Algebra Multiple Choice Study Guide
Answer Section
MULTIPLE CHOICE
1. ANS: B
Solve the equation.
Substitute 8 for x and simplify.
Feedback
A
B
C
D
Find the value of x by solving the equation. Then substitute it for x in the given
expression and simplify.
Correct!
Subtract the terms in the right order.
Find the value of x by solving the equation. Then substitute it for x in the given
expression and simplify.
PTS: 1
DIF: Advanced
NAT: 12.5.4.a
TOP: 2-2 Solving Equations by Multiplying or Dividing
2. ANS: C
Since is subtracted from
subtraction.
, add
to both sides to undo the
Since f is divided by 45, multiply both sides by 45 to undo the
division.
Simplify.
Feedback
A
B
C
D
First, add to undo the subtraction. Then, multiply to undo the division.
Check your signs.
Correct!
First, add to undo the subtraction. Then, multiply to undo the division.
PTS:
OBJ:
NAT:
3. ANS:
1
DIF: Average
REF: Page 93
2-3.2 Solving Two-Step Equations That Contain Fractions
12.5.4.a
TOP: 2-3 Solving Two-Step and Multi-Step Equations
A
Use the Commutative Property of Addition.
Combine like terms.
Since 10 is added to 17a, subtract 10 from both sides to undo
the addition.
Since a is multiplied by 17, divide both sides by 17 to undo the
multiplication.
Feedback
A
B
C
D
Correct!
Check your signs.
Combine like terms, and then solve.
Combine like terms, and then solve.
PTS: 1
DIF: Average
REF: Page 93
OBJ: 2-3.3 Simplifying Before Solving Equations
NAT: 12.5.3.c
TOP: 2-3 Solving Two-Step and Multi-Step Equations
4. ANS: B
Let d be the distance (in miles) to the movies, then
is the number of miles after the first mile. So a
formula for the total charge could be
first mile
charge
4.00
+
+
rate after first
mile
2.75
=
total charge
=
20.50
2.75
2.75
=
=
20.50 4.00
16.5
Subtract 4.00
from each side.
Divide both sides
by 2.75.
=
d
d
=
6
=
=
6+1
7
Add 1 to both
sides.
Feedback
A
B
C
D
Add one for the first mile.
Correct!
The mileage rate is the charge for each mile after the first mile.
Subtract the charge for the first mile.
PTS: 1
NAT: 12.5.3.b
5. ANS: D
DIF: Average
REF: Page 94
OBJ: 2-3.4 Problem-Solving Application
TOP: 2-3 Solving Two-Step and Multi-Step Equations
To collect the variable terms on one side, subtract 50q from both
sides.
Since 81 is subtracted from 2q, add 81 to both sides to undo the
subtraction.
Since q is multiplied by 2, divide both sides by 2 to undo the
multiplication.
Feedback
A
B
C
D
Check your signs.
After adding to undo the subtraction, divide to undo the multiplication.
First, collect the variable terms on one side. Then, add to undo the subtraction.
Correct!
PTS:
OBJ:
TOP:
6. ANS:
1
DIF: Average
REF: Page 100
2-4.1 Solving Equations with Variables on Both Sides
2-4 Solving Equations with Variables on Both Sides
C
Locate V in the equation.
NAT: 12.5.4.a
Since V is divided by I, multiply both sides by I to undo the division.
Feedback
A
B
C
D
Multiply both sides by I to isolate r.
Multiply both sides by I to isolate r.
Correct!
Multiply both sides by I to isolate r.
PTS:
OBJ:
TOP:
7. ANS:
1
DIF: Basic
REF: Page 108
2-5.2 Solving Formulas for a Variable
NAT: 12.5.4.f
2-5 Solving for a Variable
KEY: literal equation | solving | variables
D
Divide both sides by 7.
What numbers are 7 units from 0?
Case 1:
x–6=7
Case 2:
x – 6 = –7
Rewrite the equation as two cases.
The solutions are x = 13 or x = –1.
Feedback
A
B
C
Divide before you add or subtract. There are two cases to solve.
Absolute value means distance from zero. Solve the second case when the number
inside the absolute value is negative.
Divide before you add or subtract.
D
Correct!
PTS: 1
DIF: Average
REF: Page 294
OBJ: 2-Ext.1 Solving Absolute-Value Equations
TOP: 2-Ext Solving Absolute-Value Equations
8. ANS: C
First, isolate the absolute value expression.
Subtract 8 from both sides.
The absolute value expression is equal to a negative number, which is impossible. The equation has no
solution.
