Free Printable Midterm Review

1.

What shape is a normal distribution curve?

a)

Half curve

b)

Round curve

c)

Bell curve

d)

Square curve

2.

According to the empirical rule, what percentage of data falls within 1 standard deviation?

a)

25%

b)

68%

c)

95%

d)

99.7%

3.

According to the empirical rule, what percentage of data falls within 3 standard deviation?

a)

25%

b)

68%

c)

95%

d)

99.7%

4.

Which best describes the shaded part of this normal distribution graph?

a)

All data that is one or higher.

b)

All data that is one or more standard deviations above the mean.

c)

All data that is between 1 and 3.

d)

All data that is above the mean.

5.

The Empirical (68-95-99.7) Rule can be applied only if data is _______

a)

Normally Distributed

b)

Uniform

c)

Skewed

d)

Symmetric

6.

Use the following information and the Empirical Rule to estimate the answer.

The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4. Find the percentage of golfers that are between 30 and 46 years old. (Remember to draw a curve with the values to help you.)

a)

68%

b)

94%

c)

95%

d)

99.7%

7.

If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

a)

20

b)

15

c)

40

d)

30

8.

The normal curve is symmetrical about the mean.

a)

True

b)

False

9.

This data is normally distributed. What percent of the data is in the shaded region?

a)

68%

b)

32%

c)

16%

d)

50%

10.

This data is normally distributed. What percent of the data is in the shaded region?

a)

5%

b)

95%

c)

2.5%

d)

50%

11.

The mean life of a tire is 30,000 km. The standard deviation is 2000 km. Then, 68% of all tires will have a life between ___________ km and __________ km.

(Remember to draw a curve with the values to help you.)

a)

28,000 km and 32,000 km.

b)

24,000 km and 34,000 km.

c)

26,000 km and 34,000 km.

d)

27,000 km and 31,000 km.

12.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 12 and 15 days?

(Remember to draw a curve with the values to help you.)

a)

68%

b)

34%

c)

16%

d)

2.5%

13.

What is the formula to find the z-score for population?

a)

z=X-M

b)

z=σ-M/μ

c)

^z/M=μ

d)

z=X-μ/σ

14.

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

a)

True

b)

False

15.

Find the z-score value corresponding if the location is below the mean by 2 standard deviations

a)

+2.00

b)

-2.00

c)

+1.25

d)

-1.00

16.

Find the z-scores value corresponding if the location is above the mean by 1/2 standard deviations

a)

-0.50

b)

+1.00

c)

+0.50

d)

-1.00

17.

Find the Z-score.

Mean = 27

Standard Deviation: 1.4

x = 11

a)

-11.43

b)

7.85

c)

-2.33

d)

4.16

18.

Find the z-score.

Mean = 45

Standard Deviation: 2.1

x = 50

a)

2.38

b)

3.00

c)

3.08

d)

2.33

19.

Find the z-score.

Mean = 25

Standard Deviation: 7

x = 9.6

a)

-2.2

b)

-36

c)

5.2

d)

23.46

20.

Find the z-score.

Mean: 16

Standard Deviation: 4

x = 11

a)

-1.25

b)

+1.25

c)

16

d)

21

21.

A data set has a mean of 300 and a standard deviation of 40. What value would have a z-score of $z=-2$ ?

a)

298

b)

296

c)

220

d)

380

22.

What does it mean to have a z-score of $z=0$ on a quiz?

a)

It means you did better than zero people.

b)

It means you scored the same grade as the average grade.

c)

It means you earned a zero on the quiz.

d)

It means the average score was a zero.

23.

Use the image of the normal graph provided. What is the value of the mean?

a)

6

b)

34

c)

52

d)

70

24.

Use the image of the normal graph provided. What is the value of the standard deviation?

a)

6

b)

12

c)

36

d)

18

25.

A recent survey found that out of 400 random American adults, 89% pay their bills on time. The margin of error in this survey was 2%. What is the interval of values in which the truth is likely found?

a)

89% - 91%

b)

87% - 89%

c)

87% - 91%

d)

388 - 402

26.

Why is a sample of 1000 people better than a sample of 100 people?

a)

It reduces the margin of error.

b)

It decreases bias.

c)

Having more people is always better.

d)

More people means that our results are more accurate.

27.

What is the margin of error for the interval (6.8, 12.9)?

a)

9.85

b)

3.05

c)

3.50

d)

6.8

28.

