Algebra Multiple Choice Study Guide

Algebra Multiple Choice Study Guide

Answer Section

MULTIPLE CHOICE

1.ANS:B

/ Solve the equation.
/ Substitute 8 for x and simplify.
Feedback
A / Find the value of x by solving the equation. Then substitute it for x in the given expression and simplify.
B / Correct!
C / Subtract the terms in the right order.
D / Find the value of x by solving the equation. Then substitute it for x in the given expression and simplify.

PTS:1DIF:AdvancedNAT:12.5.4.a

TOP:2-2 Solving Equations by Multiplying or Dividing

2.ANS:C

/ Since is subtracted from , add to both sides to undo the subtraction.
/ Since f is divided by 45, multiply both sides by 45 to undo the division.
/ Simplify.
Feedback
A / First, add to undo the subtraction. Then, multiply to undo the division.
B / Check your signs.
C / Correct!
D / First, add to undo the subtraction. Then, multiply to undo the division.

PTS:1DIF:AverageREF:Page 93

OBJ:2-3.2 Solving Two-Step Equations That Contain Fractions

NAT:12.5.4.aTOP:2-3 Solving Two-Step and Multi-Step Equations

3.ANS: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 / Correct!
B / Check your signs.
C / Combine like terms, and then solve.
D / Combine like terms, and then solve.

PTS:1DIF:AverageREF:Page 93

OBJ:2-3.3 Simplifying Before Solving EquationsNAT: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 / + / / / rate after first mile / = / total charge
4.00 / + / / / 2.75 / = / 20.50 / Subtract 4.00 from each side.
/ / 2.75 / = / 20.50 4.00
/ / 2.75 / = / 16.5 / Divide both sides by 2.75.
/ = /
/ = / 6 / Add 1 to both sides.
d / = / 6 + 1
d / = / 7
Feedback
A / Add one for the first mile.
B / Correct!
C / The mileage rate is the charge for each mile after the first mile.
D / Subtract the charge for the first mile.

PTS:1DIF:AverageREF:Page 94OBJ:2-3.4 Problem-Solving Application

NAT:12.5.3.bTOP:2-3 Solving Two-Step and Multi-Step Equations

5.ANS:D

/ 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 / Check your signs.
B / After adding to undo the subtraction, divide to undo the multiplication.
C / First, collect the variable terms on one side. Then, add to undo the subtraction.
D / Correct!

PTS:1DIF:AverageREF:Page 100

OBJ:2-4.1 Solving Equations with Variables on Both SidesNAT:12.5.4.a

TOP:2-4 Solving Equations with Variables on Both Sides

6.ANS:C

/ Locate V in the equation.
/ Since V is divided by I, multiply both sides by I to undo the division.
Feedback
A / Multiply both sides by I to isolate r.
B / Multiply both sides by I to isolate r.
C / Correct!
D / Multiply both sides by I to isolate r.

PTS:1DIF:BasicREF:Page 108

OBJ:2-5.2 Solving Formulas for a VariableNAT:12.5.4.f

TOP:2-5 Solving for a VariableKEY:literal equation | solving | variables

7.ANS:D

/ Divide both sides by 7.
/ What numbers are 7 units from 0?
Case 1: / Case 2: / Rewrite the equation as two cases.
x – 6 = 7 / x – 6 = –7 / The solutions are x = 13 or x = –1.
Feedback
A / Divide before you add or subtract. There are two cases to solve.
B / Absolute value means distance from zero. Solve the second case when the number inside the absolute value is negative.
C / Divide before you add or subtract.
D / Correct!

PTS:1DIF:AverageREF: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 / An absolute value must be greater than or equal to 0.
B / Isolate the absolute value by subtracting the term outside absolute value bars.
C / Correct!
D / Subtract the term outside the absolute value bars.

PTS:1DIF:AverageREF: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 / The arrow should point in the same direction as the inequality symbol.
B / The endpoint is not a solution.
C / Correct!
D / The endpoint is not a solution.

PTS:1DIF:BasicREF:Page 170

OBJ:3-1.3 Writing an Inequality from a GraphNAT: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 / The number of yards must be greater than or equal to 500, not less than 500.
B / The number of yards must be greater than or equal to 500, not less than 500.
C / The number 500 should be included in the solution.
D / Correct!

PTS:1DIF:AverageREF:Page 170OBJ:3-1.4 Application

NAT:12.5.4.cTOP: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 in dollars / is at least / $635
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 / Correct!
B / You should be solving an inequality, not an equation.
C / Subtract from both sides of the inequality.
D / Check the endpoint to see if you get a true statement.

PTS:1DIF:AverageREF:Page 176OBJ:3-2.3 Application

NAT:12.5.4.cTOP: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

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 / 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.
B / Correct!
C / Use inverse operations to undo the operations in the inequality one at a time.
D / Check your calculations when using inverse operations to isolate the variable.

PTS:1DIF:BasicREF:Page 188

OBJ:3-4.1 Solving Multi-Step InequalitiesNAT:12.5.4.a

TOP:3-4 Solving Two-Step and Multi-Step InequalitiesKEY:solving | two-step inequality

MSC:solving | two-step inequality

13.ANS: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 / Check the endpoints to see whether they are included in the solutions.
B / Check the endpoints to see whether they are included in the solutions.
C / Correct!
D / Check the inequality symbols. A number cannot be less than 1 AND greater than or equal to 4.

