ACT Math Formulas: Essential Guide to Memorize

The ACT Math section challenges students with 60 questions in just 60 minutes, covering pre-algebra, algebra, geometry, and trigonometry—without providing a formula reference sheet. Memorizing core formulas is crucial for speed and accuracy, as they appear repeatedly across question types worth up to 24 points each in major categories. This guide breaks down the most frequent formulas, with clear explanations, worked examples, and practice strategies to build confidence.

Why Memorize Formulas for ACT Math?

Unlike the SAT, the ACT offers no math reference sheet, forcing reliance on memory under timed pressure—one minute per question. Questions span:

• Pre-Algebra/Elementary Algebra: 24 questions (basic operations, averages, probabilities).
• Intermediate Algebra/Coordinate Geometry: 18 questions (lines, quadratics, distances).
• Plane Geometry/Trigonometry: 18 questions (shapes, circles, trig ratios).

Mastering 15-20 key formulas covers 80-90% of problems, freeing mental energy for complex solving. Focus on high-yield ones first: averages, slope, distance, quadratics, and circle area.

Core Formulas for Pre-Algebra and Elementary Algebra

This foundational section tests number properties and basic solving. Expect questions on data interpretation and chance calculations.

Average (Arithmetic Mean)

Formula: Average = Total Sum of Values ÷ Number of Values.

Use this for datasets like test scores or temperatures. It levels data to a central value.

Example: What’s the average of 8, 12, 15, 19?
Sum = 8 + 12 + 15 + 19 = 54
Average = 54 ÷ 4 = 13.5

Tip: For weighted averages, multiply each value by its weight before summing.

Probability Basics

Formula: Probability = Favorable Outcomes ÷ Total Possible Outcomes.

Ideal for dice rolls, card draws, or event likelihoods (ranges 0 to 1).

Example: Probability of drawing a red marble from a bag with 3 red and 7 blue?
Probability = 3 ÷ (3 + 7) = 3/10 = 0.3

Practice Problem: In a deck of 52 cards, what’s the chance of an ace? (Answer: 4/52 = 1/13)

Percentages and Proportions

Formulas:
Percentage: (Part/Whole) × 100
Proportion: a/b = c/d

Quick conversions save time: 25% = 1/4, 50% = 1/2.

Example: 20% of 150?
(20/100) × 150 = 30

Key Formulas for Intermediate Algebra and Coordinate Geometry

These handle lines, curves, and points on planes—vital for 5-6 linear questions per test.

Slope of a Line

Formula: m = (y₂ – y₁) ÷ (x₂ – x₁).

Measures steepness; positive rises left-to-right, negative falls.

Example: Points (1, 3) and (4, 9):
m = (9 – 3) ÷ (4 – 1) = 6/3 = 2

Distance Between Points

Formula: d = √[(x₂ – x₁)² + (y₂ – y₁)²].

Pythagorean theorem applied to coordinates.

Example: From (0,0) to (3,4):
d = √[(3-0)² + (4-0)²] = √(9+16) = √25 = 5

Midpoint Finder

Formula: Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2].

Locates the center between endpoints.

Example: (-2, 5) and (4, -1):
x = (-2+4)/2 = 1
y = (5 + -1)/2 = 2
Midpoint: (1, 2)

Quadratic Equation Solver

Formula: x = [-b ± √(b² – 4ac)] / (2a), for ax² + bx + c = 0.

Discriminant (b² – 4ac) reveals roots: positive (two real), zero (one), negative (none real).

Example: x² + 4x + 4 = 0
a=1, b=4, c=4
x = [-4 ± √(16 – 16)] / 2 = -4/2 = -2 (repeated root)

Line Equation Forms

Slope-intercept: y = mx + b (m=slope, b=y-intercept).
Point-slope: y – y₁ = m(x – x₁).

Example: Slope 3 through (1,2): y – 2 = 3(x – 1) → y = 3x -1

Plane Geometry and Trigonometry Essentials

Focus on shapes, areas, and angles—use π ≈ 3.14.

Circle Properties

Formulas:
Circumference: C = 2πr
Area: A = πr².

Example: r=5: A = 3.14 × 25 ≈ 78.5

Rectangles and Triangles

Rectangle Area: A = length × width.
Triangle Area: A = (base × height)/2.

Example: Base 6, height 4: A = (6×4)/2 = 12

Trigonometric Ratios

In right triangles:
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent (SOH-CAH-TOA).

Example: Opposite=3, adjacent=4, hypotenuse=5:
sin θ = 3/5 = 0.6

Study Strategies and Practice Tips

To retain formulas:

• Flashcards: One side formula, other example.
• Daily Drills: 10 problems per category, timed.
• Full Practice Tests: Simulate 60-min section weekly.
• Mnemonics: ‘Please Excuse My Dear Aunt Sally’ for PEMDAS.

Track errors: revisit weak areas like trig if geometry scores lag.

Common Pitfalls and How to Avoid Them

• Misreading coordinates—double-check (x,y) order.
• Forgetting squares in distance formula.
• Calculator errors on quadratics—verify discriminant.
• Ignoring units in geometry (e.g., radius vs. diameter).

FAQs

Does the ACT provide any formulas?

No, unlike SAT. Memorize all.

How many formulas to learn?

20 core ones cover most; prioritize by section.

Can I derive formulas on test day?

Possible for some (e.g., distance from Pythagoras), but risky under time.

What’s the hardest section?

Geometry/trig for many; practice visuals.

Online resources for practice?

Official ACT site, Khan Academy (aligns with topics).

Sample Practice Quiz

1. Average of 5, 10, 15? (10)
2. Slope (2,1) to (5,7)? (2)
3. Distance (0,0) to (5,12)? (13)
4. Area circle r=4? (≈50.24)
5. Quadratic x² – 5x + 6=0 roots? (2,3)

Score 5/5? You’re ready. Review misses.

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Medha Deb

Medha Deb is an editor with a master's degree in Applied Linguistics from the University of Hyderabad. She believes that her qualification has helped her develop a deep understanding of language and its application in various contexts. Medha specializes in the areas of beauty, health, sports, and wellness and is committed to ensuring that the content on the website is…