SAT Math Formulas to Know for SAT

Mastering key math formulas is essential for tackling the SAT. These formulas cover various topics, from geometry to algebra, helping you solve problems efficiently and accurately. Knowing them can boost your confidence and improve your test performance.

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

   • The base (b) and height (h) must be perpendicular to each other.
   • This formula applies to all triangles, not just right triangles.
   • Understanding this formula is crucial for solving problems involving triangles in various contexts.

2. Pythagorean theorem: a² + b² = c²

   • Applies only to right triangles, where c is the hypotenuse.
   • Useful for finding the length of a side when the other two sides are known.
   • Can be extended to three-dimensional problems involving right triangular prisms.

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

   • Represents the steepness of a line on a graph.
   • A positive slope indicates an upward trend, while a negative slope indicates a downward trend.
   • Essential for understanding linear equations and graphing lines.

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

   • Used to find the roots of a quadratic equation in the form ax² + bx + c = 0.
   • The discriminant (b² - 4ac) determines the nature of the roots (real and distinct, real and equal, or complex).
   • A fundamental tool for solving quadratic equations in various applications.

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

   • Calculates the straight-line distance between two points in a coordinate plane.
   • Essential for problems involving geometry and coordinate systems.
   • Can be applied in real-world contexts, such as navigation and mapping.

6. Midpoint formula: [(x₁ + x₂)/2, (y₁ + y₂)/2]

   • Finds the exact center point between two coordinates.
   • Useful in geometry for bisecting line segments.
   • Helps in determining average positions in various applications.

7. Area of a circle: A = πr²

   • r represents the radius of the circle.
   • Important for problems involving circular shapes and real-world applications like land area.
   • Understanding this formula aids in solving problems related to circles in geometry.

8. Circumference of a circle: C = 2πr

   • Represents the distance around the circle.
   • Directly related to the radius; knowing one allows you to find the other.
   • Useful in problems involving circular motion and perimeter calculations.

9. Volume of a rectangular prism: V = l × w × h

   • l, w, and h represent the length, width, and height, respectively.
   • Essential for calculating capacity in three-dimensional space.
   • Applies to various real-world scenarios, such as packaging and storage.

10. Area of a trapezoid: A = (1/2)(b₁ + b₂)h

    • b₁ and b₂ are the lengths of the two parallel sides, and h is the height.
    • Useful for calculating areas of irregular shapes in geometry.
    • Important in applications involving land measurement and design.

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

    • 30-60-90 triangle: sides are in the ratio 1:√3:2.
    • 45-45-90 triangle: sides are in the ratio 1:1:√2.
    • Knowing these ratios simplifies calculations in trigonometry and geometry.

12. Exponential growth/decay: A = P(1 ± r)ⁿ

    • A represents the amount after time n, P is the initial amount, and r is the rate of growth/decay.
    • Important for modeling real-world scenarios like population growth and radioactive decay.
    • Understanding this formula is crucial for solving problems involving exponential functions.

13. Arithmetic sequence: aₙ = a₁ + (n - 1)d

    • a₁ is the first term, d is the common difference, and n is the term number.
    • Useful for finding specific terms in a sequence and understanding linear patterns.
    • Applies to various mathematical and real-world contexts, such as finance and scheduling.

14. Geometric sequence: aₙ = a₁rⁿ⁻¹

    • a₁ is the first term, r is the common ratio, and n is the term number.
    • Important for modeling situations involving exponential growth or decay.
    • Useful in finance, biology, and computer science for understanding patterns.

15. Probability formula: P(A) = (favorable outcomes) / (total outcomes)

    • Helps determine the likelihood of an event occurring.
    • Essential for solving problems in statistics and real-world decision-making.
    • Understanding probability is crucial for interpreting data and making informed choices.