In a survey of 2480 golfers, 15% said they were left-handed. The survey's margin of error was 3%. Construct a confidence interval for the proportion of left-handed golfers.

a)

(0.18, 0.21)

b)

(0.12, 0.18)

c)

(0.12, 0.15)

d)

(0.11, ).19)

29.

One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.

a)

Observational Study

b)

Experiment

30.

A researcher stood at a school parking lot entrance to see if the color of a car is related to the driver not wearing a seatbelt.

a)

Observational Study

b)

Experiment

31.

A professor finds that people who are obese have higher cholesterol levels than those who are not obese.

a)

Observational Study

b)

Experiment

32.

You want to compare the health of students who walk to school to the health of students who ride the bus

a)

experiment

b)

observational study

33.

A teacher asks all her students five questions about their study habits.

a)

Survey

b)

Observational Study

c)

Experiment

34.

A teacher looks at his students tests to see which topics his students are still struggling with.

a)

Survey

b)

Observational Study

c)

Experiment

35.

A teacher asks all her students five questions about their study habits.

a)

Survey

b)

Observational Study

c)

Experiment

36.

A news station asked viewers to call in about their opinions about the construction of a new stadium.

a)

Survey

b)

Observational Study

c)

Experiment

37.

To evaluate the defect rate of its memory chips, an integrated circuit manufacturer tests every 100th chip off the production line.

a)

Biased Sample

b)

Unbiased Sample

38.

Students who wish to represent the school at a school board meeting are asked to stop by the office after lunch

a)

Biased Sample

b)

Unbiased Sample

39.

To determine the most popular children’s programs, a television station asks parents to call in and complete a phone survey.

a)

Biased Sample

b)

Unbiased Sample

40.

Airline boarding passes are marked with red stars at random to decide which passengers should have their carry-on luggage inspected.

a)

Biased Sample

b)

Unbiased Sample

41.

To determine how often people eat out, every tenth person entering a Chinese restaurant is surveyed.

a)

Biased Sample

b)

Unbiased Sample

42.

Biased or Random?

Teliciah wants to determine the most popular brand of cereal in all of California. So she polls all the houses on her street to get a sample.

a)

Biased sample

b)

Random sample

43.

Biased or Random?

Marissa wants to learn what the most popular board game in the United States is, so she creates a poll and shares it on Twitter.

a)

Biased sample

b)

Random sample

44.

Biased or Random?

Justin wants to determine who the most popular Twitch/tv streamer in the United States is. So he hacks the U.S. Census and includes the question in the 2020 census form that goes to every household in America.

a)

Biased sample

b)

Random sample

45.

Determine if the question is random or biased. What is your favorite season?

a)

biased question

b)

random question

46.

Determine if the question is random or biased. Is basketball your favorite sport?

a)

biased question

b)

random question

47.

Determine if the question is random or biased. Do you want a delicious salad for lunch or the usual sandwich?

a)

biased question

b)

random question

48.

Determine the solution set of x. Identify any extraneous solutions.

\sqrt{x-2}=8

a)

$x=18$

b)

$x=66$

c)

$x=100$

d)

$x=36$

49.

Determine the solution set of x. Identify any extraneous solutions.

\sqrt{5x-3}=\sqrt{2x+6}

a)

$x=3$

b)

$x=\frac{3}{7}$

c)

$x=\frac{9}{7}$

d)

$x=1$

50.

Solve.

a)

no solution

b)

6

c)

3

d)

4

51.

Which is the graph of f(x) = √x +3

a)

A

b)

B

c)

C

d)

D

52.

Describe the transformation.

a)

Down 1

b)

Reflect over y-axis

c)

Up 1

d)

Reflect over x-axis

53.

Which of these equations shifts a radical equation right 1 time and up 2 times?

a)

y = √(x + 1) - 2

b)

y = √(x - 1) + 2

c)

y = √(x - 2) + 1

d)

y = √(x + 2) - 1

54.

a)

9

b)

-9

c)

21

d)

-21

55.

a)

-6

b)

6

c)

-5

d)

5

56.

a)

45

b)

55/3

c)

5

d)

189

57.

a)

3

b)

-3

c)

4

d)

-4

58.

Solve and check your solution.

a)

8

b)

-8

c)

0

d)

no solution

59.

$\sqrt{9-b}=\sqrt{1-9b}$

a)

-1

b)

1

c)

0

d)

no solution

60.

Match the correct equation with the given graph.

a)

y = √(x) + 2

b)

y = √(x) - 2

c)

y = √(x + 2)

d)

y = √(x - 2)

61.

