1. The mean is the average of the numbers. Sum of values / Number of values

It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count. 

For example: The mean of 4, 1, and 7 is 

=> ( 4 + 1 + 7 ) / 3 

=> 12 / 3 

=> 4  

2. Probability = Target outcomes / Total outcomes

For example: 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

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

For example: 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

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

Specifically calculates the distance between two points on a coordinate plane.

For example: 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

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

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

For example: Coordinates = (-2, -1) (4, 3)

=> s = 3 – (-1) / 4 – (-2)

=> s = 4 / 6

=> s = 2 / 3

3. Slope Intercept: y=mx+b

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

For example: Slope = 2, Intercept point (0,3)

y = 2x+3

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

Specifically calculates the midpoint between to points on a plane.

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

=> (-1 + 3) / 2, (2 + -6) / 2

=> 2 / 2, -4 / 2

=> Midpoint (1, -2)

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

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

For example: Base = 5, Height = 8

a = 1/2 (5)(8)

a = 1/2 (40)

a = 20

2. Pythagorean Theorem: a²+b²=c²

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

For example: a = 3, b = 4

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5

3. Area of Rectangle: area = length x width

Calculates specifically the total area within a rectangle shape.

For example: length = 5, width = 2

a = 5 x 2

a = 10

4. Area of Parallelogram: area = base x height

Specifically calculates the total area within a parallelogram.

For example: base = 6, height = 12

a = 6 x 12

a = 72

5. Area of Circle: π * r²

Calculates specifically the total area within a circle.

For example: radius = 4

a = π x 4²

a = π x 16

a = 50.24

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

Calculates specifically the length of the outline of a circle.

For example: radius = 7

c = 2π x 7

c = 43.98

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

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

For example: opposite = 2.8, hypotenuse = 4.9

s = 2.8 / 4.9

s = 0.57

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

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

For example: adjacent = 11, hypotenuse = 13

c = 11 / 13

c = 0.85

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

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

For example: opposite = 15, adjacent = 8

t = 15 / 8

t = 1.87