Feedback
A
B
C
D
An absolute value must be greater than or equal to 0.
Isolate the absolute value by subtracting the term outside absolute value bars.
Correct!
Subtract the term outside the absolute value bars.
PTS: 1
DIF: Average
REF: Page 295
OBJ: 2-Ext.2 Special Cases of Absolute-Value Equations
TOP: 2-Ext Solving Absolute-Value Equations
9. ANS: C
Use the variable m. The arrow points to the right, so use either > or . The solid circle at –3 means that –3 is a
solution, so use .
Feedback
A
B
C
D
The arrow should point in the same direction as the inequality symbol.
The endpoint is not a solution.
Correct!
The endpoint is not a solution.
PTS: 1
DIF: Basic
REF: Page 170
OBJ: 3-1.3 Writing an Inequality from a Graph
NAT: 12.5.4.c
TOP: 3-1 Graphing and Writing Inequalities
10. ANS: D
The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should
include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line.
Feedback
A
B
C
D
The number of yards must be greater than or equal to 500, not less than 500.
The number of yards must be greater than or equal to 500, not less than 500.
The number 500 should be included in the solution.
Correct!
PTS: 1
NAT: 12.5.4.c
DIF: Average
REF: Page 170
OBJ: 3-1.4 Application
TOP: 3-1 Graphing and Writing Inequalities
11. ANS: A
Let d represent the amount of money in dollars Denise must save to reach her goal.
$365
plus
additional amount of money is at least
$635
in dollars
365
+
d
635
Since 365 is added to d, subtract 365 from both sides to undo the
addition.
365
365
Check the endpoint 270 and a number that is greater than the endpoint.
Feedback
A
B
C
D
Correct!
You should be solving an inequality, not an equation.
Subtract from both sides of the inequality.
Check the endpoint to see if you get a true statement.
PTS: 1
DIF: Average
REF: Page 176
OBJ: 3-2.3 Application
NAT: 12.5.4.c
TOP: 3-2 Solving Inequalities by Adding and Subtracting
12. ANS: B
Use inverse operations to undo the operations in the inequality one at a time.
n – 4  3
n  –7
–10 –8
–6
–4
–2
0
2
4
6
8
10

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the
value is not included, such as with > or <.
Feedback
A
B
C
D
If you divide both sides of the inequality by a negative number, reverse the inequality
symbol. If you divide by a positive number, do not reverse the inequality symbol.
Correct!
Use inverse operations to undo the operations in the inequality one at a time.
Check your calculations when using inverse operations to isolate the variable.
PTS:
OBJ:
TOP:
MSC:
13. ANS:
1
DIF: Basic
REF: Page 188
3-4.1 Solving Multi-Step Inequalities
NAT: 12.5.4.a
3-4 Solving Two-Step and Multi-Step Inequalities
KEY: solving | two-step inequality
solving | two-step inequality
C
AND
Write the compound inequality using AND.
Solve each simple inequality.
Divide to undo the multiplication.
AND
First, graph the solutions of each simple inequality. Then, graph the intersection by finding where the two
graphs overlap.
Feedback
A
B
C
D
Check the endpoints to see whether they are included in the solutions.
Check the endpoints to see whether they are included in the solutions.
Correct!
Check the inequality symbols. A number cannot be less than 1 AND greater than or
equal to 4.
PTS: 1
DIF: Average
REF: Page 203
OBJ: 3-6.2 Solving Compound Inequalities Involving AND
TOP: 3-6 Solving Compound Inequalities
14. ANS: D
The graph intersects the x-axis at (10, 0). The x-intercept is 10.
The graph intersects the y-axis at (0, 5). The y-intercept is 5.
NAT: 12.5.4.c
Feedback
A
B
C
D
Check the x-intercept. If the x-intercept is to the left of the origin, it is negative.
The x-axis is the horizontal (left-right) axis; the y-axis is the vertical (up-down) axis.
Check the y-intercept. If the y-intercept is below the origin, it is negative.
Correct!
PTS: 1
DIF: Basic
REF: Page 303
NAT: 12.5.1.e
TOP: 5-2 Using Intercepts
KEY: linear equation | x-intercept | y-intercept | intercepts
15. ANS: B
To find the slope, use the coordinates of two points on the line.
OBJ: 5-2.1 Finding Intercepts
Starting at one point, count the units down (negative units) or up (positive units) and to the right (positive
units) or to the left (negative units) to arrive at the other point. The units up or down are the rise. The units to
the right or to the left are the run.
