Free Printable Algebra 2 Semester 2 SUPER Review

1.

$Simplify:\ \ \frac{x^2+6x-7}{x^2-49}$

a)

$\frac{x-1}{x+7}$

b)

$\frac{x+1}{x+7}$

c)

$\frac{x-1}{x-7}$

d)

$\frac{x+1}{x-7}$

2.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

$\frac{x}{x+3}$

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

3.

$Simplify:\ \ \frac{x^2+7x+10}{x^2-4}$

a)

$\frac{x-5}{x+2}$

b)

$\frac{x-5}{x-2}$

c)

$\frac{x+5}{x+2}$

d)

$\frac{x+5}{x-2}$

4.

$Simplify:\ \ \frac{x^2-25}{x^2-6x+5}$

a)

$\frac{x+5}{x-1}$

b)

$\frac{x-5}{x-1}$

c)

$\frac{x+5}{x+1}$

d)

$\frac{x-5}{x+1}$

5.

Multiply and Simplify

a)

4(x+3)/(x+2),

b)

(x+2)/4(x+1)

c)

(x+2)/4(x+3),

d)

4(x+1)/(x+2),

6.

Multiply the Rational Expression

a)

A.

b)

B.

c)

C.

d)

D.

7.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

8.

Simplify.

a)

A

b)

B

c)

C

d)

D

9.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

10.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

11.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

12.

Divide

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

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

13.

Jesse tried to reduce an expression to lowest terms.

Which step did Jesse make his mistake?

a)

b)

c)

d)

14.

Ryuto tried to reduce the following expression to lowest terms:

What mistake did Ryuto make?

a)

He didn't exclude x = -3 , which makes the numerator equal to zero.

b)

He excluded x = 2, which doesn't make the numerator in the new expression equal to zero.

c)

He excluded x = 0 , which doesn't make the denominator equal to zero.

d)

He didn't factor the numerator correctly.

15.

Ryuto tried to reduce the following expression to lowest terms:

What mistake did Ryuto make?

a)

He didn't exclude x = -3 , which makes the numerator equal to zero.

b)

He excluded x = 2, which doesn't make the numerator in the new expression equal to zero.

c)

He excluded x = 0 , which doesn't make the denominator equal to zero.

d)

He didn't factor the numerator correctly.

16.

Lindsay tried to reduce the following expression to lowest terms:

What mistake did Lindsay make?

a)

She excluded x = -3, which doesn't make the denominator equal to zero.

b)

She excluded x = 3, which doesn't make the denominator in the new expression equal to zero.

c)

She excluded x = 0, which doesn't make the numerator equal to zero.

d)

She didn't factor the numerator correctly.

17.

Simplify

a)

A.(x+7)/(x-4)

b)

B.-3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

18.

Simplify

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

19.

What is the first step when adding fractions?

a)

Add right away

b)

Flip the numerator and denominator

c)

Find the least common denominator (LCD)

d)

Find the greatest common factor (GCF)

20.

What is the first step when subtracting fractions?

a)

Find the greatest common factor (GCF)

b)

Subtract right away

c)

Add the numerator to the denominator

d)

Find the least common denominator (LCD)

21.

When you are dividing two fractions, what do you do with the second fraction before expanding?

a)

Nothing

b)

Multiply

c)

Divide

d)

Flip the fraction

22.

Which of the following statements summarizes multiplying fractions?

a)

Multiply the Tops and Multiply the Bottoms.

b)

Cross Simplify

c)

Find a common denominator, then multiply

d)

Multiply the numerators and keep the common denominator

23.

$2-\frac{7}{x^2+x-30}$ Simplify

a)

$\frac{2x^2-2x-67}{\left(x-6\right)\left(x+5\right)}$

b)

$\frac{-5}{\left(x+6\right)\left(x-5\right)}$

c)

$\frac{-5}{x^2+x-30}$

d)

$\frac{2x^2+2x-67}{\left(x+6\right)\left(x-5\right)}$

24.

