Download Chapters 9-11

CH 9_10_11
____
____
____
1. In a right triangle,  is an acute angle and
. Evaluate the other five trigonometric functions of .
a.
c.
b.
d.
2. In a right triangle,  is an acute angle and
. Evaluate the other five trigonometric functions of .
a.
c.
b.
d.
3. Solve
.
D
19°
12
f
F
d
E
a.
b.
____
c.
d.
4. Solve
.
D
39°
22
e
F
a.
b.
____
d
E
c.
d.
5. Draw an angle that measures 260° in standard position.
a.
c.
b.
____
6. Draw an angle that measures 700° in standard position.
a.
c.
b.
____
d.
d.
7. Draw an angle that measures –340° in standard position.
a.
c.
b.
____
d.
8. Convert 35° to radians.
a.
rad
b.
____
d.
rad
9. Convert
rad
rad
to degrees.
a. –6°
b. 84°
c. –96°
d. 174°
be a point on the terminal side of an angle  in standard position. Evaluate the six
____ 10. Let
trigonometric functions of .
a.
12
13
sin , csc
13
12
5
13
cos , sec
13
5
12
5
tan , cot
5
12
b.
c.
12
13
, csc
13
12
5
13
cos , sec
13
5
12
5
tan , cot
5
12
sin
c.
8
9
sin , csc
9
8
10
27
cos , sec
27
10
12
5
tan , cot
5
12
d.
sin
12
13
, csc
13
12
5
13
cos , sec
13
5
12
5
tan , cot
5
12
____ 11. Use the unit circle to evaluate the six trigonometric functions of
.
a. sin–1, csc–1
c. sin0, csc–1
cos0, sec0
cos–1, secundefined
tan0, cot0
tan0, cot undefined
b. sin–1, csc–1
cos0, secundefined
tanundefined, cot0
d. sin–1, csc–1
cosundefined, sec0
tan0, cotundefined
____ 12. Use the unit circle to evaluate the six trigonometric functions of
.
a. sin–1, cscundefined
c. sin0, cscundefined
cos0, sec–1
tanundefined, cot  0
cos–1, sec–1
tanundefined, cot0
b. sin0, cscundefined
cos–1, sec–1
tan0, cotundefined
____ 13. Find the reference angle
a. 36°
b. 239°
d. sin0, csc0
cos–1, sec–1
tan0, cot0
for
.
c. 31°
d. 329°
____ 14. Evaluate
a. 2
b. 0.5
without using a calculator.
____ 15. Evaluate
without using a calculator.
c. –0.5
d. –2
c. –0.5
d. –2
a. 0.5
b. 2
____ 16. Evaluate
without using a calculator.
a. 1
b. –1
c. 0.5
d. –0.5
____ 17. Identify the amplitude of
transformation of the graph of
a. 1
3
. Then graph the function and describe the graph of g as a
.
c. 2

3
y
y
4
4
2
2
–2

—
2

3

—
2
2
5

—
2
x
–4
The graph of g is a vertical shrink by a
1
factor of
of the graph of f.
3
b. 3
–2

—
2

3

—
2
2
5

—
2
x
–4
The graph of g is a vertical shrink by a
factor of 3 of the graph of f.
d. 6
y
y
4
4
2
2

—
2
–2
3

—
2

2
5

—
2

—
2
x
–2
–4

3

—
2
5

—
2
x
–4
The graph of g is a vertical stretch by a
factor of 3 of the graph of f.
____ 18. Identify the period of
of the graph of
a. 6
The graph of g is a vertical stretch by a
factor of 3 of the graph of f.
. Then graph the function and describe the graph of g as a transformation
.
y
2

2
3
4
5
6
7
x
–2
The graph of g is a vertical stretch by a factor of 6 of the graph of f.
b. 12
y
1

2
3
4
5
6
7
x
–1
The graph of g is a horizontal stretch by a factor of 6 of the graph of f.
c. 1

6
y
2

2
3
4
5
6
7
x
–2
The graph of g is a vertical shrink by a factor of 6 of the graph of f.
d. 1

