Algebra 2 Semester 2 Final Review

Simplify Rational Expressions

100

(x²+11x+30)/(2x²+17x+35)

(x+6)/(2x+7)

200

(2x+10)/(4x²+12x-40)

1/(2(x-2))

300

(x-3)/(2x-8) ⋅ (x²-16)/(x²-9)

(x+4)/2(x+3)

400

(x²-3x-18)/(4x+4) divided by (x²-6x-27)/(x²+9x+8)

(x-6)(x+8)/4(x-9)

500

2/(x²-3x+2) + (x+3)/(x²-1)

(x+4)/(x-2)(x+1)

Simplify Radicals/Properties of Exponents

100

∜(64x⁵y⁶)

2xy∜(4xy²)

200

∛125 ⋅ ∛8

10

300

(32m⁵n²⁰)^⅕

2mn⁴

400

√20 - ∛16 + ∛250 -√5

3∛2+√5

500

(x^(3/5)y^(-1/4))/(x^(1/5)y^(1/2))

x^(2/5)/y^3/4)

Logarithms and e

100

Simplify: 3e^4x ⋅ 4e^5x-2

12e^9x-2

200

Simplify: (2e³)⁴

16e¹²

300

Simplify: 12e^5x/3e^2x

4e^3x

400

Expand: log₃(4x²/y⁵)

log₃ 4+2 log₃ x -5 log₃ y

500

Condense: ln 5 + 3 ln x - ln 2 - 4 ln y

ln (5x³/2y⁴)

Solving with Radicals/Rationals

100

∛x-9=-1

x=512

200

⁵√(3x + 12)= -3

x= -85

300

(x-4)^(2/3)-9=16

x= 129

400

x - 6= √3x

x=12

500

(x+3)/(x-3)+x/(x-5)=(x+5)/(x-5)

x=0, 7

Solving with Logs/Exponentials

100

4^3x=7

x=0.468

200

e^4x-2=9

x= 0.5995 or x=0.6

300

log₃(x-1)=2

x=10

400

(1/4)^3x+2=16^x-1

x=0

500

log₂(x-2)+log₂(x+6)=log₂(3x+8)

x=4