Free Printable Precalculus - Unit 1

1.

What is 5π/6 radians in degrees?

a)

180

b)

150

c)

360

d)

120

2.

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

a)

540°, -120°

b)

600°, -120°

c)

425°, -240°

d)

120°, -135°

3.

Are $\frac{7\pi}{3}$ and $\frac{13\pi}{3}$ coterminal angles?

a)

Yes

b)

No

4.

Find an angle coterminal with an angle which measures 11π ∕ 3.

a)

17 π / 3

b)

4π ∕ 3

c)

π ∕ 3

d)

8π ∕ 3

5.

How many radians does a circle have?

a)

360 degrees

b)

2\pi radians

c)

$\pi radians$

d)

^{2 radians}

6.

What is 225 degrees in radians?

a)

7π/4

b)

5π/4

c)

3π/4

d)

5π/3

7.

What is 120 degrees in radians?

a)

2π/3

b)

π/3

c)

5π/3

d)

4π/3

8.

What is the length of y in this picture?

a)

45

b)

5√2

c)

90

d)

5

9.

What is the length of x in this 45-45-90 triangle?

a)

4√2

b)

4

c)

8

d)

4√3

10.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Equiangular

d)

Equilateral

11.

What type of special triangle is this?

a)

45°-45°-90°

b)

30°-60°-90°

c)

Isosceles

d)

Obtuse

12.

cotθ=

a)

cosθ/sinθ

b)

sinθ/cosθ

c)

tanθ

d)

1/cosθ

13.

secθ=

a)

1/cosθ

b)

1/sinθ

c)

1/tanθ

d)

1/cscθ

14.

Sin²θ + cos²θ equals to

a)

0

b)

0.5

c)

1

d)

2

15.

1 + tan²θ equals to

a)

csc²θ

b)

sec²θ

c)

sin²θ

d)

cos²θ

16.

1 + cot²θ equals to

a)

sec²θ

b)

sin²θ

c)

csc²θ

d)

cos²θ

17.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

18.

What is the reference angle for -30°?

a)

150°

b)

30°

c)

80°

d)

60°

19.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

20.

What is the reference angle for 275°?

a)

85°

b)

95°

c)

-85°

d)

-95°

21.

What is the reference angle for 63°?

a)

117°

b)

207°

c)

63°

d)

153°

22.

What is the reference angle?

a)

163

b)

73

c)

27

d)

107

23.

What is the reference angle?

a)

43

b)

-43

c)

47

d)

-47

24.

What is the reference angle?

a)

112

b)

68

c)

158

d)

248

25.

What is the reference angle?

a)

7

b)

63

c)

277

d)

97

26.

What is the reference angle?

a)

48

b)

138

c)

132

d)

42

27.

What is the reference angle for 30 degrees?

a)

70 degrees

b)

30 degrees

c)

150 degrees

d)

330 degrees

28.

What is the reference angle for -30 degrees?

a)

150 degrees

b)

30 degrees

c)

80 degrees

d)

60 degrees

29.

Which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

30.

Formula [Reference angle = Actual angle - 180] is for

a)

quadrant 1

b)

quadrant 2

c)

quadrant 3

d)

quadrant 4

31.

What is the reference angle for 240 degrees?

a)

60 degrees

b)

30 degrees

c)

45 degrees

d)

210 degrees

32.

Find the reference angle for an angle measuring -300⁰

a)

60⁰

b)

-60⁰

c)

30⁰

d)

45⁰

33.

What is the reference angle for 240 degrees?

a)

60 degrees

b)

30 degrees

c)

45 degrees

d)

210 degrees

34.

Find a coterminal angle to -180 degrees.

a)

180

b)

90

c)

270

d)

360

35.

Find a coterminal angle to 45 degrees.

a)

360

b)

405

c)

315

d)

295

36.

Find a coterminal angle to 200 degrees.

a)

-520

b)

-200

c)

160

d)

-380

37.

What is the degree equivalent to -135^o

a)

225^o

b)

215^o

c)

235^o

d)

45^o

38.

What is the sin(120)?

a)

-1/2

b)

1/2

c)

-root(3)/2

d)

root(3)/2

39.

What is the cos(585)?

a)

1/2

b)

root(2)/2

c)

-root(2)/2

d)

-root(3)/2

40.

What is sin(-660)?

a)

root(3)/2

b)

1/2

c)

-1/2

d)

1

41.

What is cos(810)?

a)

1/2

b)

1

c)

0

d)

-1

42.

What is sin(300)?

a)

1/2

b)

-1/2

c)

root(3)/2

d)

-root(3)/2

43.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

44.

What equation matches the graph?

a)

f(x) = 3^x

b)

f(x) = (⅓)^x

c)

f(x) = log₃(x)

45.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

46.

ln e⁵=

a)

e⁵

b)

ln 5

c)

5

d)

5e

47.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

48.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

49.

log (x) + log (x) = log (25)

a)

-5, 5

b)

5

c)

-5

d)

25

50.

Solve: 2^3x = 15

a)

2.3

b)

-2.3

c)

1.3

d)

-1.3

51.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

52.