3
2
y
1

2
3
4
5
6
x
7
–1
1
of the graph of f.
6
The graph of g is a horizontal shrink by a factor of
____ 19. Identify the amplitude of
. Then graph the function and describe the graph of g as a
transformation of the graph of
a. 1
4
.
c. 4
y
y
4
4
2
2

—
2
–2

3

—
2
2
5

—
2
x

—
2
–2

3

—
2
2
5

—
2
x
–4
–4
The graph of g is a vertical shrink by a
1
factor of
of the graph of f.
4
b. 8
The graph of g is a vertical stretch by a
factor of 4 of the graph of f.
d. 1

2
y
y
4
4
2
2
–2

—
2

3

—
2
2
5

—
2
x
–2
–4

—
2

3

—
2
2
5

—
2
x
–4
The graph of g is a vertical stretch by a
factor of 4 of the graph of f.
____ 20. Graph one period of
The graph of g is a vertical shrink by a
factor of 4 of the graph of f.
. Describe the graph of g as a transformation of the graph of
.
y
a.
30
30
20
20
10
10
 -—
 -—

-—
2
6
6 –10

—
6

—
3

—
2
 -—
 -—

-—
2
6
6 –10
x
–20
–20
–30
–30
The graph of g is a horizontal shrink by a
1
factor of
and a vertical shrink by a
3
1
factor of
of the graph of f.
3
y
b.
30
20
20
10
10

—
3

—
2
 -—
 -—

-—
2
6
6 –10
x
–20
–20
–30
–30
The graph of g is a horizontal shrink by a
1
factor of
and a vertical shrink by a
3
1
factor of
of the graph of f.
3
____ 21. Graph one period of

—
2
x

—
6

—
3

—
2
x
The graph of g is a horizontal shrink by a
1
factor of
and a vertical stretch by a
3
factor of 3 of the graph of f.
. Describe the graph of g as a transformation of the graph of
y
c.
10

-—
2

—
3
y
d.

—
6

—
6
The graph of g is a horizontal shrink by a
factor of 3 and a vertical stretch by a
factor of 3 of the graph of f.
30
 -—
 -—

-—
2
6
6 –10
a.
y
c.
y
20
10

—
2

x

-—
2

—
2
–10
–10
–20
–20
The graph of g is a horizontal stretch by a
factor of 2 and a vertical stretch by a
factor of 4 of the graph of f.

x
The graph of g is a horizontal shrink by a
1
factor of
and a vertical shrink by a
2
1
factor of
of the graph of f.
4
.
y
b.
d.
10
10

-—
2

—
2

x

-—
2

—
2
–10
–10
–20
–20
and
find the other five trigonometric functions.
a.
c.
b.
d.
____ 23. Given
a.
and

x
The graph of g is a horizontal shrink by a
factor of 2 and a vertical stretch by a
factor of 4 of the graph of f.
The graph of g is a horizontal shrink by a
1
factor of
and a vertical shrink by a
2
1
factor of
of the graph of f.
4
____ 22. Given
y
20
find the other five trigonometric functions.
c.
b.
d.
given that sin a 
____ 24. Find
a.
15
with
17
and cos b  
3
with
5
.
c. 13
85
d. 77
85
13
85
b. 77

