ACT math formulas: what to memorize, since there's no formula sheet
The ACT doesn't give you a formula sheet. The Math directions in ACT's 2025–26 practice test list only four assumptions, such as figures not being drawn to scale, and ACT's guide says knowledge of basic formulas is assumed while recall of complex formulas isn't required. In the 41 scored Math questions of that practice test, we counted 15 that needed a formula from memory. The ones to know cold: slope, distance and midpoint, the quadratic formula, area and volume of common shapes, the Pythagorean theorem and special right triangles, SOH-CAH-TOA, and mean and basic probability.
Where it shows up on the ACT
| Enhanced ACT | |
|---|---|
| Section | Math |
| Length | 45 questions (41 scored) in 50 minutes, about 67 seconds each |
| Reporting category | Runs through Preparing for Higher Math and Integrating Essential Skills |
| Share of the section | 15 of the 41 scored questions in ACT's 2025–26 practice test needed a remembered formula (our count) |
| In the Composite | Yes. The Composite averages English, Math and Reading. |
ACT doesn't publish how many questions need a formula; this is Ashore's count from one practice test, so treat it as a rough guide. Source: ACT, Preparing for the ACT 2025–2026: full practice test, directions and scoring keys.
What the questions ask you to do
- Find a slope, a midpoint or a distance between two points.
- Solve a quadratic by factoring or with the quadratic formula.
- Find the area, perimeter, surface area or volume of a shape, often one made of two simpler shapes.
- Use the Pythagorean theorem, special right triangles or a trig ratio to find a side.
- Find a term of an arithmetic or geometric sequence.
- Compute a mean, a probability or an expected value.
The formulas to memorize
Grouped by topic. None of these are printed on the test, on paper or online.
| Topic | Formula | Use it for |
|---|---|---|
| Slope | m = (y₂ − y₁) ÷ (x₂ − x₁) | Steepness of a line |
| Line | y = mx + b | Slope m, y-intercept b |
| Distance | d = √((x₂ − x₁)² + (y₂ − y₁)²) | Length between two points |
| Midpoint | ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2) | Point halfway between two points |
| Quadratic formula | x = (−b ± √(b² − 4ac)) ÷ 2a | Solving ax² + bx + c = 0 |
| Exponents | xᵃ · xᵇ = xᵃ⁺ᵇ, (xᵃ)ᵇ = xᵃᵇ | Simplifying powers |
| Arithmetic sequence | aₙ = a₁ + (n − 1)d | The nth term with common difference d |
| Geometric sequence | aₙ = a₁ · rⁿ⁻¹ | The nth term with common ratio r |
| Triangle | Area = ½ × base × height | Any triangle |
| Circle | Area = πr², circumference = 2πr | Use the radius, not the diameter |
| Arc and sector | Arc = (θ ÷ 360) × 2πr, sector = (θ ÷ 360) × πr² | Part of a circle with central angle θ in degrees |
| Circle equation | (x − h)² + (y − k)² = r² | Center (h, k), radius r |
| Box and cylinder | V = lwh, V = πr²h | Volume |
| Polygon angles | Sum of interior angles = (n − 2) × 180° | A polygon with n sides |
| Pythagorean theorem | a² + b² = c² | Right triangles, c is the hypotenuse |
| Special right triangles | 30°-60°-90°: x, x√3, 2x. 45°-45°-90°: x, x, x√2 | Sides without a calculator |
| Trig ratios | sin = opposite ÷ hypotenuse, cos = adjacent ÷ hypotenuse, tan = opposite ÷ adjacent | SOH-CAH-TOA |
| Radians | 180° = π radians | Converting angle units |
| Mean | Sum of values ÷ number of values | Also: sum = mean × count |
| Probability | Favorable outcomes ÷ total outcomes | Independent events: multiply |
| Expected value | Sum of (value × its probability) | Average result over many tries |
| Percent change | (new − old) ÷ old × 100% | Divide by the starting value |
What the formula questions were about
The 15 scored questions we counted in ACT's 2025–26 practice test, by topic.
- Geometry: four questions (the Pythagorean theorem and trig ratios in right triangles, a hexagon inside a circle, the volume of a cylinder).
- Angle facts: two questions (which side of a triangle is longest, the angles of a quadrilateral).
- Statistics and probability: three questions (mutually exclusive events, comparing standard deviations, an expected value).
- Algebra and functions: four questions (expanding a cube, a term of an arithmetic sequence, shifting a graph, degrees to radians).
- Coordinate geometry and matrices: two questions (distance on a circle, multiplying a matrix by a number).
Common mistakes
Wrong answer choices are often built around these.
- Using the diameter where the formula needs the radius. A circle with diameter 10 has area 25π, not 100π.
- Dividing by the new value in a percent change. Always divide by the starting value.
- Taking only the + in the quadratic formula. Most quadratics have two solutions, and a question may ask for their sum or the negative one.
- Swapping sine and cosine. Label the sides opposite, adjacent and hypotenuse from the angle in the question before you pick a ratio.
- Flipping slope into run over rise. The y-values go on top.
- Stopping one step early. A question that asks for a perimeter may need the Pythagorean theorem first to find a missing side.
3 example questions with answers
Written by Ashore in the style of the enhanced ACT. They aren't official ACT questions. Try each one before you open the answer.
Question 1 · Easy
A line passes through the points (2, 3) and (6, 11). What is the slope of the line?
- A1/2
- B2
- C4
- D8
Show the answer
B. Slope is the change in y over the change in x: (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2. The choice 1/2 is the change in x over the change in y, and 8 is the change in y alone.
Question 2 · Medium
A cylindrical water tank has a radius of 3 feet and a height of 5 feet. What is its volume, in cubic feet?
- F9π
- G15π
- H30π
- J45π
Show the answer
J. V = πr²h = π × 3² × 5 = 45π. 9π is the area of the circular base alone, 15π leaves out the square on the radius, and 30π is the area of the curved side (2πrh).
Question 3 · Hard
In right triangle PQR, angle P measures 30° and the hypotenuse is 14 units long. How long is the side opposite the 60° angle?
- A7
- B7√2
- C7√3
- D14√3
Show the answer
C. In a 30°-60°-90° triangle the sides are x, x√3 and 2x, with the hypotenuse 2x. Here 2x = 14, so x = 7 is the side opposite 30° and the side opposite 60° is 7√3. 7√2 comes from the 45°-45°-90° pattern.
More ACT Math guides
- What topics are on ACT Math
- Integrating Essential Skills
- Desmos and calculators
- ACT score calculator: questions right in each section to a 1–36 score and Composite.
- SAT vs ACT: which test fits you better.
- All ACT guides and free tools
Get ready for ACT Math
Ashore's ACT course is coming soon: a starting check, a daily plan up to your test date and timed practice. Join the waitlist and we'll email you once when it opens.
When ACT prep opens, it's part of the same plan as SAT and AP, at the same price. The score guarantee covers the SAT only.
Practice test 1
Example
27
Composite
(28 + 26 + 27) ÷ 3
- English28
- Math26
- Reading27
- ScienceOptional, not in the Composite25