Write in exponential form.
log₂(¹/₈) = -3

a)

2^-3 = ¹/₈

b)

2^1/8= -3

c)

-3² = ¹/₈

d)

-3^1/8 = 2

53.

Simplify the expression
log(30)-log(6)

a)

-6log(30)

b)

log(24)

c)

log(-24)

d)

log(5)

54.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

55.

When a logarithm has division inside of it, it expands using ________________.

a)

Addition

b)

Subtraction

c)

Multiplication

d)

Division

56.

Condense

a)

A

b)

B

c)

C

d)

D

57.

Condense

a)

A

b)

B

c)

C

d)

D

58.

Expand.

a)

A

b)

B

c)

C

d)

D

59.

Rewrite log₃t = 5 in exponential form.

a)

5^t=3

b)

log₃5 = log₃t

c)

t⁵=3

d)

3⁵=t

60.

log₃81 =

a)

2

b)

3

c)

4

d)

5

61.

Simplify. $4x^3\cdot2x^3$

a)

$6x^9$

b)

$8x^9$

c)

$6x^6$

d)

$8x^6$

62.

Simplify. $\frac{x^5y^6}{xy^2}$

a)

$x^4y^8$

b)

$x^4y^4$

c)

$\frac{1}{x^4y^4}$

d)

$\frac{x^4}{y^4}$

63.

Simplify. $\frac{1}{2^{-4}}$

a)

$8$

b)

$16$

c)

$\frac{1}{8}$

d)

$\frac{1}{16}$

64.

Simplify. $\frac{x^5y^6}{xy^2}$

a)

$x^4y^8$

b)

$x^4y^4$

c)

$\frac{1}{x^4y^4}$

d)

$\frac{x^4}{y^4}$

65.

Simplify. $4x^3\cdot2x^3$

a)

$6x^9$

b)

$8x^9$

c)

$6x^6$

d)

$8x^6$

66.

Simplify, $\left(4x^4y^{-4}\right)^3$

a)

$4x^7y^{-1}$

b)

$\frac{4x^{12}}{y^{12}}$

c)

$\frac{x^{12}}{64y^{12}}$

d)

$\frac{64x^{12}}{y^{12}}$

67.

Simplify. $7^{\frac{1}{4}}\cdot7^{\frac{1}{2}}$

a)

$7^{\frac{1}{6}}$

b)

$7^{\frac{3}{4}}$

c)

$7^{\frac{2}{3}}$

d)

$7^2$

68.

Simplify. $16^{\frac{1}{4}}$

a)

$4$

b)

$8$

c)

$2$

d)

$\frac{1}{2}$

69.

What is the y-intercept?

a)

(0,0)

b)

(0,1)

c)

(-3,0)

d)

(0,-3)

70.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

71.

What is the asymptote of y = 2^x ?

a)

y = 0

b)

x = 0

72.

What is the asymptote of y = 2^x - 3

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

73.

What is the asymptote of y = 2^x-3 ?

a)

y = 0

b)

y = -3

c)

x = 0

d)

x = -3

74.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

75.

Describe range of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

76.

Find the asymptote of the following: y = log₁₀x - 6

a)

x=6

b)

x=-6

c)

x= 0

d)

y=0

77.

find the asymptote: y = log₁₀ (x+3)

a)

x=-3

b)

x=3

c)

y=-3

d)

y=3

78.

Logarithms and Exponentials are what?

a)

parallel

b)

perpendiular

c)

inverses

d)

congurent

79.

What does it mean to find the inverse of a function?

a)

the x's and y's are switched

b)

the x's and y's are divided by 2

c)

the x's and y's are made negative

d)

the x's and y's are the same

80.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

81.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

82.

What is the inverse of the given coordinates: (1, 2) (3, 8) (-3, 6)

a)

(1, 2) (3, 8) (-3, 6)

b)

(1, 2) (8, 3) (-3, 6)

c)

(-1, -2) (-3, -8) (3, -6)

d)

(2, 1) (8, 3) (6, -3)

83.

If the equation of f(x) goes through (-1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, -1) and (6, 4)

84.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

85.

If f^-1(-25) = 7 then what is f(7) =

a)

25

b)

7

c)

No enough information.

d)

-25

86.

Which is the inverse of the table?

a)

b)

c)

d)

87.

Are these the graphs of two inverse functions?

a)

Yes

b)

No

c)

No way to tell

88.

The function shown in the graph is:

a)

Even

b)

Odd

c)

Neither Even nor Odd

d)

Not a Function

89.

Is this function even, odd or neither?

a)

Even

b)

Odd

c)

Neither

90.

Is the graph an even, odd, or neither function?

a)

Even

b)

Odd

c)

Neither

91.

Even, odd, or neither?

a)

Even

b)

Odd

c)

Neither

92.

The function in the graph is:

a)

even

b)

odd

c)

neither even nor odd

d)

both even and odd

93.

a)

Even Function

b)

Odd Function

c)

Function - Neither Even Nor Odd

d)

Both Even and Odd Function

e)

Not a Function

94.

