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