Free Printable Alg 2 Sem 2 Final Review

1.

Solve & check for extraneous solutions:

$\log\ \left(9-x\right)=\log\ \left(2x-6\right)$

a)

5

b)

-11

c)

$\frac{18}{19}$

d)

-4

2.

Solve & check for extraneous solutions:

$\log_3\left(n^2+4n\right)=\log_3\left(35+2n\right)$

a)

5

b)

5, -7

c)

-3, 5

d)

-7

3.

log₁₁b = 3

a)

1331

b)

16

c)

1000

d)

$\frac{1}{9}$

4.

$6\ +\ \log_2\ x\ =\ 6$

a)

9

b)

$\frac{1}{10}$

c)

1

d)

121

5.

$\log_9\left(r-8\right)\ =\ 2$

a)

55

b)

$\frac{11}{6}$

c)

89

d)

6

6.

$-8\ +\ \log_6\ \left(x\ +\ 1\right)\ =\ -7$

a)

5

b)

6

c)

$-\frac{1000}{9}$

d)

124

7.

$\log_4\ 7\ +\ \log_{4\ }\ \left(x\ -\ 2\right)\ =\ \log_4\ 62$

a)

$\frac{76}{7}$

b)

$-\frac{19}{6}$

c)

42

d)

$\frac{10}{3}$

8.

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

a)

-11, -17

b)

-6, -11

c)

-6

d)

-11

9.

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

a)

$\frac{1}{8}$

b)

$-\frac{60}{7}$

c)

No solution

d)

$\frac{68}{7}$

10.

Rewrite the following equation in exponential form:
$\log_636=2$

a)

$36^2=6$

b)

$2^6=36$

c)

$6^2=36$

d)

$2^{36}=6$

11.

Rewrite the equation in logarithmic form:
$12^2=144$

a)

$\log_{12}2=144$

b)

$\log_2144=12$

c)

$\log_{12}144=2$

d)

$\log_{144}12=2$

12.

Condense

a)

A

b)

B

c)

C

d)

D

13.

Condense

a)

A

b)

B

c)

C

d)

D

14.

Condense

a)

A

b)

B

c)

C

d)

D

15.

Condense the expression as a single logarithm.

log₅3 + log₅6 + log₅9

a)

log₅69

b)

log₅56

c)

log₅162

d)

log₅98

16.

Expand

a)

4 ln 3y - 3 lnx

b)

ln3 + 4 lny - 3 lnx

c)

4 ln x 3 lny - 3 lnx

d)

ln3 + lny⁴ - lnx³

17.

Expand $\log\left(a^2b\right)$

a)

2log(a) + log(b)

b)

2log(a) + 2log(b)

c)

log(a) + log(b)

d)

2log(a) * log(b)

18.

Expand . Choose the best answer. $\log\ \frac{x^2}{y^3}$

a)

log x² + log y³

b)

2 log x - 3 log y

c)

log x - log y

d)

2 log x $\div$ 3 log y

19.

a)

b)

c)

d)

20.

a)

b)

c)

d)

21.

a)

A.

b)

B.

c)

C.

d)

D.

22.

What are the restricted values?

a)

x = - 3 and x = 4

b)

x = 3 and x = - 4

c)

x = 3 only

d)

x = - 4 only

23.

Multiply

a)

A.

b)

B.

c)

C.

d)

D.

24.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

25.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

26.

Simplify.

a)

A

b)

B

c)

C

d)

D

27.

Solve and check for extraneous solutions

a)

x=5

b)

x= -5

c)

No Solution

28.

Solve

a)

x = -1, 5

b)

No Solution

c)

x = -4, 5

d)

x= -4

29.

Identify the LCM

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

30.

Solve and check for extraneous solutions

a)

x = -3

b)

x = -3, 5

c)

x = 3, 5

d)

x = 5

31.

State the vertical asymptote.

a)

x = -2/5

b)

x = -5/2

c)

x = -5

d)

x = 2

32.

Which of the following represents the vertical asymptote(s) for the function below?
$f\left(x\right)=\frac{5}{x^2\left(x-4\right)\left(x+2\right)}$

a)

$x=0,-4,2$

b)

$x=4,-2$

c)

$x=0,4,\ -2$

d)

$x=-4,2$

33.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

34.

