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Intermediate Algebra 2e

Review Exercises

Intermediate Algebra 2eReview Exercises
  1. Preface
  2. 1 Foundations
    1. Introduction
    2. 1.1 Use the Language of Algebra
    3. 1.2 Integers
    4. 1.3 Fractions
    5. 1.4 Decimals
    6. 1.5 Properties of Real Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Solving Linear Equations
    1. Introduction
    2. 2.1 Use a General Strategy to Solve Linear Equations
    3. 2.2 Use a Problem Solving Strategy
    4. 2.3 Solve a Formula for a Specific Variable
    5. 2.4 Solve Mixture and Uniform Motion Applications
    6. 2.5 Solve Linear Inequalities
    7. 2.6 Solve Compound Inequalities
    8. 2.7 Solve Absolute Value Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Graphs and Functions
    1. Introduction
    2. 3.1 Graph Linear Equations in Two Variables
    3. 3.2 Slope of a Line
    4. 3.3 Find the Equation of a Line
    5. 3.4 Graph Linear Inequalities in Two Variables
    6. 3.5 Relations and Functions
    7. 3.6 Graphs of Functions
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Systems of Linear Equations
    1. Introduction
    2. 4.1 Solve Systems of Linear Equations with Two Variables
    3. 4.2 Solve Applications with Systems of Equations
    4. 4.3 Solve Mixture Applications with Systems of Equations
    5. 4.4 Solve Systems of Equations with Three Variables
    6. 4.5 Solve Systems of Equations Using Matrices
    7. 4.6 Solve Systems of Equations Using Determinants
    8. 4.7 Graphing Systems of Linear Inequalities
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomials and Polynomial Functions
    1. Introduction
    2. 5.1 Add and Subtract Polynomials
    3. 5.2 Properties of Exponents and Scientific Notation
    4. 5.3 Multiply Polynomials
    5. 5.4 Dividing Polynomials
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Factoring
    1. Introduction to Factoring
    2. 6.1 Greatest Common Factor and Factor by Grouping
    3. 6.2 Factor Trinomials
    4. 6.3 Factor Special Products
    5. 6.4 General Strategy for Factoring Polynomials
    6. 6.5 Polynomial Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Rational Expressions and Functions
    1. Introduction
    2. 7.1 Multiply and Divide Rational Expressions
    3. 7.2 Add and Subtract Rational Expressions
    4. 7.3 Simplify Complex Rational Expressions
    5. 7.4 Solve Rational Equations
    6. 7.5 Solve Applications with Rational Equations
    7. 7.6 Solve Rational Inequalities
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Roots and Radicals
    1. Introduction
    2. 8.1 Simplify Expressions with Roots
    3. 8.2 Simplify Radical Expressions
    4. 8.3 Simplify Rational Exponents
    5. 8.4 Add, Subtract, and Multiply Radical Expressions
    6. 8.5 Divide Radical Expressions
    7. 8.6 Solve Radical Equations
    8. 8.7 Use Radicals in Functions
    9. 8.8 Use the Complex Number System
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Quadratic Equations and Functions
    1. Introduction
    2. 9.1 Solve Quadratic Equations Using the Square Root Property
    3. 9.2 Solve Quadratic Equations by Completing the Square
    4. 9.3 Solve Quadratic Equations Using the Quadratic Formula
    5. 9.4 Solve Quadratic Equations in Quadratic Form
    6. 9.5 Solve Applications of Quadratic Equations
    7. 9.6 Graph Quadratic Functions Using Properties
    8. 9.7 Graph Quadratic Functions Using Transformations
    9. 9.8 Solve Quadratic Inequalities
    10. Key Terms
    11. Key Concepts
    12. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Exponential and Logarithmic Functions
    1. Introduction
    2. 10.1 Finding Composite and Inverse Functions
    3. 10.2 Evaluate and Graph Exponential Functions
    4. 10.3 Evaluate and Graph Logarithmic Functions
    5. 10.4 Use the Properties of Logarithms
    6. 10.5 Solve Exponential and Logarithmic Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Conics
    1. Introduction
    2. 11.1 Distance and Midpoint Formulas; Circles
    3. 11.2 Parabolas
    4. 11.3 Ellipses
    5. 11.4 Hyperbolas
    6. 11.5 Solve Systems of Nonlinear Equations
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  13. 12 Sequences, Series and Binomial Theorem
    1. Introduction
    2. 12.1 Sequences
    3. 12.2 Arithmetic Sequences
    4. 12.3 Geometric Sequences and Series
    5. 12.4 Binomial Theorem
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  14. 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
    12. Chapter 12
  15. Index

Review Exercises

Simplify Expressions with Roots

Simplify Expressions with Roots

In the following exercises, simplify.

