Embed Size (px)
Citation preview
Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Algebra 2: Semester 1 Final Exam Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. Using the graph of f(x) = x2 as a guide, describe
the transformations, and then graph the function
g(x) = (x + 6)2
− 2.
a. g(x) is f(x) translated 2 units right and 6 units
up.
b. g(x) is f(x) translated 6 units left and 2 units
down.
c. g(x) is f(x) translated 2 units left and 6 units
down.
d. g(x) is f(x) translated 6 units right and 2 units
up.
2. Identify the axis of symmetry for the graph of
f(x) = x2
+ 2x − 3.
a. x = −1
b. y = −4
c. y = −1
d. x = −4
Name: ________________________ ID: A
2
3. Consider the function f(x) = −4x2
− 8x + 10.
Determine whether the graph opens upward or
downward. Find the axis of symmetry, the vertex
and the y-intercept. Graph the function.
a. The parabola opens downward.
The axis of symmetry is the line x = −1.
The vertex is the point (−1,14).
The y-intercept is 10.
b. The parabola opens upward.
The axis of symmetry is the line x = −1.
The vertex is the point (−1,−6).
The y-intercept −5.
c. The parabola opens downward.
The axis of symmetry is the line x = −1.
The vertex is the point (−1,7).
The y-intercept is 5.
d. The parabola opens upward.
The axis of symmetry is the line x = −1.
The vertex is the point (−1,14).
The y-intercept 10.
4. Find the zeros of the function h x( ) = x2
+ 23x + 60
by factoring.
a. x = 4 or x = 15
b. x = −20 or x = −3
c. x = −4 or x = −15
d. x = 20 or x = 3
Name: ________________________ ID: A
3
5. Solve the equation x2
− 10x + 25 = 54.
a. x = 5 ±3 6
b. x = 5 +3 6
c. x = 5 −3 6
d. x = 5 ± 6 3
6. Solve the equation 2x2
+ 18 = 0.
a. x = 3 ± i
b. x = ±3
c. x = ±3i
d. x = ±3 + i
7. Find the zeros of f(x) = x2
+ 7x + 9 by using the
Quadratic Formula.
a. x = −7 ± 13
b. x =−7 ± 13
2
c. x =3 ± 7
2
d. x = 3 ± 7
8. Solve the inequality x2
− 14x + 45 ≤ −3 by using
algebra.
a. x ≤ 5 or x ≥ 9
b. x ≤ 6 or x ≥ 8
c. 6 ≤ x ≤ 8
d. 5 ≤ x ≤ 9
9. Determine whether the data set could represent a
quadratic function. Explain.
x –4 –2 0 2 4
y 15 5 –1 –3 –1
a. The x-values are not evenly spaced, so this
could not be a quadratic function.
b. The first differences between y-values are
constant for equally spaced x-values, so it
could represent a quadratic function.
c. The 2nd differences between y-values are
constant for equally spaced x-values, so it
could represent a quadratic function.
d. The 2nd differences between y-values are not
constant, so this could not be a quadratic
function.
10. Find the absolute value −7 − 9i| |.
a. –16
b. 4
c. 4 2
d. 130
11. Subtract. Write the result in the form a + bi.
(5 – 2i) – (6 + 8i)
a. –1 – 10i
b. 7 – 2i
c. –3 – 8i
d. 11 + 6i
12. There are 7 singers competing at a talent show. In
how many different ways can the singers appear?
a. 49 ways
b. 42 ways
c. 720 ways
d. 5,040 ways
13. Joel owns 12 shirts and is selecting the ones he will
wear to school next week. How many different
ways can Joel choose a group of 5 shirts? (Note
that he will not wear the same shirt more than once
during the week.)
a. 792 ways
b. 17 ways
c. 95,040 ways
d. 60 ways
14. An experiment consists of rolling a number cube.
What is the probability of rolling a number greater
than 4? Express your answer as a fraction in
simplest form.
a.1
3
b.1
6
c.2
3
d.1
2
Name: ________________________ ID: A
4
15. An experiment consists of spinning a spinner. The
table shows the results. Find the experimental
probability that the spinner does not land on red.
Express your answer as a fraction in simplest form.
Outcome Frequency
red 10
purple 11
yellow 13
a.21
34
b.12
17
c.5
17
d.13
34
16. A grab bag contains 8 football cards and 2
basketball cards. An experiment consists of taking
one card out of the bag, replacing it, and then
selecting another card. Determine whether the
events are independent or dependent. What is the
probability of selecting a football card and then a
basketball card? Express your answer as a decimal.
a. independent; 0.18
b. dependent; 0.04
c. dependent; 0.64
d. independent; 0.16
17. Find the probability of rolling a 5 or an odd number
on a number cube. Express your answer as a
fraction in simplest form.
a.2
3
b.1
2
c.1
6
d. 1
18. Constellations are made up of more than one star. The table shows the number of stars that make up various
constellations. Find the mean, median, and mode of the data set.