What is the equation of the Horizontal Asymptote of $y=\frac{3}{x-4}+2$

a)

$x=2$

b)

$y=2$

c)

$x=4$

d)

$y=4$

e)

No Horizontal Asymptote

35.

If y and x vary directly, and x = 2 and y = 8, find x when y = 64.

a)

7

b)

16

c)

13

d)

17

36.

If y varies inversely as x, and y = 32 when x = 3, find x when y = 15.

a)

3/5

b)

8/5

c)

16/5

d)

32/5

37.

Evaluate without a calculator (get same base & argument)
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

38.

Evaluate without a calculator (get same base & argument)

log₂₅0.2

a)

-¹/₂

b)

-2

c)

2

d)

¹/₂

39.

Evaluate without a calculator

log₁₂1

a)

1

b)

0

c)

-1

d)

¹/₂

40.

Evaluate without a calculator (get same base & argument)

log₃(¹/₃)

a)

-2

b)

-¹/₂

c)

-1

d)

¹/₂

41.

Simplify the expression.

a)

b)

c)

d)

42.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

43.

Solve: 7^-x = 49

a)

x = 1

b)

x = -1

c)

x = 2

d)

x = -2

44.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

45.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

46.

Solve each equation. Select the closest answer.

a)

4.5

b)

1.5

c)

1.8

d)

5

47.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

48.

Using a calculator, solve for x:

2.8^x = 41

a)

0.277

b)

3.607

c)

-0.282

d)

3.684

49.

Write an explicit rule for the following sequence:

4, 12, 36, 108...

a)

a_n = 4(3^n-1)

b)

a_n = 4(3ⁿ)

c)

a_n = 4+3n

d)

a_n = 4(3n)

50.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

51.

Write an explicit rule for the given sequence:

125, 25, 5, ....

a)

a_n = (125)(1/5)^(n-1)

b)

a_n = 625(1/5)^(n-1)

c)

a_n = 625(5)^(n-1)

d)

a_n = 125 + 5n

52.

Find a₂₀ in the arithmetic sequence:

5, 12, 19, 26...

a)

145

b)

144

c)

142

d)

138

53.

Write an explicit rule for the sequence:

2, 5, 8, 11, ...

a)

a_n= -11n + 14

b)

a_n= 3n - 1

c)

a_n= -3n + 14

d)

a_n= 2n + 1

54.

Which of the following sequence is an arithmetic sequence?

a)

5, 12, 21, 32, 45, . . .

b)

3, 6, 12, 24, 48, . . .

c)

–8, –5, –2, 1, 4, . . .

d)

12, 7, 11, 6, 10, 5, . . .

55.

What is the sum of the first 50 terms of the series 2 + 17 + 32 + 47 + ...? (use formula)

a)

1,600

b)

18,235

c)

18,475

d)

19,125

56.

What is the summation notation for the series?

7 + 11 + 15 + ... + 203 + 207

a)

b)

c)

d)

57.

What is the summation notation for the series?

(-3) + (-6) + (-9) + ... + (-30)

a)

b)

c)

d)

58.

Find S₁₁ in the series:
14 + 23 + 32 + 41 + ...

a)

1296

b)

1298

c)

2604

d)

649

59.

a)

149

b)

11,200

c)

5,600

d)

140

60.

Find S₈ in the series:

$1-2+4-8+...$

a)

$\frac{1}{3}$

b)

-86

c)

-87

d)

-85

61.

Evaluate $\sum_{k\ =\ 1}^7\left(-2\right)^{k\ -1\ }$

a)

44

b)

$\frac{1}{3}$

c)

43

d)

49

62.

Find the sum of the infinite geometric series, if it exists. $\sum_{n=1}^{\infty}8\left(\frac{1}{5}\right)^{n-1}$

a)

8

b)

8/5

c)

10

d)

Does not exist

63.

Evaluate

a)

36352

b)

52428

c)

46121

d)

41131

e)

-4/5

64.

$\sum_{k=1}^{\infty}\left(\frac{4}{5}\right)^{k-1}$ Find the sum of the series if it exists.

a)

4/5

b)

5

c)

6.5

d)

Does not exist

65.