85

____ 25. Simplify the expression
.
a. cos x
b. –sin x
c. sin x
d. –cos x
____ 26. Simplify the expression
.
c. –sin x
d. –cos x
a. cos x
b. sin x
____ 27. For a family with 3 children what is the probability that they have exactly 1 boy and 2 girls?
a. 1
c. 1
4
3
b. 3
d. 2
8
3
____ 28. A card is chosen at random from a deck of 24 cards, 4 red, 8 black, 6 blue, and 6 green. Then, the card is
returned to the deck and a new card is chosen. The table below shows the results of choosing 18 cards. For
which color of card is the experimental probability the same as the theoretical probability?
Results
red
black
blue
green
3
5
2
8
a. blue
b. black
c. red
d. green
____ 29. A research study asked 2892 homeowners how many bedrooms were in their homes. The results are shown in
the table below. What is the probability that a homeowner chosen at random has 3 bedrooms?
Number of
Bedrooms
2 or less
Number of
Homeowners
318
3
1099
4
781
5 or more
694
a. about 11%
b. about 38%
c. about 24%
d. about 27%
____ 30. You play a game that requires rolling a six-sided die then randomly choosing a colored card from a deck
containing 3 red cards, 8 blue cards, and 6 yellow cards. Find the probability that you will roll a 2 on the die
and then choose a blue card.
a. 4
c. 8
51
17
b. 1
d. 1
6
17
____ 31. At a sandwich shop, 42% of customers buy a drink with their sandwich. Only 28% of customers buy a drink
and chips with their sandwich. What is the probability that a customer who buys a drink also buys chips?
a. about 66.7%
c. 70%
b. 1.5%
d. 14%
____ 32. A group of large and small dog owners are surveyed about whether they feed their dogs dry or wet dog food.
Below is a two-way table that shows the joint and marginal relative frequencies for the survey results.
Large Dog
Owner
Small Dog
Owner
Total
Dry Dog
Food
Wet Dog
Food
Total
0.355
0.169
0.525
0.131
0.344
0.475
0.486
0.514
1
Find the missing value in the table below showing the conditional relative frequencies based on the row totals.
Dry Dog Food
Wet Dog Food
Large Dog
Owner
Small Dog
Owner
a. 0.73
b. 0.355
c. 0.676
d. 0.525
____ 33. A custom furniture builder wants to earn at least $30 per hour building four different types of furniture:
dressers, nightstands, armoires, and chests. Over the course of a year, the builder records the selling and hours
worked for each piece and determines whether or not the earning goal is met. The table shows these findings.
Which type of furniture best helps meet the earning goal?
 $30 per Hour
Dresser
Nightstand
< $30 per Hour
Armoire
Chest
a. Chest
b. Nightstand
c. Dresser
d. Armoire
____ 34. You spin a spinner with 9 equal spaces numbered 1 through 9. What is the probability that the spinner lands
on a 5 or a 9.
a. 8
c. 1
9
9
b. 7
d. 2
9
9
____ 35. An amusement park has two featured rides that require an additional ticket, the Slingshot and the Scream
Flyer. On a summer day, 1279 visitors entered the park. 280 visitors bought tickets for either the Slingshot or
the Scream Flyer. 247 visitors bought a ticket for the Slingshot and 237 visitors bought a ticket for the Scream
Flyer. What is the probability that a randomly selected visitor bought tickets for both the Slingshot and the
Scream Flyer?
a. 0.159
c. 0.378
b. 0.219
d. 0.597
____ 36. A process engineer is implementing a quality assurance system on a breakfast cereal production line. A new
sensor is installed on the line that tests the weight of the filled boxes and rejects any product outside the
correct package weight. Historically, 90% of the product manufactured on this line is within the correct
weight range. The sensor rejects boxes of incorrect weight 98% of the time. The sensor rejects boxes of
correct weight 1% of the time. What is the probability that a correct weight box of cereal will get rejected by
the sensor?
a. 0.9%
c. 0.2%
b. 90%
d. 1.8%
____ 37.
In how many ways can you arrange 5 of the numerals 1 through 7?
a. 5040
c. 120
b. 2520
d. 35
____ 38. Your shirt drawer contains 8 different colored shirts that you will wear over the next 8 days. What is the
probability that you will randomly choose the orange shirt to wear today and the red shirt to wear tomorrow?
a. 1
c. 1
8
56
b. 1
d. 1
16
4
____ 39. Use the probability distribution to determine the probability of an odd number.
P(x)
Probability
0.6
0.5
0.4
0.3
0.2
0.1
1
2
3
Outcome
4
a.
x
c. 1
2
d. 7
10
3
10
b. 1
5
a. 0.9985
b. 0.975



















