Free Printable PreCalculus Mixed Review

1.

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

2.

Which expression represents g(f(x)) if f(x) = 2x - 8
and
g(x) = 4x

a)

8x - 32

b)

8x² - 32x

c)

8x - 8

d)

6x - 8

3.

cos(60°)

a)

0

b)

1/2

c)

√3/2

d)

1

4.

cos 150^o

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

5.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

6.

What is the radius of a unit circle?

a)

1

b)

2

c)

1/2

d)

0

7.

What is the exact value of sin 150°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

8.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

9.

sinθ 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

10.

cosθ 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

11.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

12.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

13.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

14.

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)

15.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

16.

cos(π)=

a)

0

b)

1

c)

-1

d)

1/2

17.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

18.

What is the value of cosine at 0

a)

0

b)

1/2

c)

1

d)

√3 / 2

19.

Simplify the following:
(x³)⁶

a)

x⁹

b)

x¹⁸

c)

x⁶

d)

x³

20.

What is the value of:
z⁰

a)

z²

b)

z

c)

0

d)

1

21.

Simplify the following:
x^-3

a)

1/x^-3

b)

x³

c)

1/x

d)

1/x³

22.

Simplify the following:
x²x³

a)

x³

b)

x²

c)

x⁶

d)

X⁵

23.

What is the value of:
(3/4)⁰

a)

1

b)

0

c)

3/4

d)

3/16

24.

What is the value of:
4^-2

a)

1/4

b)

1/16

c)

16

d)

4

25.

Simplify:
$\frac{x^5}{x^3}$

a)

x²

b)

x

c)

1

d)

x⁸

26.

The natural logarithm $\ln\left(x\right)$ has what base?

a)

10

b)

0

c)

e

d)

-e

27.

What is the amplitude of the graph?

a)

1

b)

3

c)

6

d)

9

28.

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

a)

7

b)

-2

c)

3

d)

6

29.

what is the period of y= -3sinx

a)

π

b)

2π

c)

3π

d)

4π

30.

What is the period?

a)

π/4

b)

π/2

c)

3π/4

d)

π

31.

What is the period of y=4cos5x

a)

2π/5

b)

π

c)

5

d)

5π

32.

What is 90 degrees in radians?

a)

π/4

b)

π/2

c)

π/6

d)

3π/2

33.

What is the amplitude and period of y = 2sin(πx)

a)

2 and 2

b)

π and 2

c)

2 and π

d)

2π and 2

34.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

35.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

36.

What do m, n, p and q equal in this scalar matrix multiplication?

a)

m=8, n=9, p=-4, q=4

b)

m=15, n = -45, p=20, q=-5

c)

m=20, n=-5, p=15, q=-45

d)

m=-5, n=20, p=-45, q=15

37.

Multiply

a)

20 15 -10
30 -5 0

b)

-20 15 -10
30 -5 0

c)

1 8 3
11 4 5

d)

20 -15 10
-30 5 0

38.

Evaluate the following logarithm:

log₃27

a)

3

b)

2

c)

-3

d)

¹/₃

39.

Evaluate the following logarithm:

log₃3

a)

1

b)

0

c)

-1

d)

¹/₂

40.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

41.

Evaluate the following logarithm:

log₁₂1

a)

1

b)

0

c)

-1

d)

¹/₂

42.

Evaluate the following logarithm:

log₁₅1

a)

1

b)

0

c)

-1

d)

¹/₂

43.

Evaluate the following logarithm:

log₆36

a)

3

b)

2

c)

1

d)

0

44.

Evaluate the following logarithm:

log₆6

a)

3

b)

2

c)

1

d)

0

45.

log(x+6) = 1

a)

4

b)

4.222

c)

-5

d)

-9.550

46.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

47.

Change to Logarithmic Form:
5³ = 125

a)

log ₅ 125 = 3

b)

log₃125 = 5

c)

log ₅ 3 =125

d)

log₁₂₅ 3 = 5

48.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

49.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

50.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

51.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

52.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

53.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

54.

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

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

55.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

56.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

57.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

58.

Find the inverse of
f(x) = 1/4x - 7

a)

f^-1(x) = 4x + 7

b)

f^-1(x) = -4x + 28

c)

f^-1(x) = -4x - 7

d)

f^-1(x) = 4x + 28

59.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = √(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) =√(x+5)

d)

f^-1(x) = x² - 5

60.

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

a)

25

b)

7

c)

No enough information.

d)

-25

61.

If f(x) = 3x-9, what is f^-1(12)?

a)

25

b)

9

c)

11

d)

7

62.

If the domain of f(x) is x ≥ 4, then the ____ of ____ is y ≥ 4

a)

domain, f^-1(x)

b)

range, f(x)

c)

range, f^-1(x)

d)

domain, f(x)

63.

In an inverse function, the _____ and _______ are switched from the original

a)

f(x) and g(x)

b)

input and output

c)

positives and negatives

d)

slope and intercept

64.

What's the name of the inverse of g(x)?

a)

f(x)

b)

f^-1(x)

c)

y

d)

g^-1(x)

65.

Given f(x) = x+3, find f^-1(-2).

a)

-1

b)

1

c)

5

d)

-5

66.

Given that f(x) = x² + x and g(x) = 3x + 1, find the value of g(f(-2)).

a)

-14

b)

20

c)

6

d)

7

67.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

68.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

69.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

70.

Where is the removable discontinuity?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

71.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

72.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

73.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

74.

What is/are the Vertical Asymptote(s)?

a)

x= -4

b)

x= -4,5

c)

x= -5,5

d)

x= 4

75.

How will you know that the graph illustrates a removable discontinuity?

a)

If the graph is continuous

b)

If the graph has a closed dot

c)

If the graph has a hole

d)

If the graph has lots of coordinates

PreCalculus Mixed Review

Total questions: 75

Worksheet time: 3hrs 30mins

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