AnswersAL-Algebra II with StatisticsUnit Test

Unit Test — Cumulative exam Answers

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1
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Which of the following shows the extraneous solution to the logarithmic equation below?

Question illustration
A
x = negative 6
Option A
B
x = negative 4
Option B
C
x = negative 2
Option C
D
x = negative 1
Option D
2
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What is one possible solution for the triangle below?

Question illustration
A
Y Z similar to 43 point 0, m angle X similar to 94 point 6 degree, m angle Z similar to 17 point 4 degree.
Option A
B
Y Z similar to 19 point 3, m angle X similar to 85 point 4 degree, m angle Z similar to 26 point 6 degree.
Option B
C
Y Z similar to 12 point 9, m angle X similar to 17 point 4 degree, m angle Z similar to 94 point 6 degree.
Option C
D
Y Z similar to 95 point 4, m angle X similar to 26 point 7 degree, m angle Z similar to 85 point 4 degree.
Option D
3

The histogram below shows the number of weeks Jimmy spent different amounts of money to fill the gas tank in his car. If the graph is redrawn so that the scale on the y-axis begins with zero, which aspect of the graph will change the most?

Question illustration
A
The difference in the heights of the bars will not appear as great.
B
The difference in the heights of the bars will be more pronounced.
C
The graph will appear more skewed to the left.
D
The graph will appear more skewed to the right.
4

The histogram below shows the average number of days per year in 117 Oklahoma cities where the high temperature was greater than 90 degrees Fahrenheit.Which is an accurate comparison?

Question illustration
A
The mean is likely greater than the median because the data is skewed to the right.
B
The mean is likely greater than the median because the data is skewed to the left.
C
The median is likely greater than the mean because the data is skewed to the right.
D
The median is likely greater than the mean because the data is skewed to the left.
5

A company has an opportunity to bid on three contracts. Determine which would be the best investment given the information in the table below.Probability of Profit and Loss by ContractContractProfit, Probability of ProfitProbability to Break EvenLoss, Probability of LossSoutheast$45,000, 50%30%$6,000, 20%Southwest$60,000, 35%40%$10,000, 25%California$112,000, 20%40%$40,000, 40%

A
Southeast
B
Southwest
C
California
D
All contracts include a probability for loss.
6

Which statement best compares the graphs of and ?

Question illustration
A
The two graphs are exactly the same.
B
The open and closed circles are reversed.
C
The graph of is shifted up compared to the graph of , and the open and closed circles are reversed.
Option C
D
The graph of is shifted up compared to the graph of , and the open and closed circles are the same.
Option D
7

Veronique has a spinner with three sections of equal size, red (r), green (g), and blue (b).The spinner is spun twice. The sample space for the possible outcomes is S = {rr, rb, rg, gr, gg, gb, br, bg, bb}. If the number of times red is spun is the random variable, X, which graph represents the probability distribution?

A
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.43; 1 time is 0.43; 2 times is 0.1.
Option A
B
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.33; 1 time is 0.33; 2 times is 0.33.
Option B
C
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.55; 1 time is 0.32; 2 times is 0.11.
Option C
D
A probability distribution has number of times on the x-axis and probability on the y-axis. The probability of 0 times is 0.5; 1 time is 0.38; 2 times is 0.12.
Option D
8

Which expression is equivalent to ?

Question illustration
A
log Subscript 2 Baseline 9 + 3 log Subscript 2 Baseline x
Option A
B
log Subscript 2 Baseline x + 3 log Subscript 2 Baseline 9
Option B
C
3 log Subscript 2 Baseline x minus log Subscript 2 Baseline 9
Option C
D
3 log Subscript 2 Baseline 9 minus log Subscript 2 Baseline x
Option D
9

A customer deposits $1,000 in an account in which the interest is compounded annually. The table below shows the balances in the account at the end of each year.Amount in Account vs. Number of YearsAmount in Account, ANumber of Years After Initial Deposit, t1,00001,08011,166.4021,259.7131,360.494Which equation best represents the data in the table?

