If you’re like most students, you prefer having access to a calculator when you’re taking a math test. Thankfully, the ACT permits the use of a calculator for the entire Math test.
You’re even allowed to use powerful devices like the TI-84 family of graphing calculators. While many students have used such calculators, they often aren’t familiar with all the “tricks” that can help them improve their ACT scores. That’s why securing the services of an experienced ACT math tutor is so important.
Getting into the ACT mindset
In principle, the ACT Math section covers high school math up through precalculus. However, many of its questions are formatted differently than what you have seen on your math tests, and the scope of topics covered may be broader than what you experienced in your classes.
Thankfully, the ACT consists entirely of multiple-choice questions and lets you use a calculator for all 60 of them. Those two conditions drive the entire ACT prep process—call it the “ACT mindset”: for every question you encounter, one of the five answer choices listed is the correct one, and you may use your calculator as much as you want. A skilled test prep tutor will help you get into that mindset so that you feel confident navigating the wide variety of questions on the test.
Establishing what calculators are allowed and which model you should use
Although the ACT lets you use a calculator through the entire Math test, there are some restrictions on what models you can use. What calculators can you use on the ACT? Well, the generous ACT calculator policy allows advanced graphing calculators, including those in the TI-84 series. You are not permitted to use your phone or a tablet, and any calculator with a CAS (computer algebra system)—such as the TI-Nspire CAS or TI-89—is forbidden.
Since the entire TI-84 series are calculators allowed on the ACT, it’s best that you obtain one as soon as possible so you can become familiar with its features. Texas Instruments is the brand most teachers use in their classrooms and most tutors are familiar with.
TheTI-84 Plus CE is the most advanced of the permitted calculators, so the directions listed below will be for that model. Many strategies described can be done on other calculators, but the key actions won’t look the same. While all the tips will definitely work on the TI-84 Plus and the TI-84 Plus C Silver Edition, there may be minor changes to the sequence of steps.
Learning the basics of the TI-84
- Keypad layout: Almost every key has more than one operation associated with it. To access the features in blue, press the blue “2nd” key first. For the options in green, press “Alpha” first.
- Modes: On the TI-84 Plus CE, your current modes are always on display at the top of your screen. If you should need to change a mode, press “Mode” to access this menu:
To change a mode, scroll using the navigational keys and press “Enter” to select a new setting. For the ACT, you shouldn’t mess with any of these other than Radian/Degree. When you’re on the home screen, it’s best to be in Degree mode, although you may need to change that for a particular problem. For graphing trigonometric functions, always switch to Radian mode.
- Shortcut menus: The gray keys at the top of the keypad control the graphing operations, but the ones with f1-f4 labels will connect you to dropdown menus that provide shortcuts to several features of the calculator (remember to press “Alpha” first).
F1 brings up the Fraction submenu. Option 1 lets us type fractions and rational expression with a horizontal fraction bar. Option 2 enables the entry of mixed numbers. Option 3 changes improper fractions to mixed numbers. Option 4 changes decimals into fractions and vice versa.
F2 accesses the Function submenu. While options 2-4 helpful features, they really aren’t useful on the ACT. Option 1 gives you absolute value bars, while Option 5 and 6 enable you to enter logarithms of any base and roots of any index. Options 7 and 8 are programmed to calculate permutations and combinations. Option 9 lets you do factorials.
F3 brings up the Matrix menu—more on that a little later!
F4 calls up a list of Y-variables. This list could have use on the ACT, but it probably wouldn’t provide any real advantage—so we won’t be learning about it.
- Changing decimals to fractions: Any time a calculation produces a rational number, you can change it into fraction form using either the shortcut menu or the Math menu. That means no worrying about finding common denominators and simplifying fractions! Suppose you had entered this calculation:
Select the “Math” key to bring up this screen:
Choose the first option and then hit “Enter” to complete the operation. (Note when you see “Ans” on the screen, that’s the calculator’s way of saying that it’s using the last number displayed.)
