The SAT formula sheet provides basic formulas for circles, area, triangles, and volume. But there many additional formulas it will be helpful to know on test day so you can fly through the math section with confidence.

## Problem Solving and Data Analysis

### Percents

OR change words to an algebraic equation and solve

Example: 40% of what is 20?

Percent increase or decrease:

### Mean (the average)

### Median

Middle value when items are arranged from least to greatest

### Range

The difference between the max value and min value

### Mode

Value that occurs the most in a set

### Standard Deviation

Shows how spread data points are.

**Low standard deviation: ** data points are closer to the mean

**High standard deviation: ** data is spread over a wider range

### Probability of an Event

**Joint or conditional probability **

**Mutually exclusive probability**

### Fundamental Counting Principle

Pick 1 from each group, multiply the number of options in each group

### Permutation

A combination of events occurring when order matters and the items cannot be repeated

### Combination

A combination of events occurring when the order does NOT matter

### Arithmetic Sequences

Each term (*t*) is the previous term plus a common difference (*d*)

to find the nth term:

### Geometric Sequences

Each term (*t*) is the previous term times a common ratio (*r*)

to find the *n*th term:

Key Math Section Strategy for the ACT or SAT

## Heart of Algebra and Passport to Advanced Math

### Domain

Set of possible values of *x* that can be plugged into a function (Input).

### Range

Set of possible values of *y* that a function takes on (Output).

### Lines

Slope of the line:

Parallel lines have the same slope and Perpendicular lines have slopes that are negative reciprocals

**Slope-intercept form: **

**Point-slope form:**

### Midpoint Formula

### Distance Formula

### Direct Variation

*y*=*kx* where *k *is the constant of variation

### Indirect Variation

where *k* is the constant of variation

### Standard Form of a Quadratic

To find the solutions: set *y* equal to 0, and solve for *x* by factoring or use the Quadratic Formula

To find the vertex:

plug value back into the equation to find y-coordinate

### Vertex Form of a Quadratic

The vertex is (*h, k*).

### Factored Form of a Quadratic

x-intercepts/solutions/zeros are *x=p *&* x=q*

### Exponential Functions

Shows growth if *b>1*or decay if *0<b<1*

Growth/Decay when *r* is a percent:

Interest compounded *n* times for *t* years:

### Exponents & Roots

## Additional Topics in Math

### Complex Numbers

Use the conjugate to eliminate the imaginary:

### Triangles

Degrees sum to 180°

Sides: No side can be greater than the sum or less than the difference in length of the other two. Side lengths are in the same ratio as opposite angle measures

**Special Right Triangles**

Complementary angles sum to 90°

Supplementary angles sum to 180°

Exterior angles for ANY polygon sum to 360°.

Interior angles for a polygon sum to 180°(*n*-2) where *n* is the number of sides in the polygon.

### Trigonometric Ratios

### Trigonometric Relationships

### Circle

**Degrees in a Circle: **

Find radians of given degrees:

Find degrees of given radians:

**Standard Form of a Circle**:

**Vertex Form of a Circle:**

where* (h,k)* is center and *r* is radius