$\frac{1}{6x}+\frac{1}{6}=\frac{1}{2x}$ Solve. Check for extraneous solutions.

a)

$x\ =\ 2$

b)

$x\ =\ 3$

c)

$x\ =\ 0$

d)

$x\ =\ 1$

25.

$\frac{1}{5n^2}+\frac{2}{5n}=\frac{n+5}{n^2}$ Solve. Check for extraneous solutions.

a)

$n\ =\ 4$

b)

$n\ =\ 8$

c)

$n\ =\ 2$

d)

$n=-8$

26.

$\frac{8}{x+2}=\frac{10}{1}$

What is the domain of the equation?

a)

$x\ne2$

b)

$x=2$

c)

$x\ne-2$

d)

All Real Numbers

e)

$x=-2$

27.

$\frac{3}{x+2}+\frac{5}{x+2}\ =\ 10$

What is the domain of the equation?

a)

$x\ne2$

b)

$x\ne-2$

c)

$x=-2$

d)

All Real numbers

e)

$x=2$

28.

Solve for v

29.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

30.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

31.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

32.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

33.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

34.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

35.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

36.

Solve the equation.

a)

A

b)

B

c)

C

d)

D

37.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

38.

Classify the following graph.

a)

Exponential Growth

b)

Exponential Decay

c)

Logarithmic

39.

What is the asymptote of the parent function y=2^x?

a)

x=0

b)

y=0

c)

x=2

d)

y=2

40.

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

a)

300

b)

1.16

c)

.16

d)

x

41.

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

a)

f(x) = 417(3.75)^x

b)

f(x) = 417(0.0375)^x

c)

f(x) = 417(1.0375)^x

d)

f(x) = 417(1.375)^x

42.

Match the following formulas with the scenarios that would use them to find the answer:

a)

$A=P\left(1+\frac{r}{n}\right)^{nt}$

1.

Jim invested $400 in an account giving 7.1% interest, compounded quarterly

b)

$A=P\left(1-r\right)^t$

2.

The value of a car depreciates 18% each year

c)

$A=P\left(1+r\right)^t$

3.

The population in Syracuse, NY grows 4% each year.

d)

$A=Pe^{rt}$

4.

Karen deposited $700 in an account that earns 2.3% interest, compounded continuously

e)

$y=a\cdot b^{\left(x-h\right)}+k$

5.

State the transformations and graph the function

43.

State the transformations from the parent function for the equation $h\left(x\right)=2\cdot4^{\left(x+6\right)}+7$

a = (a) h = (b) k = (c)

Transformation:

The graph was (d) , shifted (e) 6 units, and shifted up 7 units

Choose from the below words

2

-6

7

stretched

left

6

compress

right

-7

4

44.

State the following for the equation $h\left(x\right)=2\cdot4^{\left(x+6\right)}+7$

Horizontal Asymptote: (a)

Domain: (b)

Range: (c)

Choose from the below words

y = 7

$\left(-\infty,\infty\right)$

$\left(7,\infty\right)$

x=7

7

$\left(-6,\infty\right)$

$\left(-\infty,7\right)$

$\left(7,-\infty\right)$

45.

State whether the following functions are examples of exponential growth or decay:

a. $f\left(x\right)=\left(\frac{9}{4}\right)^x$ Exponential (a)

b. $g\left(x\right)=\left(0.87\right)^x$ Exponential (b)

Choose from the below words

growth

decay

46.

Put the steps in the correct order to solve the equation.

$5^{\left(3x-1\right)}\cdot5^{\left(2x-5\right)}=5^{\left(x+6\right)}$

a)

$\left(3x-1\right)+\left(2x-5\right)=x+6$

b)

$5x-6=x+6$

c)

$4x-6=6$

d)

$4x=12$

e)

$x=3$

1)

2)

3)

4)

5)

47.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

48.

Solve 8 = 2^5x+7

a)

x = ⅘

b)

x = ¼

c)

x = -⅘

d)

x = -¼

49.