- Getting back to the home screen: Any time you’re in an application and can’t figure out how to exit, you can click the blue “2nd” key then “Mode (Quit)” to return to the home screen.
Using the table features to expedite the Plugging in the Answers strategy
Almost every student is familiar with the Plugging in the Answers (PITA) strategy, but most of them don’t know how to do it efficiently. When a question presents an equation or a word problem that can be modeled with an equation, and the answer is numeric, then you can take the answer choices and plug them into the equation for the proper variable. When an answer choice makes the equation true, you have found the correct one.
The TI-84 has operations as part of its graphing feature that makes PITA a smooth process, regardless of how complicated the question may be. Consider this exponential equation:
Go to “Y=” and enter the expression on the left for Y1 and the one on the right for Y2. Yes, the problem uses the variable n, but the letter itself is arbitrary: we’ll use X instead. Use the the variable key to enter an X.
Each answer choice has two solutions, and both must satisfy the equation for that choice to be correct. Yes, you could try plugging in those answers by hand, but several of the possible solutions are fractions. If we use the table feature of the TI-84, we can avoid human error and frustration.
First, access the Table Setup menu by clicking “2nd” then “Tblset.”
The default setting for the independent variable is Auto, in which the calculator generates x-values based on the parameters we set: TblStart lets the calculator know what value to begin the table with, while ΔTbl (“change in table”) tells it how to count in order to determine the next value to plug into the functions.
For this problem, though, we want to be able to enter our own x-values because the possible solutions are not all integers. Rather than messing around trying to figure out what ΔTbl setting would enable us to see all the necessary values, we can just change the setting so that we can do the entries ourselves. Scroll down to Indpnt, then scroll right to Ask and hit “Enter.”
Now, we access the Table feature. Since we set the Table on Ask, both columns are blank.
We now just have to enter in the answer choices and see what their y-values are. Note that since the first value of each answer choice is unique, we only need to plug those in: if the first value checks out, then the second will as well.
Since our original equation showed the two exponential expressions as being equal, we are looking for the answer choice that produces the same output value for both Y1 and Y2. We see that is the case for the fifth entry, so choice E is the correct answer.
Storing numbers as variables to execute the Plugging in Numbers strategy
In contrast to PITA, the Plugging in Numbers (PIN) approach is primarily used when the answer choices have variables in them—i.e., they are mathematical expressions rather than equations. For any input value we may select, only one of the answers choices will always yield the same output value as that of the original expression. Since every question on the ACT is multiple choice, you can use process of elimination to get rid of the choices that don’t match the output value generated by the original expression
With the TI-84, the Store operation makes this process efficient and less prone to careless error. Here is a question from the tail end of a test that looks daunting:
Normally, this would make most students panic, but one doesn’t need a deep understanding of factorials to work this question. Using some basic features in conjunction with the Store operation, we can quickly narrow the answers down to the correct one.
First, store a number as the variable X (remember that the letter itself is arbitrary). Let’s start with x=1:
Next, we can use the shortcut menu to access the horizonal fraction bar (option 1 on the FRAC menu) and the factorial command (option 9 on the FUNC menu) so we can type out the original expression.
When we hit “Enter”, the calculator evaluates the expression and gives us the output value—call it the check value—for our input value of 1. Next, we evaluate the answer choices for the same input value to see which one matches the check value.
Since our check value is 240 for the original expression, we know that answer A is a possible solution. Remember that since we’re eliminating the choices that don’t match the check value, though, we have to check all the answer choices.
Answer choices B and C are numeric and don’t match the check value, so we disregard them. Finally, enter the final two answer choices and get rid of any that don’t match our check value.
Since only answer A matched our check value of 240, we know it’s the right answer!
Performing matrix operations
Even if you have never worked with matrices, you can do most matrix problems on the ACT using the TI-84. A matrix is an arrangement of numbers with a certain number of rows and columns, referred to as the dimensions of the matrix.
This problem would be brutal if we had to calculate by hand—many students wouldn’t even know how to approach it!
