ACT math study guide

Slope-Intercept Form

y=mx+b. m is the slope, b is the y-intercept

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

Special Products (FOIL)

(x+y)^2 =x^2 +2xy+y^2. (x−y)^2 =x^2 −2xy+y^2. (x+y)(x−y)=x^2−y^2.

Function Notation

f(x) is another way of writing y.

Pythagorean Theorem

a²+b²=c²

Area of a Circle

A=πr²

Circumference of a Circle

C=2πr or C=πd.

Area of a Triangle

A=1/2bh

Special Right Triangles (45-45-90)

Ratios are x, x, x√2

Special Right Triangles (30-60-90)

Ratios are x, x√3, 2x

Volume of a Cylinder

V=πr²h

SOH CAH TOA

sin= opposite/hypo; cos= adjacent/hypo; and tan= opposite/ adjacent

The "Pythagorean Identity"

sin²θ + cos²θ = 1

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

Slope Formula

y2-y1/x2-x1

Mean

average

Median

The middle number of an ordered list.

Mode

The number that appears most often.

Range

the difference between the highest and lowest values (greatest - least = range)

Probability

number of desired outcomes / number of total outcomes

Use Parentheses

Crucial for fractions and negative numbers with exponents.

Check Your Mode

Your calculator must be in DEGREE mode for trigonometry problems.

Use the "y=" function

Graph equations to find intersections or roots.