Free Printable Final Exam Math IV Fall 2023

1.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

2.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

3.

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

a)

-3

b)

-1

c)

1

d)

3

4.

When x is less than or equal to 2, what equation is shown in the graph?

a)

f(x) = 3

b)

f(x) = x

c)

f(x) = | x |

d)

f(x) = | x - 1 |

5.

How many pieces is this Piecewise Function composed of?

a)

1

b)

2

c)

3

d)

4

6.

What is the domain of the graph?

a)

1≤ x ≤ 4

b)

1 < x < 4

c)

1≤ y ≤ 4

d)

1 < y < 4

7.

A set of data is given: 3, 7, 11, 11, 16
Jesse calculated a measure of central tendency and got 9.6, which measure of central tendency did he just calculate?

a)

Mean

b)

Median

c)

Mode

d)

Range

8.

Kayte took a sample of 50 pieces of data. She added up all of the pieces of data and then divided by 50. What measure of center is she working on?

a)

Mean

b)

Median

c)

Mode

d)

Range

9.

This statistical number is the middle number of the data set.

a)

Mean

b)

Median

c)

Mode

d)

Range

10.

Calculate the median for this set of data
22, 32, 44, 11, 5, 28, 19, 30.

a)

Median=22

b)

Median=24.5

c)

Median=25

d)

Median=28

11.

What is an outlier?

a)

A value that is much less or much greater than the other values in a data set.

b)

The difference between the upper and lower quartiles of a data set.

c)

The mean of the distances from each data value in a set to the mean of a set.

d)

The difference between the greatest and least numbers in a data set.

12.

The mode score on the 9th grade math test was 94! Which of these interpretations must be correct?

a)

99 was the highest score on the test.

b)

More students received a 94 than any other score

c)

No student scored below a 50

d)

A score of 91 was slightly below average.

13.

What is the range of the set of data?

a)

70

b)

65

c)

80

d)

55

14.

Madison has test scores of 93, 82, 86, and 75. What must she score on her next test to have an average of 86?

a)

94

b)

90

c)

86

d)

88

15.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

16.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

17.

Write in logarithmic form.
2^-4 = ¹/₁₆

a)

log₂(¹/₁₆) = -4

b)

log_-4(¹/₁₆) = 2

c)

log_-4 2 = ¹/₁₆

d)

log₂(-4) = ¹/₁₆

18.

Write in exponential form.
log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

19.

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

20.

Evaluate:
log₄16

a)

2

b)

4

c)

1/2

d)

-2

21.

log₄1 =

a)

0

b)

1

c)

4

d)

DNE

22.

Solve for x
5^x = 17

a)

x = log₁₇5

b)

x = log 5 + log 17

c)

x = log₅17

d)

x = (log 5)/(log 17)

23.

Solve for x
log₈(x) = 2

a)

x = 256

b)

x = 64

c)

x = 16

d)

x = 32

24.

Solve for x:

a)

1

b)

2

c)

.5

d)

4

25.

log₅(25) = y

a)

y = 2

b)

y = 0.5

c)

y = 5

d)

y = (1/2)

26.

log₃(1) = y

a)

y = 0

b)

y = 1

c)

y = (1/3)

d)

y = 2

27.

log₁₆(4) = y

a)

y = 2

b)

y = 4

c)

y = (1/2)

d)

y = (1/4)

28.

log₂(1/8) = y

a)

y = -3

b)

y = (1/3)

c)

y = 3

d)

y = 0

29.

log₃(4x) = 2

a)

x=4/9
x=4/9

b)

x=9/4

c)

x=3/2

d)

x=2/3

30.

log₂(x + 5) = 3

a)

3

b)

4

c)

5

d)

6

31.

Solve for x:
log₃3^x = 5

a)

5

b)

4

c)

3

d)

243

32.

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

a)

14

b)

68

c)

63

d)

71

33.

Create the explicit formula for the sequence:
2, 8, 14, ...
(Hint: Write your formula and then simplify it.)

a)

a_n=2+6n

b)

a_n=-6+6n

c)

a_n=6n-4

d)

a_n=4-6n

34.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

35.