A
A = 1000 (1.08) Superscript t
Option A
B
A = 1080 Superscript t
Option B
C
A = 1000 (1.8) Superscript t
Option C
D
A = 800 Superscript t
Option D
10

In the triangle below, angle B measures 60° and BC is 18. What is the length of AC?

Question illustration
A
9 StartRoot 3 EndRoot
Option A
B
StartFraction 9 Over StartRoot 3 EndRoot EndFraction
Option B
C
9
D
StartFraction StartRoot 3 EndRoot Over 9 EndFraction
Option D
11

Which transformations are needed to change the parent sine function to the sine function below?

Question illustration
A
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit up, phase shift of units left
Option A
B
vertical stretch of 2, horizontal compression to a period of , vertical shift of 2 units up, phase shift of units left
Option B
C
vertical stretch of , horizontal compression to a period of , vertical shift of 1 unit up, phase shift of units left
Option C
D
vertical compression of , horizontal stretch to a period of , vertical shift of 1 unit down, phase shift of units left
Option D
12

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at pi.
Option A
B
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 1 cycle at 2 pi.
Option B
C
On a coordinate plane, a curve crosses the y-axis at (0, 0). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option C
D
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a maximum of 1 and a minimum of negative 1. It goes through 2 cycles at 2 pi.
Option D
13

Which function is the same as ?

Question illustration
A
y = 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option A
B
y = negative 3 sine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option B
C
y = 3 cosine (2 (x + StartFraction pi Over 4 EndFraction)) minus 2
Option C
D
y = negative 3 cosine (2 (x + StartFraction pi Over 2 EndFraction)) minus 2
Option D
14

Consider the inverse function. Which conclusions can be drawn about f(x) = x2 + 2? Select three options.f(x) has a limited range.f(x) has a restricted domain.f(x) has an x-intercept of (2, 0).f(x) has a maximum at the point (0, 2).f(x) has a y-intercept at the point (0, 2).

Question illustration
A
f(x) has a limited range.
B
f(x) has a restricted domain.
C
f(x) has an x-intercept of (2, 0).
D
f(x) has a maximum at the point (0, 2).
E
f(x) has a y-intercept at the point (0, 2).
15

The times of all 15 year olds who run a certain race are approximately normally distributed with a given mean = 18 sec and standard deviation = 1.2 sec. What percentage of the runners have times less than 14.4 sec?

Question illustration
A
0.15%
B
0.30%
C
0.60%
D
2.50%
16

Ashley is a member of the Movie-a-Month Club, where she rents movies each month. She uses the table below to keep track of the number of movies she rents each month and the total cost, which includes her monthly membership fee.Number of Movies vs. Total CostNumber of Movies1215922Total Cost$35.00$42.50$27.50$60.00Ashley graphed the relationship in the table. What is the slope of the graph, and what does it represent?

A
The slope of the graph is 2.50, and it represents the cost of each movie.
B
The slope of the graph is 2.50, and it represents the amount of the membership fee.
C
The slope of the graph is 5, and it represents the cost of each movie.
D
The slope of the graph is 5, and it represents the cost of the membership fee.
17

Melanie simplified the expression as shown below.Step 1:Step 2:Step 3:Step 4:In which step did Melanie make the first error, and which expression should she have written in that step?

Question illustration
A
step 1;
Option A
B
step 1;
Option B
C
step 4; cos(x)
D
step 4; csc(x)
18

Jake and Maddie each take the closest path from their homes to the store. Based on the picture below, what is the approximate difference in the distance each person traveled to the store?

Question illustration
A
1.4 m
B
5.9 m
C
6.4 m
D
7.7 m
19

What is the solution to

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
mc004-4.jpg
Option C
D
mc004-5.jpg
Option D
20

Which function has the same maximum value as f(x) = – |x + 3| – 2?

A
Option
Option A
B
f(x) = (x + 3)2 – 2
C
Option
Option C
D
f(x) = –(x – 6)2 – 3

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