Math Formulas We Wish Every Student Had Memorized

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Want to score higher on SAT and ACT math sections? Memorize these formulas before you begin prepping. 

 

1. Average or mean = Sum of values / Number of values

Ex: (10 + 12 + 14 + 16) / 4 = 13

 

2. Probability = Target outcomes / Total outcomes

Used to calculate the chances of something occurring from a set of possible outcomes.

Ex: A jar contains five blue marbles, five red marbles, and ten white marbles. What is the probability of picking a red marble at random?

5 / 20 = .25 or 25%

 

3. Quadratic Formula: x = −b ± √b²-4ac/2a

Used for determining the x-intercepts of a quadratic (parabolic) equation.

Ex: A = 1, B = -4, C = 4

  • x = -4 ± √4² – 4 (1)(4) / 2(1)
  • x = -4 ± √ 16 – 4(4) / 2
  • x = -4 ± √16 – 16 / 2
  • x = -4 ± √ 0 / 2
  • x = -4 / 2
  • x = -2

 

4. Distance Formula: d=√(x₁ – x₂)² + (y₁ – y₂)²

Ex. Find the distance between points (6, 6) and (2, 3)

  • d=√(6 – 2)² + (6 – 3)²
  • d=√(4)² + (3)²
  • d=√16 + 3
  • d=√25
  • d = 5

 

5. Slope Formula: Slope = y₂ – y₁ /  x₂ – x₁

Calculate the slope (angle) of a line that connects two points on a plane.

Ex: Coordinates = (-2, -1) (4, 3)

  • s = 3 – (-1) / 4 – (-2)
  • s = 4 / 6
  • s = 2 / 3

 

6. Slope Intercept: y=mx+b

Formula the defines a line on a plane, given a known slope and y-intercept.

Ex: Slope = 2, Intercept point (0,3)

  • y = 2x+3

 

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

Calculates the midpoint between to points on a plane.

Ex: Find the midpoint between (-1, 2) and (3, -6)

  • (-1 + 3) / 2, (2 + -6) / 2
  • 2 / 2, -4 / 2
  • Midpoint (1, -2)

 

8. Area of Triangle: area = (1/2) (base) (height)

Calculate the total area within a triangle based on the lengths of the sides.

Ex: Base = 5, Height = 8

  • a = 1/2 (5)(8)
  • a = 1/2 (40)
  • a = 20

 

9. Pythagorean Theorem: a²+b²=c²

Used to calculate the length of an unknown side of a right triangle, given two sides are known.

Ex: a = 3, b = 4

  • c² = 3² + 4²
  • c² = 9 + 16
  • c² = 25
  • c = √25
  • c = 5

 

10. Area of Rectangle: area = length x width

Calculates the total area within a rectangle shape.

Ex: length = 5, width = 2

  • a = 5 x 2
  • a = 10

 

11. Area of Parallelogram: area = base x height

Calculates the total area within a parallelogram.

Ex: base = 6, height = 12

  • a = 6 x 12
  • a = 72

 

12. Area of Circle: π * r²

Calculates the total area within a circle.

Ex: radius = 4

  • a = π x 4²
  • a = π x 16
  • a = 50.24

 

13. Circumference of Circle: circumference = 2π *  r

Calculate the length of the outline of a circle.

Ex: radius = 7

  • c = 2π x 7
  • c = 43.98

 

14. Sine (SOH): Sine = opposite / hypotenuse

A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle.

Ex: opposite = 2.8, hypotenuse = 4.9

  • s = 2.8 / 4.9
  • s = 0.57

 

15. Cosine (CAH): Cosine = adjacent / hypotenuse

A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle.

Ex: adjacent = 11, hypotenuse = 13

  • c = 11 / 13
  • c = 0.85

 

16. Tangent (TOA): Tangent = opposite / adjacent

A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle.

Ex: opposite = 15, adjacent = 8

  • t = 15 / 8
  • t = 1.87