____ 40. A normal distribution has mean  and standard deviation  An x-value is randomly selected from the
distribution. Find
.
c. 0.025
d. 0.0015
____ 41. A normal distribution has mean  and standard deviation  An x-value is randomly selected from the
distribution. Find
.
a. 0.0265
c. 0.975
b. 0.9735
d. 0.9985
____ 42. A normal distribution has mean of 90 and standard deviation of 10 Find the probability that a randomly
selected x-value from the distribution is at most 120.
a. 0.025
c. 0.0015
b. 0.9985
d. 0.975
____ 43. A study finds that the number of gallons of water used each month per household in a residential
neighborhood are normally distributed with a mean of 470 gallons and a standard deviation of 50 gallons. A
household is randomly selected. What is the probability that the household uses 480 gallons of water or less
per month?
a. 0.4207
c. 0.5793
b. 0.0793
d. 0.5398
____ 44. Determine whether the histogram has a normal distribution.
Pay Rates of Babysitters
Relative frequency
0.2
0.15
0.1
0.05
1
2
3
4
5
6
7
8
9
10
Dollars per hour
a. no
b. yes
____ 45. In the United States, a survey of 3563 married women found that 1746 of them suffer from allergies. Identify
the population and the sample.
a. The population consists of the responses of all women in the United States, and the sample
consists of the responses of the 3563 women in the survey.
b. The population consists of the responses of the 3563 women in the survey, and the sample
consists of the responses all of married women in the United States.
c. The population consists of the responses of all married women in the United States, and
the sample consists of the responses of the 1746 women in the survey.
d. The population consists of the responses of all married women in the United States, and
the sample consists of the responses of the 3563 women in the survey.
____ 46. A sample of 14 students in Mr. Lee's math class is taken, and the standard deviation of the students' grades is
5%. Is the standard deviation of the students' grades a parameter or a statistic?
a. parameter
b. statistic
____ 47. In a survey of 9444 people in the U.S., 47% say that they own a bicycle. What is the margin of error for the
survey? Give an interval that is likely to contain the exact percent of all people who own a bicycle.
; between 39.7% and 54.3%
a. about
; between 46% and 48%
b. about
; between 46.5% and 47.5%
c. about
about
; between 32.4% and 61.6%
d.
____ 48. Which angle is coterminal with 153°?
a. –27°
b. 63°
c. –117°
d. 513°
____ 49. Which angle is coterminal with –186°?
a. –456°
b. –96°
c. –546°
d. –366°
____ 50. A surveyor is working to determine the gradient of a hill. The surveyor knows the hill starts at an elevation of
1755 feet and peaks at an elevation of 2105 feet. The distance of the hill from the bottom to the top is
910 feet. Select the responses that represent the angle of elevation of the hill (rounded to the nearest degree)
and the trigonometric functions of the angle of elevation.
a. 23°
b.
d.
cos 
12
13
e.
13
csc 
5
f.
12
csc 
13
13
5
c. 67°
cos 
51. A yard game requires players to toss a bean bag onto a board as shown below. The bean bag is equally likely
to land on any part of the board. Which region does the bean bag have a higher probability of landing on,
region D or region B?
6
4
A
6
B
C
4
2
10
D
52. You roll a six-sided die and then flip a coin. Use a sample space to determine whether rolling a 6 first and
getting tails second are independent events.
53. You are packing clothes for vacation and don’t want to take any t-shirts. You randomly choose 3 shirts from a
drawer containing 4 t-shirts, 3 polo shirts, and 3 button-downs.
a. What is the probability that the first 3 shirts are t-shirts when you replace each shirt before choosing the
next one?
b. What is the probability that the first 3 shirts are t-shirts when you do not replace each shirt before
choosing the next one?
c. Compare the probabilities.
54. An Eastern Caribbean tourism agency surveyed visitors to three different islands and asked whether they
stayed in a beachfront resort or condominium. The results, given as joint relative frequencies, are shown in
the two-way table.
Location
Beachfront Resort
U.S. Virgin
Islands
0.28
St. Lucia
Barbados
0.27
0.28
Condominium
0.04
0.05
0.08
a. What is the probability that a randomly selected visitor to Barbados stayed in a beachfront resort?
b. What is the probability that a randomly selected visitor who did not stay in a beachfront resort visited St.
Lucia?
c. Determine whether staying in a beachfront resort and visiting St. Lucia are independent events.
____ 55. A group of 152 men and 190 women are asked if they will vote in next year’s election. 132 men and 165
women say they will vote. Which of the following statements are true?