Find the local maximum and minimum

a)

Local max at x = -3

Local min at x = -3

b)

Local max at x = 1

Local min at x = -3

c)

Local max at x = -3

Local min at x = 1

d)

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

95.

Identify the local minimum

a)

x = 8

b)

x = 4

c)

$\infty$

d)

x = 2

96.

Identify the global (or absolute) maximum.

a)

-2

b)

1

c)

$\infty$

d)

$-\infty$

97.

What is the location of the absolute maximum for the graphed function?

a)

x = 1

b)

x = 3

c)

x = 4

d)

x = 5

e)

Does Not Exist

98.

What is the location of the relative maximum within the given interval of the graphed function?

-5\le x\le0

a)

x = -4

b)

x = -2

c)

x = 0

d)

x = 3

e)

Does Not Exist

99.

What are the extrema of the graph?

a)

Max = (2, -3), (1, 2)

Min = (-3, -1), (-1, 4)

b)

Max = (-3, -1), (-1, 4)

Min = (2, -3), (1, 2)

c)

Max = (-1, -3), (4, -1)

Min = (-3, 2), (2, 1)

d)

Max = (-3, 2), (2, 1)

Min = (-1, -3), (4, -1)

100.

How many extrema are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

101.

What type of slope does the graph have?

a)

Positive

b)

Negative

c)

Zero Slope

d)

Undefined

102.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

103.

Find the slope of the line that passes through (10, -8) and (1, 12).

a)

20/9

b)

-20/9

c)

4/9

d)

9/4

104.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

105.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

106.

Is this is a function or not a function?

a)

Function

b)

Not a Function

107.

What is the domain of the function?

a)

x≥0

b)

y≥0

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

108.

What is the range?

a)

x≥0

b)

y≥0

c)

All real numbers

d)

{0, 1, 2, 3, 4,...}

109.

State the coordinates of the vertex:

a)

(0, 2)

b)

(2, 0)

c)

(3, 1)

d)

(-1, 3)
R:(0,∞)

110.

Daniel is paid $10 per week for selling newspaper subscriptions. He is also paid $3.50 for each new customer (x) that signs up for the subscription. Which equation represents the amount (y) Daniel earns per week?

a)

y = 3.5x

b)

y= 10 + x

c)

y = 10 + 35x

d)

y = 10 + 3.5x

111.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

112.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

113.

Is this table a function or not a function?

a)

Function

b)

Not a Function

114.

Is this table a function or not a function?

a)

Function

b)

Not a Function

115.

Is this set of ordered pairs a function and how can you tell?

a)

Yes its a function because no y values repeat

b)

No it's not a function because there are negative numbers

c)

No it isn't a function because an x value repeats but has different y values

d)

No it isn't a function because an y value repeats but has different x values

116.

a)

Function

b)

Not a Function

117.

a)

Function

b)

Not a Function

118.

Is this a function? Explain.

a)

Yes; it passes the horizontal line test.

b)

No; it is not a straight line.

c)

Yes; it passes the vertical line test.

d)

No; there is a line connecting the dots.

119.

What is the definition of function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

120.

.

a)

Function

b)

Not a Function

121.

Is this a function?

a)

Yes, it is a function.

b)

No, it is not a function.

122.

Is this mapping a function or not a function?

a)

Function

b)

Not a Function

123.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

124.

Is this graph a function or not a function?

a)

Function

b)

Not a Function

125.

What is the Domain?

a)

{-3, -1, 1, 3, 5, 7, 9}

b)

{-3, -2, -1, 0, 1, 2, 3}

c)

-3 ≤ x ≤ 3

d)

-3 ≤ x ≤ 9

126.

What is the domain?

a)

{-4, -1, 0, 2, 7}

b)

{-5, -4, -1, 0, 1, 2, 4, 7}

c)

{-5, 0, 1, 2, 4}

d)

{5}

127.

What is the Domain?

a)

-3 ≤ x < 5

b)

-3 ≤ y < 5

c)

-8 ≤ x < 5

d)

-8 ≤ y < 5

128.

The student council set its members on four field trips during the school year. The number of buses needed to transport the members on each trip is a function of the number of members who went on the trip. This function consists of only the ordered pairs (52, 3), (72, 4), (86, 5), and (105, 6). What is the domain for this situation?

a)

{52, 105}

b)

{3, 4, 5, 6}

c)

{52, 72, 86, 105}

d)

{3, 4, 5, 52, 72, 86, 105}

129.

The amount of money that Li spends on video games depends on how many games he purchases. If Li has at most $90 to spend on games for his Xbox 360 and the games cost $22.50 each, what is the domain of this function?

a)

{0 ≤ x ≤ 90}

b)

{0 ≤ x ≤ 4}

c)

{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

d)

{0, 1, 2, 3, 4}

130.

Find the Domain.

a)

All real numbers

b)

x > 3

c)

x > 0

d)

x ≥ 0

Precalculus - Unit 1 - 3 Review

Total questions: 130

Worksheet time: 6hrs 54mins

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