 # 8 tips for Using the TI-84 Graphing Calculator on the SAT

When it comes to advantages on any math test, access to a calculator — especially a graphing calculator — is perhaps the greatest one. While there the SAT has both a No Calculator and a Calculator section, approximately two-thirds of the SAT Math questions permit the use of a calculator.

Because the SAT has a separate No Calculator section, The College Board allows almost any calculator on the Calculator section. Basically, as long as your device (1) can’t access the internet, (2) doesn’t have a QWERTY keyboard, (3) doesn’t have to be plugged in, and (4) doesn’t have printing capabilities, then you can use it on the SAT. For a list of SAT approved calculators, check out the SAT Calculator policy.

If your school is like most high schools, your math classes favor the use of Texas Instruments calculators. The most popular one by far is the TI-84, although there are several versions of that model. The tips given in this article are for the TI-84 Plus CE, but they will also work for the TI-84 Plus C Silver Edition and most models of the TI-84 Plus.

With older models such as the TI-83, TI-83 Plus, or TI-84, some of the functions described are not available. More advanced Texas Instruments calculators (such as the TI-89 and the TI-Nspire) can do all the maneuvers listed, but the instructions given will not apply to those models.

If you have already made that commitment to preparing for the SAT, then you are surely looking for every advantage you can get. In all likelihood, you have sought out an experienced SAT Prep tutor to help direct your preparation. Hopefully, you have a plan in place that will unlock your potential to achieve the best possible score. Now it’s time to improve your SAT Calculator score by learning how to use a graphing calculator effectively.

## 1. Converting fractions to decimals

Any time you have a decimal on the Calculator section, you can change it into a fraction, provided the decimal is a rational number. Just hit the MATH button, then choose Option 1 from the first menu that comes up:

You can type in a decimal first and then choose the option:

Or if you already have calculated a decimal, choosing the option will transform the last number on the screen into a fraction:

## 2. Using the shortcut menu

Both the TI-84 Plus CE and the TI-84 Plus C Silver Edition have shortcut menus that provide quicker access to some of the calculator’s regular functions.

The five buttons directly below the graphing window have function codes in green that correspond to secondary features (F1, F2, F3, F4, F5) you can access by pushing the ALPHA key before pushing the primary feature key.

The FRAC menu has four operations that can come in useful.

• Option 1 gives you a horizontal fraction bar and enables you to type in fractions or rational expressions.
• Option 2 lets you enter mixed numbers.
• Option 3 transforms improper fractions to mixed numbers
• Option 4 changes fractions to decimals, and vice versa

The other four menus are FUNC, MTRX, and YVAR. For the most part, these are not menus that you will be using on the SAT. One that may come in handy is Option 1 on the FUNC menu, which will let you work with absolute value operations and functions.

If you have the TI-84 Plus, you may have access to the shortcut menus. However, not all versions of the TI-84 Plus come equipped with that capability.

## 3. Adjusting the graphing window

The default Window setting on the TI-84 is from –10 to 10 for both the X and Y axes. Sometimes it’s necessary to change settings so that you can either zoom in on a portion of the graph or zoom out to see an area not on the standard grid. If you hit the WINDOW button right underneath the screen, it will take you to this screen with the default settings.

The Xmin, Xmax, Ymin, and Ymax settings determine the extreme ends of the graphing grid that will be visible on the screen. If you need to zoom in and see more detail, you can set those minimum and maximum values to be narrower than the standard span; if you need to zoom out to see a portion of the graph not on the standard screen, you can chose values broader than the default settings. The Xscl and Yscl settings allow you to adjust how the grid is scaled—that is, what each tick mark on the axes represents. If you have zoomed in, then you can have the axes count by a decimal less than 1; if you have zoomed out, then you can set the axes to count by a value greater than 1.

Any time you need to return the graph to a standard –10-to-10 grid, just tap the ZOOM button and choose Option 6: ZStandard.

