Alg2 - CH2 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
____
1. Dan paid a total of $25.80 last month for his international calls. He makes international calls only
to England. Dan pays $0.06 per minute in addition to $10.98 fixed monthly payment. How many
minutes of international calls did Dan make last month?
a. 247 minutes
c. 419 minutes
b. 430 minutes
d. 613 minutes
2. Solve −4(24 + 8y) = −64.
a. y = 4
c. y = –1
b. y = –11
d. y = 5
3. A recipe for trail mix requires 2 parts peanuts, 3 parts raisins, and 4 parts granola by weight. Chiwa
has 30 ounces of peanuts, 63 ounces of raisins, and 40 ounces of granola. How many ounces of
trail mix can she make? How many ounces of raisins will she need?
a. 90 oz; 30 oz
b. 135 oz; 45 oz
c. 113 oz; 38 oz
d. 133 oz; 63 oz
4. Find the slope of the line that passes through the points (1, 3) and (9, 7).
a. 2
c. 1
1
b.
d. −2
2
____
5. In slope-intercept form, write the equation of the line that contains the points in the table.
x
y
____
−2
−3
0
1
2
5
4
9
6
13
a. y = 2x + 1
c. y = 2x − 1
b. y = x + 2
d. y = −x − 2
6. Solve 34 ÊÁË 5x − y ˆ˜¯ < 3 for y. Graph the solution.
a. y < 5x − 4
c. y > 5x − 4
b. y > −5x + 4
____
____
d. y > 5x + 4
7. Give two different combinations of transformations that would transform f( x ) = 5x + 3 into
g( x ) = 15x − 12.
a. 1. A vertical shift 15 units down, followed by a horizontal compression by a factor
of 13 .
2. A vertical stretch by a factor of 3, followed by a vertical shift 21 units down.
b. 1. A horizontal compression by a factor of 1 , followed by a vertical shift 15 units
3
down.
2. A vertical shift 21 units down, followed by a vertical stretch by a factor of 3.
c. 1. A horizontal shift 15 units left, followed by a horizontal compression by a factor
of 13 .
2. A vertical stretch by a factor of 3, followed by a vertical shift 21 units down.
d. 1. A horizontal stretch by a factor of 3, followed by a vertical shift 15 units down.
2. A vertical compression by a factor of 13 , followed by a vertical shift 21 units
down.
8. There is a known relationship between forearm length (f) and body height (h). The table and
accompanying scatter plot show arm lengths and heights from a randomly selected sample of
people. Find the correlation coefficient r and the line of best fit.
Forearm length
(cm)
Body height (cm)
____
24
27
24
26
32
30
29
28
157 177 164 175 195 178 180 172
a. h = 0.23f − 12.49; r = 0.84
c. h = 3.64f + 74.57; r = 0.83
b. h = 2.34f + 56.23; r = 6.43
d. h = −1.16f + 43.24; r = 0.91
9. The data set shows the amount of funds raised and the number of participants in the fundraiser at
the Family House organization branches. Make a scatter plot of the data with number of
participants as the independent variable. Then, find the correlation coefficient and the equation of
the line of best fit and draw the line.
Family House Fundraiser
Number of
participants
Funds raised ($)
6
10
15
20
25
13
15
18
450 550 470 550 650 600 600 650
a.
c.
y = 8.5x + 435.3; r ≈ 0.66
y = 8.4x + 450.3; r ≈ 0.76
b.
d.
y = 0.05x − 14.28; r ≈ 0.66
____
10. Solve the inequality | 12 + 4x | > 16 and graph the solution set.
a. (−∞, ∞)
c. (−∞, − 7) ∪ (1, ∞)
b. (−7, 1)
____
d. (1, ∞)
| x − 12 |
≤ 1 and graph the solution set.
4
a. −16 ≤ x ≤ 16
c. 8 ≤ x and 16 ≤ x
11. Solve
b. 8 ≥ x and 16 ≤ x
No solution.
____
y = 9.3x + 422.8; r ≈ 0.73
d. 8 ≤ x ≤ 16
12. Translate f( x ) = | x | so that the vertex is at (–5, –3). Then graph.
a. g( x ) = | x − 5 | + 3
c. g( x ) = | x − 3 | + 5
b. g( x ) = | x + 3 | − 5
d. g( x ) = | x + 5 | − 3
Numeric Response
13. A 5-foot-tall student casts a shadow 7 feet long. At the same time, a flagpole casts a shadow that is
35 feet long. How many feet tall is the flagpole?
14. Elena bought a sweatshirt in London that cost 16 pounds. At the time, $1 was worth 0.56 pounds.
Find the cost of the sweatshirt in dollars. If necessary, round your answer to the nearest cent.
