# ACT and SAT Math

## 74 terms · to help on the ACT and SAT

[-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, ...

### Factors

ex. factors of 52 are 2, 4, 13, and 26

### Multiples

ex. multiples of 20 are 40, 60, 80, 100, ...

### 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

### fundamental counting principle

if an event can happen in N ways, and another, independent event can happen in M ways, then both events together can happen in N x M ways.

### probability

probability = number of desired outcomes / number of total outcomes

x^a · x^b = x^(a+b)

### subtracting exponents

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

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

### multiplying exponents

(x^a)^b = x^(a·b)

1

√(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+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 = (1/2)bh

### 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

pi · r^2

2 · pi · r

= 360 degrees

### length of arc

(n degree / 360 degrees) · 2 · pi · r

### area of sector

(n degree / 360 degrees) · pi · r^2

area = lw

area = lh

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

### equation of circle

with midpoint (h,k) ... (x - h)^2 + (y - k)^2 = r^2

### logarithms

y = log(little b)x asks b^y = x

### complex numbers

i^0 = 1; i^1 = i; i^2 = -1; i^3 = -i; i^4 = 1; i^5 = i; i^6 = -1; i^7 = -i

opp / hyp

### special sin cos relationship

sin^2(angle) + cos^2(angle) = 1

degree# · (pi / 180 degrees)

radian# · (180 degrees / pi)

### trapezoid area

area = [(base1 + base2) / 2] · h

y=kx

y=k/x

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

dotted line

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

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