ACT Math: Essential Formulas and Concepts You Must Memorize

Why Memorizing Formulas Matters on the ACT

Unlike the SAT, which provides a reference sheet with key formulas, the ACT gives you nothing. Every formula you need must come from your own memory. This means that students who invest time memorizing the essential formulas have a significant advantage — they spend less time deriving and more time solving.

The good news: the ACT draws from a predictable set of math concepts. Below are the formulas and concepts that appear most frequently, organized by topic.

Algebra Essentials

Slope of a line: m = (y₂ – y₁) / (x₂ – x₁). You’ll use this constantly. Also know slope-intercept form (y = mx + b), point-slope form (y – y₁ = m(x – x₁)), and standard form (Ax + By = C). Be able to convert between all three.

Midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2). Straightforward but easy to mess up under pressure.

Distance formula: d = √((x₂ – x₁)² + (y₂ – y₁)²). This is just the Pythagorean theorem in coordinate form. If you forget it, sketch a right triangle between the two points and use a² + b² = c².

Quadratic formula: x = (-b ± √(b² – 4ac)) / 2a. This solves any equation in the form ax² + bx + c = 0. The discriminant (b² – 4ac) tells you the number of solutions: positive = two real solutions, zero = one real solution, negative = no real solutions.

FOIL and factoring: Know how to expand (a + b)(c + d) and reverse the process. Common patterns to recognize: difference of squares (a² – b² = (a+b)(a-b)), perfect square trinomials (a² + 2ab + b² = (a+b)²).

Geometry Formulas (High Priority)

Geometry makes up 30–40% of ACT Math — more than any other standardized test. These formulas are non-negotiable.

Triangles: Area = ½ × base × height. The Pythagorean theorem: a² + b² = c² (for right triangles only). The sum of interior angles is always 180°. Know the special right triangles cold: in a 30-60-90 triangle, the sides are in ratio x : x√3 : 2x. In a 45-45-90 triangle, the sides are x : x : x√2.

Circles: Area = πr². Circumference = 2πr (or πd). Arc length = (central angle / 360) × 2πr. Sector area = (central angle / 360) × πr². Know that an inscribed angle is half the central angle that subtends the same arc.

Rectangles and parallelograms: Rectangle area = length × width. Parallelogram area = base × height (the height is perpendicular to the base, not the slant side). Perimeter = 2l + 2w.

Trapezoids: Area = ½(b₁ + b₂) × h, where b₁ and b₂ are the parallel sides.

3D Solids: Rectangular prism volume = lwh. Cylinder volume = πr²h. Cone volume = ⅓πr²h. Sphere volume = (4/3)πr³. Surface area of a cylinder = 2πr² + 2πrh.

Trigonometry

The ACT tests basic trigonometry more heavily than the SAT. You’ll typically see 4–6 trig questions.

SOH-CAH-TOA: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. Memorize this mnemonic — it’s the foundation for every trig question.

Key identities: sin²θ + cos²θ = 1. tan(θ) = sin(θ)/cos(θ). sin(90° – θ) = cos(θ) and vice versa.

Law of Sines: a/sin(A) = b/sin(B) = c/sin(C). Use when you know two angles and a side, or two sides and a non-included angle.

Law of Cosines: c² = a² + b² – 2ab·cos(C). Use when you know two sides and the included angle, or all three sides.

Unit circle values: Know the sine and cosine values for 0°, 30°, 45°, 60°, and 90°. These come up frequently: sin(30°) = ½, cos(30°) = √3/2, sin(45°) = cos(45°) = √2/2, sin(60°) = √3/2, cos(60°) = ½.

Statistics and Probability

Mean (average): sum of all values / number of values. If the ACT tells you the average of 5 numbers is 80, the sum is 400.

Median: the middle value when data is arranged in order. For an even number of values, it’s the average of the two middle values.

Probability: P(event) = favorable outcomes / total outcomes. For independent events, P(A and B) = P(A) × P(B). For mutually exclusive events, P(A or B) = P(A) + P(B).

Counting principle: If you have m choices for one decision and n choices for another, you have m × n total combinations. Permutations (order matters): nPr = n! / (n-r)!. Combinations (order doesn’t matter): nCr = n! / (r!(n-r)!).

How to Actually Memorize All This

Don’t try to memorize everything in one sitting. Use spaced repetition — review a set of formulas, then come back to them the next day, then three days later, then a week later. Each review session locks the information more firmly into long-term memory.

Create flashcards (physical or digital) with the formula on one side and an example problem on the other. Practice recalling the formula before looking at the answer. Active recall is far more effective than passively re-reading a formula sheet.

Most importantly, practice using these formulas in context. Knowing that the area of a circle is πr² is useless if you can’t identify which problems require it. The more ACT practice problems you solve, the faster you’ll recognize which formula to apply.

Drill These Formulas with Real ACT Practice

Memorizing formulas is only half the battle — you need to apply them under timed conditions. Take a free ACT Math practice test on XMocks to see which formulas you actually know cold and which ones you still fumble with. Our topic-specific drills let you isolate geometry, trigonometry, or algebra so you can practice exactly what you need. And when you get stuck, our AI Tutor walks you through the solution step by step.