Algebra II Review*

Polynomial and Rational Functions

100

Factor completely:

x²+6x+9

(x+3)²

200

Determine the x-intercept(s) of:

f(x)=x²−2x−15

x=−3 and x=5

300

Find all vertical asymptotes of:

f(x)=(x+7)/(x²−36)

x=−6 and x=6

400

Calculate the horizontal asymptote of:

f(x)=(6x²+4)/(7x²-3x+2)

y=6/7

500

Simplify completely and state any restrictions:

(x²−4x)/(x²−16)

x/(x+4), x does not equal ±4

Sequences and Series

100

Find the 5th term:

1,  4,  7,  10,…

13

200

Find the sum of the first 7 terms:

3,  6,  12,  24,...

381

300

Write an explicit formula for:

−2,  −6,  −18,  −54,…

a_n=−2(3)ⁿ⁻¹

400

Find the 8th term:

a_n=5+2(n−1)

19

500

A geometric series has a₁=81, r=1/3. Find a₄.

3

Exponential and Logarithmic Functions

100

Solve:

2^x=1024

10

200

Rewrite in exponential form:

log⁡₅(125)=x

5^x=125

300

Solve:

log₄(x)=3/2

x=8

400

Expand:

log⁡₂(x²/y)

2log₂x−log₂y

500

Solve:

(x+1)⁴=81

x=2

Probability

100

A coin is flipped once. What is the probability of heads?

1/2

200

A bag contains 3 red, 5 blue, and 2 green marbles. Probability of blue?

5/10 = 1/2

300

Two dice are rolled. Probability the sum is 7?

6/36 = 1/2

400

A card is drawn from a standard deck. Probability it is a face card or a heart?

22/52 = 11/26

500

A bag contains 4 red, 3 blue, and 5 green marbles. Two marbles are drawn without replacement. What is the probability both marbles are red?

(4/12)*(3/11) = 1/11

Trigonometric Functions and Identities

100

Evaluate:

sin⁡2(30∘)+cos⁡2(30∘)

1

200

Find the exact value:

cos⁡(0∘)

1

300

For the function

y=2sin⁡(x)−5

state the amplitude and midline.

amplitude = 2, midline y=−5

400

Find the period of the function:

y=(1/3)cos⁡(3x)

120∘ (or 2π/3)

500

For the function

y=sin⁡(4(x−π))

state the amplitude, period, and phase shift.

• Amplitude: 1
• Period: π/2
• Phase shift: right π