15. Using data from a new data set, the relationship between the height in centimeters and the length
of a woman’s humerus bone is modeled by the equation h ≈ 2.71l + 72.8. Use this equation to
approximate the height of a woman whose humerus bone is 28 centimeters long. Give your answer
to the nearest tenth of a centimeter.
Matching
Match each vocabulary term with its definition.
a. equation
b. expression
c.
d.
e.
f.
g.
h.
____
____
____
____
____
____
16.
17.
18.
19.
20.
21.
solution set of an equation
contradiction
identity
absolute value
linear equation in one variable
inequality
an equation that can be written in the form ax = b where a and b are constants and a ≠ 0
a statement that compares two expressions by using one of the following signs: <, >, ≤, ≥, or ≠
an equation that is not true for any value of the variable
an equation that is true for all values of the variables
a mathematical sentence that shows that two expressions are equivalent
the set of values that make a statement true
Match each vocabulary term with its definition.
a. x-axis
b. x-intercept
c. y-axis
d. slope-intercept form
e. slope
f. point-slope form
g. y-intercept
h. linear function
____
____
22. a line with slope m and y-intercept b that can be written in the form y = mx + b.
23. the y-coordinate of the point where a graph intersects the y-axis
24. a function that can be written in the form y = mx + b, where x is the independent variable and m and
b are real numbers
25. the x-coordinate of the point where a graph intersects the x-axis
26. y − y1 = m(x − x1), where m is the slope and (x1, y1) is a point on the line
____
27. a measure of the steepness of a line
____
____
____
Alg2 - CH2 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: A
Let x represent the number of international call minutes Dan made last month.
number of
fixed monthly
cost per
total monthly
plus
times international =
payment
minute
payment
call minutes
10.98
+
0.06
•
x
=
25.80
Solve 10.98 + 0.06x = 25.80.
10.98 + 0.06x = 25.80 Subtract 10.98 from both sides of the equation.
0.06x = 14.82 Divide both sides by 0.06 to find x.
x = 247
Feedback
A
B
C
D
Correct!
Subtract 10.98 from both sides of the equation.
First subtract 10.98 from both sides of the equation. Then divide both sides by
0.06.
Subtract 10.98 from both sides of the equation. $25.80 is the total monthly
payment.
PTS: 1
NAT: 12.5.4.a
2. ANS: C
−4(24 + 8y)
−96 − 32y
−32y
y
DIF: Average
REF: Page 91
OBJ: 2-1.1 Application
TOP: 2-1 Solving Linear Equations and Inequalities
= −64
= −64
= 32
= −1
Distribute –4.
Add 96 to both sides.
Divide by −32.
Feedback
A
B
C
D
Distribute over all the terms inside the parentheses.
Distribute before solving the equation.
Correct!
To isolate the variable after distributing, add the opposite of the constant term to
both sides of the equation.
PTS: 1
DIF: Basic
REF: Page 91
OBJ: 2-1.2 Solving Equations with the Distributive Property
NAT: 12.5.4.a
TOP: 2-1 Solving Linear Equations and Inequalities
3. ANS: A
To simplify the calculations, suppose that one serving of trail mix has 2 + 3 + 4 = 9 ounces of trail
mix.
Step 1 Find the limiting ingredient. To do this, for each ingredient divide the number of ounces
available to the number of ounces required to make a 9-ounce serving of trail mix.
peanuts:
raisins:
granola:
30
2
63
3
40
4
= 15
=
21
= 10
The limiting ingredient is the ingredient with the minimum ratio. The minimum ratio represents
the number of 9-ounce servings of trail mix that Chiwa can make with the ingredients available.
Thus, the limiting ingredient is granola. There is enough granola to make 10 servings of trail mix.
Step 2 Calculate the ounces of trail mix in 10 servings.
Serving size × number of servings = amount of trail mix in 10 servings.
9 ⋅ 10 = 90 oz
Step 3 Calculate the ounces of raisins in 10 servings.
Ounces of raisins per serving × number of servings = ounces of raisins in 10 servings.
3 ⋅ 10 = 30 oz
Feedback
A
B
C
D
Correct!
Choose a convenient size for a single serving of trail mix. Then calculate the
number of ounces of each ingredient in a serving of trail mix. The number of
servings of trail mix that can be made is limited by one of the ingredients.
Choose a convenient size for a single serving of trail mix. Then calculate the
number of ounces of each ingredient in a serving of trail mix. The number of
servings of trail mix that can be made is limited by one of the ingredients.
Choose a convenient size for a single serving of trail mix. Then calculate the
number of ounces of each ingredient in a serving of trail mix. The number of
servings of trail mix that can be made is limited by one of the ingredients.
PTS: 1
DIF: Advanced
TOP: 2-2 Proportional Reasoning
4. ANS: B
Let (x1, y1) be (1, 3) and (x2, y2) be (9, 7).
m=
y2 − y1 7 − 3 4 1
=
= =
x2 − x1 9 − 1 8 2
The slope of the line is 12 .
