ACT Math Formulas You Need to Memorize (There's No Formula Sheet)

The ACT Math section has 45 questions in 50 minutes. You can use a permitted calculator for the whole section, but the ACT gives you no formula sheet. Any formula you need has to be in your head. Here are the ones worth memorizing, grouped by the section's content areas.

Algebra and functions

• Slope between two points: m = (y₂ − y₁) / (x₂ − x₁)
• Slope-intercept form: y = mx + b. Point-slope form: y − y₁ = m(x − x₁)
• Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals.
• Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac tells you how many real solutions there are.
• Vertex of y = ax² + bx + c has x-coordinate −b / 2a.
• Exponent rules: a^m·aⁿ = a^m+n; a^m/aⁿ = a^m−n; (a^m)ⁿ = a^mn; a⁰ = 1; a⁻ⁿ = 1/aⁿ
• Logarithms: log_bx = y means b^y = x.

Related: What to Expect on the ACT: Format, Scoring, and How to Prepare

Coordinate geometry

• Distance: d = √((x₂ − x₁)² + (y₂ − y₁)²)
• Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)
• Circle with center (h, k) and radius r: (x − h)² + (y − k)² = r²

Plane and solid geometry

• Triangle area: ½ × base × height. Interior angles of a triangle sum to 180°.
• Pythagorean theorem: a² + b² = c². Common triples: 3-4-5 and 5-12-13.
• Special right triangles: 45-45-90 sides x, x, x√2; 30-60-90 sides x, x√3, 2x.
• Circle: area πr², circumference 2πr. Arc length = (θ/360) × 2πr; sector area = (θ/360) × πr².
• Rectangle area lw; parallelogram bh; trapezoid ½(b₁ + b₂)h.
• Interior angles of an n-sided polygon sum to (n − 2) × 180°.
• Volume: rectangular box lwh; cylinder πr²h.

Trigonometry

• SOHCAHTOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
• sin²θ + cos²θ = 1, and tan θ = sin θ / cos θ.

Statistics and probability

• Mean = sum ÷ count. Median = middle value of ordered data. Mode = most frequent value.
• Probability = favorable outcomes ÷ total outcomes. For independent events, P(A and B) = P(A) × P(B).
• Counting: multiply the number of choices at each step.

Sequences and percents

• Arithmetic sequence: a_n = a₁ + (n − 1)d. Geometric sequence: a_n = a₁rⁿ⁻¹.
• Percent change = (new − old) ÷ old × 100.

How to make them stick

Memorizing a list isn't enough; you need to recognize when a formula applies. Practice with timed question sets, and when you miss a question, write down the formula it needed. About 70 seconds per question doesn't leave time to reconstruct a formula from scratch.