Chapter 0 Review of Prerequisites 0.1 Sets and the Real Number Line 0 Concept Connections
Provide the missing information. 1) A is a collection of items called elements. Answer: set Type: SA Var: 1 Objective: Concept Connections
2) W = {0, 1, 2, 3, ...} is called the set of
numbers.
Answer: whole Type: SA Var: 1 Objective: Concept Connections
3) N = {1, 2, 3, ...} is called the set of
numbers.
Answer: natural Type: SA Var: 1 Objective: Concept Connections
4) Z = {... , -3, -2, -1, 0, 1, 2, 3, ...} is called the set of
.
Answer: integers Type: SA Var: 1 Objective: Concept Connections
5) A set can be defined using
-
notation by using a description of the set.
Answer: set, builder Type: SA Var: 1 Objective: Concept Connections
6) Listing elements in a set within set braces is called the
method to define a set.
Answer: roster Type: SA Var: 1 Objective: Concept Connections
7) Real numbers that can be expressed as a ratio of two integers are called
numbers.
Answer: rational Type: SA Var: 1 Objective: Concept Connections
8) An
number is a real number that cannot be expressed as a ratio of two integers.
Answer: irrational Type: SA Var: 1 Objective: Concept Connections
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9) The statement x < y means that x lies to the
of y on the number line.
Answer: left Type: SA Var: 1 Objective: Concept Connections
10) The
of x is denoted by x .
Answer: absolute, value Type: SA Var: 1 Objective: Concept Connections
11) Write an absolute value expression to represent the distance between a and b on the number line: . Answer: a - b or b - a Type: SA Var: 1 Objective: Concept Connections
12) Given the expression bn, the value of b is called the
and n is called the
Answer: base, exponent or power Type: SA Var: 1 Objective: Concept Connections
13) The symbol x represents the principal
root of x.
Answer: square Type: SA Var: 1 Objective: Concept Connections
14) The expression
0
equals
, whereas
5
5
is
.
0
Answer: 0, undefined Type: SA Var: 1 Objective: Concept Connections 1 Identify Subsets of the Set of Real Numbers
Determine whether the statement is true or false. 1) 3 N A) True Answer: A
B) False
Type: BI Var: 10 Objective: Identify Subsets of the Set of Real Numbers
2) 7.5 ∉ Z A) True Answer: A Type: BI Var: 50+ Objective: Identify Subsets of the Set of Real Numbers
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B) False
.
3) 6 ∈ N A) False
B) True
Answer: B Type: BI Var: 20 Objective: Identify Subsets of the Set of Real Numbers
4) 0.15 ∈ Z A) False
B) True
Answer: A Type: BI Var: 36 Objective: Identify Subsets of the Set of Real Numbers 2 Use Inequality Symbols and Interval Notation
Write the statement as an inequality. 1) u is at least 10. A) u < 10 B) u ≤ 10
C) u > 10
D) u ≥ 10
C) t + 4 ≥ 31
D) t + 4 > 31
Answer: D Type: BI Var: 10 Objective: Use Inequality Symbols and Interval Notation
2) The quantity (t + 4) exceeds 31. A) t + 4 ≤ 31 B) t + 4 < 31 Answer: D Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation
Determine whether the statement is true or false. 3) 13 < - 13 A) True
B) False
Answer: B Type: BI Var: 18 Objective: Use Inequality Symbols and Interval Notation
4) -3.51 > -3.51 A) False
B) True
Answer: A Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation
Express the set in interval notation. 5) A) [-3, ∞]
-3 B) [-3, ∞)
Answer: D Type: BI Var: 40 Objective: Use Inequality Symbols and Interval Notation
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C) (-∞, -3)
D) (-3, ∞)
6) 9 B) (-∞, 9]