REF: Page 103
KEY: multi-step
Use the slope formula.
NAT: 12.1.4.c
Feedback
A
B
C
D
The slope is the ratio of the difference in the y-values to the difference in the
corresponding x-values.
Correct!
The slope is the ratio of the difference in the y-values to the difference in the
corresponding x-values.
Check your signs.
PTS: 1
DIF: Basic
REF: Page 116
OBJ: 2-4.2 Finding the Slope of a Line Given Two or More Points
NAT: 12.5.3.d
TOP: 2-4 Writing Linear Functions
5. ANS: A
First, find the slope. Let (x1, y1) be (0, 1) and (x2, y2) be (4, 9).
m=
y2 − y1 9 − 1 8
=
= =2
x2 − x1 4 − 0 4
Next, choose a point to find the equation of a line.
Using (0, 1):
y − y1 = m(x − x1)
y − 1 = 2(x − 0)
y = 2x + 1
Substitute.
Distribute. Simplify.
The equation of the line is y = 2x + 1.
Feedback
A
B
C
D
Correct!
First, choose two points to find the slope. Then, use the slope to find the
equation of the line.
First, choose two points to find the slope. Then, use the slope to find the
equation of the line.
First, choose two points to find the slope. Then, use the slope to find the
equation of the line.
PTS: 1
DIF: Average
REF: Page 117
OBJ: 2-4.3 Writing Equations of Lines
NAT: 12.5.3.d
TOP: 2-4 Writing Linear Functions
6. ANS: C
3 Á
Ê
˜ˆ
4 Ë 5x − y ¯ < 3
4
3 Ê
ˆ˜ 4
Á
Multiply both sides by 43 .
3 ⋅ 4 Ë 5x − y ¯ < 3 ⋅ 3
5x − y < 4
−y < 4 − 5x
Subtract 5x from both sides.
y > 5x − 4
Multiply by −1, and reverse the inequality symbol.
Graph the solution. Use a dashed line for inequalities using >, and shade above the line.
Feedback
A
B
C
D
Reverse the inequality symbol when you multiply or divide by a negative
number.
Multiply both sides of the equation by –1.
Correct!
Multiply each term on the right side by –1.
PTS: 1
DIF: Average
REF: Page 127
OBJ: 2-5.4 Solving and Graphing Linear Inequalities
NAT: 12.5.4.d
TOP: 2-5 Linear Inequalities in Two Variables
7. ANS: A
Combination 1
A vertical shift 15 units down transforms f( x ) = 5x + 3 into h( x ) = 5x + 3 − 15, or h( x ) = 5x − 12.
A horizontal compression by a factor of
1
3
transforms h( x ) = 5x − 12 into g( x ) = 11 ⋅ 5x − 12 or
3
g( x ) = 15x − 12.
Combination 2
A vertical stretch by a factor of 3 transforms f( x ) = 5x + 3 into h( x ) = 3( 5x + 3 ), or h( x ) = 15x + 9.
A vertical shift 21 units down transforms h( x ) = 15x + 9 into g( x ) = 15x + 9 − 21, or g( x ) = 15x − 12.
Feedback
A
B
C
D
Correct!
The order of the transformations in the second combination is reversed.
A horizontal shift 15 units left transforms f(x) into 5(x – 15) + 3.
A horizontal stretch by a factor of 3 transforms f(x) into f((1/3)x). A vertical
compression by a factor of 1/3 transforms f(x) into (1/3)f(x).
PTS: 1
DIF: Advanced
NAT: 12.5.2.d
TOP: 2-6 Transforming Linear Functions
8. ANS: C
To find the value of r and the equation for the line of best fit, use a calculator’s LinReg feature.
h = 3.64f + 74.57. The correlation coefficient r is approximately 0.91. The data shows a good
positive correlation that is very close to linear. It can be concluded that the taller the person, the
larger the forearm.
Feedback
A
B
C
Forearm length is the independent variable (shown on the x-axis).
The correlation coefficient is between 0 and 1.
Correct!
D
The slope of the data in the scatter plot is positive.
PTS: 1
DIF: Average
REF: Page 144
OBJ: 2-7.2 Application
NAT: 12.4.1.a
TOP: 2-7 Curve Fitting by Using Linear Models
9. ANS: A
Make a scatter plot of the data with number of participants as the independent variable (i.e., along
the x-axis) and the money raised as the dependent variable (i.e., along the y-axis).
Use the calculator’s LinReg feature to find r the correlation coefficient, and the equation of the line
of best fit.
Feedback
A
B
C
D
Correct!
You reversed the values of x and y. The number of participants should be the
independent variable.
There are two points whose x-value is 15. You graphed only one of them.
Some of the points are not graphed according to the table.
