The Top 75 ACT Math Questions

Based on the last 10 tests, as of June 2023.

This is an analysis of the most common math questions on the last 10 released ACTs (through June 2023). I need to know this information in order to make the questions and question-selection algorithms for Mathchops. So I tagged every question from the most recent ACTs a bunch of different ways. Then one of my partners helped me make a Python script and we did a ton of data analysis. 

Guaranteed To Show Up

These have to be rock solid because A) they’ll definitely show up and B) they’ll often be combined with other skills.

Fractions and Decimals – All four operations. Mixed numbers.

Average – Also called the arithmetic mean. There is always a basic version and usually an advanced one, like the average sum trick (see below).

Probability – Know the basic part:whole versions. There is usually a harder one also (like one with two events).

Percents – Know all basic variations. More advanced ones are common also.

Exponents – All operations. Fractional and negative exponents are very common too (see below).

Linear Equations/Slope – Find the slope when given two points. Be able to isolate y (to create y = mx + b). All the standard stuff from 8th grade Algebra.

Solving Equations – Be very comfortable with ax + b = cx + d. Distribute. Combine like terms. You also need to be able to create these equations based on word problems.

Picking Numbers – You never have to use this but it will be a useful option on every test.

Ratio – Part:part, part:whole.

Quadratic skills – Factor. FOIL. Set parenthesis equal to zero. Graph parabolas.

Area/Perimeter of basic shapes – Triangles, rectangles, circles.

Negatives – Be comfortable with all operations.

SOHCAHTOA – Every variation of right triangle trig, including word problems.

Plug in answers – Like picking numbers, it’s not required but it’s often helpful.

Absolute Value – Sometimes basic arithmetic, sometimes an algebraic equation or inequality.

Radicals – Basic operations. Translate to fractional exponents.

Extremely Likely

(> 80% chance)

Average sum trick – 5 tests, average is 80. After the 6th test, the average is 82. What was the 6th test score?

MPH – The concept of speed in miles per hour is very common (sometimes combined with other conversion).

System of Equations – Elimination. Substitution. Word problems.

Angle chasing – 180 in a line. 180 in a triangle. Corresponding angles. Vertical angles.

Time – Hours to minutes, minutes to seconds.

Pythagorean Theorem – Sometimes asked directly, other times required as part of something else (like SOHCAHTOA or finding the distance between two points).

Composite function – As in g(f(x)).

Probability, two events – If there's a .4 probability of rain and a .6 probability of tacos, what is the probability of rain and tacos?

Factoring – Mostly the basics. Almost never involves a leading coefficient.

LCM – Straight up. In word problems. In algebraic fractions.

Order of operations – Sometimes directly tested, other times part of a harder question.

FOIL – This has to be automatic.

Imaginary numbers – Powers of i. What is i^2? The complex plane.

Very Likely

(> 50% chance)

Matrices – Adding, subtracting, multiplying. Knowing when products are possible.

Mixed Numbers – all four operations. Often combined with word problems.

Function shifts – Horizontal shifts, vertical shifts. Stretches. You should recognize y = 2(x+1)^2 - 5 right away and know exactly what to do.

Negative exponents – Know what they do and how to combine them with other exponents.

Fractional Exponents – Rewrite radicals as fractional exponents and vice versa.

Midpoint – Given two ordered pairs, find the midpoint. Sometimes they’ll give you the midpoint and ask for one of the pairs.

Median – Middle when organized from low to high. Even number of numbers. What happens when you make the highest number higher or the lowest number lower?

Apply formula – they give you a formula (sometimes in the context of a word problem) and you have to plug stuff in.

Special right triangles – 30:60:90, 45:45:90.

Scientific notation – Go back and forth between standard and scientific notation. All four operations.

Algebra LCD – Find the lowest common denominator, then combine the numerators.

Logarithms – Rewrite in exponential form. Basic operations.

Remainders – Can be simple or pattern based, as in “If 1/7 is written as a repeating decimal, what is the 400th digit to the right of the decimal point?”

Difference of two squares – (x + y)(x - y) = x^2 - y^2

Change the base – If 9^x = 27^5, what is x?

Worth Knowing

(>25% chance)

Multistep conversion – For example, they might give you a mph and a cost/gallon and then ask for the total cost.

Weird shape area – It’s an unusual shape but you can use rectangles and triangles to find the area.

Parallelogram – Know that adjacent angles add to 180. Area formula.

Arithmetic sequence – Usually asks you to find a specific term, sometimes asks you to find the formula.

Circle equations – (x-h)^2 + (y-k)^2 = r^2. Sometimes you have to complete the square.

Linear inequality – Be comfortable solving algebraic inequalities. Graphs appear sometimes also.

Law of Cosines – They almost always give you the formula. Then you just have to plug things in.

Triangle opposite side rule – There is a relationship between an angle and the side across from that angle.

Geometric sequence – You usually just need to find a subsequent term (not the formula).

Venn – There are 30 kids. 18 are in Algebra. 20 are in French. How many are in both?

Vectors – Add, subtract, multiply (scalar), i and j notation.

Volume of a prism – Know that the volume = area of something x height. Sometimes the base will be a weird shape.

Shaded area – The classic one has a square with a circle inside.

Similar triangles – Relate the sides with a proportion.

Probability with “not” – 3 reds, 5 blue, 6 green. Probability of picking one that’s not red?

Permutation – You have 5 plants and 3 spots. How many ways can you arrange them?

Undefined – You can’t have 0 in the denominator.

Periodic function graph – The basics of sine and cosine graphs (shifts, amplitude, period).

Amplitude – If y = 5 sin(x) + 2, what is the amplitude?

Toy Soldier (volume) – What happens to the height of the water when you drop an object in the bucket?

Ellipses – Know how to graph basic versions.

Mixtures – There’s a 10L container. 20% of it is OJ concentrate, but the rest is water. If you combine those 10L with 8L of water, what percentage of the resulting mixture is pure OJ concentrate?

Mode – The number that shows up the most. For example, 5 is the mode of [1, 2, 5, 5, 12].

Use the radius – A circle will be combined with another shape and you have to use the radius to find the essential info about that other shape.

Conjugates – Rationalize denominators that include radicals or imaginary numbers. Know that imaginary roots come in pairs.

Inverse trig – Use right triangle ratios to find angles.

Find inverse function – Switch y and x, then isolate y.

Prime numbers – Usually combined with something else, like basic probability.

Line of best fit – They’ll sometimes ask you to find the predicted value, or the difference between the predicted and actual values.

Counting principle – License plate questions.

Domain – Usually you can think of it as “possible x values”.

To practice the most common questions on the ACT, visit mathchops.com or check our podcast on Tests and the Rest. Mathchops picks the best questions for students to practice based on their previous answers.