A) [-∞, 9]
C) (-∞, 9)
D) (9, ∞)
C) (-∞, -9)
D) [-9, -7]
C) (6, 7]
D) (-∞, 6)
C) [3, 9)
D) (-∞, 3)
Answer: B Type: BI Var: 40 Objective: Use Inequality Symbols and Interval Notation
7) -9 A) (-9, ∞)
-7 B) (-9,-7]
Answer: D Type: BI Var: 36 Objective: Use Inequality Symbols and Interval Notation
8) 6 A) [6, 7]
7 B) [6, 7)
Answer: B Type: BI Var: 36 Objective: Use Inequality Symbols and Interval Notation
9) 3 A) [3,9]
9 B) (3, 9]
Answer: B Type: BI Var: 36 Objective: Use Inequality Symbols and Interval Notation
Graph the set and express it in interval notation. 10) {x | x > 5} Answer: (5, ∞) Type: SA Var: 1 Objective: Use Inequality Symbols and Interval Notation
11) {x | x < –1} Answer: (–∞, –1] Type: SA Var: 1 Objective: Use Inequality Symbols and Interval Notation
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Write the subset of real numbers in set-builder notation. 12) (-4, 4] A) {x -4 < x ≤ 4} B) {x -4 ≤ x < 4}
C) {x -4 ≤ x ≤ 4}
D) {x -4 < x < 4}
Answer: A Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation
For the following exercise, interval notation is given for several sets of real numbers. Graph the set and write the corresponding set-builder notation. 13) (-∞, 1.1 A)
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
x | x < 1.1 B)
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
x | x > 1.1 C)
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
x | x ≤ 1.1 D)
-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
x | x ≥ 1.1 Answer: C Type: BI Var: 50+ Objective: Use Inequality Symbols and Interval Notation
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3 Find the Union and Intersection of Sets
List the elements of . 1) A = {-29, 14, 13, -20, 11, -2} and B = {-27, -10, 13, 11} A) {13} B) { } C) {13, 11} D) {-29, 14, 13, -20, 11, -2, -27, -10} Answer: C Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets
Determine the intersection X ∩ Y. Express the answer in interval notation. 2) X = {x x ≥ 18} and Y = {x x < 11} A) (-∞, 11] ∪ (18, ∞) B) [11, 18) C) (11, 18] D) { } Answer: D Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets
Determine the union X ∪ Y. Express the answer in interval notation. 3) X = {x x > 14} and Y = {x x ≤ 11} A) (11, 14] B) [11, 14) C) (-∞, 11] ∪ (14,∞) D) { } Answer: C Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets
4) X = {x x > -9} and Y = {x x ≤ 16} A) All real numbers C) (16, -9]
B) { } D) (-∞, 16] ∪ (-9,∞)
Answer: A Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets
Determine the intersection X ∩ Y. Express the answer in interval notation. 5) X = {x x ≥ -2} and Y = {x x < -6} A) { } B) [-6, -2) C) (-∞, -6] ∪ (-2, ∞) D) (-6, -2] Answer: A Type: BI Var: 50+ Objective: Find the Union and Intersection of Sets
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4 Evaluate Absolute Value Expressions
Simplify by writing the expression without absolute value bars. 1) 1 A) 1 B) -1 Answer: A Type: BI Var: 20 Objective: Evaluate Absolute Value Expressions
2) w - 2 for w < 2 A) w - 2
B) -w + 2
C) -w - 2
D) w + 2
C) x - 7
D) x + 7
C) -1
D) -15
Answer: B Type: BI Var: 20 Objective: Evaluate Absolute Value Expressions
3) x + 7 for x ≥ -7 A) - x +7
B) - x - 7
Answer: D Type: BI Var: 17 Objective: Evaluate Absolute Value Expressions
15 - z 4)
15 - z
for z < 15
A) 15
B) 1
Answer: B Type: BI Var: 18 Objective: Evaluate Absolute Value Expressions 5 Use Absolute Value to Represent Distance