Identify the common difference.
97, 86, 75, 64, ...

a)

8

b)

11

c)

-11

d)

-8

36.

Identify the common difference.
3, 7, 11, 15, ...

a)

6

b)

5

c)

4

d)

2

37.

The next two terms of the sequence 4,7,10,13 are ....

a)

16 and 19

b)

15 and 19

c)

16 and 18

d)

15 and 18

38.

Find the sum of the 1st 20 terms: 2+5+8+......

a)

1220

b)

610

c)

600

d)

612

39.

Find the sum: 11 + 15 + 19 + .......+ 83

a)

19

b)

83

c)

893

d)

624

40.

Find the sum: 50 + 33 + 16 + ..... -18

a)

162

b)

9

c)

-150

d)

-162

41.

Find the sum: 400 + 394 + 388 + .... - 32

a)

400

b)

13432

c)

432

d)

73

42.

What are the next 3 terms in the following geometric sequence:

512, 256, 128, ___, ___, ___, ...

a)

1024, 2048, 4096

b)

32, 8, 2

c)

64, 32, 16

d)

92, 66, 38

43.

Find the next three terms: -4, -12, -36, -108, ...

a)

36, -108, 324

b)

-324, -972, -2916

c)

324, -972, 2916

d)

-108, 324, -972

44.

What is the common ratio for the sequence:
28, 14, 7, 3.5...

a)

2

b)

1/2

c)

-14

d)

-7

45.

Find the common ratio: 4, -16, 64, -256, ...

a)

r = -4

b)

r = 2

c)

r = -2

d)

r = 4

46.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

47.

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

48.

Find a₁₂ in the sequence -1, -3, -9, -27, ...

a)

-177,147

b)

-19,683

c)

-59,049

d)

118,098

49.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

50.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

51.

Determine whether the sequence is arithmetic, geometric, or neither.

a)

arithmetic

b)

geometric

c)

neither

52.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

53.

Find the sum of 125 + 25 + 5 +... + S₉

a)

$\frac{488280}{3125}$

b)

$\frac{488281}{3125}$

c)

$\frac{3125}{488280}$

d)

$\frac{3125}{488281}$

54.

9 + 6 + 4 + ..., the find S₇

a)

$\frac{2059}{81}$

b)

$-\frac{2059}{81}$

c)

$-\frac{81}{2059}$

d)

$\frac{81}{2059}$

55.

Find the sum of the first 10 terms of a geometric sequence 5, 10, 20, ...

a)

5115

b)

5114

c)

5113

d)

5112

56.

What side is opposite $\angle W$ ?

a)

VW

b)

VX

c)

WX

57.

What is the length of the hypotenuse $\Delta WVX$ ?

a)

21

b)

28

c)

35

d)

49

58.

What the name of the hypotenuse?

a)

VW

b)

VX

c)

WX

59.

Name the side adjacent to $\angle S$ .

a)

UT

b)

SU

c)

ST

60.

Which side is the hypotenuse?

a)

5

b)

12

c)

13

61.

What is the length of the side adjacent to ∠C?

a)

30

b)

40

c)

50

62.

For angle A, the opposite leg equals

a)

8

b)

15

c)

17

d)

Does not apply

63.

For angle B, the adjacent side is

a)

8

b)

15

c)

17

d)

Does not apply

64.

What is the length of the side adjacent to ∠A?

a)

30

b)

40

c)

50

65.

What is the length of the side opposite ∠X?

a)

16

b)

30

c)

34

66.

Which side is adjacent to ∠B?

a)

AB

b)

BC

c)

AC

d)

∠C

67.

What is the ratio for Sine?

a)

$\frac{hyp}{opp}$

b)

$\frac{opp}{hyp}$

c)

$\frac{opp}{adj}$

d)

$\frac{adj}{opp}$

68.

