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Chapter P
Practice Test
It is suggested that you complete this practice test prior to the review day. You will
maximize the benefits if you complete your homework first, work out each question (showing
the details) on your own paper without the use of notes and attempt to rework questions you
missed. Discuss solutions with your classmates and ask me questions! Your exam will not
be multiple choice so you must be able to show your work.
Evaluate the algebraic expression for the given value or values of the variable(s).
1) -9x + 5;
x = -1
A) 14
B) -4
C) 4
D) -14
C) 876
D) 120
Objective: (0.1) Evaluate Algebraic Expressions
2) 3x2 + 9y;
x = 8 and y = 4
A) 228
B) 612
Objective: (0.1) Evaluate Algebraic Expressions
List all numbers from the given set B that are members of the given Real Number subset.
3) B = {5,
5, -5, 0, 0.4,
4} Integers
A) 5, -5, 0
B) 5, 0
C) 5, 0,
4
B) 1, 0,
16
D) 5, -5, 0,
Objective: (0.1) Recognize Subsets of the Real Numbers
4) B = {1,
7, -8, 0,
A) 1, -8, 0,
C)
7,
4
,
5
4
,
5
16, 0.6, 0.42} Rational numbers
16, 0.42, 0.6
16
D)
7,
4
, 0.42
5
Objective: (0.1) Recognize Subsets of the Real Numbers
Rewrite the expression without absolute value bars.
5)
2 - 10
A)
2 - 10
B) -8
C) 10 -
2
D) 8
Objective: (0.1) Evaluate Absolute Value
Evaluate the expression for the given values of x and y.
|x| |y|
6)
;
x = 5 and y = -2
+
x
y
A) 2
B) -1
C) 0
Objective: (0.1) Evaluate Absolute Value
1
D) 1
4
Simplify the algebraic expression.
7) (12z + 6) - (5z - 4)
A) 7z + 10
B) 7z + 2
C) 7z - 10
D) 17z + 10
C) x2
D) 2x2
C) -14x12
D) -14x8
C) x4
D) x10
C) x6 y4
D) xy5
C) -1
D) 1
C) -81
D)
Objective: (0.1) Simplify Algebraic Expressions
Simplify the exponential expression.
8) x · x2
A) x3
B) 2x3
Objective: (0.2) Use the Product Rule
9) (7x6 )(-2x2)
A) 14x12
B) 14x8
Objective: (0.2) Use the Product Rule
10)
x9
x5
A) x14
B)
1
x4
Objective: (0.2) Use the Quotient Rule
11)
x12y11
x5y6
A) x6y5
B) x7 y5
Objective: (0.2) Use the Quotient Rule
12) 9 0
A) 0
B) 9
Objective: (0.2) Use the Zero-Exponent Rule
13) 3 -4
A)
1
81
B) 81
1
12
Objective: (0.2) Use the Negative-Exponent Rule
14) x-6 · x3
A) x3
B) -x3
C)
1
x3
D) -
C)
6x7
y9
D)
1
x3
Objective: (0.2) Use the Negative-Exponent Rule
15) 6x-7 y9
A)
6
7
x y9
B)
y9
6x7
Objective: (0.2) Use the Negative-Exponent Rule
2
6y9
x7
16)
x-2
y-8
A)
1
x2 y8
B) x2 y8
C)
x2
y8
D)
y8
x2
Objective: (0.2) Use the Negative-Exponent Rule
17) (x8)5
A) x40
B) 5x40
C) 5x8
D) x13
C) -8x4
D) 16x
C) x28y4
D) x11y5
C) 375
D) 128
C) -16
D) 256
C) 814,000
D) 81,400,000
C) 0.000006233
D) 0.00006233
C) 2.8 × 10-4
D) 2.8 × 105
Objective: (0.2) Use the Power Rule
18) (-2x)4
A) 16x4
B) -8x
Objective: (0.2) Find the Power of a Product
19) (x7y) 4
A) x11y
B) x28y
Objective: (0.2) Find the Power of a Product
20) 5 3 · 3
A) 45
B) 3375
Objective: (0.2) Simplify Exponential Expressions
21) -44
A) -256
B) 16
Objective: (0.2) Simplify Exponential Expressions
Write the number in decimal notation without the use of exponents.
22) 8.14 × 106
A) 488.4
B) 8,140,000
Objective: (0.2) Use Scientific Notation
23) 6.233 × 10-6
A) -6,233,000
B) 0.0000006233
Objective: (0.2) Use Scientific Notation
Write the number in scientific notation.