Write an absolute value expression to represent the distance between the two points on the number line and simplify. 1) -3 and 2 A) -3 - 2 ; 5 B) -3 + 2 ; 1 C) -3 - 2 ; -5 D) -3 - 2 ; -1 Answer: A Type: BI Var: 50+ Objective: Use Absolute Value to Represent Distance 6 Apply the Order of Operations
Evaluate the expression. 1) (-11)2 A) -9
B) -121
Answer: D Type: BI Var: 10 Objective: Apply the Order of Operations
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C) -22
D) 121
Evaluate the root without using a calculator or note that root is not a real number. 2)
3
64 A) 4 C) -4
B) 5 D) Not a real number
Answer: A Type: BI Var: 5 Objective: Apply the Order of Operations 3
3)
-125 A) –5 C) 5 Answer: A
B) 6 D) Not a real number
Type: BI Var: 1 Objective: Apply the Order of Operations 7 Simplify Algebraic Expressions
Apply the associative property of addition. 1) (r + 3) + 7 A) r + 3 B) r + 7
C) r + 10
D) r +4
C) -55p
D) 6p
6 C) w 5
D)
Answer: C Type: BI Var: 24 Objective: Simplify Algebraic Expressions
Apply the associative property of multiplication. 5 11 2) p 5 11 A) -5p
B) p
Answer: B Type: BI Var: 20 Objective: Simplify Algebraic Expressions
Apply the commutative property of multiplication. 5 3) w · 6 5 6 B) w · A) - w 6 5 Answer: D Type: BI Var: 18 Objective: Simplify Algebraic Expressions
Clear parentheses and combine like terms. 4) -11z3 - 8z3 - z3 Answer: -20z3 Type: SA Var: 50+ Objective: Simplify Algebraic Expressions
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5 6
w
5) 3(2x - 5) + 14x A) 6x - 15 + 14x
B) 20x - 5
C) 20x - 15
D) 15x
C) 4s + 9t + 7
D) 4s - 9t + 7
Answer: C Type: BI Var: 40 Objective: Simplify Algebraic Expressions
6) -2x(4 - 3x) + 16x2 - 7x Answer: 22x2 - 15x Type: SA Var: 50+ Objective: Simplify Algebraic Expressions
7) 2[3.5(2.5 - 3x) - x(5 + 0.5x)] + 7.5x2 Answer: 6.5x2 - 31x + 17.5 Type: SA Var: 50+ Objective: Simplify Algebraic Expressions
Clear parentheses by applying the distributive property. 8) -(-4s + 9t + 7) A) 4s - 9t - 7 B) -4s - 9t - 7 Answer: A Type: BI Var: 50+ Objective: Simplify Algebraic Expressions
9) 4(4s - 4)- 1(8t - 2u) A) 16s - 4 - 8t - 2u C) 16s - 16 - 8t - 2u Answer: D Type: BI Var: 50+ Objective: Simplify Algebraic Expressions
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B) 16s - 4 - 8t + 2u D) 16s - 16 - 8t + 2u
8 Write Algebraic Models
Solve the problem. 1) A new diet program guarantees you will lose 1.6 lb per week. A male with a starting weight of 220 lb is modeled by W = 220 - 1.6t where t is the number of weeks after starting the diet. Use the model to determine the male's weight after 19 weeks. 250 200 150 W (lb) 100 50
2
4
6
8 10 12 14 16 18
t (weeks)
A) 170.6 lb
B) 189.6 lb
C) 218.4 lb
D) 208.6 lb
Answer: B Type: BI Var: 50+ Objective: Write Algebraic Models
2) A tool rental store charges a flat fee of $6.50 to rent a chain saw, and $3.75 for each day, including the first. Write an equation that expresses the cost y of renting this saw if it is rented for x days. A) y = 6.50x + 3.75 B) y = 3.75(x + 6.50) C) y = 3.75x + 6.50 D) y = 3.75x - 6.50 Answer: C Type: BI Var: 50+ Objective: Write Algebraic Models
3) A tool rental store charges a flat fee of $8.50 to rent a chain saw, and $4.00 for each day, including the first. Use a linear equation to find the cost of renting the saw for one week. A) $32.50 B) $36.50 C) $12.50 D) $28.00 Answer: B Type: BI Var: 50+ Objective: Write Algebraic Models
