MATH 120 Final Exam Review

Quadratics

100

Factor: 

x^2-7x-18 

(x-9)(x+2)

x=-2,9

200

Factor using the slide and divide method:

2x^2-5x+2

(x-2)(2x-1)

x=1/2,2

300

Solve using the quadratic formula: 

3x^2-4x-5=0

x=(4-sqrt76)/6

x=(4+sqrt76)/6

400

Solve using any method:

x^2-11x+19=-5

(x-3)(x-8)

x=3,8

500

Find the vertex form:

y=-6x^2-12x-13

y=-6(x+1)^2-7

Logarithms and Exponentials

100

log₄ 1/8 = ?

-3/2

200

Convert to exponential form:

log_yx=18

y^18=x

300

Convert to logarithmic form:

a^b=52/47

log_a(52/47)=b

400

Solve the equation: 

-2e^(7v+5)-10=-17

v=-0.535

500

Solve the equation:

-10+log₃(n+3)=-10

n=-2

Polynomials

100

Find the greatest common factor:

-90x^3-81xy+18x^2

9x(-10x^2-9y+2x)

200

Determine the end behavior:

f(x)=x^2-6x+11

as x -> ∞, f(x) -> ∞

as x -> -∞, f(x) -> ∞

300

Determine the end behavior:

f(x)=x^5-4x^3+5x+2

as x -> ∞, f(x) -> ∞

as x -> -∞, f(x) -> -∞

400

Divide using synthetic division:

(v^3-2v^2-14v-5)÷(v+3)

v^2-5v+1-8/(v+3)

500

Divide using polynomial long division:

(x^4+3x^2+1)÷(x^2-2x+3)

x^2+2x+4+(2x-11)/(x^2-2x+3)

Equation Solving

100

Solve for n:

(n-31)/4=2

n=39

200

Solve for p:

-3(7p+5)=27

p=-2

300

Solve for n:

4n-1=6n+8-8n+15

n=12

400

Solve for k:

sqrt(2k+40)=sqrt(-16-2k)

k=-14

500

Solve for x:

8(x-2)+3(2x+3)=3(x-6)

x=1

Inverses

100

Find the inverse function:

f(x)=4x

f^-1(x)=x/4

200

Find the inverse function:

f(x)=-x+3

f^-1(x)=-x+3

300

Find the inverse function:

g(x)=-4x+1

g^-1(x)=-1/4x+1/4

400

Find the inverse function:

g(x)=(7x+18)/2

g^-1(x)=(2x-18)/7

500

Find the inverse function:

h(x)=2x^3+3

h^-1(x)=root(3)((x-3)/2)