## 4. Adjusting the Table Setup to assist with Plugging in the Answers

Plugging in the Answers (PITA) is one of the most useful test-taking skills for multiple-choice questions in the SAT. On the Calculator section, adjusting the Table Setup will help you work backwards from the answers much more efficiently.

The Table Setup is the second function of the WINDOW key, so you have to press the 2ND key first. Note that all secondary functions are in blue, so this one appears as TBLSET.

The default settings look like this:

This means that the table is automatically generated by the calculator, beginning with 0 and counting by 1. (The triangle is the Greek letter delta, meaning “change in.”

Consider this problem:

You would begin by entering both functions into the grapher using the Y= key. Then you can access the TABLE by clicking on the second feature of the GRAPH key.

Since the goal of this question is to find an ordered pair that is a solution to both equations, the default settings aren’t of much help for this problem (although they can be just what we need for others). The only rational value in the answer choices is 5, and our table shows that the two functions are not equal at that value.

In such a situation, you would want to adjust the table so that you can enter in the x-values yourself. To do so, go back the Table Setup and change the independent variable (Indpnt) to ASK. Move the cursor so it’s on top of ASK, then click ENTER:

When you go back to the table, it will be blank. That’s because you are now entering the x-values, and the calculator will return the corresponding y-values. This is a great feature when the answer choices have fractions or irrational numbers. When we apply this to our example, we see that the correct answer choice is A, as it’s the one that produces the same y-value for each equation.

## 5. Storing numbers for repeated substitution

Another convenient method for applying the PITA method is to use the STORE feature to save a value as a variable, then using that variable to substitute into algebraic equations.

Let’s look at this example:

You begin by entering the answer choice for A and clicking the Store Variables key. Next, tell the calculator what variable to store that value as. Click on the variable key to store the variable as X:

(The other variables on the X key are used when the calculator is put into other modes, but none of those other modes will ever be used when taking the SAT. Also, don’t worry about storing a value using that key, as the calculator will still interpret it as an unknown variable when you’re using the graphing features.)

The next step is to simply type in the expression in the original equation and see if it equals 0.

That one does indeed equal 0, so it’s our answer. However, if we need to enter in more than one answer choice, we can store another value and repeat the process. On the TI-84 Plus CE, the TI-84 Plus C Silver Edition, and some TI-84 Plus models, you can scroll up and “grab” entries: once the blue cursor in on the expression you want, click ENTER to bring it down.

Once you bring it down and click ENTER again, the calculator will find the value of the expression with the new stored value.

This x-value did not produce an expression value of 0, so we know it’s not the correct answer.

## 6. Graphing polynomial functions

The SAT likes problems with polynomial functions, expressions, and equations, but specifically questions dealing with quadratics. This is where the graphing features of the TI-84 calculators come in handy.

Let’s take a look at this question:

One way to solve this is by graphing the quadratic equations by clicking on Y=, then entering all four functions into the Y1 through Y4 positions. Once they’re entered, press the GRAPH key to see the all four graphs at the same time:

One nice thing about the TI-84 Plus CE and the TI-84 Plus C Silver Edition is that they have color codes for each function you enter, thus making it easier for you to match up the entered functions with the answer choices. For this graph, the blue graph matches the one in the question, so that means answer A is the correct choice.

## 7. Making lists and analyzing data

The SAT Calculator section is full of Problem-Solving and Data Analysis questions, so sometimes it can be helpful to organize and analyze data using the features on the STAT menu.

Suppose you get this problem on the test:

You can enter that data into lists by pressing the STAT key and then hitting ENTER for the first option on the EDIT menu. That will bring you to the list tables. If there are any previous lists in the table, just move the cursor up so that it’s on the list name (L1, L2, etc.) and click CLEAR. When you go back down into the table, all that list’s entries will be blank. Then enter the data given in the question into L1:

Once you have your data entered into the list, go ahead and exit that menu, then push the STAT button again. This time scroll to the right to access the CALC menu: click on the first option 1-Var Stats.