a. Given that the person is a man, the conditional relative frequency that he will vote is
approximately 0.868.
b. The probability that a person who will not vote is a woman is approximately 0.444.
c. The marginal frequency of people who will vote is 45.
d. The joint relative frequency of men who will vote is approximately 0.386.
e. The joint frequency of men who will vote is 132.
f. The marginal relative frequency of people who will not vote is approximately 0.868.
Identify the type of sample described.
____ 56. You want to determine whether students like the new healthy options for the school lunch. You ask every
fifth student in line for lunch.
a. self-selected
b. systematic
c. stratified
d. cluster
e. convenience
____ 57. You want to determine whether students like the new healthy options for the school lunch. You place
questionnaires in lockers and use the ones returned to you.
a. self-selected
b. systematic
c. stratified
d. cluster
e. convenience
____ 58. The owner of the local library wants to know whether patrons like the new summer reading programs for
kids. The owner leaves questionnaires at the checkout counter and uses the ones returned.
a.
b.
c.
d.
e.
self-selected
systematic
stratified
cluster
convenience
____ 59. The CEO of a company wants to determine whether employees are satisfied with their jobs. The CEO
randomly surveys three employees from each department.
a. self-selected
b. systematic
c. stratified
d. cluster
e. convenience
Identify the method of data collection each situation describes.
____ 60. Members of a prom committee at your school ask every seventh student who enters the dance whether they
like the decorations.
a. experiment
c. survey
b. observational study
d. simulation
____ 61. A city employee paints half of the park benches with an oil-based paint and half with a latex paint. The
employee then compares the benches after six months and determines which method is better.
a. experiment
c. survey
b. observational study
d. simulation
____ 62. A financial advisor uses a computer program to predict the movement of stocks in the stock market.
a. experiment
c. survey
b. observational study
d. simulation
____ 63. A hospital has a critical shortage of O negative blood. A recent survey of 10,050 donors in the United States
found that only 804 have this type of blood. The hospital sends out a mobile blood donation unit that can
serve about 50 donors per day, with each giving about one liter of blood. The hospital’s goal is to collect
32 liters of O negative blood in 4 days.
You simulate the number of donors with blood type O negative out of 50 donors by repeatedly drawing
200 random samples of size 50. The histogram shows the results.
S imulation of 50 Blood Donors
Relative frequency
0.25
0.2
0.15
0.1
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.05
Proportion of 50 donors with O negative blood
Which of the following statements are true?
a.
b.
c.
d.
e.
The population is all people in the United States.
The statistic is the 8% of donors with O negative blood.
It is not likely that the hospital will reach its goal.
The parameter is the 10,050 donors in the United States who were surveyed.
The sample is the 804 donors who have O negative blood.
____ 64. A national polling company claims 26% of U.S. adults say they own more than 30 pairs of shoes. You survey
a random sample of 50 adults. The pairs of shoes owned for a random sample of 50 adults are shown in the
table.
20
40
21
12
21
22
16
28
12
9
Pairs of Shoes Owned
21
15
25
17
9
28
9
25
32
28
20
25
26
31
23
28
34
36
6
35
12
21
15
29
12
11
30
17
37
10
18
35
28
25
4
38
17
26
38
3
To analyze this claim you simulate choosing 70 random samples of size 50 using a random number generator.
The dot plot shows the results.
Simulation: Polling 50 Adults
0.1
0.2
0.3
0.4
P roportion of 50 adults who ow n more than 30 pairs of shoes
Which of the following statements are true?
a. The company’s claim is probably not accurate.
.
b. The margin of error on the results of your survey is about
c. If the national polling company surveyed 3122 adults, then the margin of error on the
results of its survey is about
.
d. The estimated population mean of your survey is 22 pairs of shoes.
e. The company’s claim is probably accurate.
f. Assuming the true population proportion is 0.26, the variation among sample proportions
using samples of size 50 could range from 0.2 to 0.32.
Match the description below with its value.
A Labor Day 5K race is run for charity each year. The mean time that it takes the runners to complete the
course is 44 minutes with a standard deviation of 8 minutes. The race has 54 people registered to run this
year.
a. 0.24
f. 1
b. 0.82
g. 50
c. 53
h. 1.4