4) A tool rental store charges a flat fee of $9.00 to rent a chain saw, and $4.00 for each day, including the first. If you need to rent the saw and absolutely refuse to spend more than $49.00, what's the maximum number of days you can keep the saw? A) 7 days B) 5 days C) 14 days D) 10 days Answer: D Type: BI Var: 50+ Objective: Write Algebraic Models
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5) The width of a rectangle is 2 ft less than 4 times the length. Write a model for the width W in terms of the length L. A) W = 2L - 4 B) W = 2L + 4 C) W = 4L + 2 D) W = 4L - 2 Answer: D Type: BI Var: 15 Objective: Write Algebraic Models 9 Mixed Exercises
Evaluate the expression for the given values of the variables. -q 1) for q = -3, t = 2 4t 3 3 3 B) C) A) 8 2 8
D) -
1 8
Answer: A Type: BI Var: 50+ Objective: Mixed Exercises
2) Under selected conditions, a sports car gets 14 mpg in city driving and 19 mpg for highway driving. 1 1 The model G = c + h represents the amount of gasoline used (in gal) for c miles driven in the 14 19 city and h miles driven on the highway. Determine the amount of gas required to drive 98 mi in the city and 399 mi on the highway. A) 37 gal B) 28 gal C) 33 gal D) 34 gal Answer: B Type: BI Var: 50+ Objective: Mixed Exercises 10 Expanding Your Skills
Write the set as a single interval. 1) -∞, 5 ∩ -6, 8 ∩ [1,6] A) 1, 5
B) 1, 6
C) -6, 5
D) -∞, 8
2) -∞, 7 ∪ 12, ∞ ∩ 10, 15 A) 10, 15 B) 10, ∞
C) -∞, 15
D) 12, 15
Answer: A Type: BI Var: 5 Objective: Expanding Your Skills
Answer: D Type: BI Var: 16 Objective: Expanding Your Skills
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11 Technology Connections
Solve the problem. 1) If n > 0, then 9n - 9n = A) n
B) 9n
C) 0
D) 1
C) 0
D) 1
Answer: C Type: BI Var: 8 Objective: Technology Connections
2) If z > 0, then 5z + 5z = A) 10z
B) 5z
Answer: A Type: BI Var: 8 Objective: Technology Connections
0.2 Integer Exponents and Scientific Notation 0 Concept Connections
Provide the missing information. 1) For a nonzero real number b, the value of b0 =
.
Answer: 1 Type: SA Var: 1 Objective: Concept Connections
2) For a nonzero real number b, the value b□ =
1
. bn
Answer: -n Type: SA Var: 1 Objective: Concept Connections
3) A number expressed in the form a × 10n, where 1 ≤ a < 10 and n is an integer is said to be written in notation. Answer: scientific Type: SA Var: 1 Objective: Concept Connections
4) From the properties of exponents, bmbn = b□. Answer: m + n Type: SA Var: 1 Objective: Concept Connections
5) If b ≠ 0, then
bm
□ n =b .
b Answer: m - n
Type: SA Var: 1 Objective: Concept Connections
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6) From the properties of exponents, bm n = b□. Answer: m · n Type: SA Var: 1 Objective: Concept Connections 1 Simplify Expressions with Zero and Negative Exponents
Simplify. 1)
19 0 9 A) 1
B)
19
C) 0
9
D)
1 9
Answer: A Type: BI Var: 50+ Objective: Simplify Expressions with Zero and Negative Exponents
2) 4-2 A)
1 16
B) 2
C) -16
D) -8
Answer: A Type: BI Var: 14 Objective: Simplify Expressions with Zero and Negative Exponents
4 -3 3) 5 A)
1 2
B) -
12 5
125 64
D) -
256 C) x 4
4 D) x 4
C)
64 125
Answer: C Type: BI Var: 33 Objective: Simplify Expressions with Zero and Negative Exponents
4) 4x -4 1 A) 256x 4
1 B)4x 4
Answer: D Type: BI Var: 27 Objective: Simplify Expressions with Zero and Negative Exponents
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5)
6p -3r 6 q -9 9 6
6q r A)
p3
6q B)
9
p 3r 6
3 6
6p r
3 6 9
C) 6p r q
D)
q9
Answer: A Type: BI Var: 50+ Objective: Simplify Expressions with Zero and Negative Exponents 2 Apply Properties of Exponents
Simplify the expression. Write your answer with positive exponents only. 1) 64 · 67 A) 6-3 B) 611 C) 3611
