The ACT Math Subject Test is a standardized test that measures your mathematical skills and knowledge. The ACT Math test is designed to assess your knowledge of topics, as described in Table 1 and your ability to apply them in problem-solving situations.
Table 1: ACT Math Format
| No. of Questions | Question Type | Time Limit | Time/Question |
| 60 | Multiple-choice with 4 answer choices | 60 Minutes | 1 Minute |
Table 2: Distribution of question types and skills you can expect to encounter on the ACT Mathematics test
| Question Types | Subtopics | Question Distribution (approx.) |
| Pre Algebra | Basic operations using whole numbers, fractions, decimals, and integers, Scientific notation, Square roots, Ratio, proportion, and percent, Linear equations, Ordering numbers by value, Simple probability, Simple descriptive statistics, Data collection, representation, and interpretation, |
12-15 questions (20 to 25%) |
| Elementary Algebra | Substitution method for evaluating algebraic expressions, Expressing functional relationships using variables Understanding algebraic operations , Quadratic equations (with and without factoring) |
9-12 questions (15 to 20%) |
| Intermediate Algebra | Quadratic formula, Absolute value equations, Inequalities, Quadratic inequalities, Rational and radical expressions, Systems of equations, Modelling, Matrices, Complex numbers. Polynomial roots |
9-12 questions (15 to 20%) |
| Statistics and Probability | Data collection methods Probabilities, Sample space |
6-7 questions (8% – 12%) |
| Coordinate Geometry | Slope, Parallel and perpendicular lines, Midpoints, Graphing (in the context of equations and graphs), Distance, Conics |
9-12 questions (15 to 20%) |
| Plane Geometry | Properties of plane figures, Properties of circles, triangles, rectangles, trapezoids, and parallelograms Proving basics and techniques, Volume, Three-dimensional measurements |
12-15 questions (20 to 25%) |
| Trigonometry | Trigonometric identities, Trigonometric functions (values and properties). Graphing trigonometric functions. Modelling using trigonometric functions, Solving trigonometric equations |
3-6 questions (5 to 10%) |
| Functions | Functions (definition, notation, representation, and application), Linear functions, Radical functions, Polynomials, Logarithmic functions |
7-9 questions (12% – 15%) |
| Integrating essential skills | Rates, Percentages, Proportional relationships, Area, Surface area, Volume, Average/median |
12-15 questions (20 to 27%) |
Here are the ACT formulas students must know before taking the test this fall:
Table 3. Pre-Algebra
| Scientific Notation | Scientific notation is a way of writing very large or very small numbers using powers of 10. For example: The number 3,500,000 can be expressed in scientific notation as 3.5 x 10^6. The number 0.000012 can be expressed in scientific notation as 1.2 x 10^-5. |
| Square Roots | The square root of a product: ?(ab) = ?a × ?b The square root of a quotient: ?(a/b) = (?a) / (?b) |
| Ratio, proportion, and percent | Direct and Indirect Proportion ( (a1/b1)=(a2/b2) and (a1a2 = b1b2) Ratio: The ratio of two quantities a and b can be written as a:b or a/b. |
| Linear equations | y = mx + b |
Table 4. Elementary Algebra
| Elementary Algebra | The distributive property: a(b + c) = ab + ac The commutative property: a + b = b + a, ab = ba The associative property: (a + b) + c = a + (b + c), (ab)c = a(bc) The identity property: a + 0 = a, a x 1 = a The inverse property: a + (-a) = 0, a x 1/a = 1 |
Table 5. Intermediate Algebra: Linear Equations and Functions
| Matrices: | Matrix addition and subtraction: A + B = B + A, A – B = A + (-B) Scalar multiplication: k(A + B) = kA + kB, (k + l)A = kA + lA · Matrix multiplication: AB = C, where C[i,j] = ?k A[i,k]B[k,j] |
| Complex Numbers: | The imaginary unit: i^2 = -1T he complex conjugate of a+bi is a-bi Addition and subtraction: (a+bi) + (c+di) = (a+c) + (b+d)i, (a+bi) – (c+di) = (a-c) + (b-d)i Multiplication: (a+bi)(c+di) = (ac-bd) + (ad+bc)i Division: (a+bi) / (c+di) = ((ac+bd)/(c^2+d^2)) + ((bc-ad)/(c^2+d^2))i |
Table 6. Statistics and Probability
| Mean | Sum of the terms / the number of different terms |
| Average speed | Total distance / total time |
| Probability | Probability = Target outcomes / Total outcomes |
Table 7. Coordinate Geometry
| Slope | Slope = y? – y? / x? – x? |
| Slope-Intercept Form | y=mx+b |
| Midpoint Formula | (x?+x?) / 2, (y?+y?) / 2 |
| Distance Formula | d=?(x? – x?)² + (y? – y?)² |
| Logarithms | Log_b(x.y) = log_bx + log_by Log_b{x/y} = log_bx – log_by |
Table 8. Plane Geometry
| Rectangles | Area of Rectangle: area = length x width Perimeter: 2l+2w Volume: lwh a (h is the height of the figure) |
| Triangles | Area of Triangle: area = (1/2) (base) (height) Pythagorean Theorem: a2 + b2 = c2 |
| Trapezoids | Area: [parallel side a + parallel side b)/2]h |
| Circles | Area of Circle: ? * r² Circumference = 2? * r Length of an Arc: (2?r)(degree measure center of arc/360) Equation of a Circle: (x – h)^2 + (y – k)^2 = r^2 where (h,k) are the center of the circle |
| Cylinder | Volume of a cylinder: ?r2h |
Table 9. Trigonometry
| SOH CAH TOA | sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent |
To learn more about ACT, download ACT’s free e-book to learn more about the ACT. For a comprehensive diagnostic report, students can also grade ACT practice test bubble sheets online using Socrato’s test grading software.