Constellation Number Number of Stars in Constellation
Constellation 1 23
Constellation 2 30
Constellation 3 37
Constellation 4 23
Constellation 5 48
a. mean = 46.3; median = 30;
mode = 29
c. mean = 32.2; median = 30;
mode = 23
b. mean = 32.2; median = 37;
mode = 23
d. mean = 46.3; median = 37;
mode = 23
19. The table shows the probability distribution for the number of people who contract a disease in a scientific study.
Find the expected number of people who contract the disease. Round your answer to the nearest tenth.
Number of People 2 3 4 5 6
Probability 0.20 0.32 0.288 0.1536 0.0384
a. 3.5 b. 2.5 c. 4.0 d. 3.0
Name: ________________________ ID: A
5
20. Make a box-and-whisker plot of the data. Find the
interquartile range.
7,9,11,12,13,15,12,17,18,12,9,7,12,15,18,10
a.
Interquartile range: 5.5
b.
Interquartile range: 5
c.
Interquartile range: 5.5
d.
Interquartile range: 5
21. A scientist studies a herd of mule deer to learn
about their dietary habits. Identify the population
and sample.
a. Population: The deer in the herd being sampled
Sample: All mule deer
b. Population: All mule deer
Sample: The deer in the herd being sampled
22. Decide whether the sampling method could result
in a biased sample. Explain your reasoning.
The Candlelit-Dinner Candle Store surveys its
Monday customers to find out their opinion on a
new scented candle.
a. The sample is probably not biased. It is a
random sample.
b. The sample could be biased. The sample does
not include customers who shop there on days
other than Monday.
23. Determine which sampling method is more likely to be representative of the population. Justify your answer.
Sampling Method Results of Survey
Tom surveys 40 moviegoers by randomly choosing their ticket
numbers.
60% like the movie.
Kim surveys 40 moviegoers that entered the movie theater in
the first hour.
80% like the movie.
a. Kim’s method is more likely to be representative of the population because she uses a
convenience sample. People that attend early showings of the movie may be more
representative of the entire population of moviegoers than those in a random sample.
b. Tom’s method is more likely to be representative of the population because he uses a
random sample. All of the moviegoers are equally likely to be selected.
Name: ________________________ ID: A
6
24. Explain whether the situation is an experiment or
an observational study.
A researcher asks people how many hours they
exercise per week and examines whether this
affects the amount of sleep they get.
a. This is an experiment. The researcher gathers
data instead of applying a treatment.
b. This is an observational study. The researcher
gathers data instead of applying a treatment.
c. This is an experiment. The researcher is
applying a treatment (exercise) instead of
simply gathering data.
d. This is an observational study. The researcher
is applying a treatment (exercise) instead of
simply gathering data.
25. Explain whether the research topic is best
addressed through an experiment or an
observational study. Then explain how you would
set up the experiment or the observational study.
Do people who speak at least two languages
fluently tend to earn more money than those who
speak only one language?
a. The treatment (learning to speak a second
language fluently) is impractical. Use an
observational study. Randomly choose a group
of people who speak more than one language.
Randomly choose another group of similar
people who speak only one language. Monitor
the incomes of both groups at regular intervals.
b. The treatment (learning to speak a second
language fluently) is not ethical. Use an
observational study. Randomly choose a group
of people who speak more than one language.
Randomly choose another group of similar
people who speak only one language. Monitor
the incomes of both groups at regular intervals.
c. The treatment (learning to speak a second
language fluently) is both ethical and practical
because it is not known to have any negative
effects. Use an experiment. Randomly choose a
group of people who speak only one language.
Randomly select half of those people to learn
another language of their choice. Monitor the
incomes of both groups at regular intervals.
d. The treatment (learning to speak a second
language fluently) is both ethical and practical
because it is not known to have any negative
effects. Use an experiment. Randomly choose a
group of people who speak at least two
languages. Randomly select another group of
people who speak only one language, and have
those people learn another language of their
choice. Monitor the incomes of both groups to
see how long it takes the second group to catch
up to the first.
Name: ________________________ ID: A
7
26. A speed reading course claims that it can boost
reading speeds to 1050 words per minute.
In a random sample of 49 people who took the
course, the average was 1020 words per minute,
with a standard deviation of 90 words per minute.
What is the z-value rounded to the nearest
hundredth? Is there enough evidence to reject the
claim?
a. The z-value is –2.33.
There is enough evidence to reject the claim.
b. The z-value is –16.33.
There is enough evidence to reject the claim.
c. The z-value is –1.96.
There is not enough evidence to reject the
claim.
d. The z-value is –2.33.
There is not enough evidence to reject the
claim.
27. In 2009, 1672 cats, 1114 dogs, and 639 other
animals (such as rabbits and hamsters) were
adopted at an animal shelter. The shelter president
wants to survey the people who adopted pets.