481.

225225 1616

482.

169169 −8−8

483.

8383 814814 24352435

484.

−5123−5123 −814−814 −15−15

Estimate and Approximate Roots

In the following exercises, estimate each root between two consecutive whole numbers.

485.

6868 843843

In the following exercises, approximate each root and round to two decimal places.

486.

3737 843843 12541254

Simplify Variable Expressions with Roots

In the following exercises, simplify using absolute values as necessary.

487.


a33a33
b77b77

488.


a14a14
w24w24

489.


m84m84
n205n205

490.


121m20121m20
64a264a2

491.


216a63216a63
32b20532b205

492.


144x2y2144x2y2
169w8y10169w8y10
8a51b638a51b63

Simplify Radical Expressions

Use the Product Property to Simplify Radical Expressions

In the following exercises, use the Product Property to simplify radical expressions.

493.

125125

494.

675675

495.

62536253 12861286

In the following exercises, simplify using absolute value signs as needed.

496.


a23a23
b83b83
c138c138

497.


80s1580s15
96a7596a75
128b76128b76

498.


96r3s396r3s3
80x7y6380x7y63
80x8y9480x8y94

499.


−325−325
−18−18

500.


8+968+96
2+4022+402

Use the Quotient Property to Simplify Radical Expressions

In the following exercises, use the Quotient Property to simplify square roots.

501.

72987298 2481324813 69646964

502.

y4y8y4y8 u21u115u21u115 v30v126v30v126

503.

300m564300m564

504.


28p7q228p7q2
81s8t3381s8t33
64p15q12464p15q124

505.


27p2q108p4q327p2q108p4q3
16c5d7250c2d2316c5d7250c2d23
2m9n7128m3n62m9n7128m3n6

506.


80q55q80q55q
625353625353
80m745m480m745m4

Simplify Rational Exponents

Simplify expressions with a1na1n

In the following exercises, write as a radical expression.

507.

r12r12 s13s13 t14t14

In the following exercises, write with a rational exponent.

508.

21p21p 8q48q4 436r6436r6

In the following exercises, simplify.

509.


6251462514
2431524315
32153215

510.


(−1,000)13(−1,000)13
1,000131,00013
(1,000)13(1,000)13

511.


(−32)15(−32)15
(243)15(243)15
1251312513

Simplify Expressions with amnamn

In the following exercises, write with a rational exponent.

512.


r74r74
(2pq5)3(2pq5)3
(12m7n)34(12m7n)34

In the following exercises, simplify.

513.


25322532
932932
(−64)23(−64)23

514.


64326432
64326432
(−64)32(−64)32

Use the Laws of Exponents to Simplify Expressions with Rational Exponents

In the following exercises, simplify.

515.


652·612652·612
(b15)35(b15)35
w27w97w27w97

516.


a34·a14a104a34·a14a104
(27b23c52b73c12)13(27b23c52b73c12)13

Add, Subtract and Multiply Radical Expressions

Add and Subtract Radical Expressions

In the following exercises, simplify.

517.


72327232
7p3+2p37p3+2p3
5x33x35x33x3

518.


11b511b+311b11b511b+311b
811cd4+511cd4911cd4811cd4+511cd4911cd4

519.


48+2748+27
543+1283543+1283
6543280465432804

520.


80c720c780c720c7
2162r104+432r1042162r104+432r104

521.

375y2+8y48300y2375y2+8y48300y2

Multiply Radical Expressions

In the following exercises, simplify.

522.


(56)(12)(56)(12)
(−2184)(94)(−2184)(94)

523.


(32x3)(718x2)(32x3)(718x2)
(−620a23)(−216a33)(−620a23)(−216a33)

Use Polynomial Multiplication to Multiply Radical Expressions

In the following exercises, multiply.

524.