Write the repeating decimal, 0.373737... as a simplified fraction using a series

a)

37/100

b)

37/99

c)

17/99

d)

38/100

66.

Write the repeating decimal 0.66666... as a simplified fraction using a series

a)

33/50

b)

6/9

c)

6/10

d)

2/3

67.

Conveert 210 degrees to radians

a)

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

b)

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

c)

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

d)

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

68.

Convert -460 degrees to radians

a)

$\frac{9\pi}{23}$

b)

$\frac{23\pi}{9}$

c)

$-\frac{23\pi}{9}$

d)

$-\frac{9\pi}{23}$

69.

Convert $\frac{5\pi}{6}$ to degrees

a)

140 degrees

b)

150 degrees

c)

210 degrees

d)

216 degrees

70.

Convert $\frac{4\pi}{3}$ to degrees

a)

150 degrees

b)

240 degrees

c)

270 degrees

d)

300 degrees

71.

Evaluate cos $210\degree$ using special right triangles

a)

$-\frac{1}{2}$

b)

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

c)

$\frac{1}{2}$

d)

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

72.

What is the reference angle of $315\degree$

a)

$25\degree$

b)

$35\degree$

c)

$20\degree$

d)

$45\degree$

73.

Evaluate tan $315\degree$

a)

1

b)

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

c)

-1

d)

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

74.

What is the reference angle of $265\degree$ ?

a)

$73\degree$

b)

$75\degree$

c)

$85\degree$

d)

$90\degree$

75.

If the terminal side of contains the point (5,-3), find the exact value of cot $\theta$

a)

5

b)

-3

c)

$-\frac{5}{3}$

d)

$-\frac{3}{5}$

76.

Standard position is when .....

a)

the initial side of the angle is on the positive x-axis.

b)

the initial side of the angle is on the negative x-axis.

c)

the initial side of the angle is on the positive y-axis.

d)

the initial side of the angle is on the negative y-axis.

77.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

78.

Find the reference angle.

a)

-65°

b)

125°

c)

-55°

d)

55°

79.

Find the reference angle.

a)

-15°

b)

15°

c)

-165°

d)

165°

80.

Find the exact value of the trig function.

a)

-1

b)

1

c)

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

d)

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

81.

Find the exact value of the trig function.

a)

1

b)

$\sqrt{3}$

c)

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

d)

$-\sqrt{3}$

82.

Find the exact value of the trig function.

a)

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

b)

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

c)

1

d)

-1

83.

cos π =

a)

0

b)

1

c)

-1

d)

undefined

84.

Which trig equation is correct based on the diagram?

a)

b)

c)

d)

e)

The correct answer is not listed

85.

Which trig equation is correct based on the diagram?

a)

b)

c)

d)

e)

The correct answer is not listed

86.

Evaluate csc(270⁰)

a)

1

b)

0

c)

-1

d)

undefined

e)

The correct answer is not listed

87.

When graphing cosine, what is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

88.

What is the period of the equation

y = 2cos(2x)?

a)

$2\pi$

b)

$\frac{\pi}{2}$

c)

$4\pi$

d)

$\pi$

89.

What is the period for

y = 4 cos (¹/₂x +π) - 2 ?

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

$\frac{\pi}{4}$

d)

$4\pi$

90.

What is the amplitude of y=3sin(7x)-2

a)

7

b)

-2

c)

3

d)

6

91.

Find the amplitude of y = -4 sin[2(x+π)].

a)

-4

b)

4

c)

π

d)

2

92.

Find the vertical shift.

y=2\sin\ \left(5x-\frac{π}{3}\right)-4

a)

down 4

b)

up 4

c)

right π/3

d)

left π/3

93.

Write an equation for the cosine function with amplitude 3, period of $2\pi$ , phase shift of $\pi$ , and vertical shift of 5.

a)

$y=5\cos(x-\pi)+3$

b)

$y=3\cos(x-\pi)+5$

c)

$y=3\cos2\left(x-\pi\right)+5$

d)

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

94.

4. Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

95.

7. What is the phase shift for y = 4cos(¹/₂x +π) - 2?

a)

left pi/2

b)

right pi/2

c)

right 2pi

d)

left 2pi

96.

