ACT Math Formulas to Memorize for ACT

Mastering key math formulas is crucial for success on the ACT. These formulas cover areas, volumes, and geometric relationships, helping you tackle a variety of questions efficiently. Familiarity with these concepts will boost your confidence and performance on test day.

1. Area of a rectangle: A = lw

   • A rectangle's area is calculated by multiplying its length (l) by its width (w).
   • Units of area are always squared (e.g., square meters).
   • Understanding this formula is essential for solving problems involving rectangular spaces.

2. Area of a triangle: A = 1/2bh

   • The area of a triangle is half the product of its base (b) and height (h).
   • This formula is crucial for calculating areas in various geometric contexts.
   • Remember that the height must be perpendicular to the base.

3. Area of a circle: A = πr²

   • The area of a circle is determined by squaring the radius (r) and multiplying by π (approximately 3.14).
   • This formula is vital for problems involving circular shapes and sectors.
   • Ensure to use the radius, not the diameter, in calculations.

4. Circumference of a circle: C = 2πr

   • The circumference is the distance around a circle, calculated by multiplying the diameter by π or using the radius.
   • This formula is important for understanding the relationship between radius and diameter.
   • Useful in problems involving circular motion or perimeter calculations.

5. Pythagorean theorem: a² + b² = c²

   • This theorem applies to right triangles, relating the lengths of the legs (a and b) to the hypotenuse (c).
   • It is essential for solving problems involving distances and triangle properties.
   • Can be used to determine if a triangle is a right triangle.

6. Slope formula: m = (y₂ - y₁) / (x₂ - x₁)

   • The slope (m) measures the steepness of a line, calculated by the change in y over the change in x.
   • Important for understanding linear equations and graphing lines.
   • A positive slope indicates an upward trend, while a negative slope indicates a downward trend.

7. Midpoint formula: ((x₁ + x₂)/2, (y₁ + y₂)/2)

   • The midpoint of a line segment is found by averaging the x-coordinates and y-coordinates of the endpoints.
   • Useful for determining the center point between two coordinates.
   • Essential in coordinate geometry problems.

8. Distance formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

   • This formula calculates the distance between two points in a coordinate plane.
   • It is derived from the Pythagorean theorem and is crucial for geometry and algebra problems.
   • Always ensure to square the differences before taking the square root.

9. Quadratic formula: x = [-b ± √(b² - 4ac)] / 2a

   • This formula provides the solutions to quadratic equations in the form ax² + bx + c = 0.
   • It is essential for finding roots of polynomials and solving various algebraic problems.
   • The discriminant (b² - 4ac) indicates the nature of the roots (real and distinct, real and equal, or complex).

10. Volume of a rectangular prism: V = lwh

    • The volume is calculated by multiplying the length (l), width (w), and height (h) of the prism.
    • Units of volume are cubed (e.g., cubic meters).
    • Important for problems involving three-dimensional space.

11. Volume of a cylinder: V = πr²h

    • The volume is found by multiplying the area of the base (circle) by the height (h).
    • Essential for calculating capacities and storage in cylindrical shapes.
    • Remember to use the radius for the base area calculation.

12. Surface area of a rectangular prism: SA = 2(lw + lh + wh)

    • The surface area is the total area of all the faces of the prism.
    • Important for problems involving material costs or painting surfaces.
    • Units of surface area are squared.

13. Surface area of a cylinder: SA = 2πrh + 2πr²

    • This formula combines the lateral area and the area of the two circular bases.
    • Useful for determining the amount of material needed to cover a cylinder.
    • Remember to include both the curved surface and the bases.

14. SOHCAHTOA for trigonometry ratios

    • A mnemonic for remembering the definitions of sine, cosine, and tangent.
    • SOH: Sine = Opposite/Hypotenuse; CAH: Cosine = Adjacent/Hypotenuse; TOA: Tangent = Opposite/Adjacent.
    • Essential for solving right triangle problems and understanding trigonometric functions.

15. Special right triangle ratios (30-60-90 and 45-45-90)

    • In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.
    • In a 45-45-90 triangle, the sides are in the ratio 1:1:√2.
    • Knowing these ratios allows for quick calculations without needing to use the Pythagorean theorem.