11(8+411)11(8+411)
33(93+183)33(93+183)

525.


(327)(547)(327)(547)
(x35)(x33)(x35)(x33)

526.

(27511)(47+911)(27511)(47+911)

527.


(4+11)2(4+11)2
(325)2(325)2

528.

(7+10)(710)(7+10)(710)

529.

(3x3+2)(3x32)(3x3+2)(3x32)

Divide Radical Expressions

Divide Square Roots

In the following exercises, simplify.

530.


48754875
813243813243

531.


320mn−545m−7n3320mn−545m−7n3
16x4y−23−54x−2y4316x4y−23−54x−2y43

Rationalize a One Term Denominator

In the following exercises, rationalize the denominator.

532.

8383 740740 82y82y

533.

11131113 75437543 33x2333x23

534.

144144 93249324 69x3469x34

Rationalize a Two Term Denominator

In the following exercises, simplify.

535.

726726

536.

5n75n7

537.

x+8x8x+8x8

Solve Radical Equations

Solve Radical Equations

In the following exercises, solve.

538.

4x3=74x3=7

539.

5x+1=−35x+1=−3

540.

4x13=34x13=3

541.

u3+3=uu3+3=u

542.

4x+532=−54x+532=−5

543.

(8x+5)13+2=−1(8x+5)13+2=−1

544.

y+4y+2=0y+4y+2=0

545.

28r+18=228r+18=2

Solve Radical Equations with Two Radicals

In the following exercises, solve.

546.

10+2c=4c+1610+2c=4c+16

547.

2x2+9x183=x2+3x232x2+9x183=x2+3x23

548.

r+6=r+8r+6=r+8

549.

x+1x2=1x+1x2=1

Use Radicals in Applications

In the following exercises, solve. Round approximations to one decimal place.

550.

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of 75 square feet. Use the formula s=As=A to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.

551.

Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was 175 feet. Use the formula s=24ds=24d to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Use Radicals in Functions

Evaluate a Radical Function

In the following exercises, evaluate each function.

552.

g(x)=6x+1,g(x)=6x+1, find
g(4)g(4)
g(8)g(8)

553.

G(x)=5x1,G(x)=5x1, find
G(5)G(5)
G(2)G(2)

554.

h(x)=x243,h(x)=x243, find
h(−2)h(−2)
h(6)h(6)

555.

For the function
g(x)=44x4,g(x)=44x4, find
g(1)g(1)
g(−3)g(−3)

Find the Domain of a Radical Function

In the following exercises, find the domain of the function and write the domain in interval notation.

556.

g(x)=23xg(x)=23x

557.

F(x)=x+3x2F(x)=x+3x2

558.

f(x)=4x2163f(x)=4x2163

559.

F(x)=107x4F(x)=107x4

Graph Radical Functions

In the following exercises, find the domain of the function graph the function use the graph to determine the range.

560.

g(x)=x+4g(x)=x+4

561.

g(x)=2xg(x)=2x

562.

f(x)=x13f(x)=x13

563.

f(x)=x3+3f(x)=x3+3

Use the Complex Number System

Evaluate the Square Root of a Negative Number

In the following exercises, write each expression in terms of i and simplify if possible.

564.


−100−100
−13−13
−45−45

Add or Subtract Complex Numbers

In the following exercises, add or subtract.

565.

−50+−18−50+−18

566.

(8i)+(6+3i)(8i)+(6+3i)

567.

(6+i)(−24i)(6+i)(−24i)

568.

(−7−50)(−32−18)(−7−50)(−32−18)

Multiply Complex Numbers

In the following exercises, multiply.

569.

(−25i)(−4+3i)(−25i)(−4+3i)

570.

−6i(−32i)−6i(−32i)

571.

−4·−16−4·−16

572.

(5−12)(−3+−75)(5−12)(−3+−75)

In the following exercises, multiply using the Product of Binomial Squares Pattern.

573.

(−23i)2(−23i)2

In the following exercises, multiply using the Product of Complex Conjugates Pattern.

574.

(92i)(9+2i)(92i)(9+2i)

Divide Complex Numbers

In the following exercises, divide.

575.

2+i34i2+i34i

576.

−432i−432i

Simplify Powers of i

In the following exercises, simplify.

577.

i48i48

578.

i255i255

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