Algebra 2 Semester 2 Review

Rationals

100

Simplify the following rational expression:

15n/10n³

3/2n²

200

Multiply the following rational expressions:

1/(x+10)  *  (10x+30)/(x+3)

10/(x+10)

300

Divide the following rational expressions:

7/(8r-40) /  1/(8r-40)

7

400

Add the following rational expressions:

3/(x+7) + 4/(x-8)

(7x+4) / (x+7)(x-8)

500

Solve the following rational equation:

1/x = 6/5x + 1

x = -1/5

Exponentials

100

Simplify the following exponential expression

6x^-8 * 5x³

30x^-5

200

Solve the following exponential equation:

9^x * 9^2x-5 = 9¹⁶

x = 7

300

Solve the following exponential equation:

6^1-n = 6³

n = -2

400

Solve the following exponential equation:

4^1-2x = 8

x = -1/4

500

Solve the following exponential equation:

16^-3x * 1/4 = 16

x = -1/2

Logarithms

100

Rewrite as an exponential:

log_2 (8) = 3

2³ = 8

200

Rewrite the following as a logarithm:

8² = 64

log_8(64) = 2

300

Evaluate the following logarithm:

log_5(125)

3

400

Condense the following logarithmic expression:

log_3(x) + 2 log_3(y) + log_3(z)

log_3(xy²z)

500

Expand the following logarithm:

log (xy⁵)³

3 log (x) + 15 log(y)

Graphing

100

Does the function 2^x - 1 show growth or decay?

Growth

200

Given a parent function of (1/2)^x, what kind of transformation is given by (1/2)^x-3 ?

Shift 3 units right

300

Where does the graph 2^x have an asymptote?

y = 0 or the x-axis

400

Given a parent function of 3^x, what transformation is given by 3^x/2 ?

Squish to the x-axis

500

Where does the graph 2^x have a y-intercept?

y = 1

Trivia!

100

When is Mr. Dooley's birthday?

Christmas

200

What two oceans are connected by the Panama Canal?

Pacific and Atlantic

300

What is the name of the mathematician who discovered the number e?

Euler

400

What is the capital of New York?

Albany

500

Where is Mr. Dooley going to teach in the fall?

Jacksonville, Florida