PTS:1DIF:AverageREF:Page 203

OBJ:3-6.2 Solving Compound Inequalities Involving ANDNAT:12.5.4.c

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.

Feedback
A / Check the x-intercept. If the x-intercept is to the left of the origin, it is negative.
B / The x-axis is the horizontal (left-right) axis; the y-axis is the vertical (up-down) axis.
C / Check the y-intercept. If the y-intercept is below the origin, it is negative.
D / Correct!

PTS:1DIF:BasicREF:Page 303OBJ:5-2.1 Finding Intercepts

NAT:12.5.1.eTOP: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.

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 / To find the slope, choose two points on the line. Divide the rise from one point to the next by the run.
B / Correct!
C / When finding slope, the numerator should be the rise (change in y-values) and the denominator should be the run (change in x-values).
D / 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:1DIF:BasicREF:Page 311OBJ:5-3.3 Finding Slope

NAT:12.5.2.bTOP:5-3 Rate of Change and SlopeKEY:line | slope

16.ANS:D

/ Use the slope formula.
/ Substitute for and for .
= / Simplify.
Feedback
A / Divide the difference in y-values by the difference in x-values.
B / Use the slope formula.
C / 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.
D / Correct!

PTS:1DIF:BasicREF:Page 320

OBJ:5-4.1 Finding Slope by Using the Slope FormulaNAT: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 / Correct!
B / Check the sign.
C / Slope is the ratio of rise to run.
D / First, find the x- and y-intercepts. Then, substitute those points into the slope formula.

PTS:1DIF:AverageREF:Page 322

OBJ:5-4.4 Finding Slope from an EquationNAT: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 / Correct!
B / Put the lines in slope-intercept form and look for lines with equal slopes.
C / 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.
D / Put the lines in slope-intercept form and look for lines with equal slopes.

PTS:1DIF:AverageREF:Page 349OBJ:5-8.1 Identifying Parallel Lines

NAT:12.3.3.gTOP: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 / Substitute for x in one of the original equations.
0– 6y = 12 / Simplify and solve for y.
– 6y = 12
y = –2
(0, –2) / Write the solution as an ordered pair.
Feedback
A / 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.
B / You switched the x- and y-coordinates.
C / Correct!
D / Add the equations to eliminate the variable, not subtract.

PTS:1DIF:BasicREF:Page 398OBJ:6-3.1 Elimination Using Addition

NAT:12.5.4.gTOP: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 / Correct!
B / Write an equation expressing the total cost and a second equation expressing the total number of fish. Solve for z and n using elimination.
C / You switched the prices of zebra fish and neon tetras.
D / 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:1DIF:AverageREF:Page 400OBJ:6-3.4 Application

NAT:12.5.4.gTOP: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 / Write both equations in slope-intercept form to see if the lines are parallel.
B / 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.
C / Write both equations in slope-intercept form to see if the lines are parallel.
D / Correct!

PTS:1DIF:AverageREF:Page 406OBJ:6-4.1 Systems with No Solution

NAT:12.5.4.gTOP:6-4 Solving Special Systems

22.ANS:A

Substitute (8, 5) for (x, y) in .

, false

(8, 5) is not a solution of .

Feedback
A / Correct!
B / Substitute the values for (x, y) into the inequality to see if the ordered pair is a solution.

PTS:1DIF:BasicREF:Page 414

OBJ:6-5.1 Identifying Solutions of InequalitiesNAT:12.5.4.a

TOP:6-5 Solving Linear Inequalities

23.ANS:C

Step 1. Solve the inequality for y.

Step 2. Graph the boundary line . Use a dashed line for .

Step 3. The inequality is , so shade above the line.

Feedback
A / The shaded region includes points that make the inequality true.
B / Check the boundary and the shading.
C / Correct!
D / The line is solid only when the operator is not > or <.

PTS:1DIF:AverageREF:Page 415

OBJ:6-5.2 Graphing Linear Inequalities in Two VariablesNAT:12.5.4.a

TOP:6-5 Solving Linear Inequalities

24.ANS:BPTS:1DIF:L2

REF:Thinking with Mathematical Models | Multiple Choice

OBJ:Investigation 2: Linear Models and Equations

TOP:Problem 2.4 Intersecting Linear ModelsKEY:slope | parallel

25.ANS:CPTS:1DIF:L2

REF:Thinking with Mathematical Models | Multiple ChoiceOBJ:Investigation 3: Inverse Variation

NAT:NAEP A2a| NAEP A2b| NAEP A3a| NAEP D1a| NAEP D2e

TOP:Problem 3.2 Inverse Variation PatternsKEY:inverse variation

26.ANS:DPTS:1DIF:L2

REF:Thinking with Mathematical Models | Multiple ChoiceOBJ:Investigation 3: Inverse Variation

NAT:NAEP A2a| NAEP A2b| NAEP A3a| NAEP D1a| NAEP D2e

TOP:Problem 3.2 Inverse Variation PatternsKEY:inverse variation

27.ANS:BPTS:1DIF:L2

REF:Thinking with Mathematical Models | Multiple ChoiceOBJ:Investigation 3: Inverse Variation

NAT:NAEP A2a| NAEP A2b| NAEP A3a| NAEP D1a| NAEP D2e

TOP:Problem 3.2 Inverse Variation PatternsKEY:inverse variation

28.ANS:DPTS:1DIF:L1

REF:Growing GrowingGrowing | Skills Practice Investigation 1

OBJ:Investigation 1: Exponential GrowthNAT:NAEP G3d

KEY:exponent | power