.

Use the left and right arrows to highlight a character you would like to overwrite.

If you would like to insert a character, use the [2nd] [del = ins] option to toggle into insert mode. It will stay in insert mode until you use the arrows or hit [enter], at which point it defaults back to overwrite mode.

#### Calculus:

If you have functions in the [y=] window and you want to quickly access them to, for example, calculate a definite integral or the derivative at a specific value, you can access them with [alpha] [trace = f4].

### [Math]

If you’re reading this in order with your calculator in hand, then you’ve already used one of the most useful things under this button: converting rational numbers to reduced fractions.

I highly recommend playing around with the options under this button.

Under the MATH column, scroll up to find [A: logBASE(] which lets you set the base of a logarithm.

Under the NUM column, you’ll find things like the absolute value function (which can be used while graphing) and a least common multiple and greatest common divisor functions (these take two inputs at a time, separated by a comma which can be found to the left of the parentheses buttons).

Under CMPLX, you will find some operations that are specific to complex numbers.

Under PROB,
you can find permutations (2: nPr), combinations (3: nCr), and factorial (4: !).

Under FRAC, you can format rational numbers, but as long as you use parentheses effectively in your calculations, this column of options is more hassle than help.

In any menu, if you know the number of the option you want to select, you can press that number button rather than using the up or down arrow to scroll to that option. Some menus have more options than can display in a single window, so try using the up arrow to loop up and see the options near the bottom of a long menu.

#### Calculus:

Notice [8: nDeriv] and [9: fnInt(] under the MATH column under the [math] button; these aren’t symbolic solvers, so you’ll need to evaluate the derivative at a specific value or plug in bounds for your integral.

### Go Home

If you’re in a menu where you’re editing things and you need to stop editing that thing, use [2nd] [mode = quit] to get out of there and go back to the home screen.

### Graphing on Your Graphing Calculator

#### Inputting Functions: [y=]

When you want to input your independent variable, use the [$$X,T,\theta,n$$] button.

Use the left arrow to see some different options. You can deselect a function if you don’t want to clear it and you don’t want it graphing. You can also change the display to different inequalities or a dashed line.

#### Choosing a Window or Zoom Setting

[zoom]  will reset your window to -10 to 10 in both the x and y directions.

[zoom]  will use the xmin and xmax that you have set in your [window] and will set the ymin and ymax to fit the function in the window. This can be an efficient way to find a maximum or minimum y value over an interval of x values.

#### Calculating Values on the Graph

[trace] lets you scoot back and forth along a function with the left and right arrows and toggle between functions with the up and down arrows, but it isn’t ideal for calculating important points.

[2nd] [trace = calc] pulls up a menu of things you can calculate.

[1: value] lets you input an x value and get the corresponding y value. If you have more than one function displayed, use the up and down arrows to toggle between them.

[2: zero] lets you find an x-intercept aka root aka zero of the function. It will ask you to set a left bound, then a right bound, and then confirm that you want the calculator to try and estimate the root in between those bounds. If you need to switch functions, do so before locking in your left bound. You can use the left and right arrows to move to the x value that you want to set, or you can type in the x value to jump straight there.

[3: minimum] and [4: maximum] work like [2: zero] does and let you find the min or max y value over the interval that you set.

[5: intersect] will find the intersection nearest to where your cursor is when you make the selections, so if you need to find more than one intersection point, just do this process more than once and scroll near the one you want to find first.

The last two options are for calculus.

Piecewise:

[y=] [math], scroll up to [B: piecewise], choose how many pieces with the left and right arrows and click [enter].

When you need to input the domain for each piece, use [2nd] [math = test] and select the relational operator that you need. (The pieces will graph from left to right, no matter what order you input them in.)

### Complex Numbers

You can find $$i=\sqrt{-1}$$ above the decimal point, so click [2nd] [ . ] to access it.

You can find some functions specific to complex numbers under the [math] button under the CMPLX column.

The NUM column under the [math] button has an absolute value function as the first option, and it works just like the CMPLX option 5 works for absolute values: it finds the “modulus” of the complex number (which is basically just like the length aka magnitude of a vector or the absolute value of a real number).

### Mode

Working with trig functions, you may need to toggle this mode:

RADIAN $$\:\:\:\:\:\:\:\:$$ DEGREE

If you need a reminder about scientific notation, try switching from NORMAL to SCI mode and running some calculations. You will typically want to stay in NORMAL mode for most of your calculations.

#### Calculus and some Pre-Calculus:

You may want to switch your calculator to polar or parametric modes, and this is where you do that. If you’ve ever wondered why the button for a variable looks like [$$X,T,\theta,n$$], notice that the options for different graphing modes are FUNCTION, PARAMETRIC, POLAR, SEQ.

### Matrices

Access matrix options with [2nd] [$$x^{-1}$$].

EDIT is where you can edit a matrix. First, you set the dimensions, and then you fill. It automatically starts in the top left corner and fills across the top if you hit [enter] between entries. Once done, go home by clicking [2nd] [mode = quit]. If you need to edit more than one matrix, exit back to the home screen between them.

NAME is where you pull a matrix in for a calculation.

The MATH column has some functions that are specific to matrices.

Note: Matrix multiplication is not commutative. If you are running calculations with matrices in your calculator, remember to type them in exactly as you see them on the page.

### Statistics and Linear or Quadratic Fit

If you have a list of data (with or without an accompanying frequency list) and you want the mean, median, and/or standard deviation, or if you want to fit a quadratic function through three points, you’ll want to input a list. Oddly, [2nd] [stat = list] is not how you edit a list; just click that [stat] button. The first option is the EDIT column and the [1: Edit…] option. Once in the editing screen, if you use the up arrow to highlight the list title and click [clear], you can clear the entire list. If you need x and y coordinates, use two lists and make sure the pairs line up. If you need a data and corresponding frequency, also use two columns and make sure the pairs line up. Use [2nd] [mode = quit] when you’re done editing.

That [stat] button, under the CALC column, has 1-Var Stats, which is good for mean, median, and standard deviation, and LinReg(ax+b) and QuadReg which are good for fitting a linear or quadratic function to coordinate pairs. The TESTS column has some functions that are useful for a statistics course but won’t come up on an ACT or SAT.

#### AP Statistics:

You’ll want to look at [2nd] [vars = distr] to find some of the important distributions like normalcdf and invNorm.

You might want to store a regression equation to graph over a scatter-plot, and you can do that if you “Store RegEQ:” with [alpha] [trace = f4] and select which y you’d like to store it in.

### [2nd] [mode]

If you read through this article, then you know what [2nd] [mode] does: it gets you back to the home screen. I think I’ve mentioned the main tips and tricks and functions that I use with students frequently. It does make for a dense read, so if you’d like to talk through any of this out loud rather than slogging through text on the page, please reach out to me; I would love to help you get the most out of your calculator and your math courses.