Answer Key - Master High-Frequency Concepts and Skills for Algebra Proficiency—FAST - Easy Algebra Step-by-Step

Easy Algebra Step-by-Step: Master High-Frequency Concepts and Skills for Algebra Proficiency—FAST! (2012)

Answer Key

Chapter 1 Numbers of Algebra
Exercise 1

1. 10 is a natural number, a whole number, an integer, a rational number, and a real number.

2. Image is a rational number and a real number.

3. Image is a rational number and a real number.

4. –π is an irrational number and a real number.

5. –1000 is an integer, a rational number, and a real number.

6. Image is an irrational number and a real number.

7. Image is an irrational number and a real number.

8. Image is a rational number and a real number.

9. 1 is a natural number, a whole number, an integer, a rational number, and a real number.

10. Image = 0.1 is a rational number and a real number.

11. Closure property of multiplication

12. Commutative property of addition

13. Multiplicative inverse property

14. Closure property of addition

15. Associative property of addition

16. Distributive property

17. Additive inverse property

18. Zero factor property

19. Associative property of multiplication

20. Multiplicative identity property

Chapter 2 Computation with Real Numbers
Exercise 2

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3. Image

4. “Negative nine plus the opposite of negative four equals negative nine plus four”

5. “Negative nine minus negative four equals negative nine plus four”

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8. Image

9. Image

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11. Image

12. Image

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14. Image

15. Image

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17. Image

18. Image

19. Image

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Chapter 3 Roots and Radicals
Exercise 3

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2. Image

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5. Image

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7. Image

8. Image

9. Image

10. Image

11. Image

12. Image

13. Image

14. Image

15. Image

16. Image

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18. Image

19. Image

20. Image

Chapter 4 Exponentiation
Exercise 4

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5. Image

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9. Image

10. Image

11. Image

12. Image

13. Image

14. Image

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16. Image

17. Image

18. Image

19. Image

20. Image

Chapter 5 Order of Operations
Exercise 5

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5. Image

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Chapter 6 Algebraic Expressions
Exercise 6

1. Name the variable(s) and constant(s) in the expression 2π r, where r is the measure of the radius of a circle. Answer: The letter r stands for the measure of the radius of a circle and can be any real nonzero number, so r is a variable. The numbers 2 and π have fixed, definite values, so they are constants.

2. –12 is the numerical coefficient

3. 1 is the numerical coefficient

4. Image is the numerical coefficient

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11. Image

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13. Image

14. Image

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16. Image

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Chapter 7 Rules for Exponents
Exercise 7

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3. Image

4. Image

5. Image

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10. Image

11. Image

12. (2x + 1)2 is a power of a sum. It cannot be simplified using only rules for exponents.

13. (3x – 5)3 is a power of a difference. It cannot be simplified using only rules for exponents.

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15. Image

Chapter 8 Adding and Subtracting Polynomials
Exercise 8

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Chapter 9 Multiplying Polynomials
Exercise 9

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Chapter 10 Simplifying Polynomial Expressions
Exercise 10

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Chapter 11 Dividing Polynomials
Exercise 11

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The quotient is Image and the remainder is 0.

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The quotient is Image and the remainder is 0.

3. Image

The quotient is Image and the remainder is 0.

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The quotient is Image and the remainder is 0.

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The quotient is Image and the remainder is 0.

6. Image

The quotient is –6 and the remainder is 5.

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The quotient is Image and the remainder is 0.

8. Image

The quotient is x – 1 and the remainder is 0.

9. Image

The quotient is x–5 and the remainder is 0.

10. Image

The quotient is Image and the remainder is 98.

Chapter 12 Factoring Polynomials
Exercise 12

1. False

2. False

3. False

4. False

5. False

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Chapter 13 Rational Expressions
Exercise 13

1. Image

2. Image

3. Image

4. Image is simplified.

5. Image

6. Image

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8. Image

9.

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10. Image

11. Image

12. Image

13. Image

14.

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15. Image

Chapter 14 Solving Linear Equations and Inequalities
Exercise 14

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2. Image

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4. Image

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Chapter 15 Solving Quadratic Equations
Exercise 15

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There is no real solution because the discriminant is negative.

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Chapter 16 The Cartesian Coordinate Plane
Exercise 16

1. True

2. False

3. True

4. False

5. True

6. False

7. rise

8. run

9. negative

10. positive

11. zero

12. Image

13. Image

14. undefined

15. Image

The point K is 6 units to the left of the y-axis and 5 units below the x-axis, so (–6, –5) is the ordered pair corresponding to point K.

16. Image

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17. Image

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18. Image

19. Image

20. Image

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Chapter 17 Graphing Linear Equations

Exercise 17

1. Image

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6. Image

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Chapter 18 The Equation of a Line

Exercise 18

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3. Image

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7. Image

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10. Image

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Chapter 19 Basic Function Concepts
Exercise 19

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Only f, h, and t are functions. Note that in t, (8, 9) and (8, 9) are the same point.

2. The domain is {4, 6, 7, 8} and the range is {5, 7, 9}.

Image The domain is the set of all real numbers.

b. Image

Image

Image · The domain is the set of all real numbers greater than or equal to

c. Image The domain is the set of all real numbers except 5.

d. Image

Set Image and solve.

x = ±2 The domain is the set of all real numbers except 2 and –2.

4. a. Image

b. Image

c. Image

d. Image There is no real number solution because the square root of a negative number is not a real number.

5. Only graphs b and c are functions.

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Chapter 20 Systems of Equations
Exercise 20

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