Math Review

Exponents

100

88²-1⁰

7743

200

(4²)(2⁴)(27^1/3)

768 :)

300

64^a=8^a+2

a=2

8^2a=8^a+2

2a=a+2

400

8^x-1=2^x+2

x=5/2

2^3x-3=2^x+2

3x-3=x+2

2x=5

x=5/2

500

5^x-2=4

5^x_/25=4

5^x=100

x=log₅100

Functions

100

√(x-4)

Find the domain 

x ≥ 4

200

1/√(x-2)

x>2

300

f(x)=x^2

g(x)=6

f(g(x))=?

36

400

g(x)=√(2x-3)

What is the inverse?

g(x)^-1=(x²+3)/2 or x²/3 + 3/2

500

g(x)=8/4-3x

h(x)=2x-9/5 

h( g(4))

g(4)=8/-8=-1

h(-1)=-2-9/5

h(g(4))=-11/5 or -2.2

Factoring

100

x²+7x+12

factor

(x+3)(x+4)

200

3x²-18x+24

factor

3(x-4)(x-2)

300

3x³-2x²-12x+8

(x²-4)(3x-2) 

OR...

(x+2)(x-2)(3x-2)

400

7x⁴-14x³+21x²

^{Leave in simplest factored form}

7x²(x²-2x+3)

500

32x⁵- 8x³+4x²-1

factor

(4x²-2x+1)(2x+1)²(2x-1)

Algebraic Equations

100

2x+3y=-11

5x-3y=56 

What is (x,y)

(8,-9)

200

2²(x+3)+9-5=32

Solve for X?

x= 4

300

6^x+6^y=42

x+y=3

What is (x)(y)

x times y=?

x=1, y=2

xy=2

400

6x+3y=33

6x-y=5

What is (x,y)

x=2, y=7 

(2,7)

500

x²+y²=25

2x+y=10

x+y=?

Bonus:Give both solutions

x+y=5 or x+y=7

Solution sets: (5,0) and (3,4)