Classify each sampling method. Which is most
accurate? Which is least accurate? Explain your
reasoning.
Method A: Leave 300 surveys at the adoption desk
for people to pick up and fill out.
Method B: Randomly select 300 people from all of
the people who adopted pets.
Method C: Randomly select 100 people who
adopted cats, 100 who adopted dogs, and 100 who
adopted other animals.
a. Method A is a stratified sample; Method B is a
simple random sample, and Method C is a
self-selected sample.
Method B is the most accurate because every
member of the population is equally likely to
be included.
Method C is the least accurate because it
underrepresents people who adopted cats..
b. Method A is a simple random sample; Method
B is a stratified sample, and Method C is a
self-selected sample.
Method C is the most accurate because it
includes an equal number of people for each
type of pet.
Method A is the least accurate because it is
likely to overrepresent cat adopters.
c. Method A is a self-selected sample; Method B
is a simple random sample, and Method C is a
stratified sample.
Method B is the most accurate because every
member of the population is equally likely to
be included.
Method A is the least accurate because it is
likely to overrepresent or underrepresent
certain types of people--for instance, people
who adopt on weekends may have more time to
fill out a survey than those who adopt on
weekdays.
d. Method A is a self-selected sample; Method B
is a simple random sample, and Method C is a
stratified sample.
Method C is the most accurate because it
includes an equal number of people for each
type of pet.
Method A is the least accurate because it is the
most likely to include only cat and dog
adopters.
Name: ________________________ ID: A
8
28. According to a random survey, 56% plan to vote
for candidate A in an upcoming mayoral election
and 44% plan to vote for candidate B. The survey’s
margin of error is ±7%.
Determine whether the survey clearly projects the
winner. Explain your response.
a. The survey does not clearly project the winner;
44% ± 7% = 37% to 51% plan to vote for
candidate A and 56% ± 7% = 49% to 63% plan
to vote for candidate B. The intervals overlap,
so the survey does not clearly project the
winner.
b. The survey does not clearly project the winner;
up to 56% – 14% = 42% might vote for
candidate A and only 44% + 14% = 58% might
vote for candidate B. The intervals overlap, so
the survey does not clearly project the winner.
c. The survey does not clearly project the winner;
56% ± 7% = 49% to 63% plan to vote for
candidate A and 44% ± 7% = 37% to 51% plan
to vote for candidate B. The intervals overlap,
so the survey does not clearly project the
winner.
d. The survey clearly projects that candidate A
will win; 56% ± 3.5% = 52.5% to 59.5% plan
to vote for candidate A and 44% ± 3.5% =
40.5% to 47.5% plan to vote for candidate B.
The intervals do not overlap, so the survey
clearly projects the winner.
29. Use the Binomial Theorem to expand the binomial (2x − 4y)4.
a. 16x4
− 128x3y + 384x
2y
2− 512xy
3+ 256y
4
b. 16x4
+ 256y4
c. 16x4
− 256y4
d. 16x4
+ 128x3y + 384x
2y
2+ 512xy
3+ 256y
4
Name: ________________________ ID: A
9
30. The heights of adult males in the United States are approximately normally distributed. The mean height is 70
inches (5 feet 10 inches) and the standard deviation is 3 inches.
Use the table to estimate the probability that a randomly-selected male is more than 74.5 inches tall. Express your
answer as a decimal.
a. 0.07 c. 0.93
b. 0.83 d. 0.5
ID: A
1
Algebra 2: Semester 1 Final Exam Review
Answer Section
MULTIPLE CHOICE
1. ANS: B
Because h = + 6, the graph is translated 6 units left. Because k = − 2, the graph is translated 2 units down.
Therefore, g(x) is f(x) translated 6 units left and 2 units down.
Feedback
A Check that you graphed the function correctly.
B Correct!
C Check that you graphed the function correctly.
D Check the horizontal and vertical shifts.
PTS: 1 DIF: Average REF: 155fb74e-4683-11df-9c7d-001185f0d2ea
OBJ: 2-1.2 Translating Quadratic Functions NAT: NT.CCSS.MTH.10.9-12.F.BF.3
STA: FL.NGSSS.MTH.07.9-12.MA.912.A.2.10
LOC: MTH.C.10.07.16.01.01.002 | MTH.C.10.07.16.02.001 | MTH.C.10.07.16.02.002
TOP: 2-1 Using Transformations to Graph Quadratic Functions
KEY: quadratic | graph MSC: DOK 3
ID: A
2
2. ANS: A
If a function has one zero, use the x-coordinate of the vertex to find the axis of symmetry.
If a function has two zeros, use the average of the two zeros to find the axis of symmetry.
Feedback
A Correct!
B The axis of symmetry of a parabola is a vertical line. All the points it contains have the
same x-value, so the variable in the equation should be x and not y.
