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. is a rational number and a real number.
3. 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. is an irrational number and a real number.
7. is an irrational number and a real number.
8. 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. = 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
3.
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”
8.
9.
11.
12.
14.
15.
17.
18.
19.
Chapter 3 Roots and Radicals
Exercise 3
2.
5.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
18.
19.
20.
Chapter 4 Exponentiation
Exercise 4
5.
9.
10.
11.
12.
13.
14.
16.
17.
18.
19.
20.
Chapter 5 Order of Operations
Exercise 5
5.
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. is the numerical coefficient
11.
13.
14.
16.
Chapter 7 Rules for Exponents
Exercise 7
3.
4.
5.
10.
11.
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.
15.
Chapter 8 Adding and Subtracting Polynomials
Exercise 8
Chapter 9 Multiplying Polynomials
Exercise 9
Chapter 10 Simplifying Polynomial Expressions
Exercise 10
Chapter 11 Dividing Polynomials
Exercise 11
The quotient is and the remainder is 0.
The quotient is and the remainder is 0.
3.
The quotient is and the remainder is 0.
The quotient is and the remainder is 0.
The quotient is and the remainder is 0.
6.
The quotient is –6 and the remainder is 5.
The quotient is and the remainder is 0.
8.
The quotient is x – 1 and the remainder is 0.
9.
The quotient is x–5 and the remainder is 0.
10.
The quotient is and the remainder is 98.
Chapter 12 Factoring Polynomials
Exercise 12
1. False
2. False
3. False
4. False
5. False
Chapter 13 Rational Expressions
Exercise 13
1.
2.
3.
4. is simplified.
5.
6.
8.
9.
10.
11.
12.
13.
14.
15.
Chapter 14 Solving Linear Equations and Inequalities
Exercise 14
2.
4.
Chapter 15 Solving Quadratic Equations
Exercise 15
There is no real solution because the discriminant is negative.
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.
13.
14. undefined
15.
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.
17.
18.
19.
20.
Chapter 17 Graphing Linear Equations
Exercise 17
1.
6.
Chapter 18 The Equation of a Line
Exercise 18
3.
7.
10.
Chapter 19 Basic Function Concepts
Exercise 19
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}.
The domain is the set of all real numbers.
b.
· The domain is the set of all real numbers greater than or equal to
c. The domain is the set of all real numbers except 5.
d.
Set and solve.
x = ±2 The domain is the set of all real numbers except 2 and –2.
4. a.
b.
c.
d. 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.
Chapter 20 Systems of Equations
Exercise 20