SAT Math

quadratic formula

[-b ± √(b² - 4ac)] / (2a)

slope formula

(y₂- y₁) / (x₂- x₁)

integers

…, -3, -2, -1, 0, 1, 2, 3, …

rationals

fractions (anything expessable as a ratio of integers)

reals

integers, rationals, plus special #s (like √2 or pi)

order of opperations

PEMDAS (Parentheses / Exponents / Multiply / Divide / Add / Subtract)

Arithmetic Sequences

t₁, t₁+ d, t₁+2d, …

Geometric Sequences

t₁, t₁· r, t₁· r², …

percentages

part = (percent / 100) x whole

average

average = sum of terms / number of terms

average speed

average speed = total distance / total time

sum

sum = average x (number of terms)

mode

mode = value in the list that appears most often

median

median = middle value in the list

probability

probability = number of desired outcomes / number of total outcomes

adding exponents

x^a · x^b = x^(a+b)

subtracting exponents

x^a / x^b = x^(a-b)

negative exponents

1 / x^b = x^(-b)

multiplying exponents

(x^a)^b = x^(a·b)

x^0

1

roots

√(xy) = √x · √y

FOIL

(x+a)(x+b) = x^2 + (b+a)x + ab

difference of squares

a^2 -b^2 = (a+b)(a-b)

a^2 + 2ab + b^2

(a+b)^2

a^2 - 2ab + b^2

(a-b)(a-b)

distance formula

√[(x₂- x₁)^2 + (y₂- y₁)^2)]

mid-point formula

[(x₁+ x₂)/2 , (y₁+ y₂)/2]

intersecting lines

opposite angles are equal (each pair of angles along the same line add to 180 degrees)

area of triangle

area = (1/2)bh

angles of triangle

add up to 180 degrees

length of triangle sides

length of 1 side is always less than the sum of the other 2

equilateral

three equal sides, all angles = 60 degrees

isosceles

2 equal sides, 2 equal angles

similar

same shape, corresponding angles are equal, corresponding sides are in proportion

circle area

pi · r^2

circle circumference

2 · pi · r

full circle

= 360 degrees

length of arc

(n degrees / 360 degrees) · 2 · pi · r

area of sector

(n degree / 360 degrees) · pi · r^2 (fraction of circle’s area)

rectangle area

area = lw

parallelogram area

area = lh

rectangular solid volume

volume = lwh

right cylinder volume

volume = pi · r^2 · h

prime factors

2, 3, 5, 7, 11, …

Greatest Common Factor

ex. GCF of 200 and 60 is 20

Least Common Multiple

ex. LCM of 200 and 60 is 600

trapezoid area

area = [(base1 + base2) / 2] · h

Slope intercept form

y=mx+b

Point-Slope form

y - y₁= m(x - x₁)

standard form

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative

Dividing by a negative number in an inequality

You must flip the sign

Graphing < or > on a coordinate plane

dotted line

Graphing ≥ or ≤ on a coordinate plane

solid line

Graphing ≥ or > on a coordinate plane

shade upwards or to the right

Graphing ≤ or < on a coordinate plane

shade downwards or to the left

circle perimeter

2 pi r

Chord

The distance from one point on the circle to another point on the circle.

Sector

The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.

arc

Part of a circle connecting two points on the circle.

Central Angle

An angle whose vertex is the center of the circle

Percent Change

old(1 +/- %) = new

<

1. less than
2. fewer than

>

1. greater than
2. exceeds
3. more than

≤

1. at most
2. less than or equal to
3. no more than

≥

1. greater than or equal to
2. no less than
3. at least

Exponential growth

y = a(1 +/- r)^t

a = initial value

r = growth rate

t = time

Vertex Form

y = a(x-h)^2 + k

(h,k) = A vertex

Distance =

rt

Sine and Cosine

sin(x) = cos(90-x)

Sum of solutions

-b/a

The discriminant

b^2 - 4ac

-3 < 0 = NO SOL

0 = 0 = 1 REAL SOL

7 > 0 = 2 REAL SOL

Area of equilateral triangle

s^2√3/4

Sum of angles in polygon

(n-2)180

Circle Equation

(x-h)^2 + (y-k)^2 = r^2

Weighted average

sum of terms/number of terms

Part

Percent x whole

Odd num + even num =

Odd num

Percent Increase

100 + (asked percent increase)/100 x whole number

Interior Angles

180 (n - 2)

30-60-90 Triangle

Short Leg: x

Second Leg: x√3

Hypotenuse: 2x

45-45-90 Triangle

Short Leg: x

Second Leg: x

Hypotenuse: x√5

3-4-5 Triangle

Short Leg: 3x

Second Leg: 4x

Hypotenuse: 5x