PTS: 1
DIF: Average
REF: Page 145
OBJ: 2-7.3 Application
NAT: 12.4.1.a
TOP: 2-7 Curve Fitting by Using Linear Models
10. ANS: C
Rewrite the absolute value as a disjunction. Then subtract 12 from both sides and divide by 4.
| 12 + 4x | > 16
12 + 4x > 16
4x > 4
x>1
or 12 + 4x < −16
or
4x < −28
or
x < −7
Feedback
A
B
Write the absolute value as a disjunction. Then solve the problem.
This answer is a conjunction. Write the problem as a disjunction.
C
D
Correct!
Write the absolute value as a disjunction. Then solve the problem.
PTS:
OBJ:
TOP:
11. ANS:
1
DIF: Average
REF: Page 152
2-8.3 Solving Absolute-Value Inequalities with Disjunctions
2-8 Solving Absolute-Value Equations and Inequalities
D
Multiply both sides by 4.
| x − 12 |
≤1
4
| x − 12 | ≤ 4
x − 12 ≤ 4 and x − 12 ≥ −4
x ≤ 16 and x ≥ 8
Rewrite the absolute value as a conjunction.
Simplify.
Graph the solution on a number line. As the inequality symbols include equality, circles should be
filled in at the limits indicated by each expression. “Greater than” means values larger than a limit
will be included. “Less than” indicates values less than the limit will be included. If there are no
solutions that satisfy both inequalities, there is no solution. If all values satisfy the requirements,
the solution includes all real umbers.
Feedback
A
B
C
D
Multiply the solution by –1 when making the conjunction.
Change the inequality sign when making the conjunction.
Check that the graph matches the solution set.
Correct!
PTS:
OBJ:
TOP:
12. ANS:
1
DIF: Average
REF: Page 153
2-8.4 Solving Absolute-Value Inequalities with Conjunctions
2-8 Solving Absolute-Value Equations and Inequalities
D
g( x ) = | x − h | + k
g( x ) = || x − ( −5 ) || + ( − 3 )
Substitute.
g( x ) = | x + 5 | − 3
The graph of g( x ) = | x + 5 | − 3 is the graph of f( x ) = | x | after a vertical shift 3 units down and a
horizontal shift 5 units left.
Feedback
A
B
C
D
g(x) = |x – h| + k where (h, k) are the coordinates of the vertex.
g(x) = |x – h| + k where (h, k) are the coordinates of the vertex.
g(x) = |x – h| + k where (h, k) are the coordinates of the vertex.
Correct!
PTS:
1
DIF:
Average
REF: Page 159
OBJ: 2-9.2 Translations of an Absolute-Value Function
TOP: 2-9 Absolute-Value Functions
NUMERIC RESPONSE
13. ANS: 25
PTS: 1
NAT: 12.3.2.e
14. ANS: $28.57
DIF: Average
OBJ: 2-2 Proportional Reasoning
KEY: proportions | similarity
PTS: 1
NAT: 12.3.2.e
15. ANS: 148.7
DIF: Average
KEY: proportion
OBJ: 2-2 Proportional Reasoning
PTS: 1
NAT: 12.3.2.e
DIF: Average
KEY: proportion
OBJ: 2-2 Proportional Reasoning
MATCHING
16. ANS:
TOP:
17. ANS:
TOP:
18. ANS:
TOP:
19. ANS:
TOP:
20. ANS:
TOP:
21. ANS:
TOP:
G
PTS: 1
DIF: Basic
2-1 Solving Linear Equations and Inequalities
H
PTS: 1
DIF: Basic
2-1 Solving Linear Equations and Inequalities
D
PTS: 1
DIF: Basic
2-1 Solving Linear Equations and Inequalities
E
PTS: 1
DIF: Basic
2-1 Solving Linear Equations and Inequalities
A
PTS: 1
DIF: Basic
2-1 Solving Linear Equations and Inequalities
C
PTS: 1
DIF: Basic
2-1 Solving Linear Equations and Inequalities
REF: Page 90
22. ANS:
TOP:
23. ANS:
TOP:
24. ANS:
TOP:
25. ANS:
TOP:
26. ANS:
TOP:
27. ANS:
D
PTS: 1
2-3 Graphing Linear Functions
G
PTS: 1
2-3 Graphing Linear Functions
H
PTS: 1
2-3 Graphing Linear Functions
B
PTS: 1
2-3 Graphing Linear Functions
F
PTS: 1
2-4 Writing Linear Functions
E
PTS: 1
REF: Page 92
REF: Page 92
REF: Page 92
REF: Page 90
REF: Page 90
DIF:
Basic
REF: Page 107
DIF:
Basic
REF: Page 106
DIF:
Basic
REF: Page 105
DIF:
Basic
REF: Page 106
DIF:
Basic
REF: Page 116
DIF:
Basic
REF: Page 106
TOP: 2-3 Graphing Linear Functions