C The axis of symmetry of a parabola is a vertical line. All the points it contains have the
same x-value, so the variable in the equation should be x and not y.
D Look at the graph. Does the line you found divide the parabola into two symmetrical
halves?
PTS: 1 DIF: Average REF: 1566b752-4683-11df-9c7d-001185f0d2ea
OBJ: 2-2.1 Identifying the Axis of Symmetry NAT: NT.CCSS.MTH.10.9-12.F.IF.7
STA: FL.NGSSS.MTH.07.9-12.MA.912.A.7.6 LOC: MTH.C.10.07.06.01.007
TOP: 2-2 Properties of Quadratic Functions in Standard Form MSC: DOK 3
ID: A
3
3. ANS: A
Because a is −2, the graph opens downward.
The axis of symmetry is given by x =−(−8)
2(−4)=
8
−8= −1.
x = −1 is the axis of symmetry.
The vertex lies on the axis of symmetry, so x = −1.
The y-value is the value of the function at this x-value.
f(−1) = −4(−1)2
− 8(−1) + 10 = −4 + 8 + 10 = 14
The vertex is (−1,14).
Because the last term is 10, the y-intercept is 10.
Feedback
A Correct!
B If the leading coefficient is negative, then the graph opens downward.
C Use the last term to find the y-intercept.
D If the leading coefficient is negative, then the graph opens downward.
PTS: 1 DIF: Average REF: 156919ae-4683-11df-9c7d-001185f0d2ea
OBJ: 2-2.2 Graphing Quadratic Functions in Standard Form NAT: NT.CCSS.MTH.10.9-12.F.IF.7
STA: FL.NGSSS.MTH.07.9-12.MA.912.A.2.6 LOC: MTH.C.10.07.06.01.001
TOP: 2-2 Properties of Quadratic Functions in Standard Form MSC: DOK 3
4. ANS: B
h x( ) = x2
+ 23x + 60
x2
+ 23x + 60 = 0 Set the function equal to 0.
(x + 20)(x + 3) = 0 Factor: Find factors of 60 that add to 23.
x + 20 = 0 or x + 3 = 0 Apply the Zero-Product Property.x = −20 or x = −3 Solve each equation.
Feedback
A To factor h(x), find factors of the constant term whose sum is the coefficient of the x
term. Set each factor equal to 0 and solve for x.
B Correct!
C To factor h(x), find factors of the constant term whose sum is the coefficient of the x
term. Set each factor equal to 0 and solve for x.
D To factor h(x), find factors of the constant term whose sum is the coefficient of the x
term. Set each factor equal to 0 and solve for x.
PTS: 1 DIF: Basic REF: 157040c2-4683-11df-9c7d-001185f0d2ea
OBJ: 2-3.2 Finding Zeros by Factoring
NAT: NT.CCSS.MTH.10.9-12.A.REI.4 | NT.CCSS.MTH.10.9-12.F.IF.8
LOC: MTH.C.10.07.06.018 TOP: 2-3 Solving Quadratic Equations by Graphing and Factoring
KEY: solve quadratic equations MSC: DOK 3
ID: A
4
5. ANS: A
x2
− 10x + 25 = 54
x − 5( )2
= 54 Factor the perfect square trinomial.
x − 5 = ± 54 Take the square root of both sides.
x = 5 ± 54 Add 5 to each side.
x = 5 ±3 6 Simplify.
Feedback
A Correct!
B Does the right side of the equation have only a positive square root?
C Does the right side of the equation have only a negative square root?
D You switched the number to the left of the radical sign with the number under the
radical sign.
PTS: 1 DIF: Average REF: 15752c8a-4683-11df-9c7d-001185f0d2ea
OBJ: 2-4.1 Solving Equations by Using the Square Root Property
NAT: NT.CCSS.MTH.10.9-12.A.REI.4 LOC: MTH.C.10.06.04.01.002
TOP: 2-4 Completing the Square MSC: DOK 3
6. ANS: C
2x2
+ 18 = 0
2x2
= −18 Add −18 to both sides.
x2
= −9 Divide both sides by 2.
x = ± −9 Take square roots.
x = ±3i Express in terms of i.
Feedback
A The square root of a negative number is not a sum or a difference. It is a product of i
and the square root of the opposite number.
B The square root of a negative number is an imaginary number.
C Correct!
D The square root of a negative number is not a sum. It is a product of i and the square
root of the opposite number.