D) 628
Answer: B Type: BI Var: 1 Objective: Apply Properties of Exponents
1812 2)
185 A) 1817
B) 187
C) 1812 - 185
D) 1812/5
Answer: B Type: BI Var: 19 Objective: Apply Properties of Exponents
3) (x9)4 36
A) x
5
B) x
6,561
C) x
13
D) x
Answer: A Type: BI Var: 25 Objective: Apply Properties of Exponents
z2y3 4)
y-3z6
y6
1 A)
z4
B)
z4
Answer: B Type: BI Var: 44 Objective: Apply Properties of Exponents
5) (-2a2b4c4)3 Answer: -8a6b12c12 Type: SA Var: 50+ Objective: Apply Properties of Exponents
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1
4 3
C) z y
D)
z4y6
2x-4y4 -3 6) 5x5y-5 125x27 Answer:
8y27
Type: SA Var: 50+ Objective: Apply Properties of Exponents
7) (t3z)2(3t-2z4)-2 z7 t A) 9
t10 B)
1 C) 81t4z20
9z6
9z10 D)
t
Answer: B Type: BI Var: 1 Objective: Apply Properties of Exponents
8)
-2 20 1 -23 12 10x 2y -5 x y
-1
A)
x 27y 22
5y 2
x 19
2 B)
5y 22
C)
x 19
x 27 D)
2y 2
Answer: C Type: BI Var: 50+ Objective: Apply Properties of Exponents
(4vw-3x2)2 9)
3 2 -4 -3 3 2 -2 4 · (-v w x )
(2v w x ) x24 A)
v23w8
x24 B) -
v19w20
x16 C)
v19w8
4x16 D) -
v23w20
Answer: B Type: BI Var: 50+ Objective: Apply Properties of Exponents 3 Apply Scientific Notation
Write the number in scientific notation. 1) 528,000,000 Answer: 5.28 × 108 Type: SA Var: 50+ Objective: Apply Scientific Notation
2) 0.00000063 A) 63 × 10-8
B) 6.3 × 10-7
Answer: B Type: BI Var: 1 Objective: Apply Scientific Notation
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C) 0.63 × 10-6
D) 6.3 × 107
Perform the indicated operation and write the answer in scientific notation. 3) (1.2 ×106)(3.8 ×107) A) 5 × 1013 B) 4.56 × 10013 C) 4.56 ×1042
D) 4.56 × 1013
Answer: D Type: BI Var: 50+ Objective: Apply Scientific Notation
Answer the question. 4) How old (in whole years) is someone that has been alive for 1.6 × 104 days? Answer: 43 years Type: SA Var: 20 Objective: Apply Scientific Notation
5) How many miles (to the nearest hundredth of a mile) is a trip that is 1.5 × 106 inches? A) 23.67 miles B) 11.835 miles C) 2,367.42 miles D) 47.34 miles Answer: A Type: BI Var: 21 Objective: Apply Scientific Notation
Perform the indicated operation and write the answer in scientific notation. 31.5 × 10 16 6) 4.5 × 10 6 A) 7 × 10 10
B) 7 × 10 22
C) 27 × 10 22
D) 27 × 10 10
Answer: A Type: BI Var: 50+ Objective: Apply Scientific Notation
0.3 Rational Exponents and Radicals 0 Concept Connections
Provide the missing information. 1) b is an nth-root of a if b□ = a. Answer: n Type: SA Var: 1 Objective: Concept Connections n
2) Given the expression
a, the value a is called the
and n is called the
.
Answer: radicand, index Type: SA Var: 1 Objective: Concept Connections
3) The expression am/n can be written in radical notation as number. Answer:
n
m
a
or
n m
a
Type: SA Var: 1 Objective: Concept Connections
Page 16
, provided that
n
a is a real
4) The expression a1/n can be written in radical notation as number. Answer:
n
, provided that
n
a is a real
a
Type: SA Var: 1 Objective: Concept Connections
5) If x represents any real number, then x2 =
.
Answer: x Type: SA Var: 1 Objective: Concept Connections
6) If x represents any real number, then
3 3
x =
.
Answer: x Type: SA Var: 1 Objective: Concept Connections
7) The product property of radicals indicates that represent real numbers. Answer:
n
n
a·
n
b=
provided that
n
a and
n
a· b
Type: SA Var: 1 Objective: Concept Connections
8) Removing a radical from the denominator of a fraction is called
the denominator.