d. 1.6
i. –1.1
e. 0.84
____ 65. probability that a runner finishes between 28 and 52 minutes
____ 66. approximate number of runners predicted to finish in less than 28 minutes
____ 67. z-score of a runner finishing in 35.2 minutes
____ 68. probability that a runner finishes between 32 and 40 minutes
____ 69. approximate number of runners predicted to finish in more than 32 minutes
____ 70. z-score of a runner finishing in 56.8 minutes
71. A game spinner is evenly divided into 9 numbered sections. While playing the game, you get a six on 4 out
the first 5 spins. You suspect that the spinner favors the number six. The game maker claims that the spinner
is fair. You simulate spinning 50 times by repeatedly drawing 200 random samples of size 50. The histogram
shows the results. What should you conclude when you spin 50 times and get (a) 2 sixes and (b) 6 sixes?
S imulation of 50 S pins
0.22
0.2
0.18
Relative frequency
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.02
Proportion of 50 spins that result in a six
72.
Health News
Patch Helps Smokers Quit
To test a new patch to quit smoking, a
company conducted an experiment. The
company identified 500 heavy smokers and
randomly divided them into two groups.
One group received the new patch and the
other group received a placebo patch. After
six months, 45% of smokers who used the
new patch quit smoking.
73.
Exercise Watch
Herbal Supplements Improve Workouts
At a fitness center, students were given the
choice of whether to take a
performance-enhancing herbal supplement.
Sixty students who took the supplement and
60 students who did not take the supplement
were monitored for two months. After the two
months, the students who took the supplement
had improved physical activity.
CH 9_10_11
Answer Section
1. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: evaluating trigonometric functions of acute angles | sine | cosine | tangent | cosecant | secant | cotangent
NOT:
Example 2
2. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: evaluating trigonometric functions of acute angles | sine | cosine | tangent | cosecant | secant | cotangent
NOT:
Example 2
3. ANS: A
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: solving right triangles
NOT: Example 4
4. ANS: A
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: solving right triangles
NOT: Example 4
5. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
6. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
7. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: drawing angles in standard position | standard position | measure of an angle
NOT: Example 1
8. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
9. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: degrees | radians | converting between degrees and radians
NOT: Example 3
10. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: trigonometric function | standard position
NOT: Example 1
11. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2
KEY: evaluating trigonometric functions of any angle | trigonometric function | unit circle
NOT: Example 2
12. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2
KEY: evaluating trigonometric functions of any angle | trigonometric function | unit circle
NOT: Example 2
13. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | finding reference angles
NOT: Example 3
14. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | using reference angles to evaluate functions
NOT: Example 4
15. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | using reference angles to evaluate functions
NOT: Example 4
16. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.3
NAT: HSF-TF.A.2 KEY: reference angle | using reference angles to evaluate functions
NOT: Example 4
17. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.4
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: graphing sine functions |sine function | graph of a periodic function | describing transformations of
graphs of periodic functions | amplitude | periodic function | period
NOT: Example 1
18. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.4
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: graphing sine functions |sine function | graph of a periodic function | describing transformations of
graphs of periodic functions | amplitude | periodic function | period
NOT: Example 1
19. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.4
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: graphing cosine functions | cosine function | graph of a periodic function | describing transformations
of graphs of periodic functions | amplitude | period | periodic function
NOT: Example 2
20. ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.5
