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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Review Exercises

Add and Subtract Polynomials

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

494.

y2+8y20y2+8y20

495.

−6a4−6a4

496.

9x319x31

497.

n33n2+3n1n33n2+3n1

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

498.

16x240x2516x240x25

499.

5m+95m+9

500.

−15−15

501.

y2+6y3+9y4y2+6y3+9y4

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

502.

4p+11p4p+11p

503.

−8y35y3−8y35y3

504.

Add 4n5,n5,−6n54n5,n5,−6n5

505.

Subtract 10x210x2 from 3x23x2

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

506.

(4a2+9a11)+(6a25a+10)(4a2+9a11)+(6a25a+10)

507.

(8m2+12m5)(2m27m1)(8m2+12m5)(2m27m1)

508.

(y23y+12)+(5y29)(y23y+12)+(5y29)

509.

(5u2+8u)(4u7)(5u2+8u)(4u7)

510.

Find the sum of 8q3278q327 and q2+6q2q2+6q2

511.

Find the difference of x2+6x+8x2+6x+8 and x28x+15x28x+15

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

512.

200x15x2200x15x2 when x=5x=5

513.

200x15x2200x15x2 when x=0x=0

514.

200x15x2200x15x2 when x=15x=15

515.

5+40x12x25+40x12x2 when x=10x=10

516.

5+40x12x25+40x12x2 when x=−4x=−4

517.

5+40x12x25+40x12x2 when x=0x=0

518.

A pair of glasses is dropped off a bridge 640640 feet above a river. The polynomial −16t2+640−16t2+640 gives the height of the glasses tt seconds after they were dropped. Find the height of the glasses when t=6.t=6.

519.

The fuel efficiency (in miles per gallon) of a bus going at a speed of xx miles per hour is given by the polynomial 1160x2+12x.1160x2+12x. Find the fuel efficiency when x=20x=20 mph.

Use Multiplication Properties of Exponents

Simplify Expressions with Exponents

In the following exercises, simplify.

520.

6363

521.

(12)4(12)4

522.

(−0.5)2(−0.5)2

523.

3232

Simplify Expressions Using the Product Property of Exponents

In the following exercises, simplify each expression.

524.

p3·p10p3·p10

525.

2·262·26

526.

a·a2·a3a·a2·a3

527.

x·x8x·x8

Simplify Expressions Using the Power Property of Exponents

In the following exercises, simplify each expression.

528.

(y4)3(y4)3

529.

(r3)2(r3)2

530.

(32)5(32)5

531.

(a10)y(a10)y

Simplify Expressions Using the Product to a Power Property

In the following exercises, simplify each expression.

532.

(8n)2(8n)2

533.

(−5x)3(−5x)3

534.

(2ab)8(2ab)8

535.

(−10mnp)4(−10mnp)4

Simplify Expressions by Applying Several Properties

In the following exercises, simplify each expression.

536.

(3a5)3(3a5)3

537.

(4y)2(8y)(4y)2(8y)

538.

(x3)5(x2)3(x3)5(x2)3

539.

(5st2)3(2s3t4)2(5st2)3(2s3t4)2

Multiply Monomials

In the following exercises, multiply the monomials.

540.

(−6p4)(9p)(−6p4)(9p)

541.

(13c2)(30c8)(13c2)(30c8)

542.

(8x2y5)(7xy6)(8x2y5)(7xy6)

543.

(23m3n6)(16m4n4)(23m3n6)(16m4n4)

Multiply Polynomials

Multiply a Polynomial by a Monomial

In the following exercises, multiply.

544.

7(10x)7(10x)

545.

a2(a29a36)a2(a29a36)

546.

−5y(125y31)−5y(125y31)

547.

(4n5)(2n3)(4n5)(2n3)

Multiply a Binomial by a Binomial

In the following exercises, multiply the binomials using various methods.

548.

(a+5)(a+2)(a+5)(a+2)

549.

(y4)(y+12)(y4)(y+12)

550.

(3x+1)(2x7)(3x+1)(2x7)

551.

(6p11)(3p10)(6p11)(3p10)

552.

(n+8)(n+1)(n+8)(n+1)

553.

(k+6)(k9)(k+6)(k9)

554.