What is the ratio for Cosine?

a)

$\frac{opp}{hyp}$

b)

$\frac{opp}{adj}$

c)

$\frac{adj}{opp}$

d)

$\frac{adj}{hyp}$

69.

What is the ratio for Tangent

a)

$\frac{opp}{hyp}$

b)

$\frac{adj}{opp}$

c)

$\frac{opp}{adj}$

d)

$\frac{hyp}{opp}$

70.

Find the measure of the indicated angle.

a)

9.39

b)

55.2

c)

20.2

d)

19.4

71.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

72.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

73.

A ramp is being built next to a 4-inch high sidewalk. The ramps angle of inclination is 10 degrees. Estimate the length of the ramp to the nearest tenth of an inch.

a)

4.1 inches

b)

3.9 inches

c)

22.7 inches

d)

0.7 inches

74.

Sam views a deer from a height of 45 feet. The horizontal distance between the tourist and the deer is 130 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

a)

19^o

b)

45^o

c)

71^o

d)

138^o

75.

Solve for m∠N

a)

14

b)

65

c)

76

d)

53

76.

Find x round to the nearest tenth.

a)

46.1

b)

4.9

c)

73.5

d)

68.6

77.

Which class has the higher median?

a)

1st period

b)

2nd period

c)

They have the same median

78.

A radio station asks its listeners to dial one of two numbers to indicate their preference for one of two candidates in an upcoming election. Of the responses received, 76% favored candidate A. If there are 1,500 registered voters, how many will vote for candidate A?

a)

1,140

b)

6

c)

1,974

d)

100

79.

Ana wants to know the average student’s opinion of the tardy policy at her school. Which group of students should she survey in order to achieve the most accurate results?

a)

thirty students who are often tardy

b)

thirty students who are rarely tardy

c)

thirty of her friends

d)

thirty randomly selected students from her school

80.

What is the DOMAIN of the function?

a)

All real numbers

b)

x ≤ 4

c)

x < 4

d)

0 ≤ x ≤ 4

81.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

82.

Match the graph with the correct equation.

a)

b)

c)

d)

83.

A house painter charges $12 per hour for the first 40 hours he works, $18 for the ten hours after that, and $24 for all hours after that.

How much does he earn for a 70 hour week?

a)

$1020

b)

$1140

c)

$840

d)

He works for free!

84.

Which is the best way to represent answering 25 multiple-choice questions with 4 choices for each answer?

a)

spin a spinner with four sections 25 times

b)

roll a die 25 times

c)

flip a coin 25 times

d)

roll a die 4 times

85.

What statement does the shaded region represent

a)

A or B

b)

Not A

c)

A and B

d)

Not B

86.

How many senior boys play football or wrestle?

a)

9

b)

21

c)

30

d)

39

87.

Add

a)

11 8
-4 2

b)

3 2
-6 -6

c)

-3 2
-4 -6

d)

10 8
-6 2

88.

Subtract

a)

3 -8
0 -1

b)

3 -4
8 -13

c)

-3 8
0 1

d)

3 -8
-8 1

89.

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

90.

What are the dimensions of this matrix?

a)

2 x 3

b)

3 x 2

c)

6 x 1

d)

1 x 6

91.

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

92.

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

a)

8

b)

9.01

c)

6

d)

1

93.

What comes first in the order?

a)

Row

b)

Column

94.

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.

95.

You can multiply a 2X3 matrix by which matrix?

a)

2X2

b)

2X12

c)

3X12

d)

2X3

96.

What is the entry at f₄₂?

a)

23

b)

-81

c)

-44

d)

99

e)

-56

97.

Simplify √-28

a)

-√28

b)

-2i√7

c)

2i√7

d)

28i

98.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

99.

Simplify:
-3i(4 + 2i)

a)

6 - 12i

b)

6 + 12i

c)

-12i - 6i²

d)

-12i + 6i²

100.

(4-5i)(4+5i)

a)

41

b)

-9

c)

41+40i

d)

-9+40i

Final Exam Math IV Fall 2023

Total questions: 100

Worksheet time: 6hrs 38mins

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