That will bring up this screen:

You want L1 as your list choice, but leave the FreqList (frequency list) blank. That selection can be used when a separate list gives us how often certain data values appear, but in this problem we don’t have such a list. Click on Calculate to bring up the analysis of the data:

The first entry is the average (arithmetic mean). The Sx and the one below it (that’s the Greek letter sigma) are both standard deviation—don’t worry, the difference between the two formulas doesn’t matter on the SAT. If you scroll down, we can see more statistics from our list:

Here we see the median (Med) and the other elements for a box-and-whisker-plot: the minimum value (minX), quartile 1 (Q1), quartile 3 (Q3), and the maximum value (maxX).

For our question, we can work backwards from the answers by entering additional values into out lists and generating a new list of 1-Var Stats.

Since answer D yields a mean value of 169, it’s the correct one.

## 8. Taking advantage of the pre-programmed apps

The TI-84 Plus CE, the TI-84 Plus C Silver Edition, and some of the TI-84 Plus models have special graphing calculator functions loaded on already. Unlike programs you may download after purchasing a calculator, these functions won’t be wiped out by clearing the memory. Sometimes test proctors will have test-takers reset the calculator back to factory defaults, but that will only affect the programs you download yourself.

To access the Applications menu, press the APPS key:

On the TI-84 Plus CE, Option 8: PlySmlt2 is the Polynomial Root Finder and Simultaneous Equation Solver. On other models, it may be a different option. If you click on that option, it will bring you to this screen:

Let’s look at a problem where we can use Option 2:

First, we enter in how many unknown quantities there are and how many equations we need. For this problem we need 2 for each. (Just leave the rest of the options as they are.)

Once we have entered that in, we click the key right below NEXT at the bottom right (the GRAPH key) and enter in the systems. Note that only the TI-84 Plus CE will display these equations in this manner. Both the TI-84 Plus C Silver Edition and the TI-84 Plus will display a matrix where you can enter the coefficients and constants.

Once you have that entered in, click on the GRAPH key again to SOLVE.

We see that x=3, meaning that a=3 in our problem. However, remember that the question is asking for 10a, so the correct response would be 30, which is answer D.

Another useful app is Option 6 on the TI-84 Plus CE: Inequalz (Inequality Graphing) Again, other models of the TI-84 may have that app at a different option number. Once you choose that option, you will be taken to the graphing screen where you can enter in functions, only now you can also do inequalities.

Let’s say you get this question:

After we put the second two inequalities into slope-intercept form, we can enter them in. Scroll to the left and click ENTER in order to bring up a screen where you can put in the correct inequality symbol. (With models other than the TI-84 Plus CE, the inequality symbols can be set with keys at the bottom of the screen.)

The third inequality in the problem is not a function, but the app allows you to enter vertical line inequalities. Just scroll up to the upper left portion of the screen and click on X= to put in that inequality.

Once you have all three inequalities entered in, you can graph the system of inequalities and see where they overlap:

If you have the TI-84 Plus CE, you can get an even better look at the solution area of the system by accessing the CALCULATE menu:

Scroll to the right to the INEQUALITY menu, then click on Option 2: Inequal Intersection.

That selection will produce a graph where only the solution area is shown:

This really helps us see the dimensions of the triangle: the base is clearly equal to 8, while the height appears to be 2.5. (We could adjust the window if we wish to get a closer look.) Since the problem asks for the area, we apply the area formula for a triangle (remember that you can find that formula on the reference sheet at the beginning of the Calculator test) and get the answer of (½)(8)(2.5)=10.

If you’re planning on also taking the ACT, these tips can be utilized on the ACT Math test as well. However, the ACT covers topics that the SAT doesn’t, so you’ll want to familiarize yourself with the differences between the two tests in order to determine what other calculator “tricks” can be used in the ACT Math section.

## Connect with an expert

Incorporating solid calculator skills is essential to your SAT Math Prep process. Too many students waste time on the SAT Calculator section because they don’t know how to use their TI-84 calculators efficiently. Learning these tips will certainly help you navigate the test more smoothly, but working with a qualified SAT Math tutor will help you master the skills and even learn some additional ones. It’s best to have every advantage possible so you can achieve your best SAT Calculator score.