Describe the transformation.

a)

Right 10

b)

Up 10

c)

Down 10

d)

Left 10

62.

Sketch the graph of each function.

a)

b)

c)

d)

63.

What are the transformations of this functions compared to the parent function?

a)

right 5, down 2, and reflection

b)

Reflection, stretch, and right 5

c)

Reflection, stretch, and left 5

d)

right 5, down 2

64.

What function best describes this graph?

a)

f(x)= -√(x+4) -2

b)

f(x)= √(x-4) -2

c)

f(x)= -√(x-4) -2

d)

f(x)= √(x+4) +2

65.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

66.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

67.

Jack invest $600 earning 5% interest rate. How much will he have after 5 years?

a)

$630

b)

$729.30

c)

$765.77

d)

$4556.25

68.

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

a)

300

b)

1.16

c)

.16

d)

x

69.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1 + 0.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1+ 0.15)^x

70.

Write an equation that models the following situation:

Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1+ 0.14)^x

d)

y=6(1 - 0.14)^x

71.

Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

a)

$23,219.72

b)

$136.72

c)

$51,710.94

d)

$16,710.94

72.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

73.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

74.

log₅25 = ?

a)

2

b)

5

c)

125

d)

10

75.

Evaluate log₅20 to the third decimal place

a)

0.537

b)

2.996

c)

1.301

d)

1.861

76.

The common logarithm has what base? For example: What base does log 100=2 have?

a)

10

b)

0

c)

e

d)

-e

77.

Find the value for x to the third decimal place: 10^x =20

a)

2

b)

1.301

c)

0.5

d)

No Correct Answer

78.

Solve the exponential equation algebraically. (Round to three decimal places)
2^x+13=35

a)

11

b)

4.690

c)

4.459

d)

2.802

79.

Solve: 7ⁿ⁺¹⁰−8 = 6

a)

-7.374

b)

-7.360

c)

-8.644

d)

-8.853

80.

Change the following into logarithmic form: h = p ^g

a)

log _gp = h

b)

log _p h = g

c)

log _pg = h

d)

log _hp = g

81.

Change log₄ 19 to be an expression with a base of 5. Do not evaluate.

a)

(log ₅ 19)/(log 4)

b)

(log 19)/(log 4)

c)

(log 19)/(log ₅4)

d)

(log ₅ 19)/(log ₅ 4)

82.

Solve the following equation:
4 + 3 log (2x) = 16

a)

x = 3000

b)

x = 0

c)

x = 5000

d)

x = 1,000,000

83.

a)

No Solution

b)

x = 4

c)

x = 7

d)

x = 9

84.

Write in exponential form
∛x⁷

a)

x⁷∕ ³

b)

x3⁄7

c)

3x⁷

d)

7x³

85.

Simplify 4^1/3 x 4^4/3

a)

4^5/3

b)

4

c)

2⁵

86.

(6^3/4)^1/3

a)

6^1/4

b)

6^3/12

c)

6^4/7

d)

6^9/12

87.

Simplify. Your answer should only contain positive exponents.

a)

A

b)

B

c)

C

d)

D

88.

Rewrite in radical form.

a)

A

b)

B

c)

C

d)

D

89.

Evaluate without a calculator.

a)

A

b)

B

c)

C

d)

D

90.

a)

2^1/6

b)

64

c)

6^1/2

d)

2⁶

91.

an exponent 1/2 means

a)

square root

b)

cube root

c)

fourth root

d)

fifth root

92.

In the following, what is my base $\left(-2\right)^{\frac{1}{3}}$

a)

-2

b)

2

93.

Your exponents denominator is the (a) ?

94.

Simplify . Your answer should contain only positive exponents. $4v^{\frac{2}{3}}\cdot v^{-1}$

a)

$4v^{\frac{1}{3}}$

b)

$\frac{4}{v^{\frac{1}{3}}}$

c)

$\frac{v^{\frac{1}{3}}}{4}$

d)

$\frac{1}{4v^{\frac{1}{3}}}$

95.

Simplify . Your answer should contain only positive exponents. $\left(6b\right)^{\frac{-4}{3}}$

a)

$\frac{1}{6^{\frac{4}{3}}b^{\frac{4}{3}}}$

b)

$\frac{6}{b^{\frac{4}{3}}}$

c)

$\frac{b^{\frac{4}{3}}}{6}$

d)

$\frac{6^{\frac{4}{3}}}{b^{\frac{4}{3}}}$

Midterm Review

Total questions: 95

Worksheet time: 4hrs 27mins

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