Top 75 ACT Math Questions – By Topic

Publication Date: May 8, 2024.

This is an analysis of the most common math questions on the last 10 released ACTs (through April 2024).

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.

  1. Fractions and Decimals – All four operations. Mixed numbers.
  2. Exponents – All operations. Fractional and negative exponents are very common too (see below).
  3. Probability – Know the basic part:whole versions. There is usually a harder one also (like one with two events).
  4. Negatives – Be comfortable with all operations.
  5. Average – Also called the arithmetic mean. There is always a basic version and usually an advanced one, like the average sum trick (see below).
  6. 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.
  7. Quadratic skills – Factor. FOIL. Set parenthesis equal to zero. Graph parabolas.
  8. Ratio – Part:part, part:whole.
  9. Area/Perimeter of basic shapes – Triangles, rectangles, circles.
  10. Percents – Know all basic variations. More advanced ones are common also.
  11. Absolute Value – Sometimes basic arithmetic, sometimes an algebraic equation or inequality.
  12. Picking Numbers – You never have to use this but it will be a useful option on every test.
  13. Plug in answers – Like picking numbers, it’s not required but it’s often helpful.
  14. 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.
  15. Radicals – Basic operations. Translate to fractional exponents.

Extremely Likely

(> 80% chance)

  1. FOIL – This has to be automatic.
  2. SOHCAHTOA – Every variation of right triangle trig, including word problems.
  3. 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?
  4. Average sum trick – 5 tests, average is 80. After the 6th test, the average is 82. What was the 6th test score?
  5. MPH – The concept of speed in miles per hour is very common (sometimes combined with other conversion).
  6. System of Equations – Elimination. Substitution. Word problems.
  7. Composite function – As in g(f(x)).
  8. Order of operations – Sometimes directly tested, other times part of a harder question.
  9. Pythagorean Theorem – Sometimes asked directly, other times required as part of something else (like SOHCAHTOA or finding the distance between two points).
  10. Time – Hours to minutes, minutes to seconds, time elapsed.
  11. Angle chasing – 180 in a line. 180 in a triangle. Corresponding angles. Vertical angles.
  12. LCM – Straight up. In word problems. In algebraic fractions.
  13. Imaginary numbers – Powers of i. What is i^2? The complex plane.
  14. Negative exponents – Know what they do and how to combine them with other exponents.Very Likely(>50% chance)
  15. Factoring – Mostly the basics. Almost never involves a leading coefficient.
  16. Fractional Exponents – Rewrite radicals as fractional exponents and vice versa.
  17. Logarithms – Rewrite in exponential form. Basic operations.
  18. Mixed Numbers – all four operations. Often combined with word problems.
  19. 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?”
  20. Matrices – Adding, subtracting, multiplying. Knowing when products are possible.
  21. Venn – There are 30 kids. 18 are in Algebra. 20 are in French. How many are in both?
  22. 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?
  23. Algebra LCD – Find the lowest common denominator, then combine the numerators.
  24. Geometric sequence – You usually just need to find a subsequent term (not the formula).
  25. Change the base – If 9^x = 27^5, what is x?
  26. Given points, find equation – You’re given two ordered pairs and must find the linear equation.Worth Knowing(> 25% chance)
  27. Apply formula – they give you a formula (sometimes in the context of a word problem) and you have to plug stuff in.
  28. Domain – Usually you can think of it as “possible x values”.
  29. 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?”
  30. Law of Cosines – They almost always give you the formula. Then you just have to plug things in.
  31. Midpoint – Given two ordered pairs, find the midpoint. Sometimes they’ll give you the midpoint and ask for one of the pairs.
  32. Scientific notation – Go back and forth between standard and scientific notation. All four operations.
  33. Shaded area – The classic one has a square with a circle inside.
  34. Similar triangles – Relate the sides with a proportion.
  35. Weird shape area – It’s an unusual shape but you can use rectangles and triangles to find the area.
  36. Conjugates – Rationalize denominators that include radicals or imaginary numbers. Know that imaginary roots come in pairs.
  37. Difference of two squares – (x + y)(x – y) = x^2 – y^2
  38. Graph translations – Horizontal shifts, vertical shifts. Stretches. You should recognize y = 2(x+1)^2 – 5 right away and know exactly what to do.
  39. Multistep conversion – For example, they might give you a mph and a cost/gallon and then ask for the total cost.
  40. Parallelogram – Know that adjacent angles add to 180. Area formula.
  41. Prime numbers – Usually combined with something else, like basic probability.
  42. Probability with “not” – 3 reds, 5 blue, 6 green. Probability of picking one that’s not red?
  43. Undefined – You can’t have 0 in the denominator.
  44. Special right triangles – 30:60:90, 45:45:90.
  45. Amplitude – If y = 5 sin(x) + 2, what is the amplitude?
  46. Arithmetic sequence – Usually asks you to find a specific term, sometimes asks you to find the formula.
  47. 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?
  48. Volume of a prism – Know that the volume = area of something x height. Sometimes the base will be a weird shape.
  49. Circle equations – (x-h)^2 + (y-k)^2 = r^2. Sometimes you have to complete the square.
  50. Compare numbers – Be able to order square roots, decimals, and fractions.
  51. Find inverse function – Switch y and x, then isolate y.
  52. Permutation – You have 5 plants and 3 spots. How many ways can you arrange them?
  53. Line of best fit – They’ll sometimes ask you to find the predicted value, or the difference between the predicted and actual values.
  54. Linear inequality – Be comfortable solving algebraic inequalities. Graphs appear sometimes also.
  55. Triangle opposite side rule – There is a relationship between an angle and the side across from that angle.
  56. Inverse trig – Use right triangle ratios to find angles.
  57. Toy Soldier (volume) – What happens to the height of the water when you drop an object in the bucket?
  58. 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.
  59. Periodic function graph – The basics of sine and cosine graphs (shifts, amplitude, period).
  60. Value/frequency table – Find the median and mean in this format.

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