24) 280,000
A) 2.8 × 10-5
B) 2.8 × 104
Objective: (0.2) Use Scientific Notation
3
25) 0.000167
A) 1.67 × 104
B) 1.67 × 10-3
C) 1.67 × 10-4
D) 1.67 × 10-5
Objective: (0.2) Use Scientific Notation
Perform the indicated computation. Write the answer in scientific notation.
8.82 × 108
26)
3 × 10-7
A) 5.88 × 1015
B) 2.94 × 101
C) 2.94 × 1015
D) 5.88 × 101
C) -128
D) Not a real number
C)
D) 13
Objective: (0.2) Use Scientific Notation
Evaluate the expression or indicate that the root is not a real number.
27) - 256
A) 16
B) -16
Objective: (0.3) Evaluate Square Roots
28)
144 + 25
A) 169
B) 17
119
Objective: (0.3) Evaluate Square Roots
Use the product rule to simplify the expression.
29)
175
A) 5 7
B) 35
C) 7 5
D) 13
Objective: (0.3) Use the Product Rule to Simplify Square Roots
30)
6
A) 2 3
B)
6
C) 2
D) 3 2
Objective: (0.3) Use the Product Rule to Simplify Square Roots
Use the quotient rule to simplify the expression.
25
31)
4
A) 2
B)
5
2
C)
5
2
D)
5
2
Objective: (0.3) Use the Quotient Rule to Simplify Square Roots
Add or subtract terms whenever possible.
32) 9 2 - 2 2
A) 11 2
B) -18 4
C) 7 2
D) 7 4
C) 5 2
D) 26 2
Objective: (0.3) Add and Subtract Square Roots
33) -2 2 - 8 18
A) -26 2
B) -10 2
Objective: (0.3) Add and Subtract Square Roots
4
Rationalize the denominator.
1
34)
5
A)
5
5
B)
1+ 5
5
C)
5
D) 1 +
5
Objective: (0.3) Rationalize Denominators
35)
7
8- 2
A)
56 + 7 2
6
B)
56 + 7 2
62
C)
56 - 7 2
62
D)
7
7
8
2
Objective: (0.3) Rationalize Denominators
Evaluate the radical expressions or indicate that the root is not a real number.
5
36) 32
A) 32
B) -2
C) 2
D) not a real number
Objective: (0.3) Evaluate and Perform Operations with Higher Roots
Evaluate the expression without using a calculator.
37) 9 1/2
A) 1.5
B) 3
C) 6
D) 12
C) 256
D) 1024
Objective: (0.3) Understand and Use Rational Exponents
38) 644/3
A) 4096
B) 16,384
Objective: (0.3) Understand and Use Rational Exponents
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form.
39) 5x - 7 + 4x2
B) Yes; 4x2 + 5x - 7
A) No
Objective: (0.4) Understand the Vocabulary of Polynomials
Find the degree of the polynomial.
40) -18x4 - 3x3 + 5x - 5x5 - 5
A) degree 3
B) degree 5
C) degree -18
D) degree 4
Objective: (0.4) Understand the Vocabulary of Polynomials
Perform the indicated operations. Write the resulting polynomial in standard form.
41) (7x5 + 10x2 - 17) - (4x5 - 2x2 + 13)
A) 3x5 + 14x2 - 4
B) 3x5 + 12x2 - 4
C) -15x7
Objective: (0.4) Add and Subtract Polynomials
5
D) 3x5 + 12x2 - 30
Find the product.
42) (9x - 1)(x2 - 2x + 1)
A) 9x3 - 18x2 + 9x + 1
B) 9x3 - 17x2 + 7x - 1
D) 9x3 - 19x2 + 11x - 1
C) 9x3 + 19x2 - 11x + 1
Objective: (0.4) Multiply Polynomials
43) (2x + 1)(2x - 1)
A) 4x2 + 4x - 1
B) 4x2 - 1
C) 4x2 - 4x - 1
D) x2 - 1
Objective: (0.4) Use Special Products in Polynomial Multiplication
44) (5x - 2)2
A) 25x2 - 20x + 4
B) 5x2 - 20x + 4
C) 25x2 + 4
D) 5x2 + 4
Objective: (0.4) Use Special Products in Polynomial Multiplication
45) (x - 3)3
A) x3 - 9x2 + 27x - 27
B) x3 - 9x2 + 9x - 27
C) x3 - 9x2 + 15x - 27
D) x3 - 3x2 + 15x - 27
Objective: (0.4) Use Special Products in Polynomial Multiplication
Perform the indicated operations.