PTS: 1 DIF: Average REF: 157e8eea-4683-11df-9c7d-001185f0d2ea
OBJ: 2-5.2 Solving a Quadratic Equation with Imaginary Solutions
NAT: NT.CCSS.MTH.10.9-12.A.REI.4 LOC: MTH.C.10.03.003 | MTH.C.10.06.04.01.002
TOP: 2-5 Complex Numbers and Roots KEY: complex numbers
MSC: DOK 3
ID: A
5
7. ANS: B
x2
+ 7x + 9 = 0 Set f(x) = 0.
x =−b ± b
2− 4ac
2aWrite the Quadratic Formula.
x =−7 ± (7)
2− 4(1)(9)
2(1)Substitute 1 for a, 7 for b, and 9 for c.
x =−7 ± 49 − 36
2Simplify.
x =−7 ± 13
2Write in simplest form.
Feedback
A Rewrite the equation in standard form to get the values of a, b, and c for the Quadratic
Formula.
B Correct!
C Set f(x) = 0, and then use the Quadratic Formula.
D Use the Quadratic Formula.
PTS: 1 DIF: Average REF: 15837ab2-4683-11df-9c7d-001185f0d2ea
OBJ: 2-6.1 Quadratic Functions with Real Zeros NAT: NT.CCSS.MTH.10.9-12.A.REI.4
LOC: MTH.C.10.06.04.01.005 | MTH.C.10.07.06.018 TOP: 2-6 The Quadratic Formula
KEY: quadratic formula MSC: DOK 3
ID: A
6
8. ANS: C
Step 1
x2
− 14x + 45 = −3 Write the related equation.
x2
− 14x + 48 = 0 Write the equation in standard form.
(x − 6)(x − 8) = 0 Factor.
Step 2x − 6 = 0 or x − 8 = 0 Find the critical values.x = 6 or x = 8 The critical values are 6 and 8.
Step 3
The critical values divide the number line into three intervals: x < 6, 6 <x < 8, or x > 8.
Test an x-value in each interval in the original inequality to determine which intervals make the inequality true.
The solution is 6 ≤ x ≤ 8.
Feedback
A Subtract values from both sides of the equal sign when solving an equation.
B The critical values are correct. Test values of x to find the intervals satisfy the
inequality.
C Correct!
D Subtract values from both sides of the equal sign when solving an equation.
PTS: 1 DIF: Average REF: 158d0422-4683-11df-9c7d-001185f0d2ea
OBJ: 2-7.3 Solving Quadratic Inequalities Using Algebra NAT: NT.CCSS.MTH.10.9-12.A.REI.4
LOC: MTH.C.10.08.04.01.01.002 TOP: 2-7 Solving Quadratic Inequalities
KEY: quadratic inequality MSC: DOK 3
ID: A
7
9. ANS: C
x –4 –2 0 2 4
y 15 5 –1 –3 –1
1st differences −10 −6 −2 2
2nd differences 4 4 4
As the 2nd differences are constant for equally spaced x-values, the data set could represent a quadratic function.
Feedback
A The x-values are evenly spaced.
B The first differences of y-values do not need to be evenly spaced for this to be a
quadratic function.
C Correct!
D The second differences of y-values are evenly spaced.
PTS: 1 DIF: Average REF: 1591a1ca-4683-11df-9c7d-001185f0d2ea
OBJ: 2-8.1 Identifying Quadratic Data STA: FL.NGSSS.MTH.07.9-12.MA.912.A.2.6
LOC: MTH.C.10.07.06.001 | MTH.C.10.07.06.002 TOP: 2-8 Curve Fitting with Quadratic Models
KEY: quadratic inequality MSC: DOK 3
10. ANS: D
(−7)2
+ (− 9)2 Find the square root of the sum of the squares of the real and
imaginary parts of the complex number.
130 Simplify the square root.
Feedback
A Take the square root of the sum of the squares of the real and imaginary parts.
B Take the square root of the sum of the squares of the real and imaginary parts.
C Take the square root of the sum of the squares of the real and the imaginary parts.
D Correct!
PTS: 1 DIF: Basic REF: 159d8d96-4683-11df-9c7d-001185f0d2ea
OBJ: 2-9.2 Determining the Absolute Value of Complex Numbers
NAT: NT.CCSS.MTH.10.9-12.N.CN.3 LOC: MTH.C.10.03.01.007
TOP: 2-9 Operations with Complex Numbers MSC: DOK 3
ID: A
8
11. ANS: A
To add complex numbers, add the real parts and the imaginary parts. To subtract complex numbers, subtract the
real parts and the imaginary parts.
(5 – 2i) – (6 + 8i) = (5 – (6)) + (–5 – (5))i = –1 – 10i
Feedback
A Correct!
B Add or subtract real parts and imaginary parts.
C Add or subtract real parts and imaginary parts.
D Check whether you should add or subtract the two complex numbers.
PTS: 1 DIF: Average REF: 159db4a6-4683-11df-9c7d-001185f0d2ea
OBJ: 2-9.3 Adding and Subtracting Complex Numbers NAT: NT.CCSS.MTH.10.9-12.N.CN.2
STA: FL.NGSSS.MTH.07.9-12.MA.912.A.1.6 LOC: MTH.C.10.03.01.002
TOP: 2-9 Operations with Complex Numbers MSC: DOK 3
12. ANS: D
Since the order matters, use the formula for permutations.