Write a fraction with the rise in the numerator and the run in the denominator. Simplify the fraction.
Feedback
A
B
C
D
To find the slope, choose two points on the line. Divide the rise from one point to the
next by the run.
Correct!
When finding slope, the numerator should be the rise (change in y-values) and the
denominator should be the run (change in x-values).
Check the signs for rise and run. If the line rises from left to right, the slope is positive;
if it falls, the slope is negative.
PTS: 1
NAT: 12.5.2.b
16. ANS: D
DIF: Basic
REF: Page 311
TOP: 5-3 Rate of Change and Slope
Use the slope formula.
OBJ: 5-3.3 Finding Slope
KEY: line | slope
Substitute
= 3
5
for
and
for
.
Simplify.
Feedback
A
B
C
D
Divide the difference in y-values by the difference in x-values.
Use the slope formula.
First, substitute the coordinates of the first point into (x1, x2) and the coordinates of the
second point into (y1, y2) of the slope formula. Then, simplify.
Correct!
PTS: 1
DIF: Basic
REF: Page 320
OBJ: 5-4.1 Finding Slope by Using the Slope Formula
NAT: 12.5.2.b
TOP: 5-4 The Slope Formula
17. ANS: A
Find the x-intercept by substituting x = 0 into the equation. Find the y-intercept by substituting y = 0 into the
equation. Use the two intercept points and the slope formula,
, to calculate the slope.
Feedback
A
B
C
D
Correct!
Check the sign.
Slope is the ratio of rise to run.
First, find the x- and y-intercepts. Then, substitute those points into the slope formula.
PTS: 1
DIF: Average
REF: Page 322
OBJ: 5-4.4 Finding Slope from an Equation
NAT: 12.5.2.c
TOP: 5-4 The Slope Formula
18. ANS: A
Write all the equations in slope-intercept form (y = mx + b). The equations that have the same slope but
different y-intercepts are parallel lines.
Feedback
A
B
C
D
Correct!
Put the lines in slope-intercept form and look for lines with equal slopes.
Not all the lines have the same slope. Note that Line 1 and Line 3 are in slope intercept
form, but the coefficients of x are different.
Put the lines in slope-intercept form and look for lines with equal slopes.
PTS: 1
DIF: Average
REF: Page 349
OBJ: 5-8.1 Identifying Parallel Lines
NAT: 12.3.3.g
TOP: 5-8 Slopes of Parallel and Perpendicular Lines
19. ANS: C
Step 1 3x – 6y = 12
2x + 6y = –12
The y-terms have opposite coefficients.
5x = 0
Add the equations to eliminate the y terms.
x=0
Step 2
3(0) – 6y = 12
0 – 6y = 12
– 6y = 12
y = –2
Substitute for x in one of the original equations.
Simplify and solve for y.
(0, –2)
Write the solution as an ordered pair.
Feedback
A
B
C
D
This is a solution of the first equation, but it is not a solution of the second equation.
Use elimination to find a solution of both equations.
You switched the x- and y-coordinates.
Correct!
Add the equations to eliminate the variable, not subtract.
PTS: 1
DIF: Basic
REF: Page 398
OBJ: 6-3.1 Elimination Using Addition
NAT: 12.5.4.g
TOP: 6-3 Solving Systems by Elimination
KEY: linear equations | system of equations | solving | elimination
20. ANS: A
Let z be the number of zebra fish and let n be the number of neon tetras that Marsha bought. Then solve the
following system of equations.
Marsha spent $25.80.
Marsha bought 13 fish.
Multiply the second equation by –2.10
Add the two equations to eliminate the z term.
Solve for n.
To solve for z, substitute 6 for n in the first equation.
Simplify.
Solve for z.
Feedback
A
B
C
D
Correct!
Write an equation expressing the total cost and a second equation expressing the total
number of fish. Solve for z and n using elimination.
You switched the prices of zebra fish and neon tetras.
Write an equation expressing the total cost and a second equation expressing the total
number of fish. Solve for z and n using elimination.
PTS: 1
DIF: Average
REF: Page 400
OBJ: 6-3.4 Application
NAT: 12.5.4.g
TOP: 6-3 Solving Systems by Elimination
21. ANS: D
Write each equation in slope-intercept form.
y = –x + 8
y = –x + 7
The lines both have slope –1 but different y-intercepts, so they are parallel.
Parallel lines never intersect so the system has no solutions and is inconsistent.
Feedback
A
B
C
D
Write both equations in slope-intercept form to see if the lines are parallel.