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: secant function | graph of a periodic function | describing transformations of graphs of periodic
functions | graphing secant functions
NOT: Example 3
21. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.5
NAT: HSF-IF.C.7e | HSF-BF.B.3
KEY: cosecant function | graph of a periodic function | describing transformations of graphs of periodic
functions | graphing cosecant functions
NOT: Example 4
22. ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.7
NAT: HSF-TF.C.8 KEY: trigonometric function | finding trigonometric values
NOT: Example 1
23. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.7
NAT: HSF-TF.C.8 KEY: trigonometric function | finding trigonometric values
NOT: Example 1
24. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.8
NAT: HSF-TF.C.9 KEY: sum and difference formulas
NOT: Example 2
25. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.8
NAT: HSF-TF.C.9 KEY: simplifying trigonometric expressions
NOT: Example 3
26. ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.8
NAT: HSF-TF.C.9 KEY: simplifying trigonometric expressions
NOT: Example 3
27. ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.1
NAT: HSS-CP.A.1 KEY: theoretical probability | application
NOT: Example 2
28. ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.1
NAT: HSS-CP.A.1 KEY: experimental probability | application
NOT: Example 5
29. ANS:
NAT:
NOT:
30. ANS:
NAT:
KEY:
NOT:
31. ANS:
NAT:
KEY:
32. ANS:
NAT:
NOT:
33. ANS:
NAT:
NOT:
34. ANS:
NAT:
KEY:
NOT:
35. ANS:
NAT:
NOT:
36. ANS:
NAT:
NOT:
37. ANS:
NAT:
38. ANS:
NAT:
39. ANS:
NAT:
NOT:
40. ANS:
NAT:
NOT:
41. ANS:
NAT:
NOT:
42. ANS:
NAT:
NOT:
43. ANS:
NAT:
NOT:
44. ANS:
NAT:
NOT:
45. ANS:
B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.1
HSS-CP.A.1 KEY: experimental probability | application
Example 6
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
independent events | application | probability of independent events
Example 3
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
conditional probability | application
NOT: Example 7
C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.3
HSS-CP.A.4 KEY: two-way table | application | conditional relative frequency
Example 3
C
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.3
HSS-CP.A.4 | HSS-CP.A.5
KEY: conditional probability | application
Example 5-2
D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.4
HSS-CP.A.1 | HSS-CP.B.7
application | compound event | disjoint | finding probabilities of compound events
Example 1
A
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.4
HSS-CP.A.1 | HSS-CP.B.7
KEY: application | compound event
Example 3
A
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.4
HSS-CP.A.1 | HSS-CP.B.7
KEY: application | compound event
Example 4-2
B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.5
HSS-CP.B.9 KEY: permutation NOT: Example 1
C
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.5
HSS-CP.B.9 KEY: permutation | application
NOT: Example 3
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.6
HSS-CP.B.9 KEY: probability distribution | interpreting probability distributions
Example 2
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.1
HSS-ID.A.4 KEY: normal distribution | calculating probabilities
Example 1
B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.1
HSS-ID.A.4 KEY: normal distribution | calculating probabilities
Example 1
B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.1
HSS-ID.A.4 KEY: normal distribution | calculating probabilities
Example 1
C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.1
HSS-ID.A.4 KEY: normal distribution | application | standard normal table | z-score
Example 3
A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.1
HSS-ID.A.4 KEY: recognizing normal distributions | application
Example 4
D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.2
46.
47.
48.
49.
50.
51.
NAT: HSS-IC.A.2 | HSS-IC.A.1
KEY: population | sample | distinguishing between populations and samples | application
NOT: Example 1
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.2
NAT: HSS-IC.A.2 | HSS-IC.A.1
KEY: parameter | statistic | application
NOT: Example 2
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.5
NAT: HSS-IC.A.2 | HSS-IC.B.4
KEY: application | margin of error
NOT: Example 4
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: coterminal | finding coterminal angles | coterminal angles
NOT: Example 2
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 9.2
NAT: HSF-TF.A.1 KEY: coterminal | finding coterminal angles | coterminal angles
NOT: Example 2
ANS: A, D, E
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 9.1
NAT: HSF-TF.A.1 | HSF-TF.A.2 | HSF-TF.B.5 | HSF-TF.C.8
KEY: angle of elevation | application | evaluating trigonometric functions of acute angles | solving right