(5u3)(u+8)(5u3)(u+8)

555.

(2y9)(5y7)(2y9)(5y7)

556.

(p+4)(p+7)(p+4)(p+7)

557.

(x8)(x+9)(x8)(x+9)

558.

(3c+1)(9c4)(3c+1)(9c4)

559.

(10a1)(3a3)(10a1)(3a3)

Multiply a Trinomial by a Binomial

In the following exercises, multiply using any method.

560.

(x+1)(x23x21)(x+1)(x23x21)

561.

(5b2)(3b2+b9)(5b2)(3b2+b9)

562.

(m+6)(m27m30)(m+6)(m27m30)

563.

(4y1)(6y212y+5)(4y1)(6y212y+5)

Divide Monomials

Simplify Expressions Using the Quotient Property of Exponents

In the following exercises, simplify.

564.

28222822

565.

a6aa6a

566.

n3n12n3n12

567.

xx5xx5

Simplify Expressions with Zero Exponents

In the following exercises, simplify.

568.

3030

569.

y0y0

570.

(14t)0(14t)0

571.

12a015b012a015b0

Simplify Expressions Using the Quotient to a Power Property

In the following exercises, simplify.

572.

(35)2(35)2

573.

(x2)5(x2)5

574.

(5mn)3(5mn)3

575.

(s10t)2(s10t)2

Simplify Expressions by Applying Several Properties

In the following exercises, simplify.

576.

(a3)2a4(a3)2a4

577.

u3u2·u4u3u2·u4

578.

(xx9)5(xx9)5

579.

(p4·p5p3)2(p4·p5p3)2

580.

(n5)3(n2)8(n5)3(n2)8

581.

(5s24t)3(5s24t)3

Divide Monomials

In the following exercises, divide the monomials.

582.

72p12÷8p372p12÷8p3

583.

−26a8÷(2a2)−26a8÷(2a2)

584.

45y6−15y1045y6−15y10

585.

−30x8−36x9−30x8−36x9

586.

28a9b7a4b328a9b7a4b3

587.

11u6v355u2v811u6v355u2v8

588.

(5m9n3)(8m3n2)(10mn4)(m2n5)(5m9n3)(8m3n2)(10mn4)(m2n5)

589.

42r2s46rs354rs29s42r2s46rs354rs29s

Integer Exponents and Scientific Notation

Use the Definition of a Negative Exponent

In the following exercises, simplify.

590.

6−26−2

591.

(−10)−3(−10)−3

592.

5·2−45·2−4

593.

(8n)−1(8n)−1

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

594.

x−3·x9x−3·x9

595.

r−5·r−4r−5·r−4

596.

(uv−3)(u−4v−2)(uv−3)(u−4v−2)

597.

(m5)−1(m5)−1

598.

(k−2)−3(k−2)−3

599.

q4q20q4q20

600.

b8b−2b8b−2

601.

n−3n−5n−3n−5

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

602.

5,300,0005,300,000

603.

0.008140.00814

604.

The thickness of a piece of paper is about 0.0970.097 millimeter.

605.

According to www.cleanair.com, U.S. businesses use about 21,000,00021,000,000 tons of paper per year.

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

606.

2.9×1042.9×104

607.

1.5×1081.5×108

608.

3.75×10−13.75×10−1

609.

9.413×10−59.413×10−5

Multiply and Divide Using Scientific Notation

In the following exercises, multiply and write your answer in decimal form.

610.

(3×107)(2×10−4)(3×107)(2×10−4)

611.

(1.5×10−3)(4.8×10−1)(1.5×10−3)(4.8×10−1)

612.

6×1092×10−16×1092×10−1

613.

9×10−31×10−69×10−31×10−6

Introduction to Factoring Polynomials

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

614.

5n,455n,45

615.

8a,728a,72

616.

12x2,20x3,36x412x2,20x3,36x4

617.

9y4,21y5,15y69y4,21y5,15y6

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

618.

16u2416u24

619.

15r+3515r+35

620.

6p2+6p6p2+6p

621.

10c210c10c210c

622.

−9a59a3−9a59a3

623.

−7x828x3−7x828x3

624.

5y255y+455y255y+45

625.

2q516q3+30q22q516q3+30q2

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