Write both equations in slope-intercept form to see if the lines are parallel or the same
line. Only lines with the same graph have infinitely many solutions.
Write both equations in slope-intercept form to see if the lines are parallel.
Correct!
PTS: 1
DIF: Average
REF: Page 406
NAT: 12.5.4.g
TOP: 6-4 Solving Special Systems
22. ANS: A
Substitute (8, 5) for (x, y) in
.
, false
(8, 5) is not a solution of
OBJ: 6-4.1 Systems with No Solution
.
Feedback
A
B
Correct!
Substitute the values for (x, y) into the inequality to see if the ordered pair is a solution.
PTS: 1
DIF: Basic
REF: Page 414
OBJ: 6-5.1 Identifying Solutions of Inequalities
TOP: 6-5 Solving Linear Inequalities
23. ANS: C
Step 1. Solve the inequality
for y.
Step 2. Graph the boundary line
NAT: 12.5.4.a
. Use a dashed line for .
Step 3. The inequality is , so shade above the line.
Feedback
A
B
C
D
The shaded region includes points that make the inequality true.
Check the boundary and the shading.
Correct!
The line is solid only when the operator is not > or <.
PTS:
OBJ:
TOP:
24. ANS:
REF:
OBJ:
NAT:
1
DIF: Average
REF: Page 415
6-5.2 Graphing Linear Inequalities in Two Variables
NAT: 12.5.4.a
6-5 Solving Linear Inequalities
B
PTS: 1
DIF: L2
Thinking with Mathematical Models | Multiple Choice
Investigation 2: Linear Models and Equations
NAEP A1f| NAEP A2b| NAEP A2c| NAEP A2d| NAEP A4a| NAEP A4c| NAEP A4d| NAEP D1a|
25.
26.
27.
28.
NAEP D2e
STA: 8NJ 4.1.8.C.3| 8NJ 4.3.8.A.1a| 8NJ 4.3.8.B.1b| 8NJ 4.3.8.C.1| 8NJ 4.3.8.C.2a
TOP: Problem 2.4 Intersecting Linear Models
KEY: slope | parallel
ANS: C
PTS: 1
DIF: L2
REF: Thinking with Mathematical Models | Multiple Choice
OBJ: Investigation 3: Inverse Variation
NAT: NAEP A2a| NAEP A2b| NAEP A3a| NAEP D1a| NAEP D2e
STA: 8NJ 4.1.8.A.3| 8NJ 4.3.8.A.1a| 8NJ 4.3.8.A.1b| 8NJ 4.3.8.A.1c| 8NJ 4.3.8.C.1| 8NJ 4.3.8.C.2a
TOP: Problem 3.2 Inverse Variation Patterns
KEY: inverse variation
ANS: D
PTS: 1
DIF: L2
REF: Thinking with Mathematical Models | Multiple Choice
OBJ: Investigation 3: Inverse Variation
NAT: NAEP A2a| NAEP A2b| NAEP A3a| NAEP D1a| NAEP D2e
STA: 8NJ 4.1.8.A.3| 8NJ 4.3.8.A.1a| 8NJ 4.3.8.A.1b| 8NJ 4.3.8.A.1c| 8NJ 4.3.8.C.1| 8NJ 4.3.8.C.2a
TOP: Problem 3.2 Inverse Variation Patterns
KEY: inverse variation
ANS: B
PTS: 1
DIF: L2
REF: Thinking with Mathematical Models | Multiple Choice
OBJ: Investigation 3: Inverse Variation
NAT: NAEP A2a| NAEP A2b| NAEP A3a| NAEP D1a| NAEP D2e
STA: 8NJ 4.1.8.A.3| 8NJ 4.3.8.A.1a| 8NJ 4.3.8.A.1b| 8NJ 4.3.8.A.1c| 8NJ 4.3.8.C.1| 8NJ 4.3.8.C.2a
TOP: Problem 3.2 Inverse Variation Patterns
KEY: inverse variation
ANS: D
PTS: 1
DIF: L1
REF: Growing Growing Growing | Skills Practice Investigation 1
OBJ: Investigation 1: Exponential Growth
NAT: NAEP G3d
STA: 8NJ 4.1.8.B.1a| 8NJ 4.1.8.B.1b| 8NJ 4.1.8.B.2| 8NJ 4.3.8.A.1a| 8NJ 4.3.8.A.1d| 8NJ 4.3.8.A.1e| 8NJ
4.5.8.A.3
TOP: Problem 1.2 Representing Exponential Relationships
KEY: exponent | power