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1

Square Root Rules

√ab =√​a ⋅√​b; √​b/a​​ = ​√​b/​√​a; √a^2 = a; (√a)^2

2

prime numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

3

integer facts

1. the sum of two even integers = even integer

2. the sum of two odd integers = even integer

3. the sum of an even & odd integers = odd integers

4. product of two even integers = even integer

5.product of odd integers = odd integer

6. product of an even & odd = even integer

7.product of two positives = positive integer

8.product of two negative integers = positive integer

9.product of positive & negative integer = negative

4

algebraic expressions

1. ca + cb = c(a + b)

2. ca - cb = c(a - b)

3. (a + b)^2 = a^2 + 2ab + b^2

4. (a - b)^2 = a^2 - 2ab + b^2

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

6. (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

7. (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3

5

exponent rules

A n ⋅ A m = A n+m

A n ⋅ B n = (A ⋅ B) n

A n / A m = A n-m

A n / B n = (A / B) n

(Bn)m = Bn⋅m

Bn^m = B(n^m)

m√(Bn) = B n/m

B1/n = n√B

B-n = 1 / Bn

B0 = 1

B1 = B

1n = 1

6

greater than

>

7

less than

8

greater than or equal to

9

less than or equal to

10

simple interest

A = P(1 + rt)

11

compound interest

Calculate Accrued Amount (Principal + Interest)
A = P(1 + r)t

Calculate Principal Amount, solve for P
P = A / (1 + r)t

Calculate rate of interest in decimal, solve for r
r = (A/P)1/t - 1

Calculate rate of interest in percent
R = r * 100

12

slope (rise over run)

y2 - y1 / x2 - x1

13

surface area

SA = 2(lw + lh + wh)

14

cylinder volume

v = πr^2h

15

cylinder surface area

SA = 2(πr^2) + 2πrh

16

circumference

C = 2πr

17

area of a circle

A = πr

18

special right triangles

45°; 45°; 90° Triangle
- The ratio of the base to height to hypotenuse of this triangle is 1: 1: √2.
- Base: Height: Hypotenuse = x: x: x√2 = 1: 1: √2.

30°; 60°; 90° Triangle
- The ratio of the lengths of the sides are x: x√3: 2x.
- Base: Height: Hypotenuse = x: x√3: 2x.

19

area of a triangle

A = bh/2

20

volume of a triangle

V=Bh/3