Answer: rationalizing Type: SA Var: 1 Objective: Concept Connections 1 Evaluate nth-Roots
Evaluate the root without using a calculator or note that root is not a real number. 1)
3
8 A) -2 C) 2
B) 3 D) Not a real number
Answer: C Type: BI Var: 5 Objective: Evaluate nth-Roots
2)
4
625 A) 5 C) -5
Answer: A Type: BI Var: 5 Objective: Evaluate nth-Roots
Page 17
B) 6 D) Not a real number
b
4
3) -256 A) -4 C) 5
B) 4 D) Not a real number
Answer: D Type: BI Var: 5 Objective: Evaluate nth-Roots 2 Simplify Expressions of the Forms a1/n and am/n
Convert the expression to radical form and simplify. 1) 91/2 A) 3 C)
B) 81
9
D) Not a real number
2
Answer: A Type: BI
Var: 6
Objective: Simplify Expressions of the Forms a1/n and am/n
Simplify the expression, if possible. 2) 1,2961/4 1 A) 5,184 C) 6
B) 5,184 D) Not a real number
Answer: C Type: BI Var: 5 Objective: Simplify Expressions of the Forms a1/n and am/n
3) 1963/2 A) 2,754 C) 294
B) 2,744 D) Not a real number
Answer: B Type: BI
Var: 7
Objective: Simplify Expressions of the Forms a1/n and am/n
Page 18
4) (-81)5/2 405 2
A) 59,049
B) -
C) -59,049
D) Not a real number
Answer: D Type: BI
Var: 5
Objective: Simplify Expressions of the Forms a1/n and am/n
Convert the expression to radical notation. 5) x1/7 A)
7
C)
B) 7 x
x
1
D)
7
x
x 7
Answer: A Type: BI
Var: 8
Objective: Simplify Expressions of the Forms a1/n and am/n
Write the expression by using rational exponents rather than radical notation. 6)
13
16t
Answer: (16t)1/13 Type: SA Var: 50+ Objective: Simplify Expressions of the Forms a1/n and am/n 3 Simplify Expressions with Rational Exponents
Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. 1) (x4y8)2/3 2 A) x4y8 B) x14/3y26/3 C) x4y16/3 D) x8/3y16/3 3 Answer: D Type: BI Var: 1 Objective: Simplify Expressions with Rational Exponents
2) A)
t2 1/2 t-6 t7
B) t-5
C) t-2
Answer: D Type: BI Var: 9 Objective: Simplify Expressions with Rational Exponents
Page 19
D) t4
3)
81s12r-4 3/4 16s-4r4 A)
27s6
27s12 B)
8
3s12 C)
8r6
3s16r8 D) 2
2r6
Answer: B Type: BI Var: 1 Objective: Simplify Expressions with Rational Exponents
Simply the expression. Assume that all variable expressions represent positive real numbers. c 6 -3 c 6 6 4) c-d c-d c
A)
11 11 6
B) c
11
c-d
11 6
c-d C) c 11
11 6
D) c
25
c-d
c-d Answer: C Type: BI Var: 50+ Objective: Simplify Expressions with Rational Exponents 4 Simplify Radicals
Simplify the radical. 1)
3
72 3
A) 8 36 Answer: B
3
3
B) 2 9
C) 8 9
3
D) 6 2
Type: BI Var: 1 Objective: Simplify Radicals
Simplify the radical. Assume that all variables represent positive real numbers. 54z15 2) 3z4 A) 3z5 2z Answer: A Type: BI Var: 42 Objective: Simplify Radicals
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B) 3z 2z
9
C) 9z5 2z
11 D) 3 2z
11 6
3) 9 3
c 18d 20 64
A)
9 4
cd 3 c 18d 20
B)
27
3
c 18d 20 cd
64
9 C) c 6d 6 3 d 2 4
D)
9
c 6d 7
64
Answer: C Type: BI Var: 50+ Objective: Simplify Radicals 5 Multiply Single-Term Radical Expressions
Multiply the radical expressions and simplify your answer. 1) 9 · 8 A) 36 2 B) 17 C) 6 2
D) 2 6
Answer: C Type: BI Var: 6 Objective: Multiply Single-Term Radical Expressions 6
2) -3 6x y3 · 2 10xy6 5 7
A) -24xy x y
B) -12x3y4 15xy
C) -24x3y4 15xy
Answer: B Type: BI Var: 50+ Objective: Multiply Single-Term Radical Expressions 6 Add and Subtract Radicals
Add the radical expressions. 1) 9 10 + 6 10 A) 54 10 C) 15 10
B) 15 20 D) Cannot be simplified further
Answer: C Type: BI Var: 50+ Objective: Add and Subtract Radicals
2) z2 18z + 7 98z A) (3z2 + 49) 2z C) (18z2 + 686) z Answer: A Type: BI Var: 50+ Objective: Add and Subtract Radicals
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7 9
D) -12 15x y
B) (z2 + 7) 116z D) Cannot be simplified further
Subtract the radical expressions. Assume that all variables represent positive real numbers. 3) Subtract the radical expressions. Assume that all variables represent positive real numbers. 3 72y3 - 2y A) (18y - 1) 2y
B) 17 2y3 - 2y
C) 3 72y3 - 2y
D) Cannot be simplified further
Answer: A Type: BI Var: 1 Objective: Add and Subtract Radicals
Add or subtract the radical expressions as indicated. Assume that all variables represent positive real numbers. 4) 2 3y - 12y5 + y2 48y Answer: (2 + 2y2) 3y Type: SA Var: 10 Objective: Add and Subtract Radicals 7 Mixed Exercises
Use the Pythagorean theorem to determine the length of the missing side. Write the answer as a simplified radical. 1)
14 m
7m A) 7 2 m Answer: C Type: BI Var: 9 Objective: Mixed Exercises
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B) 14 3 m
C) 7 3 m
D) 7 5 m
Solve the problem. 2) The lateral surface area A of a right circular cone is given by A = πr r2 + h2, where r and h are the radius and height of the cone. Determine the exact value (in terms of π) of the lateral surface area of a cone with radius 3 m and height 5 m. Then give a decimal approximation to the nearest square meter.