Solve for x:
(1/8)^x = 2³

a)

x=−3

b)

x=3

c)

x=−1

d)

x=1

50.

What is the graph of the equation?

a)

b)

c)

d)

51.

Solve for x.

$9^x=87$

a)

1.9395

b)

4.4659

c)

2.0325

d)

No solution

52.

Solve: $10^{3x}-1=5$ Round your answer to two decimal places.

(a)

53.

Solve: $8e^{x+1}=40$

Round your answer to two decimal places.

(a)

54.

Solve: $3\cdot\left(2\right)^{x+3}-1=8$

Round your answer to two decimal places.

(a)

55.

Find the explicit formula:

3, 6, 12, 24, ...

a)

aₙ = 6⋅(½)ⁿ ⁻ ¹

b)

aₙ = 6⋅(½)ⁿ

c)

aₙ = 3⋅2ⁿ ⁻ ¹

d)

aₙ = 3⋅2ⁿ

56.

Which of the following best describes this sequence?

\left\{135,\ 45,\ 15,\ 5,\ ...\right\}

a)

An arithmetic sequence with a common ratio of $\frac{1}{3}$

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

A geometric sequence with a common ratio of $\frac{1}{3}$

57.

Find the eighth term:

3, 6, 12, 24, ...

(a)

58.

Find the explicit formula:

8, 14, 20, 26, ...

a)

aₙ = 6n + 2

b)

aₙ = 8n + 6

c)

aₙ = 2n + 6

d)

aₙ = 6n + 8

59.

What is the 12th term of the following sequence?

$\left\{3,-6,\ 12,\ -24,\ 48,\ ...\right\}$

a)

$6,144$

b)

$-6,144$

c)

$354,294$

d)

$-354,294$

60.

Given the sequence, identify the $a_1$ and the common ratio:

30, 60, 120, 240....

a)

A. $a_{1\ }=\ 20;\ r\ =\frac{1}{2}$

b)

$a_{1\ }=\ 30;\ r\ =\ 2$

c)

$a_{1\ }=\ 240;\ r\ =\ 2$

d)

$a_{1\ }=\ 240;\ d=\frac{1}{2}$

61.

Evaluate the arithmetic series given the following: $a_1=42,\ a_n=146,\ n=14$ .

a)

1315

b)

1316

c)

1314

d)

1313

62.

Which sequence is arithmetic?

a)

4, 8, 16, 32, 64, ...

b)

4, 6, 10, 12, 16, ...

c)

4, 1, -2, -5, -8, ...

d)

4, 2, 1, 1/2, 1/4, ...

63.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

64.

Find S_n for the given series:
a₁=22
d=-8
n=21

a)

1911

b)

-1449

c)

-2436

d)

-1218

65.

-21, -16, -11, -6, ...

Is this sequence arithmetic, geometric, or neither?

a)

arithmetic (common difference d = 5)

b)

geometric (common ratio r = 5)

c)

neither

66.

What is the recursive rule for the sequence
2, 6, 18, 54, ...?

a)

a_n=2(3)^n-1

b)

a₁ = 2, a_n = a_n-1 + 4

c)

a₁ = 2, a_n = 3a_n-1

d)

a₁ = 3, a_n = 2a_n-1

67.

Which recursive formula best describes the following sequence:
3, 8, 13, 18, 23...

a)

a_n = (3)^n-1 ; a₁=5

b)

a_n = (5)^n-1 ; a₁=3

c)

a_n = a_n-1+3 ; a₁=5

d)

a_n = a_n-1+5 ; a₁=3

68.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

69.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

70.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

71.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

72.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

73.

Choose the correct ratio.

a)

A

b)

B

c)

C

d)

D

74.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

75.

What is the correct equation to solve for x ?

a)

tan( 46 ) = 17/x

b)

sin ( 46 ) = x/17

c)

tan (46 ) = x/17

d)

cos (46) = x/17

76.

sin A = (a)

cos A = (b)

tan A = (c)

Choose from the below words

$\frac{15}{17}$

$\frac{8}{17}$

$\frac{15}{8}$

$\frac{17}{15}$

$\frac{17}{8}$

$\frac{8}{15}$

77.

