Here’s my quick guide to what is tested on ACT Math. I’ve separated it into topics that usually appear on the first 40 questions, last 20 questions, and rare topics that are usually less than one question per test, as I find that this is typically a cut off point for students. If you can get about 40 questions right, you can typically get a 25 on the Math section, so depending on whether you’re aiming above or below a 25, you can focus your attention accordingly. If you need above a 30, study everything! I recommend this only as a time saving study strategy though – if you have time to get a basic knowledge of everything, then do, because some easy versions of hard topics can appear later on the test too.
Timing can be a really big deal on the ACT Math. If you’re struggling with that, read this .
Topics tested on ACT Math (Q1-40)
- Basic algebra: using BEDMAS, rearranging equations, isolating for x, expressing one function in terms of the other.
- Ratios, percentages, fractions – convert between each
- Square roots, cube, and higher roots, exponent laws, scientific notation
- Inequalities: solving linear inequalities and graphing on numberline
- Statistics: mean, median, mode averages, stem and leaf plots
- General functions: finding x and y intercepts, inverse functions, root, reciprocal and absolute value functions, transformations of functions, word problems with functions,compound functions such as f(g(x)) and specially defined functions.
- Linear functions: solving two simultaneously to find points of intersection (by substitution or elimination), graphing, slope (finding parallel and perpendicular), word problems.
- Quadratic Functions: factoring, roots, intercept, vertex form, application problems, using the quadratic formula including knowledge of the discriminant, quadratic inequalities.
- Circles (not centered at the origin) and ellipses on the coordinate axis.
- Shapes/Angles: polygon angle rules, properties of triangles, and types of quadrilaterals, area and volume of 2d and 3d shapes.
- General formulae: length of a line segment, midpoint of a line segment
- Basic trigonometry & triangles: Pythagorean theorem, SOHCAHTOA, sine & cosine law
Topics typically tested on ACT Math questions 40-60:
- Pythagorean triples and special triangles (it’s not essential to know these, but often time saving!).
- Solving and interpreting a system of equations with zero or infinite solutions
- More advanced trigonometry: CAST rule, trigonometric identities, graphing trig functions, solving trig word problems, triangle inequality theorem, radians.
- Inequalities: solving equations and graphing inequalities
- Variation problems (for example: P is inversely proportional to Q. If P = 20 when Q = 2, what is P when Q = 8?).
- Sequence and series
- Harder versions of all the topics in the Question 1-20 list!
Rare questions tested on ACT Math:
- Permutations and combinations, factorial formulae. These are also known as “counting problems” and involve arranging objects in order. In most cases on the ACT, they are simpler to work out without the formulae.
- Polynomial long or synthetic division.
- Knowledge of the associative, commutative and distributive laws.
- Logarithms (usually using log laws to rearrange expressions), and natural log (ln – it follows all the same rules as other logs).
- Imaginary numbers (including applications in to quadratic equations)
- Matrices: addition, subtraction, multiplication by scalar or matrix, transpose, determinant.
- Even and odd functions
- Vectors (only basic knowledge)
- Ambiguous case of Sine law
- Standard deviation (you don’t have to calculate it, but they might ask you which set of numbers has the least or greatest standard deviation).
Most study guides that I have found cover most of the topics tested on ACT Math, but usually not all of them. Depending on where you’ve studied Math, and the level you’ve studied to, you may know most, but not all of these.
You’re welcome! 🙂