Math Formulas To Know For Act

Math Formulas to Know for the ACT: A Comprehensive Guide

Meta Description: Conquer the ACT math section with confidence! This guide covers essential formulas you NEED to know, categorized for easy memorization and application. Boost your score with this cheat sheet of crucial math concepts.

The ACT Math section tests your understanding of various mathematical concepts. While you won't be explicitly given formulas, knowing certain key formulas beforehand significantly improves your speed and accuracy. This guide breaks down the essential formulas you should master before test day, categorized for easy memorization and recall.

Geometry Formulas: Shapes & Spatial Reasoning

This section covers fundamental geometric concepts frequently appearing on the ACT. Mastering these formulas is crucial for efficient problem-solving.

• Area of a rectangle: Area = length × width
• Area of a square: Area = side²
• Area of a triangle: Area = (1/2) × base × height
• Area of a trapezoid: Area = (1/2) × (base1 + base2) × height
• Area of a circle: Area = πr²
• Circumference of a circle: Circumference = 2πr or Circumference = πd (where d is the diameter)
• Volume of a rectangular prism: Volume = length × width × height
• Volume of a cube: Volume = side³
• Volume of a cylinder: Volume = πr²h
• Volume of a sphere: Volume = (4/3)πr³
• Pythagorean Theorem: a² + b² = c² (where a and b are legs of a right triangle, and c is the hypotenuse)
• Special Right Triangles: Remember the ratios of sides in 30-60-90 and 45-45-90 triangles.

Algebra Formulas: Equations & Inequalities

Algebra forms a significant part of the ACT Math section. Understanding these formulas and their applications is key to success.

• Slope of a line: Slope (m) = (y₂ - y₁) / (x₂ - x₁)
• Slope-intercept form of a line: y = mx + b (where m is the slope and b is the y-intercept)
• Point-slope form of a line: y - y₁ = m(x - x₁)
• Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a (used to solve quadratic equations of the form ax² + bx + c = 0)
• Distance Formula: Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
• Midpoint Formula: Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Trigonometry Formulas: Angles & Ratios

While not heavily emphasized, a basic understanding of trigonometry is beneficial.

• SOH CAH TOA: This mnemonic helps remember the basic trigonometric functions:
  • Sine (sin): Opposite/Hypotenuse
  • Cosine (cos): Adjacent/Hypotenuse
  • Tangent (tan): Opposite/Adjacent

Other Essential Concepts & Strategies

• Percentage Calculations: Mastering percentage increases, decreases, and finding percentages of numbers is crucial.
• Average (Mean): Know how to calculate the average of a set of numbers.
• Median & Mode: Understanding median (middle value) and mode (most frequent value) is important for data analysis questions.
• Probability: Know basic probability calculations.
• Exponents and Roots: Understand exponent rules and how to simplify expressions with roots.
• Factoring: Practice factoring quadratic expressions.

Practice Makes Perfect:

Simply memorizing these formulas isn't enough. Consistent practice with ACT-style problems is vital to solidify your understanding and build speed and accuracy. Use practice tests and focus on areas where you struggle. Good luck!