46) (5x4 y2 - 6x2 y2 + 2xy) + (4x4 y2 - 12x2y2 + 11xy)
A) 18x4 y2 - 9x2 y2 + 13xy
C) 9x4 y2 + 18x2 y2 + 13xy
B) -18x4 y2 + 9x2 y2 + 13xy
D) 9x4 y2 - 18x2 y2 + 13xy
Objective: (0.4) Perform Operations with Polynomials in Several Variables
Find the product.
47) (x - 6y)(x + 12y)
A) x2 + 3xy - 72y2
C) x2 + 6xy + 6y2
B) x + 6xy - 72y
D) x2 + 6xy - 72y2
Objective: (0.4) Perform Operations with Polynomials in Several Variables
Factor out the greatest common factor.
48) 14x4 - 4x3 + 8x2
A) 2x(7x3 - 2x2 + 4x)
B) x2 (14x2 - 4x + 8)
C) 2(7x4 - 2x3 + 4x2)
D) 2x2(7x2 - 2x + 4)
Objective: (0.5) Factor Out the Greatest Common Factor of a Polynomial
Factor by grouping. Assume any variable exponents represent whole numbers.
49) 2x3 - 4x2 + 7x - 14
A) (x - 2)(2x2 - 7)
B) (x + 2)(2x2 + 7)
C) (x - 2)(2x + 7)
D) (x - 2)(2x2 + 7)
C) (x - 5)(x + 3)
D) prime
Objective: (0.5) Factor by Grouping
Factor the trinomial, or state that the trinomial is prime.
50) x2 - 2x - 15
A) (x + 5)(x + 3)
B) (x + 5)(x + 1)
Objective: (0.5) Factor Trinomials
6
51) x2 + 10x - 24
A) (x - 12)(x + 1)
B) (x + 12)(x - 2)
C) (x - 12)(x + 2)
D) prime
C) (5x + 9)(5x + 7)
D) prime
C) (x + 7y)(x + y)
D) prime
C) (3x + 2)2
D) prime
Objective: (0.5) Factor Trinomials
52) 5x2 + 44x + 63
A) (5x + 7)(x + 9)
B) (5x + 9)(x + 7)
Objective: (0.5) Factor Trinomials
53) x2 - 12xy + 35y2
A) (x - 7y)(x - 5y)
B) (x + 7y)(x - 5y)
Objective: (0.5) Factor Trinomials
Factor the difference of two squares.
54) 9x2 - 4
A) (3x + 2)(3x - 2)
B) (3x - 2)2
Objective: (0.5) Factor the Difference of Squares
55) x4 - 256
A) (x2 + 16)(x2 + 16)
B) (x2 - 16)(x2 - 16)
C) (x2 + 16)(x + 4)(x - 4)
D) prime
Objective: (0.5) Factor the Difference of Squares
Factor the perfect square trinomial.
56) 81x2 + 18x + 1
A) (x + 9)2
C) (9x + 1)2
B) (9x + 1)(9x - 1)
D) prime
Objective: (0.5) Factor Perfect Square Trinomials
Factor using the formula for the sum or difference of two cubes.
57) x3 + 125
A) (x + 5)(x2 - 5x + 25)
C) (x - 5)(x2 + 5x + 25)
B) (x + 5)(x2 + 25)
D) prime
Objective: (0.5) Factor the Sum and Difference of Two Cubes
58) 27x3 - 125
A) (3x + 5)(9x2 - 15x + 25)
C) (3x - 5)(9x2 - 15x + 25)
B) (3x - 5)(9x2 + 15x + 25)
D) (3x - 5)(9x2 + 25)
Objective: (0.5) Factor the Sum and Difference of Two Cubes
Factor completely, or state that the polynomial is prime.