7!P7!
7!
(7 − 7)!=
7!
0!
Since 0! = 1, the number of ways is 7! = 5,040.
Feedback
A Since the order is important, use the formula for permutations.
B Since the order is important, use the formula for permutations.
C Since the order is important, use the formula for permutations.
D Correct!
PTS: 1 DIF: Average REF: 179001c2-4683-11df-9c7d-001185f0d2ea
OBJ: 7-1.2 Finding Permutations NAT: NT.CCSS.MTH.10.9-12.S.CP.9
LOC: MTH.C.13.06.02.02.004 TOP: 7-1 Permutations and Combinations
KEY: permutation | ordering MSC: DOK 3
ID: A
9
13. ANS: A
Step 1 Determine whether the problem represents a combination or a permutation.
The order does not matter because choosing a green shirt, a blue shirt, and a red shirt is the same as choosing a red
shirt, a blue shirt, and a green shirt. It is a combination.
Step 2 Use the formula for combinations.
The number of combinations of n items taken r at a time is n Cr =n!
r! (n − r)!.
12 C5 =12!
5! (12 − 5)!n = 12 and r = 5
12 C5 =12 ⋅ 11 ⋅ 10 ⋅ 9 ⋅ 8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1
5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 ⋅ (7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1)Expand.
12 C5 =12 ⋅ 11 ⋅ 10 ⋅ 9 ⋅ 8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1
5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 ⋅ (7 + 6 + 5 + 4 + 3 + 2 + 1)=
12 ⋅ 11 ⋅ 10 ⋅ 9 ⋅ 8
5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1Divide out common
factors.
12 C5 =12 ⋅ 11 ⋅ 10 ⋅ 9 ⋅ 8
5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1=
12 ⋅ 11 ⋅ 10 ⋅ 9
5 ⋅ 3= 12 ⋅ 11 ⋅ 2 ⋅ 3 = 729 Simplify.
There are 729 ways to select a group of 5 shirts from 12.
Feedback
A Correct!
B Check your formula. Find the combination nCr.
C You found the permutation nPr. Order is not important, so find the combination nCr.
D Check your formula. Find the combination nCr.
PTS: 1 DIF: Average REF: 17923d0e-4683-11df-9c7d-001185f0d2ea
OBJ: 7-1.3 Application NAT: NT.CCSS.MTH.10.9-12.S.CP.9
LOC: MTH.C.13.06.02.03.003 TOP: 7-1 Permutations and Combinations
MSC: DOK 3
ID: A
10
14. ANS: A
There are six possible outcomes when a fair number cube is rolled. Because the number cube is fair, all outcomes
are equally likely. There are two numbers greater than 4 on the number cube: 5 and 6. So the probability of rolling
one of these numbers is 2
6=
1
3.
Feedback
A Correct!
B This is the probability of rolling a 4. Find the probability of rolling a number greater
than 4.
C This is the probability of rolling a number less than or equal to 4. Find the probability
of rolling a number greater than 4.
D This is the probability of rolling a number greater than or equal to 4. Find the
probability of rolling a number greater than 4.
PTS: 1 DIF: Basic REF: 17949f6a-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.1 Finding Theoretical Probability LOC: MTH.C.13.05.03.001
TOP: 7-2 Theoretical and Experimental Probability KEY: probability | theoretical probability
MSC: DOK 2
15. ANS: B
When the spinner does not land on red, it must land on yellow or purple.
experimental probability =number of times the event occurs
number of trials=
13 + 11
34=
24
34=
12
17
Feedback
A To find the probability that the spinner does not land on a color, find the probability
that the spinner lands on either of the two other colors.
B Correct!
C This is the probability that the spinner does land on the color. The problem asked you
to find the probability that the spinner does not land on that color.
D To find the probability that the spinner does not land on a color, find the probability
that the spinner lands on either of the two other colors.
PTS: 1 DIF: Basic REF: 17998b32-4683-11df-9c7d-001185f0d2ea
OBJ: 7-2.5 Finding Experimental Probability LOC: MTH.C.13.05.02.02.001
TOP: 7-2 Theoretical and Experimental Probability MSC: DOK 2
ID: A
11
16. ANS: D
One outcome does not affect the other, so the events are independent.
To find the probability that A and B both happen, multiply the probabilities.
P(A and B) = P(A) • P(B) = 0.8 • 0.2 = 0.16.
Feedback
A To find the probability that both events happen, multiply the probabilities of the events.
B To find the probability that both events happen, multiply the probabilities of the events.
C To find the probability that both events happen, multiply the probabilities of the events.
D Correct!