$\sin^2x+\cos^2x=$

a)

$1$

b)

$-1$

c)

$\tan^2x$

d)

$\cot^2x$

97.

Simplify $\sin x\sec x$

a)

$\csc x$

b)

$\tan x$

c)

$\cot x$

d)

$\cos x$

98.

Simplify $\cos^2x\left(\sec^2x-1\right)$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\tan^2x$

d)

$\csc^2x$

99.

Simplify cotθsinθ

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

100.

Simplify secθcotθsinθ

a)

-1

b)

sin θ

c)

csc θ

d)

1

101.

Simplify cot²θ(1+tan²θ)

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

102.

Simplify sin²(x) - cos(x)sec(x)

a)

sec²(x)

b)

cos²(x)

c)

-cos²(x)

d)

-sec²(x)

103.

Simplify $\frac{\sin^2x-1}{\cos}$

a)

$-Cos\theta$

b)

$\sec\theta-Cos^2\theta$

c)

$Sin^2\theta$

d)

$Cot\theta$

104.

Use a sum or difference identity to find the EXACT value:
$\cos\left(75\degree\right)$

a)

0.2588

b)

0.9218

c)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

105.

Use a sum or difference identity to find the EXACT value:

$\cos\left(105\degree\right)$

a)

-0.2410

b)

-0.2588

c)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

106.

Use a sum or difference identity to find the EXACT value:

$\cos\left(\frac{\pi}{12}\right)$

a)

0.9659

b)

0.9999

c)

$\frac{\sqrt{2}+\sqrt{6}}{4}$

d)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

107.

Which of the following is the same as $\cos\ \left(A+B\right)$

a)

$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$

b)

$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$

c)

$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$

d)

$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$

108.

Expand and simplify $\cos\ \left(90^o-x\right)$

a)

$\cos\ x$

b)

$\sin\ x$

c)

$\tan\ x$

d)

$-\cos x$

109.

Use the angle sum/difference identity to find the exact value of

a)

b)

c)

d)

110.

Use the angle sum/difference identity to find the exact value of

a)

b)

c)

d)

111.

Solve on the domain 0 ≤ x < 360°
cos x + 1 = 0

a)

0°

b)

No solution

c)

180°

d)

270°

112.

Solve equation on the domain 0 ≤ x < 360°

$-2+\cot\theta=-3$

a)

θ = 135°, 240°, 315°

b)

θ = 135°, 315°

c)

θ = 60°, 240°

d)

θ = 135°, 240°

113.

Solve equation on the domain 0° ≤ θ < 360°

$1=5-8\cos\theta$

a)

θ = 30°, 60°, 330°

b)

θ = 30°, 330°

c)

θ = 30°

d)

θ = 60°, 300°

114.

Solve equation on 0° ≤ θ < 360°

$3\sin^2\theta+4=5+\sin^2\theta$

a)

θ = 45°, 135°, 225°

b)

θ = 45°, 315°

c)

θ = 45°, 135°

d)

θ = 45°, 135°, 225°, 315°,

115.

Solve equation on 0° ≤ θ < 360°

2cos²x + cosx = 0

a)

90°, 270°

b)

0°, 180°, 360°

c)

120°, 240°

d)

60°, 300°

116.

Solve equation on 0° ≤ θ < 360°

2sin²x - 5sinx + 2 = 0

a)

30°, 150°

b)

210°, 330°

c)

60°, 120°

d)

240°, 300°

117.

Evaluate the function: sin^-1(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

118.

Evaluate: cos^-1(-√2∕2)

a)

π/4

b)

3π/4

c)

-π/4

d)

-3π/4

119.

Evaluate: $\cos\left(\sin^{-1}\left(\frac{-\sqrt{3}}{2}\right)\right)$

a)

$\frac{1}{2}$

b)

$\frac{-\pi}{3}$

c)

$\frac{-\pi}{6}$

d)

$0$

120.

Find the exact value of $\sin\left(\tan^{-1}\left(\sqrt{3}\right)\right)$ .

a)

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

b)

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

c)

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

d)

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

Alg 2 Sem 2 Final Review

Total questions: 120

Worksheet time: 5hrs 37mins

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