Free Printable Mid Term Review Objectives 23-25,38-40 CC,AT,NM

1.

Use the change of base formula to solve the logarithm: $\log_212$

a)

3.5850

b)

0.2789

c)

0.3249

d)

3.2789

2.

Use the change of base formula to solve the logarithm: $\log_425$

a)

0.43

b)

0.84

c)

2.32

d)

0.6

3.

Expand $\log_45x^3y$

a)

$\log_45+\log_43x+\log_4y$

b)

$\log_45+3\log_4x\ +\log_4y$

c)

$\log_45-3\log_4x-\log_{x4}y$

d)

$3\log_45+\log_4x+\log_4y$

4.

Condense $\frac{1}{2}\log_{10}x+3\log_{10}\left(x+1\right)$

a)

$\log_{10}\left(\sqrt{x}\left(x+1\right)\right)$

b)

$\frac{3}{2}\log_{10}\left(2x+1\right)$

c)

$\log_{10}\left(\sqrt{x+1}\left(x^2\right)\right)$

d)

$\log_{10}\left(\sqrt{x}\left(x+1\right)^3\right)$

5.

Solve the logarithm and check for extraneous solutions. $\log_4\left(x+5\right)=\log_4\left(13-x\right)-\log_4\left(x-3\right)$

a)

4, -7 extraneous

b)

4, -7

c)

-7, 4 extraneous

d)

no solution

6.

Solve the equation and check for extraneous solutions. $e^{2x}-7e^x+10=0$

a)

5.023, 3.227

b)

1.609,0.693

c)

11.12, 8.779

d)

0.6033, 1.902

7.

Which is the correct graph of y=sin(x)?

a)

b)

c)

d)

8.

Which is the correct graph of y=cos(x)?

a)

b)

c)

d)

9.

Find the period and amplitude of the function $y=-4\cos\left(x+1\right)$

a)

Amplitude: 1

Period: $4\pi$

b)

Amplitude: 4

Period: $4\pi$

c)

Amplitude: 4

Period: $2\pi$

d)

Amplitude: 1

Period: $2\pi$

10.

Find the period and amplitude of the function $y=6\sin\left(\pi x-3\right)$

a)

Amplitude: 3
Period: 2

b)

Amplitude: 6
Period: $2\pi$

c)

Amplitude: 3
Period: $2\pi$

d)

Amplitude: 6
Period: 2

11.

Write the a sine function given the graph.

a)

$y=8\sin\left(2x+\frac{\pi}{4}\right)$

b)

$y=-4\sin\left(\frac{1}{2}x-\frac{\pi}{4}\right)$

c)

$y=4\sin\left(2x-\frac{\pi}{4}\right)$

d)

$y=-8\sin\left(\frac{1}{2}x+\frac{\pi}{4}\right)$

12.

Write a cosine function given the graph.

a)

$y=2\cos\left(x+\pi\right)+1$

b)

$y=3\cos\left(x+\pi\right)+2$

c)

$y=2\cos\left(x+\pi\right)+1$

d)

$y=3\cos\left(2x+\pi\right)+5$

Mid Term Review Objectives 23-25,38-40 CC,AT,NM

Total questions: 12

Worksheet time: 3hrs 0mins

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