PTS: 1 DIF: Average REF: 17a08b36-4683-11df-9c7d-001185f0d2ea
OBJ: 7-3.4 Determining Whether Events Are Independent or Dependent
NAT: NT.CCSS.MTH.10.9-12.S.CP.2 | NT.CCSS.MTH.10.9-12.S.CP.8
LOC: MTH.C.13.05.03.006 | MTH.C.13.05.03.007 TOP: 7-3 Independent and Dependent Events
KEY: events | independent events | outcomes | probability MSC: DOK 3
17. ANS: B
P(5 or odd)
= P(5) + P(odd) − P(5 and odd)
= 1
6 +
3
6 −
1
65 is also an odd number.
= 1
2
Feedback
A First, add the probability of the first event and the probability of the second event.
Then, subtract the probability of both events.
B Correct!
C The probability of two inclusive events occurring is the sum of their individual
probabilities minus the probability of both occurring.
D A probability of 1 means this event always happens.
PTS: 1 DIF: Basic REF: 17a54fee-4683-11df-9c7d-001185f0d2ea
OBJ: 7-5.2 Finding Probabilities of Inclusive Events NAT: NT.CCSS.MTH.10.9-12.S.CP.7
LOC: MTH.C.13.05.03.013 TOP: 7-5 Compound Events
MSC: DOK 2
ID: A
12
18. ANS: C
To find the mean, add all the values in the list and divide by 5.
To find the median, sort the values in ascending order and choose the third value, which is the middle number, in
the sorted list.
To find the mode, look for the value that appears the most times in the list.
Feedback
A To find the mean, add the data values, then divide by the number of values. To find the
mode(s), identify the most-frequently appearing value(s).
B To find the median, put the data values in order and find the middle value.
C Correct!
D To find the mean, add the data values, then divide by the number of values. To find the
median, put the data values in order and find the middle value.
PTS: 1 DIF: Average REF: 17aa14a6-4683-11df-9c7d-001185f0d2ea
OBJ: 8-1.1 Finding Measures of Central Tendency
LOC: MTH.C.13.04.02.01.01.001 | MTH.C.13.04.02.01.003 | MTH.C.13.04.02.01.004
TOP: 8-1 Measures of Central Tendency and Variation KEY: central tendency | mean | median | mode
MSC: DOK 3
19. ANS: A
The expected value is the weighted average of all the outcomes of the study.
Expected value = 2(.20) + 3(.32) + 4(.288) + 5(.1536) + 6(.0384) = 3.5104 ≈ 3.5
Feedback
A Correct!
B To find the expected value, multiply the outcomes by their probabilities.
C This is the average of the number of people. To find the expected value, multiply the
outcomes by their probabilities.
D To find the expected value, multiply the outcomes by their probabilities.
PTS: 1 DIF: Average REF: 17aa3bb6-4683-11df-9c7d-001185f0d2ea
OBJ: 8-1.2 Finding Expected Value
NAT: NT.CCSS.MTH.10.9-12.S.MD.5 | NT.CCSS.MTH.10.9-12.S.MD.4
LOC: MTH.C.13.05.05.004 TOP: 8-1 Measures of Central Tendency and Variation
MSC: DOK 3
ID: A
13
20. ANS: C
Order the data from least to greatest.
Find the minimum, maximum, median, and quartiles.
Minimum = 7
Maximum = 18
Median = 12
Lower Quartile = 9.5
Upper Quartile = 15
Interquartile range = 15 – 9.5 = 5.5
Feedback
A Order the data from least to greatest, then find the minimum, maximum, median, and
quartiles.
B Order the data from least to greatest, then find the minimum, maximum, median, and
quartiles.
C Correct!
D Order the data from least to greatest, then find the minimum, maximum, median, and
quartiles.
PTS: 1 DIF: Average REF: 17ac7702-4683-11df-9c7d-001185f0d2ea
OBJ: 8-1.3 Making a Box-and-Whisker Plot and Finding the Interquartile Range
NAT: NT.CCSS.MTH.10.9-12.S.ID.1 LOC: MTH.C.13.02.03.016 | MTH.C.13.04.02.02.009
TOP: 8-1 Measures of Central Tendency and Variation MSC: DOK 3
21. ANS: B
Feedback
A A sample is part of the population.
B Correct!
PTS: 1 DIF: Basic REF: 9074c1b9-6ab2-11e0-9c90-001185f0d2ea
NAT: NT.CCSS.MTH.10.9-12.S.IC.1 TOP: 8-2 Data Gathering
MSC: DOK 2
22. ANS: B
Feedback
A This sample is not random. Customers who do not shop on Monday have no chance of
being in the sample.
B Correct!
PTS: 1 DIF: Average REF: 90774b24-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-2.1 Determining if a Sample is Biased
NAT: NT.CCSS.MTH.10.9-12.S.IC.1 | NT.CCSS.MTH.10.9-12.S.MD.6
TOP: 8-2 Data Gathering KEY: sample | biased sample
MSC: DOK 3
ID: A
14
23. ANS: B
Feedback
A Random samples are usually more representative of a population than are convenience
samples.
