SAT Math Formulas

sat formula sheet

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 nth 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 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>1or 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

Rectangular Prism

Cylinder