78.

79.

80.

81.

82.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

83.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

84.

What is the length of the hypotenuse?

a)

16

b)

30

c)

34

85.

Convert to degrees

a)

-270 degrees

b)

-135 degrees

c)

-130 degrees

d)

-140 degrees

86.

Convert to degrees

a)

270 degrees

b)

230 degrees

c)

185 degrees

d)

460 degrees

87.

Convert to radians 390 degrees

a)

b)

c)

d)

88.

Solve for the triangle:

a)

CA = √5 , <A = 48.19 , <C = 41.81

b)

CA = 4 , <A = 41.81 , < C = 48.19

c)

CA = √13 , <C = 33.69 , < A = 56.31

89.

What is 120 degrees in radians?

a)

2π/3

b)

π/3

c)

5π/3

d)

4π/3

90.

Convert the following to degrees:
-8π/5 radians

a)

-288⁰

b)

-260⁰

c)

-275⁰

91.

$\frac{8\pi}{3}$ is equivalent to what degree measure?

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

92.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

93.

To convert from degrees to RADIANS

a)

multiply by

\frac{π}{180°}

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

94.

To convert from radians to DEGREES

a)

multiply by

\frac{π}{180°}

b)

multiply by
$\frac{180°}{π}$

c)

multiply by
$\frac{π}{\sqrt{2}}$

d)

multiply by
$\frac{π}{\sqrt{3}}$

95.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

96.

Convert 510^o to Radians

a)

25π / 3

b)

23π / 8

c)

17π / 6

d)

51π / 8

97.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

98.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

99.

What is the radius of the unit circle?

a)

0

b)

1

c)

1/2

d)

√2/2

100.

What is the value of cosine at 135

a)

0

b)

1/2

c)

√2 /2

d)

-√2 /2

101.

What is the value of sine at 330

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

102.

What radian measure corresponds to the point

a)

π/4

b)

3π/2

c)

5π/4

d)

7π/3

103.

For what angles are sine and cosine the same?

a)

0^o

b)

45^oand 135⁰

c)

45^oand 225⁰

d)

45^oand 315⁰

104.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

105.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

106.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

107.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

108.

What is the reference angle for 2pi/3

a)

pi/4

b)

7pi/6

c)

4pi/3

d)

pi/3

109.

Which of the following is a correct representation of the reference angle of $\theta=210\degree$

a)

b)

c)

d)

110.

Which of the following is a correct representation of the reference angle of $\theta=-150\degree$

a)

b)

c)

d)

111.

If θ is an angle in Quadrant I, which trig ratios will be positive

a)

sin θ

b)

cos θ

c)

tan θ

d)

All the above (sin θ, cos θ, tan θ)

112.

If θ is an angle in Quadrant IV, which trig ratios will be positive

a)

sin θ

b)

cos θ

c)

tan θ

d)

cos θ and tan θ

113.

Find a coterminal angle to 5°.

a)

365°

b)

255°

c)

-220°

d)

-365°

114.

Find a coterminal angle to 45°.

a)

360°

b)

405°

c)

315°

d)

295°

115.

Find a coterminal angle to -90°.

a)

-450°

b)

90°

c)

180°

d)

-180°

116.

Find a coterminal angle to -27°.

a)

-387°

b)

27°

c)

323°

d)

-393°

117.

In which quadrant would you find an angle measuring -740°

a)

1

b)

2

c)

3

d)

4

118.

What are the negative and positive coterminal angles of 240°?

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

119.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

120.

Which of the following angles are co-terminal to 330^o?

a)

-330^o, 330^o

b)

510^o, -210^o

c)

690^o, -30^o

d)

420^o, -330^o

121.

Which of the following is closest to the measure of the angle shown?

a)

30º

b)

40º

c)

395º

d)

440º

122.

