# Math Formulas We Wish Every Student Had Memorized

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.

• 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.

• 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