SAT Math

Standard Deviation

The spread from the average. Example: Low spread: 5, 5, 5, 5. High spread: 0, 0, 10, 10.

Vertex Form

a(x − h)² + k

Vertex Form: Vertex

(h, k) is the vertex.

No Real Solutions

If the discriminant D < 0.

One Real Solution

If the discriminant D = 0.

Two Real Solutions

If the discriminant D > 0.

Discriminant

b² − 4ac

Discriminant: What does it determine?

How many real solutions there are.

Product of the Roots

c/a

Exponential Growth and Decay

xₜ = x₀(1 + r)ᵗ

Exponential Growth and Decay: t

How often the growth or decay increases/decreases.

Exponential Growth and Decay: x₀

The initial amount.

Exponential Growth and Decay: 1 + r

The growth/decay factor.

Solutions for a Quadratic

x-intercepts and roots.

Circumference

2πr

Area of a Circle

πr²

Sector Length

(θ/360) × 2πr

Sector Area

(θ/360) × πr²

Desmos: Circle Equation

(x − h)² + (y − k)² = r²

Volume of a Cylinder

πr²h

Determining if Triangles Are Similar

Use AA, SAS, or SSS.

ASS

ASS is not enough to prove triangles are similar.

Supplementary Angles

Angles add up to 180°.

Sum of the Roots

−b/a

Complementary Angles

Angles add up to 90°.

Standard Quadratic Form

ax² + bx + c

Quadratic Formula

x = (−b ± √(b² − 4ac))/(2a)

Area of Square A Compared to Square B

If the area of square A is 3/4 the area of square B, then A = (3/4)B.

Example: Area of Square A

121 = (3/4)x

Area of a Square

x²

Perimeter of a Square

4x

Area of a Rectangle

LW

Perimeter of a Rectangle

2L + 2W

Cutting a Square in Half

Creates a 45°−45°−90° triangle.

45-45-90 Triangle Ratio

x : x : x√2

Similar Shapes: Area Ratio

If the ratio of corresponding sides is a:b, the ratio of their areas is a²:b².

Interchangeable

Systems of equations solutions, roots, and x-intercepts.

Mirroring

If the same expression appears on both sides of an equation, isolate the variable/expression to determine the solution.

Vertical Shift

Outside the parentheses; moves a graph up or down.

Horizontal Shift

Inside the parentheses; moves a graph left or right.

Same Lines

Infinitely many solutions.

Perpendicular Lines

Intersect to make a 90° angle; their slopes are opposite reciprocals.

Parallel Lines

No solutions because they do not intersect; they have the same slope.

Slope

(y₂ − y₁)/(x₂ − x₁), or rise over run.

Y-Intercept: b

The point where x = 0.

Linear Equation

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

Vertex Form: a

In a(x − h)² + k, a determines the vertical stretch/compression and whether the parabola opens up or down.

Standard Deviation

The spread from the average.

Ambiguous Percent Problem

If no specific number is given, plug in 100.

Percentage

Part/whole = x/100%.

mean

the average. Add all the numbers together, then divide by how many numbers there are.

Example:

Numbers: 2, 4, 6, 8

→ (2 + 4 + 6 + 8) ÷ 4 = 5

median

the middle number when the numbers are put in order.

Example:

Numbers: 3, 5, 7, 9, 11

= 7

***If there are two middle numbers, average them***

mode

the number that appears most often.

Example:

Numbers: 2, 3, 3, 4, 5, 3, 6

= 3