To enter the matrix operation C + AB, we can use the shortcut menu to select the dimensions of the matrices and then enter their values. Matrix A is 2×3 (two rows and three columns), matrix B is 3×2, and matrix C is 2×2.
First, we enter matrix C. Once we’re done entering it, we use the navigational keys to get the cursor out of the brackets before entering the plus sign.
Next, we enter matrix A and move the cursor outside the brackets. Note that with multiplication, we don’t need to enter any multiplication sign, as the calculator understands to multiply matrices that are next to each other.
Finally, enter matrix B and hit “Enter”.
Since the result of the calculation matches answer B, then that’s the correct choice.
Doing problems with imaginary numbers
The ACT covers imaginary numbers, but you don’t have to know much about them to do the problems. Whenever you need to enter the imaginary unit i, where:
…just press “2nd” and the decimal button.
Here’s a question that would likely be time-consuming if you had to do it by hand:
Using the shortcut menu to create a horizontal fraction bar, we can enter this expression exactly as we see it.
The answer is already in standard form, so we can easily see that K is the correct choice.
Using the graphing tools
Though the capability to graph functions is a big advantage of the TI-84, many students don’t know how to use the graphing operations efficiently. With the proper knowledge on how to make adjustments, however, using the grapher becomes an effective strategy.
Suppose we have a question about trigonometric graphs:
Making sure we are in Radian mode, we press “y=” and enter in the five answer choices as Y1 through Y5.
To see the graphs clearly, however, we’ll need to adjust the viewing window so that it matches the graph in the problem. The default Window setting look like this, showing us the minimum and maximum values shown on the screen, as well as the increments (Xscl and Yscl) that the numbers on the axis count by.
In our problem, the x-values go from –π to π, while the y-values range from –3 to 3. Also, we recognize that the x-axis counts by π/2 and the y-axis counts by 1, so those will be our entries for Xscl and Yscl. After selecting “Window” we make the necessary changes to the Window settings. (We can enter π directly using “2nd” and “Pi” buttons, but once that’s entered, the calculator will change it to a decimal.)
Once we have made those adjustments, we are ready to graph the functions.
Since the TI-84 Plus CE assigns a different color to each function, we just match the right color to the graph from the question. The green one clearly matches the graph in the question, and that corresponds to Y5—therefore, answer K is correct.
Important note – On the next graph, you may want to return to a standard graphing screen where both the x-values and y-values on the axes go from –10 to 10. To do that, just select “Zoom” and select option 6. (For any menu on the TI-84, you can either scroll down and hit “Enter” or simply type the number of the option.)
Sometimes we don’t even need to graph the functions, though. Consider this question:
First, we enter the answer choices by pressing “y=” and typing them in for Y1-Y5:
The question provides the x-intercepts, so all we need to do is plug the given values into the answer choices and find out which one returns a y-value of 0 for both x-values. Yes, we could do that using the Graph feature, but it’s more efficient to do it using the Table feature. Since one of the two values we’re entering is a fraction, we want the Table Setup to be on Ask for the independent variable.
We then enter in the x-intercepts:
Since the fourth function has zeroes for both numbers, we know that J is the right answer.
Making the most of ACT Math tutoring
There are even more handy operations that an ACT Math tutor can show you, but don’t think that ACT tutoring will only be about calculator “tricks.” You’ll learn the types of math on the ACT and how to study for the ACT as your tutor teaches you how to efficiently navigate the test. Chances are high that there is content on the test you either aren’t familiar with or are rusty on. With the assistance of an expert ACT Math tutor, however, you’ll be able to confidently attack questions on such material.
Since the ACT does not provide a reference sheet for the Math test, your tutor will walk you through all the ACT math formulas you’ll need to know. During your ACT lessons, you’ll also be provided with tips on time management and guidance on how to guess strategically. This is where access to an ACT Math tutor is most advantageous, as they can teach you to recognize what terminology to look for, what strategies to use, and what moves the makers of the test employ to “trick” students into the wrong answer. After several sessions of concentrated test prep, you’ll be ready to tackle the ACT with everything you have and achieve the score you’ve been shooting for.