triangles
NOT: Combined Concept
ANS:
region D
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.1
NAT: HSS-CP.A.1 KEY: theoretical probability | geometric probability | application
NOT: Example 4-2
52. ANS:
1
1
P(rolling a 6) = ; P(getting tails) = ;
6
2
1
P(rolling a 6 then getting tails) =
12
Because
, the events are independent
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.2
NAT: HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.5 | HSS-CP.B.8
KEY: independent events | application | determining whether events are independent
NOT: Example 1 and 2
53. ANS:
8
a.
 0.064
125
1
b.
 0.033
30
c. You are 1.9 times more likely to choose 3 t-shirts when you replace each shirt before you select the next
shirt.
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.2
NAT: HSS-CP.A.1 | HSS-CP.A.2 | HSS-CP.A.3 | HSS-CP.A.5 | HSS-CP.B.6 | HSS-CP.B.8
KEY: dependent events | application | independent events
NOT: Example 5-2
54. ANS:
a. 77.8%
b. 29.4%
c. P(St. Lucia) = 0.32; P(St. Lucia | Yes)  0.33
Because
, the two events are not independent.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 10.3
NAT: HSS-CP.A.4 | HSS-CP.A.5
KEY: two-way table | application | conditional probability
NOT: Example 4
ANS: A, D, E
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 10.3
NAT: HSS-CP.A.4 | HSS-CP.A.5
KEY: two-way table | application | conditional relative frequency | conditional probability | joint relative
frequency | marginal relative frequency
NOT: Combined Concept
ANS: B
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample
NOT: Example 1
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample
NOT: Example 1
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample
NOT: Example 1
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample
NOT: Example 1
ANS: C
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample | identifying methods of data collection
NOT: Example 4
ANS: A
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample | identifying methods of data collection
NOT: Example 4
ANS: D
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.3
NAT: HSS-IC.A.1 | HSS-IC.B.3
KEY: sample | identifying methods of data collection
NOT: Example 4
ANS: B, C
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.2
NAT: HSS-IC.A.2 | HSS-IC.A.1
KEY: analyzing hypotheses | application | population | sample | parameter | statistic
NOT: Combined Concept
ANS: C, D, E
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.5
NAT: HSS-IC.A.2 | HSS-IC.B.4
KEY: application | estimating population parameters | analyzing estimated population parameters | margin of
error NOT:
Combined Concept
ANS: B
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.1
NAT: HSS-ID.A.4
KEY: normal distribution | application | standard normal table | calculating probabilities | z-score
NOT: Combined Concept
ANS: F
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.1
NAT: HSS-ID.A.4 KEY: normal distribution | application
NOT: Combined Concept
ANS: I
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.1
NAT: HSS-ID.A.4 KEY: normal distribution | application
NOT: Combined Concept
ANS: A
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.1
NAT: HSS-ID.A.4 KEY: normal distribution | application
NOT: Combined Concept
ANS: G
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.1
NAT: HSS-ID.A.4 KEY: normal distribution | application
NOT: Combined Concept
70. ANS: D
PTS: 1
DIF: Level 2
NAT: HSS-ID.A.4 KEY: normal distribution | application
71. ANS:
a. The maker’s claim is most likely false.
b. The maker’s claim is most likely true.
REF: Algebra 2 Sec. 11.1
NOT: Combined Concept
PTS: 1
DIF: Level 2
REF: Algebra 2 Sec. 11.2
NAT: HSS-IC.A.2 | HSS-IC.A.1
KEY: analyzing hypotheses | application
NOT: Example 3-2
72. ANS:
The study is a randomized comparative experiment; The treatment is the new patch to quit smoking. The
treatment group is the smokers who received the new patch. The control group is the smokers who received
the placebo patch.
PTS: 1
DIF: Level 1
REF: Algebra 2 Sec. 11.4
NAT: HSS-IC.A.1 | HSS-IC.B.3 | HSS-IC.B.6
KEY: randomized comparative experiment | control group | treatment group | randomization | application
NOT: Example 1
73. ANS:
The study is not a randomized comparative experiment because the individuals were not randomly assigned to
a control group and a treatment group. The conclusion that herbal supplements improve physical activity may
or may not be valid. There may be other reasons why some students had increased performance.
PTS:
NAT:
KEY:
NOT:
1
DIF: Level 1
REF: Algebra 2 Sec. 11.4
HSS-IC.A.1 | HSS-IC.B.3 | HSS-IC.B.6
randomized comparative experiment | control group | treatment group | randomization | application
Example 1