5m
3m A) 6π 2 m2≈ 27 m2
B) 5π 34 m2≈ 92 m2
C) 10π 2 m2≈ 44 m2
D) 3π 34 m2≈ 55 m2
Answer: D Type: BI Var: 6 Objective: Mixed Exercises
0.4 Polynomials and Multiplication of Radicals 0 Concept Connections
Provide the missing information. 1) A in the variable x is a finite sum of terms of the form axn where a is a real number and n is a whole number. Answer: polynomial Type: SA Var: 1 Objective: Concept Connections
2) The polynomial 5x3 - 2x2 + 4 is written in
order by degree.
Answer: descending Type: SA Var: 1 Objective: Concept Connections
3) The
term of a polynomial is the term of highest degree.
Answer: leading Type: SA Var: 1 Objective: Concept Connections
4) The leading
of a polynomial is the numerical factor of the leading term.
Answer: coefficient Type: SA Var: 1 Objective: Concept Connections
5) A
is a polynomial that has two terms, and a
Answer: binomial, trinomial Type: SA Var: 1 Objective: Concept Connections
Page 23
is a polynomial with three terms.
6) The expanded form of the square of a binomial is a trinomial called a
square trinomial.
Answer: perfect Type: SA Var: 1 Objective: Concept Connections
results in a difference of squares a2 - b2.
7) The product of conjugates (a + b) · Answer: (a - b) Type: SA Var: 1 Objective: Concept Connections
8) The conjugate of 3 - x is
.
Answer: 3 + x Type: SA Var: 1 Objective: Concept Connections 1 Identify Key Elements of a Polynomial
Write the polynomial in descending order. Then identify the leading coefficient and the degree. 1) -9x + 7 - 4x6 A) -4x6 - 9x + 7; leading coefficient: -4; degree: 3 B) 7 - 4x6 - 9x; leading coefficient: 7; degree: 6 C) -4x6 - 9x + 7; leading coefficient: -4; degree: 6 D) 7 - 4x6 - 9x; leading coefficient: 7; degree: 3 Answer: C Type: BI Var: 50+ Objective: Identify Key Elements of a Polynomial
Choose the polynomial that is described. 2) A monomial in one variable of degree 4 A) 4n C) -9t4
B) -9t3 - 3n D) -9t3 - 4t2 - 3n - 8
Answer: C Type: MC Var: 50+ Objective: Identify Key Elements of a Polynomial
3) A trinomial in one variable of degree 3 A) 4r3 B) 4r2 - 9t + 7 Answer: D Type: MC Var: 50+ Objective: Identify Key Elements of a Polynomial
Page 24
C) 3r2 + 4t - 9
D) 4r3 - 9t + 7
2 Add and Subtract Polynomials
Add the polynomials and simplify. 1) (4m4 - 8m3 - 7m) + (4m4 - 7m2 - 5m) A) 4m4 - 4m3 - 7m2 - 12m C) 8m4 - 8m3 - 7m2 - 2m
B) 8m4 - 8m3 - 7m2 - 12m D) 8m4 - 8m3 - 14m2 - 5m
Answer: B Type: BI Var: 50+ Objective: Add and Subtract Polynomials
1 3 1 1 9 2) - n + n2 + 4.6n + - n3 + n2 + 4.5n 2 4 4 2 11 3 A) - n3 + n2 + 9.1n 4 4 11 1 C) - n3 + n2 + 0.1n 4 4
11 3 1 2 n - n + 0.1n 4 4 11 D) - n3 - 3 n2 + 9.1n 4 4 B) -
