math 2

1²

1

2²

4

3²

9

4²

16

5²

25

6²

36

7²

49

8²

64

9²

81

10²

100

11²

121

12²

144

1³

1

2³

8

3³

27

4³

64

5³

125

Order of Operations

PE(MD)(AS) Working from left to right

Square Facts

A= s², P=4s

Greatest common divisor (GCD)

Two integers is the largest integer that divides evenly into both. Ex. gcd(6,10)=30

Least common multiple (LCM)

Two integers is the smallest integer that is evenly divisible by both. Ex. lcm(6,10) = 30

Rectangle facts

A= l*w P=2l+2w

Triangle perimeter

P = side1 + side2 + side3

Isosceles triangle

Has exactly two sides of equal length

Equilateral triangle

Has three sides of equal length and all angles are 90 degrees

Triangle area

A = ½ bh

1/5

0.2

¼

0.25

1/3

0.3

½

0.5

2/3

0.6

¾

0.75

Trapezoid Area (only)

A = ½ (b1+b2)*h

Simple interest: The amount of money you make in interest, I, when investing P dollars in a non compounding investment with interest rate r over time

$$I=Prt$$

New/Original % Change Formula

New Amount = Original ± (% change) * Original

Uniform Motion: An object moving at a constant rate r in a straight line for time t will go a distance

$$d=rt$$

In any setting changing at a constant rate

New amount = starting amount + rate * time

Interval notation compactly express s inequalities. Use brackets, [ and ], to include endpoints. Use parentheses, ( and ), to exclude endpoints $\infty$ and -$\infty$ always use parentheses

Exponent Operation Rules

$a^{m}\cdot a^{n}=a^{m+n}$ , $\frac{a^{m}}{a^{n}}=a^{m-n}$ , $\left(a^{m}\right)^{n}=a^{m\cdot n}$

Special Powers

$a^0=1$ , $a^1=a$

Exponent Distribution

$\left(a\cdot b\right)^{n}=a^{n}\cdot b^{n}$ ,$\left(\frac{a}{b}\right)^{n}=\frac{a^{n}}{a^{n}}$

Negative Exponent Rules

$$a^{-n}=\frac{1}{a^{n}},\frac{1}{a^{-n}}=a^{n}$$

Special Powers 2

$$a^{-2}=\frac{1}{a}$$

Careful with

(a+b)^n does not equal to a^n + b^n and (a-b)^n does not equal to a^n-b^n

Root Exponent Relationship

$$\sqrt[n]{a}=a^{\frac{1}{n}}$$

Radical Distribution Rules

$\sqrt[n]{a}\cdot b=\sqrt[n]{a}\cdot\sqrt[n]{b}$ , $\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

Careful!

$\sqrt[n]{a+b}\ne\sqrt[n]{a}+\sqrt[n]{b}$ , $\sqrt[n]{a-b}\ne\sqrt[n]{a}-\sqrt[n]{b}$