B Correct!
PTS: 1 DIF: Average REF: 907c0fda-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-2.2 Determining if a Sample is Representative of a Population
NAT: NT.CCSS.MTH.10.9-12.S.IC.1 | NT.CCSS.MTH.10.9-12.S.IC.3 | NT.CCSS.MTH.10.9-12.S.MD.6
TOP: 8-2 Data Gathering KEY: sample | representative sample
MSC: DOK 3
24. ANS: B
Feedback
A In an experiment, the researcher applies a treatment.
B Correct!
C Is the researcher setting up a control group and a treatment group?
D Is the researcher setting up a control group and a treatment group?
PTS: 1 DIF: Basic REF: 90859946-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-3.1 Identifying Experiments and Observational Studies NAT: NT.CCSS.MTH.10.9-12.S.IC.3
TOP: 8-3 Surveys, Experiments, and Observational Studies KEY: experiment | observational study
MSC: DOK 2
25. ANS: A
Feedback
A Correct!
B The treatment is ethical, but it may not be practical.
C The treatment is ethical, but it may not be practical.
D The treatment is ethical, but it may not be practical.
PTS: 1 DIF: Average REF: 908a36ec-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-3.3 Designing an Experiment or Observational Study NAT: NT.CCSS.MTH.10.9-12.S.IC.3
TOP: 8-3 Surveys, Experiments, and Observational Studies KEY: experiment | observational study
MSC: DOK 3
ID: A
15
26. ANS: A
Feedback
A Correct!
B Check the z-value.
C Check the z-value.
D Is there enough evidence to reject the claim?
PTS: 1 DIF: Average REF: 9091850d-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-4.2 Using a z-Test NAT: NT.CCSS.MTH.10.9-12.S.IC.5
TOP: 8-4 Significance of Experimental Results KEY: significance | experiment | z-test
MSC: DOK 3
27. ANS: C
Feedback
A Check your classifications of the sample types.
B Check your classifications of the sample types.
C Correct!
D In Method C, does every member of the population have an equal chance of being
selected?
PTS: 1 DIF: Average REF: 909b0e79-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-5.2 Evaluating Sampling Methods NAT: NT.CCSS.MTH.10.9-12.S.IC.6
TOP: 8-5 Sampling Distributions KEY: sampling methods
MSC: DOK 3
28. ANS: C
Feedback
A Check the ranges for Candidates A and B.
B The margin of error is ±7%, not ± 14%.
C Correct!
D The margin of error is ±7%, not ± 3.5%.
PTS: 1 DIF: Average REF: 909fac1f-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-5.3 Interpreting a Margin of Error
NAT: NT.CCSS.MTH.10.9-12.S.IC.4 | NT.CCSS.MTH.10.9-12.S.IC.6
TOP: 8-5 Sampling Distributions KEY: survey | margin of error
MSC: DOK 3
ID: A
16
29. ANS: A
Use Pascal’s Triangle (or the combinations used to derive the triangle) to help determine the coefficients for each
term in the expansion:
4 C0 (2x)4(−4y)
0+ 4C1(2x)
3(−4y)
1+ 4C2 (2x)
2(−4y)
2+ 4 C3 (2x)
1(−4y)
3+ 4C4(2x)
0(−4y)
4
Calculate the combinations:
1 × 16x4
× 1 + 4 × 8x3
× (−4)y + 6 × 4x2
× 16y2
+ 4 × 2x × (−64)y3
+ 1 × 1 × 256y4
Simplify:
16x4
− 128x3y + 384x
2y
2− 512xy
3+ 256y
4
Feedback
A Correct!
B Use Pascal's Triangle to help you with the expansion.
C Use Pascal's Triangle to help you with the expansion.
D Be careful to check the plus and minus signs.
PTS: 1 DIF: Average REF: 17b39e16-4683-11df-9c7d-001185f0d2ea
OBJ: 8-6.1 Expanding Binomials NAT: NT.CCSS.MTH.10.9-12.A.APR.5
LOC: MTH.C.10.05.08.03.01.01.001 TOP: 8-6 Binomial Distributions
MSC: DOK 3
30. ANS: C
Feedback
A This is the probability that a randomly-selected male is not more than 74.5 inches tall.
B Convert 74.5 to a z-score. Then use the table to estimate the probability.
C Correct!
D Convert 74.5 to a z-score. Then use the table to estimate the probability.
PTS: 1 DIF: Average REF: 90a20e7a-6ab2-11e0-9c90-001185f0d2ea
OBJ: 8-7.2 Using Standard Normal Values NAT: NT.CCSS.MTH.10.9-12.S.ID.4
TOP: 8-7 Fitting to a Normal Distribution KEY: normal distribution | z-value
MSC: DOK 3
