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College Algebra

Review Exercises

College AlgebraReview Exercises
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  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Key Terms
    9. Key Equations
    10. Key Concepts
    11. Review Exercises
    12. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Key Terms
    6. Key Concepts
    7. Review Exercises
    8. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  8. 7 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 7.1 Systems of Linear Equations: Two Variables
    3. 7.2 Systems of Linear Equations: Three Variables
    4. 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 7.4 Partial Fractions
    6. 7.5 Matrices and Matrix Operations
    7. 7.6 Solving Systems with Gaussian Elimination
    8. 7.7 Solving Systems with Inverses
    9. 7.8 Solving Systems with Cramer's Rule
    10. Key Terms
    11. Key Equations
    12. Key Concepts
    13. Review Exercises
    14. Practice Test
  9. 8 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 8.1 The Ellipse
    3. 8.2 The Hyperbola
    4. 8.3 The Parabola
    5. 8.4 Rotation of Axes
    6. 8.5 Conic Sections in Polar Coordinates
    7. Key Terms
    8. Key Equations
    9. Key Concepts
    10. Review Exercises
    11. Practice Test
  10. 9 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 9.1 Sequences and Their Notations
    3. 9.2 Arithmetic Sequences
    4. 9.3 Geometric Sequences
    5. 9.4 Series and Their Notations
    6. 9.5 Counting Principles
    7. 9.6 Binomial Theorem
    8. 9.7 Probability
    9. Key Terms
    10. Key Equations
    11. Key Concepts
    12. Review Exercises
    13. Practice Test
  11. 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
  12. Index

Real Numbers: Algebra Essentials

For the following exercises, perform the given operations.

1.

( 532 ) 2 6 ( 532 ) 2 6

2.

64÷( 28 )+14÷7 64÷( 28 )+14÷7

3.

2 5 2 +6÷2 2 5 2 +6÷2

For the following exercises, solve the equation.

4.

5x+9=−11 5x+9=−11

5.

2y+ 4 2 =64 2y+ 4 2 =64

For the following exercises, simplify the expression.

6.

9( y+2 )÷32+1 9( y+2 )÷32+1

7.

3m( 4+7 )m 3m( 4+7 )m

For the following exercises, identify the number as rational, irrational, whole, or natural. Choose the most descriptive answer.

8.

11

9.

0

10.

5 6 5 6

11.

11 11

Exponents and Scientific Notation

For the following exercises, simplify the expression.

12.

2 2 2 4 2 2 2 4

13.

4 5 4 3 4 5 4 3

14.

( a 2 b 3 ) 4 ( a 2 b 3 ) 4

15.

6 a 2 a 0 2 a −4 6 a 2 a 0 2 a −4

16.

( xy ) 4 y 3 2 x 5 ( xy ) 4 y 3 2 x 5

17.

4 −2 x 3 y −3 2 x 0 4 −2 x 3 y −3 2 x 0

18.

( 2 x 2 y ) −2 ( 2 x 2 y ) −2

19.

( 16 a 3 b 2 ) ( 4a b −1 ) −2 ( 16 a 3 b 2 ) ( 4a b −1 ) −2

20.

Write the number in standard notation: 2.1314× 10 −6 2.1314× 10 −6

21.

Write the number in scientific notation: 16,340,000

Radicals and Rational Expressions

For the following exercises, find the principal square root.

22.

121 121

23.

196 196

24.

361 361

25.

75 75

26.

162 162

27.

32 25 32 25

28.

80 81 80 81

29.

49 1250 49 1250

30.

2 4+ 2 2 4+ 2

31.

4 3 +6 3 4 3 +6 3

32.

12 5 13 5 12 5 13 5

33.

−243 5 −243 5

34.

250 3 −8 3 250 3 −8 3

Polynomials

For the following exercises, perform the given operations and simplify.

35.

(3 x 3 +2x1)+(4 x 2 2x+7) (3 x 3 +2x1)+(4 x 2 2x+7)

36.

( 2y+1 )( 2 y 2 2y5 ) ( 2y+1 )( 2 y 2 2y5 )

37.

(2 x 2 +3x6)+(3 x 2 4x+9) (2 x 2 +3x6)+(3 x 2 4x+9)

38.

( 6 a 2 +3a+10 )( 6 a 2 −3a+5 ) ( 6 a 2 +3a+10 )( 6 a 2 −3a+5 )

39.

(k+3)(k6) (k+3)(k6)

40.

(2h+1)(3h2) (2h+1)(3h2)

41.

( x+1 )( x 2 +1 ) ( x+1 )( x 2 +1 )

42.

(m2)( m 2 +2m3) (m2)( m 2 +2m3)

43.

( a+2b )( 3ab ) ( a+2b )( 3ab )

44.

( x+y )( xy ) ( x+y )( xy )

Factoring Polynomials

For the following exercises, find the greatest common factor.

45.

81p+9pq27 p 2 q 2 81p+9pq27 p 2 q 2

46.

12 x 2 y+4x y 2 −18xy 12 x 2 y+4x y 2 −18xy

47.

88 a 3 b+4 a 2 b144 a 2 88 a 3 b+4 a 2 b144 a 2

For the following exercises, factor the polynomial.

48.

2 x 2 9x18 2 x 2 9x18

49.

8 a 2 +30a27 8 a 2 +30a27

50.

d 2 5d66 d 2 5d66

51.

x 2 +10x+25 x 2 +10x+25

52.

y 2 6y+9 y 2 6y+9

53.

4 h 2 12hk+9 k 2 4 h 2 12hk+9 k 2

54.

361 x 2 121 361 x 2 121

55.

p 3 +216 p 3 +216

56.

8 x 3 125 8 x 3 125

57.

64 q 3 27 p 3 64 q 3 27 p 3

58.

4x (x1) 1 4 +3 (x1) 3 4 4x (x1) 1 4 +3 (x1) 3 4

59.

3p ( p+3 ) 1 3 −8 ( p+3 ) 4 3 3p ( p+3 ) 1 3 −8 ( p+3 ) 4 3

60.

4r ( 2r1 ) 2 3 5 ( 2r1 ) 1 3 4r ( 2r1 ) 2 3 5 ( 2r1 ) 1 3

Rational Expressions

For the following exercises, simplify the expression.

61.

x 2 x12 x 2 8x+16 x 2 x12 x 2 8x+16

62.

4 y 2 25 4 y 2 20y+25 4 y 2 25 4 y 2 20y+25

63.

2 a 2 a3 2 a 2 6a8 5 a 2 19a4 10 a 2 13a3 2 a 2 a3 2 a 2 6a8 5 a 2 19a4 10 a 2 13a3

64.

d4 d 2 9 d3 d 2 16 d4 d 2 9 d3 d 2 16

65.

m 2 +5m+6 2 m 2 5m3 ÷ 2 m 2 +3m9 4 m 2 4m3 m 2 +5m+6 2 m 2 5m3 ÷ 2 m 2 +3m9 4 m 2 4m3

66.

4 d 2 7d2 6 d 2 17d+10 ÷ 8 d 2 +6d+1 6 d 2 +7d10 4 d 2 7d2 6 d 2 17d+10 ÷ 8 d 2 +6d+1 6 d 2 +7d10

67.

10 x + 6 y 10 x + 6 y

68.

12 a 2 +2a+1 3 a 2 −1 12 a 2 +2a+1 3 a 2 −1

69.

1 d + 2 c 6c+12d dc 1 d + 2 c 6c+12d dc

70.

3 x 7 y 2 x 3 x 7 y 2 x

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