59) 3x3 - 108x
A) x(x + 6)(3x - 18)
B) 3(x + 6)(x2 - 6x)
C) 3x(x + 6)(x - 6)
Objective: (0.5) Use a General Strategy for Factoring Polynomials
7
D) prime
60) 3x2 + 9x - 84
A) (x - 4)(3x + 21)
B) (3x - 12)(x + 7)
C) 3(x - 4)(x + 7)
D) 3(x2 + 3x - 28)
Objective: (0.5) Use a General Strategy for Factoring Polynomials
61) x3 - 2x2 - 16x + 32
A) (x - 2)(x + 4)(x - 4)
B) (x - 2)(x - 4)2
C) (x + 2)(x + 4)(x - 4)
D) prime
Objective: (0.5) Use a General Strategy for Factoring Polynomials
62) x2 + 49
A) (x + 7)(x - 7)
B) (x + 7)2
C) (x - 7)2
D) prime
Objective: (0.5) Use a General Strategy for Factoring Polynomials
Factor and simplify the algebraic expression.
63) x7/8 - x1/8
A) x(x 3/4 - 1)
B) x7/8 (1 - x 3/4 )
C) x1/8 (x3/4 - 1)
D) x1/8(x7 - 1)
Objective: (0.5) Factor Algebraic Expressions Containing Fractional and Negative Exponents
64) (x + 8)2/5 - (x + 8)12/5
A) (x + 8)(- x2 - 16x + 63)
B) (x + 8)2/5 (- x2 - 16x - 63)
D) (x + 8)((x + 8)2/5 - (x + 8)12/5)
C) (x + 8)12/5 ((x + 8)1/6 - 1)
Objective: (0.5) Factor Algebraic Expressions Containing Fractional and Negative Exponents
Find all numbers that must be excluded from the domain of the rational expression.
x-5
65)
x2 + 7x + 10
A) x ≠ -5, x ≠ -2
B) x ≠ 5, x ≠ 2
C) x ≠ 0
D) x ≠ 5
Objective: (0.6) Specify Numbers That Must Be Excluded from the Domain of a Rational Expression
Multiply or divide as indicated.
2x
6x + 3
66)
·
4x + 2
2
A)
3x
4
B)
3
2
C)
3x
2
D)
x
2
C)
x-7
x+8
D)
x-8
x+7
Objective: (0.6) Multiply Rational Expressions
67)
x2 - 15x + 56
x2 - 49
·
2
2
x + x - 56
x - x - 56
A)
x+7
x+8
B)
x+7
x-8
Objective: (0.6) Multiply Rational Expressions
8
68)
(y - 12)2 3y - 36
÷
3
9
A) y - 12
B)
1
y - 12
C)
3(y - 12)2
3y - 36
D)
(y - 12)3
9
C)
1
x+9
D)
1
2
x + 11x + 18
C)
6x - 10
x(x - 5)
D)
10x - 6
x(5 - x)
Objective: (0.6) Divide Rational Expressions
Add or subtract as indicated.
7x - 7
9 - 6x
69)
+
2
2
x + 11x + 18 x + 11x + 18
A)
1
x+2
B)
x-2
2
x + 11x + 18
Objective: (0.6) Add and Subtract Rational Expressions
70)
2
4
+
x x-5
A)
6x - 10
x(5 - x)
B)
10x - 6
x(x - 5)
Objective: (0.6) Add and Subtract Rational Expressions
71)
7
13
+
x-8 8-x
A)
20
x-8
B)
6
x-8
C) -
6
x-8
D) -
20
x-8
Objective: (0.6) Add and Subtract Rational Expressions
72)
x
x2 - 16
A)
-
5
x2 + 5x + 4
x2 + 4x + 20
(x - 4)(x + 4)(x + 1)
B)
x2 - 4
(x - 4)(x + 4)(x + 1)
C)
x2 - 4x + 20
(x - 4)(x + 4)
D)
x2 - 4x + 20
(x - 4)(x + 4)(x + 1)
D)
2
x-2
Objective: (0.6) Add and Subtract Rational Expressions
Simplify the complex rational expression.
x
-1
2
73)
x-2
A)
1
2
B) -2
C) x - 2
Objective: (0.6) Simplify Complex Rational Expressions
9
4+
74)
2
x
x 1
+
3 6
A)
12
x
B)
x
12
C) 1
D) 12
C) x - 2
D)
Objective: (0.6) Simplify Complex Rational Expressions
75)
1
x+2
3
2
x -4
A)
x-2
3
B)
3
x-2
Objective: (0.6) Simplify Complex Rational Expressions
10
x+2
3
Answer Key
Testname: PRACTICE TEST P
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A
A
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A
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D
A
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Answer Key
Testname: PRACTICE TEST P
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B
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A
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D
A
A
A
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