The Top 75 ACT Math Questions
Based on the last 10 tests, as of October 2024.
This is an analysis of the most common math questions on the last 10 released ACTs (through September 2024). 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.
Exponents – All operations. Fractional and negative exponents are very common too (see below).
Probability – Know the basic part:whole versions. There is usually a harder one also (like one with two events).
Negatives – Be comfortable with all operations.
Quadratic skills – Factor. FOIL. Set parenthesis equal to zero. Graph parabolas.
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.
Average – Also called the arithmetic mean. There is always a basic version and usually an advanced one, like the average sum trick (see below).
Area/Perimeter of basic shapes – Triangles, rectangles, circles.
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.
Percents – Know all basic variations. More advanced ones are common also.
Ratio – Part:part, part:whole.
Picking Numbers – You never have to use this but it will be a useful option on every test.
Plug in answers – Like picking numbers, it’s not required but it’s often helpful.
Factoring – Mostly the basics. Almost never involves a leading coefficient.
SOHCAHTOA – Every variation of right triangle trig, including word problems.
Extremely Likely
(> 80% chance)
Absolute Value – Sometimes basic arithmetic, sometimes an algebraic equation or inequality.
System of Equations – Elimination. Substitution. Word problems.
Radicals – Basic operations. Translate to fractional exponents.
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?
MPH – The concept of speed in miles per hour is very common (sometimes combined with other conversion).
Pythagorean Theorem – Sometimes asked directly, other times required as part of something else (like SOHCAHTOA or finding the distance between two points).
Imaginary numbers – Powers of i. What is i^2? The complex plane.
Time – Hours to minutes, minutes to seconds, time elapsed.
FOIL – This has to be automatic.
Order of operations – Sometimes directly tested, other times part of a harder question.
Angle chasing – 180 in a line. 180 in a triangle. Corresponding angles. Vertical angles.
Add/subtract fractions – often part of a more difficult question, like adding rational expressions.
Very Likely
(>50% chance)
Venn – There are 30 kids. 18 are in Algebra. 20 are in French. How many are in both?
Average sum trick – 5 tests, average is 80. After the 6th test, the average is 82. What was the 6th test score?
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?”
Negative exponents – Know what they do and how to combine them with other exponents.
Composite function – As in g(f(x)).
Graph translations – Horizontal shifts, vertical shifts. Stretches. You should recognize y = 2(x+1)^2 - 5 right away and know exactly what to do.
Logarithms – Rewrite in exponential form. Basic operations.
Mixed Numbers – all four operations. Often combined with word problems.
Change the base – If 9^x = 27^5, what is x?
Matrices – Adding, subtracting, multiplying. Knowing when products are possible.
Shaded area – The classic one has a square with a circle inside.
Midpoint – Given two ordered pairs, find the midpoint. Sometimes they’ll give you the midpoint and ask for one of the pairs.
Fractional Exponents – Rewrite radicals as fractional exponents and vice versa.
LCM – Straight up. In word problems. In algebraic fractions.
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.
Algebra LCD – Find the lowest common denominator, then combine the numerators.
Given points, find equation – You’re given two ordered pairs and must find the linear equation.
Difference of two squares – (x + y)(x - y) = x^2 - y^2
Worth Knowing
(> 25% chance)
Linear inequality – Be comfortable solving algebraic inequalities. Graphs appear sometimes also.
Arithmetic sequence – Usually asks you to find a specific term, sometimes asks you to find the formula.
Geometric sequence – You usually just need to find a subsequent term (not the formula).
Scientific notation – Go back and forth between standard and scientific notation. All four operations.
Prime numbers – Usually combined with something else, like basic probability.
Domain – Usually you can think of it as “possible x values”.
Given sine, find cosine – They give you one trig ratio and ask you to find another. As in, “If the sine of x is 4/5, what is the cosine?”
Law of Cosines – They almost always give you the formula. Then you just have to plug things in.
Undefined – You can’t have 0 in the denominator.
Line of best fit – They’ll sometimes ask you to find the predicted value, or the difference between the predicted and actual values.
Similar triangles – Relate the sides with a proportion.
Weird shape area – It’s an unusual shape but you can use rectangles and triangles to find the area.
Expected value – There is a 0.3 chance of winning $100 in Game A and 0.2 chance of winning $200 in Game B, which is unrelated to Game A. If you place bets on both games, what is the expected value of your bets?
Multistep conversion – For example, they might give you a mph and a cost/gallon and then ask for the total cost.
Value/frequency table – Find the median and mean in this format.
Parallelogram – Know that adjacent angles add to 180. Area formula.
Probability with “not” – 3 reds, 5 blue, 6 green. Probability of picking one that’s not red?
Special right triangles – 30:60:90, 45:45:90.
Volume of a prism – Know that the volume = area of something x height. Sometimes the base will be a weird shape.
Circle equations – (x-h)^2 + (y-k)^2 = r^2. Sometimes you have to complete the square.
Inverse trig – Use right triangle ratios to find angles.
Law of Sines – Know the difference between this and the Law of Cosines, apply to basic triangles.
Find inverse function – Switch y and x, then isolate y.
Permutation – You have 5 plants and 3 spots. How many ways can you arrange them?
Conjugates – Rationalize denominators that include radicals or imaginary numbers. Know that imaginary roots come in pairs.
Triangle opposite side rule – There is a relationship between an angle and the side across from that angle.
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
Ice cream problem – There are 10 flavors, 5 toppings, and 3 cone types. You can choose one flavor, one topping, and one cone. How many different combinations can you create?
Ellipses – Know how to graph basic versions.
To practice the most common questions on the ACT, visit mathchops.com or check our podcast on Tests and the Rest.