Free Printable Pre-Calculus Final Exam Study Guide

1.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

2.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

3.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

4.

On the graph, which portion of the piecewise function is represented in red?

a)

x

b)

0.5x + 2.5

c)

-1

d)

0.5x + 2

5.

What is the RANGE of the function?

a)

All real numbers

b)

y ≤ 4

c)

y < 4

d)

0 ≤ y ≤ 4

6.

What is the domain restriction of the blue piece of this function?

a)

x > 0

b)

x ≥ 0

c)

x > 2

d)

x ≥ 2

7.

What is the value of f(0)?

a)

-2

b)

2

c)

4

d)

0

8.

Find f(-2)

a)

-3

b)

6

c)

8

d)

-6

9.

Given g(x)= -3x and f(x)=x²+2, find f(g(x)).

a)

f(g(x))= -3x²-6

b)

f(g(x))= -3x²+2

c)

f(g(x))=9x²+2

d)

f(g(x))= -9x²+2

10.

Given g(x)= -3x and f(x)=x²+2, find g(f(x)).

a)

g(f(x))= -3x²-6

b)

g(f(x))= -3x²+2

c)

g(f(x))=9x²+2

d)

g(f(x))= -9x²+2

11.

g(x)=3x+4
h(x)=3x-1
Find (g∘h)(x)

a)

-9x+11

b)

4x²+4x

c)

9x+1

d)

9x+11

12.

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

a)

19

b)

23

c)

-10

d)

None of these.

13.

a)

9 - √17

b)

4

c)

2

d)

√8

14.

f(x) = 9-3x
g(x) = 5x-7
Find f(x)+g(x).

a)

14x-10

b)

-8x+2

c)

2x+2

d)

2x-2

15.

f(n)=2n+1
g(n)=3n
Find f(n)+g(n)

a)

5n+1

b)

-5n+1

c)

-2n+1

d)

-6n-1

16.

a)

-2x+3

b)

-2x-9

c)

-8x+9

d)

-8x-9

17.

Given p(x) = x - 2, find p(-4).

a)

-6

b)

6

c)

2

d)

-2

18.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

19.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

20.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

21.

What do w, x, y and z equal in this matrix subtraction?

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

22.

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

23.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

24.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

25.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

26.

Find A+B

a)

8 10
8 1

b)

12 25
7 1

c)

10 30
0 1

d)

can't add two together because the rows dont match columns

27.

What do w, x, y and z equal in this matrix subtraction?

a)

w = 13, x = 4, y = 7, z = 23

b)

w = 13, x = -4, y = 11, z = 23

c)

w = 13, x = 4, y = 11, z = 23

d)

w = 13, x = 4, y = 11, z = 17

28.

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

29.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

30.

Perform the indicated operation. If it’s not possible, select Not Possible.

a)

7
-7
-6
20

b)

7
-9
-6
20

c)

Not Possible

d)

7
-9
2
20

31.

find: B*A

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

32.

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

33.

Subtract

a)

-5
-8
3
10

b)

-9
8
3
2

c)

5
-8
3
10

d)

-5
8
3
2

34.

In Matrix R (pictured) what element is in the second row, third column?

a)

8

b)

9.01

c)

6

d)

1

35.

What comes first in the order?

a)

Row

b)

Column

36.

What must be true in order to ADD two matrices?

a)

They must be square.

b)

The dimensions must be equal.

c)

The determinant can't equal 0.

d)

The column of the 1st must equal the row of the 2nd.

37.

You can multiply a 2X3 matrix by which matrix?

a)

2X2

b)

2X12

c)

3X12

d)

2X3

38.

find: B*A

a)

47 30
9 5

b)

17 15
42 35

c)

10 25
7 1

d)

not possible because rows do not match columns

39.

In Matrix R (pictured) what element is in the second row, third column?

a)

8

b)

9.01

c)

6

d)

1

40.

What comes first in the order?

a)

Row

b)

Column

41.

You can multiply a 2X3 matrix by which matrix?

a)

2X2

b)

2X12

c)

3X12

d)

2X3

42.

Can the operation be performed?

a)

Yes

b)

No

c)

Sometimes

d)

only Mrs. Jordan knows

43.

How many columns are in a 5 x 4 matrix?

a)

5

b)

4

c)

20

d)

9

44.

