### Cheat Sheet with Formulas

Cheat Sheet – You may print this page for your own reference.

However, this sheet may not be electronically reproduced or posted on online forums or document-sharing platforms.

#### Cheat Sheet for Coordinate Geometry

**Midpoints:**

Midpoint x: (x_{1} + x_{2}) ÷ 2

Midpoint y: (y_{1} + y_{2}) ÷ 2

**x and y intercepts:**

These are the points where the line on a two-dimensional graph intersects with the x and y axes.

You will see an algebraic equation which represents the line on the two-dimensional graph.

The equation will contain the variables x and y.

To calculate the x intercept, substitute 0 for y.

To calculate the y intercept, substitute 0 for x.

**Slope:**

y = mx + b

m = slope

b = y intercept

x, y = points on the graph or in the equation

#### Cheat Sheet for Plane Geometry

**Area of circle:**

π × R^{2} (radius squared)

**Area of square or rectangle:**

length × width

**Area of triangle:**

(base × height) ÷ 2

**Arcs:**

Arc length is the distance on the outside of a circle.

Calculate the circumference for the part of circle for the degrees stated.

**Chords:**

A chord is a straight line which is drawn inside a circle.

That line connects two points on the circumference of the circle.

Use the degrees stated for the given angle to calculate chord length.

**Circumference of a circle:**

π × diameter

diameter = radius × 2

**Cone volume:**

(π × radius^{2} × height) ÷ 3

**Cylinder volume:**

V = πr^{2}h

Volume = π times the radius squared times the height

**Hypotenuse length:**

Length of hypotenuse = square root of the sum of the squares of the other two sides

**Perimeter of squares and rectangles:**

(length × 2) + (width × 2)

#### Cheat Sheet for Trigonometry

**Radians:**

θ = s ÷ r

θ = radians

s = arc length

r = radius

π × 2 × radians = 360°

π × radians = 180°

π ÷ 2 × radians = 90°

π ÷ 4 × radians = 45°

π ÷ 6 × radians = 30°

**Tangent, sine, and cosine:**

cos^{2} A + sin^{2} A = 1

cos^{2} A = 1 − sin^{2} A

sin^{2} A = 1 − cos^{2} A

tan A = sin A ÷ cos A

You can get more math help for the ACT from our **math formulas** section, our **free sample test**, and our **ACT download**.