Free Printable PreCalc Sem2 Exam: Log/Exp, unit circle trig/graphing

1.

Convert to logarithmic form.

a^b=c

a)

$\log_ca=b$

b)

$\log_ac=b$

c)

$\log_ab=c$

d)

$\log_bc=a$

2.

81^3-x = (1/3)^5x-6

a)

6

b)

-6

c)

9/2

d)

3/2

3.

Solve: $-8e^{\left(6-2x\right)}+2=-62$

a)

$\frac{\ln8-6}{-2}$

b)

$\frac{\ln6-2}{8}$

c)

$\frac{\ln2-8}{6}$

d)

$\frac{\ln8+2}{6}$

4.

Evaluate the following logarithm:

log₃81

a)

3

b)

2

c)

1

d)

4

5.

Evaluate log₄1

a)

1

b)

0

c)

4

d)

undefined

6.

Evaluate: $\log\left(\frac{1}{100000}\right)$

a)

5

b)

-5

c)

1/5

d)

-1/5

7.

Match the following

a)

$\log_24$

1.

2

b)

$\log_381$

2.

4

c)

$\log_4\ \frac{1}{16}$

3.

-2

d)

$\log_93$

4.

0.5

e)

$\log_22$

5.

1

8.

Solve. Leave your answer in calculator ready form:

$3\ \ln\left(x-3\right)+2=29$

a)

$e^9+3$

b)

$\frac{e^{29}-2}{3}+3$

c)

$\frac{e^{29}+3}{3}-2$

d)

$\frac{1}{3}e^{27}+3$

9.

$\log_6\ \left(x\ +\ 8\right)\ +\ \log_{6\ }\left(x\ +\ 9\right)\ =\ 1$

a)

-11, -17

b)

-6, -17

c)

-6

d)

-11

10.

$\log_{7\ }\left(x\ +\ 3\right)\ -\ \log_{7\ }x\ =\ 1$

a)

$\frac{9}{8}$

b)

No solution

c)

$\frac{19}{3}$

d)

$\frac{1}{2}$

11.

$\log_7\ \left(x\ +\ 4\right)\ -\ \log_{7\ }x\ =\ \log_{7\ }33$

a)

$\frac{1}{8}$

b)

$-\frac{60}{7}$

c)

No solution

d)

$\frac{68}{7}$

12.

The terminal side passes through (-4, -3) for angle $\theta.$
What is sin $\theta?$

a)

3/5

b)

-5/4

c)

-3/5

d)

-4/5

13.

Given the point (-7, $\sqrt{15}$ ) on the terminal side of the angle $\theta.$

What is cos $\theta?$

a)

-8/7

b)

$-\frac{\sqrt{15}}{7}$

c)

-7/8

d)

$-\frac{7\sqrt{15}}{15}$

14.

Find $\sin\left(\theta\right)$ given that $\cot\left(\theta\right)=-\frac{\sqrt{2}}{5}$ and $\theta$ is in quadrant 4.

a)

$-\frac{5\sqrt{3}}{9}$

b)

$\frac{\sqrt{6}}{3}$

c)

$\frac{5\sqrt{2}}{2}$

d)

$-\frac{5}{9}$

15.

Tan\left(\frac{5\pi}{3}\right)

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$-\frac{\sqrt{3}}{2}$

16.

\cos\left(\frac{3\pi}{4}\right)

a)

1

b)

-1

c)

$\frac{\sqrt{2}}{2}$

d)

$\frac{-\sqrt{2}}{2}$

17.

$\tan\left(\pi\right)$

a)

0

b)

1

c)

-1

d)

Undefined

18.

$\sin\left(\frac{7\pi}{4}\right)$

a)

1

b)

-1

c)

$\frac{\sqrt{2}}{2}$

d)

$\frac{-\sqrt{2}}{2}$

19.

$\tan\left(-\frac{5\pi}{6}\right)$

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$-\frac{\sqrt{3}}{3}$

20.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

21.

Solve for $\theta$ , where $0\le\theta<360\degree$

$\csc\ \theta\ =\ -\ \sqrt[]{2}$

a)

$\frac{7\pi}{6},\frac{11\pi}{6}$

b)

$\frac{\pi}{4},\ \frac{7\pi}{4}$

c)

$\frac{5\pi}{4},\ \frac{7\pi}{4}$

d)

$\frac{\pi}{4},\ \frac{3\pi}{4}$

22.

10. What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

23.

13. What is the equation of the graph?

a)

y = -2 cos x - 3

b)

y = 3 cos x - 2

c)

y = -7 cos x - 3

d)

y = -3 cos x - 4

24.

What is the equation for the graph shown.

a)

y = 4sinθ - 2

b)

y = 3tcosθ - 1

c)

y = 2tanθ - 4

d)

y = 2-4tanθ + 2

25.

What is the equation of the graph shown?

a)

y = 4cosθ/2 - 6

b)

y = 4cosθ/2 - 2

c)

y = -2cosθ/4 - 2

d)

y = 4cosθ/4 + 2

26.

Which function below matches this graph?

a)

y=cot(x)

b)

y=cot4(x)

c)

y=cot8(x)

d)

y=π/4cot(x)

27.

2. Determine an equation for this graph:

a)

y=sec(x)

b)

y=2sec(x)

c)

y=2csc(x)

d)

y= csc(2x)

28.

1. Determine an equation for this graph:

a)

y=2csc(x)

b)

y=csc(x) + 1

c)

y=2csc(x) + 1

d)

y= csc(x) + 2

PreCalc Sem2 Exam: Log/Exp, unit circle trig/graphing

Total questions: 28

Worksheet time: 21mins

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