How many rows are in a 7 x 3 matrix?

a)

7

b)

3

c)

21

d)

10

45.

Find the product of the two matrices.

a)

undefined

b)

-3 16
17 12
8 -10

c)

3 12
-15 -8
-1 -3

46.

In Matrix R (pictured) what element is a₂₃?

a)

8

b)

9.01

c)

6

d)

1

47.

Given matrices A & B:
A is a (4x33) matrix
B is a (33x1) matrix
What are the dimensions of the product of A times B?

a)

4x1

b)

4x33

c)

33x1

d)

Matrix does not exist

48.

Evaluate the determinant of the matrix.

a)

$9$

b)

$-1$

c)

$1$

d)

$19$

49.

How long is the hypotenuse of this triangle?

(a)

50.

Find the missing side.

a)

18

b)

16

c)

17

d)

19

51.

Find the missing side.

a)

11

b)

12

c)

13

d)

14

52.

Find the value of the following expression. Assume that all angles are in Quadrant I.

\sin^{-1}\left(\frac{\sqrt{2}}{2}\right)

a)

$45\degree$

b)

$60\degree$

c)

$90\degree$

d)

$0\degree$

53.

Find the value of the following expression. Assume that all angles are in Quadrant I.

\cos^{-1}\left(0\right)

a)

$45\degree$

b)

$60\degree$

c)

$90\degree$

d)

$0\degree$

54.

Find the value of the following expression. Assume that all angles are in Quadrant I.

\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)

a)

$45\degree$

b)

$60\degree$

c)

$30\degree$

d)

$0\degree$

55.

Find the value of the following expression. Assume that all angles are in Quadrant I.

\tan\left(\sin^{-1}\left(\frac{1}{2}\right)\right)

a)

$\sqrt{3}$

b)

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

c)

$\frac{1}{2}$

d)

$1$

56.

Find the value of the following expression. Assume that all angles are in Quadrant I.

\sin\left(\cos^{-1}\left(0\right)\right)

a)

$0$

b)

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

c)

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

d)

$1$

57.

What is the amplitude of

y = -3sin (7x) -2

a)

7

b)

-2

c)

3

d)

-3

58.

What is the period of either graph?
y = sin(x) & y = cos (x)

a)

Pi

b)

2Pi

c)

Pi/2

d)

Pi/4

59.

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

60.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

61.

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

62.

What is the vertical shift?

a)

Down 1

b)

Down 5

c)

Down 3

d)

Down 4

63.

Name the function and how many units the graph shifted vertically.

a)

sine, 2 units up

b)

cosine, 2 units down

c)

cosine, 2 units up

d)

sine, 2 units up

64.

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

a)

up 2

b)

left 2

c)

right 2

d)

down 2

65.

What is another name for a phase shift?

a)

Horizontal Dilation

b)

Horizontal Shift/Translation

c)

Vertical Dilation

d)

Vertical Shift/Translation

66.

A trig function has an amplitude of 4 and a minimum value of 5. What is its maximum value?

a)

7

b)

9

c)

11

d)

13

67.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

68.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

69.

Convert 150⁰ to radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

70.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

71.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

72.

What is 225 degrees in radians?

a)

7π/4

b)

5π/4

c)

3π/4

d)

5π/3

73.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

74.

What are the negative and positive coterminal angles of -225 degrees?

a)

375°, -600°

b)

125°, -356°

c)

135°, -585°

d)

60°, -120°

75.

What is 150 degrees in radians?

a)

5π/6

b)

7π/6

c)

5π/4

d)

π/6

76.

What is 120 degrees in radians?

a)

2π/3

b)

π/3

c)

5π/3

d)

4π/3

77.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

78.

Which of the following formulas shows the Law of Cosines?

a)

c² = a² + b² - 4ac + cosA

b)

c² = a² - b² - 2abcosC

c)

c² = a² + b² - 2abcosC

d)

(cos A)/a = (cos B)/b

79.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

80.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

81.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

82.

Based on the given information determine the number of unique triangles that may exist.
A= 37°, a=8, b=14

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

83.

Based on the given information determine the number of unique triangles that may exist.
J = 98°, j = 29, p = 6

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

84.

Find angle A

a)

53.6

b)

13.3

c)

113.1

85.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

Pre-Calculus Final Exam Study Guide

Total questions: 85

Worksheet time: 21hrs 15mins

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