Negative angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

123.

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.

124.

Which of the following shows $-210\degree$ graphed in standard position?

a)

b)

c)

d)

125.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

126.

Evaluate

$\sin\left(\frac{\pi}{3}\right)=$

127.

Select all that are equal to 1

a)

$\cos\left(2\pi\right)$

b)

$\sin\left(\frac{\pi}{2}\right)$

c)

$\sin\left(270^o\right)$

d)

$\cos\left(\pi\right)$

128.

Name the largest freshwater lake in the world

a)

Lake Michigan

b)

Lake Placid

c)

Lake Superior

d)

Lake Winnebago

129.

What is someone who shoes horses called?

a)

Hoofer

b)

Veterinarian

c)

Podiatrist

d)

Farrier

130.

Which chess piece can only move diagonally?

a)

Rook

b)

Queen

c)

Pawn

d)

Bishop

131.

Who was the first character to speak in Star Wars?

a)

C-3PO

b)

Luke Skywalker

c)

Darth Vader

d)

Obi Wan Kenobi

132.

Which potion in Harry Potter and the Half-Blood Prince grants good luck?

a)

Polyjuice Potion

b)

Felix Felicis

c)

Amortentia

d)

Veritaserum

133.

What is a haboob?

a)

A malformed body part

b)

A type of bird

c)

A type of sandstorm

d)

A type of iced drink served in India.

134.

Orecchiette is a type of...

a)

Cheese

b)

Pasta

c)

Flower

d)

Pizza

135.

SpongeBob's pet snail is named...

a)

Larry

b)

Jerry

c)

Dairy

d)

Gary

136.

What is the plastic end of your shoe string called?

a)

Aglet

b)

Tippend

c)

Tie End

d)

Gangler

137.

What is an octothorpe?

a)

A type of bug with a hard shell and 8 legs

b)

A conglomerate of 8 companies

c)

Another name for the hashtag symbol

d)

Another name for the infinity symbol

138.

What is the national animal of Scotland?

a)

Highland Cow

b)

Lochness Monster

c)

Hawk

d)

Unicorn

139.

What is the definition of a sesquipedalianist?

a)

A biker who can ride without their hands on the handles.

b)

A person who uses long and complicated words.

c)

Someone squishy.

d)

Any animal who acts vaguely human-like.

140.

The stinging cells on a jellyfish are called?

a)

Stingers

b)

Tentacles

c)

Nematocysts

d)

Ctenophores

141.

Which file size is bigger?

a)

10 mb

b)

1000 kb

c)

1gb

d)

1000000 b

142.

Which animal below has the longest lifespan?

a)

Human

b)

Galapagos Tortoise

c)

Gopher Tortoise

d)

Blue-Ringed Octopus

143.

Which hand is the torch of the statue of liberties in?

a)

left

b)

right

144.

On a traffic light is the red where is the red light?

a)

middle

b)

top

c)

bottom

d)

there is no red light!

145.

The last inmate to be issued a prisoner number at Alcatraz was?

a)

Al Capone

b)

Tony Giunobli

c)

Frank Weatherman

d)

George Whitaker

146.

The 23rd President of the United States was?

a)

Benjamin Harrison

b)

Abraham Lincoln

c)

George Bush

d)

Dwight D. Eisenhower

147.

The deepest point in the ocean is the

a)

Mid-Atlantic Ridge

b)

Marianas Trench

c)

Challenger Deep

d)

Indian Ocean

148.

How many bones are there in an adult human body?

a)

210

b)

106

c)

110

d)

206

149.

Match the characters

a)

1.

Freddy

b)

2.

Bonnie

c)

3.

Chica

d)

4.

Foxy

150.

What color was Oscar the Grouch originally before turning green?

a)

Orange

b)

Yellow

c)

Brown

d)

Pink

Algebra 2 Semester 2 SUPER Review

Total questions: 150

Worksheet time: 8hrs 30mins

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