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Intermediate Algebra

Review Exercises

Intermediate AlgebraReview 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

Use the Language of Algebra

Identify Multiples and Factors

385.

Use the divisibility tests to determine whether 180 is divisible by 2, by 3, by 5, by 6, and by 10.

386.

Find the prime factorization of 252.

387.

Find the least common multiple of 24 and 40.

In the following exercises, simplify each expression.

388.

24÷3+4(52)24÷3+4(52)

389.

7+3[64(54)]327+3[64(54)]32

Evaluate an Expression

In the following exercises, evaluate the following expressions.

390.

When x=4,x=4, x3x3 5x5x 2x25x+32x25x+3

391.

2x24xy3y22x24xy3y2 when x=3,x=3, y=1y=1

Simplify Expressions by Combining Like Terms

In the following exercises, simplify the following expressions by combining like terms.

392.

12y+7+2y512y+7+2y5

393.

14x29x+118x2+8x614x29x+118x2+8x6

Translate an English Phrase to an Algebraic Expression

In the following exercises, translate the phrases into algebraic expressions.

394.


the sum of 4ab24ab2 and 7a3b27a3b2
the product of 6y26y2 and 3y3y
twelve more than 5x5x
5y5y less than 8y28y2

395.


eleven times the difference of yy and two
the difference of eleven times yy and two

396.

Dushko has nickels and pennies in his pocket. The number of pennies is four less than five the number of nickels. Let nn represent the number of nickels. Write an expression for the number of pennies.

Integers

Simplify Expressions with Absolute Value

In the following exercise, fill in <,>,<,>, or == for each of the following pairs of numbers.

397.


|7|___|−7||7|___|−7|
−8___|−8|−8___|−8|
|−13|___13|−13|___13
|−12|___(−12)|−12|___(−12)

In the following exercises, simplify.

398.

9|3(48)|9|3(48)|

399.

123|14(42)|123|14(42)|

Add and Subtract Integers

In the following exercises, simplify each expression.

400.

−12+(−8)+7−12+(−8)+7

401.


157157
−15(−7)−15(−7)
−157−157
15(−7)15(−7)

402.

−11(−12)+5−11(−12)+5

403.

23(−17)23(−17) 23+1723+17

404.

(711)(35)(711)(35)

Multiply and Divide Integers

In the following exercise, multiply or divide.

405.

−27÷9−27÷9 120÷(−8)120÷(−8) 4(−14)4(−14) −1(−17)−1(−17)

Simplify and Evaluate Expressions with Integers

In the following exercises, simplify each expression.

406.

(−7)3(−7)3 7373

407.

(711)(613)(711)(613)

408.

63÷(−9)+(−36)÷(−4)63÷(−9)+(−36)÷(−4)

409.

63|4(12)(75)|63|4(12)(75)|

410.

(−2)424÷(135)(−2)424÷(135)

For the following exercises, evaluate each expression.

411.

(y+z)2(y+z)2 when
y=−4,z=7y=−4,z=7

412.

3x22xy+4y23x22xy+4y2 when
x=−2,y=−3x=−2,y=−3

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

413.

the sum of −4−4 and −9,−9, increased by 23

414.

the difference of 17 and −8−8 subtract 17 from −25−25

Use Integers in Applications

In the following exercise, solve.

415.

Temperature On July 10, the high temperature in Phoenix, Arizona, was 109°, and the high temperature in Juneau, Alaska, was 63°. What was the difference between the temperature in Phoenix and the temperature in Juneau?

Fractions

Simplify Fractions

In the following exercises, simplify.

416.

204228204228

417.

270x3198y2270x3198y2

Multiply and Divide Fractions

In the following exercises, perform the indicated operation.

418.

(1415)(1021)(1415)(1021)

419.

6x25÷9y206x25÷9y20

420.

4982149821

Add and Subtract Fractions

In the following exercises, perform the indicated operation.

421.

518+712518+712

422.

1136154811361548

423.

58+3458+34 58÷3458÷34

424.

3y10563y1056 3y10·563y10·56

Use the Order of Operations to Simplify Fractions

In the following exercises, simplify.

425.

4·32·5−6·3+2·34·32·5−6·3+2·3

426.

4(73)2(49)−3(4+2)+7(36)4(73)2(49)−3(4+2)+7(36)

427.

4342(45)24342(45)2

Evaluate Variable Expressions with Fractions

In the following exercises, evaluate.

428.

4x2y24x2y2 when
x=23x=23 and y=34y=34

429.

a+baba+bab when
a=−4,a=−4, b=6b=6

Decimals

Round Decimals

430.

Round 6.7386.738 to the nearest hundredth tenth whole number.

Add and Subtract Decimals

In the following exercises, perform the indicated operation.

431.

−23.67+29.84−23.67+29.84

432.

54.310054.3100

433.

79.38(−17.598)79.38(−17.598)

Multiply and Divide Decimals

In the following exercises, perform the indicated operation.

434.

(−2.8)(3.97)(−2.8)(3.97)

435.

(−8.43)(−57.91)(−8.43)(−57.91)

436.

(53.48)(10)(53.48)(10)

437.

(0.563)(100)(0.563)(100)

438.

$118.35÷2.6$118.35÷2.6

439.

1.84÷(−0.8)1.84÷(−0.8)

Convert Decimals, Fractions and Percents

In the following exercises, write each decimal as a fraction.

440.

13201320

441.

2402524025

In the following exercises, convert each fraction to a decimal.

442.

5858

443.

14111411

In the following exercises, convert each decimal to a percent.

444.

2.432.43

445.

0.04750.0475

Simplify Expressions with Square Roots

In the following exercises, simplify.

446.

289289

447.

−121−121

Identify Integers, Rational Numbers, Irrational Numbers, and Real Numbers

In the following exercise, list the whole numbers integers rational numbers irrational numbers real numbers for each set of numbers

448.

−8,0,1.95286...,125,36,9−8,0,1.95286...,125,36,9

Locate Fractions and Decimals on the Number Line

In the following exercises, locate the numbers on a number line.

449.

34,34,113,−123,72,5234,34,113,−123,72,52

450.

3.23.2 −1.35−1.35

Properties of Real Numbers

Use the Commutative and Associative Properties

In the following exercises, simplify.

451.

58x+512y+18x+712y58x+512y+18x+712y

452.

−32·9·58−32·9·58

453.

(1115+38)+58(1115+38)+58

Use the Properties of Identity, Inverse and Zero

In the following exercises, simplify.

454.

47+815+(47)47+815+(47)

455.

1315·917·15131315·917·1513

456.

0x3,x30x3,x3

457.

5x70,5x705x70,5x70

Simplify Expressions Using the Distributive Property

In the following exercises, simplify using the Distributive Property.

458.

8(a4)8(a4)

459.

12(23b+56)12(23b+56)

460.

18·56(2x5)18·56(2x5)

461.

(x5)p(x5)p

462.

−4(y3)−4(y3)

463.

126(x+3)126(x+3)

464.

6(3x4)(−5)6(3x4)(−5)

465.

5(2y+3)(4y1)5(2y+3)(4y1)

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