Answer: A Type: BI Var: 50+ Objective: Add and Subtract Polynomials
Subtract the polynomials and simplify. 3) (-6m2 - 7m + 8) - (2m2 - 5m - 9) A) -4m2 - 12m - 1 C) -8m2 - 7m2 + 5m + 17
B) -8m2 - 12m - 1 D) -8m2 - 2m + 17
Answer: D Type: BI Var: 50+ Objective: Add and Subtract Polynomials
4)
2 2 1 p - pq + 3 q2 + 14 - 9 p2 + 4 pq - 5 q2 + 11 2 14 14 14 7 7 5 2 15 pq + 4 q2 + 3 p 14 14 7 5 1 C) - p2 + pq - 1 q2 + 25 14 14 7
A) -
B) D)
5 2 15 pq + 4 2 + 25 p q 14 14 7
13 2 1 pq - 1 2 + 25 p + q 14 14 7
Answer: A Type: BI Var: 50+ Objective: Add and Subtract Polynomials
5) Subtract (-7m3 - 6m - 6) from (-5m3 - 4m - 8). A) -5m3 + 7m2 + 2m - 2 C) 2m3 + 2m - 2 Answer: C Type: BI Var: 50+ Objective: Add and Subtract Polynomials
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B) 2m3 - 10m - 14 D) -2m3 - 2m + 2
3 Multiply Polynomials
Multiply the polynomials by using the distributive property. 1) (8t7u3)(3t4u5) A) 11t11u8 B) 24t3u-2 C) 24t11u8
D) 24t28u15
Answer: C Type: BI Var: 50+ Objective: Multiply Polynomials
2) (n - 6p)(n2 - 5np + 3p2) A) n3 - 6p - 5np - 18p3 C) n3 - 11n2p + 33np2 - 18p3
B) n3 - 6np + 33np2 - 18p3 D) n3 + 22n2p2 - 18p3
Answer: C Type: BI Var: 50+ Objective: Multiply Polynomials
Write an expression for the area and simplify your answer. 3) Rectangle
4x - 9
3x + 6 [The figure is not necessarily drawn to scale.] B) 12x2 - 3x - 54 C) 12x2 + 51x - 54
A) 12x2 - 54 Answer: B
Type: BI Var: 50+ Objective: Multiply Polynomials
Write an expression for the volume and simplify your answer. 4)
3x
x+4 x+1 A) 3x + 12x C) 3x3 + 15x2 + 12x 3
Answer: C Type: BI Var: 50+ Objective: Multiply Polynomials
Page 26
B) 3x3 + 15x +12 D) x3 + 5x2 + 4x
D) 12x2 + 3x - 54
4 Identify and Simplify Special Case Products
Multiply. 1) (-6m2 - 9n)2 A) 36m2 + 108mn + 81n2 C) 36m4 + 81n2
B) 36m4 + 108m2n + 81n2 D) 36m4 - 81n2
Answer: B Type: BI Var: 50+ Objective: Identify and Simplify Special Case Products
2) [(-8y - 9) + z][(-8y - 9)- z] A) 64y2 + 81 - z2 C) 64y2 + 288y + 81 - z2
B) 64y2 + 144y + 81 - z2 D) 64y2 + 144y - 16yz + 81- 19z2
Answer: B Type: BI Var: 50+ Objective: Identify and Simplify Special Case Products
3) (5m - 4n)3 A) 125m3 - 200m2n + 160mn2 - 64n3 C) 125m3 - 300m2n + 240mn2 - 64n3
B) 125m3 - 64n3 D) 125m3 - 40mn - 64n3
Answer: C Type: BI Var: 24 Objective: Identify and Simplify Special Case Products 5 Multiply Radical Expressions Involving Multiple Terms
Multiply the radical expressions and simplify your answer. 1) 2( 2 - 3) A) 2 - 6 B) 2 2 - 6 C) 2 - 3
D) 2 + 6
Answer: A Type: BI Var: 5 Objective: Multiply Radical Expressions Involving Multiple Terms
2) ( 108 - 1)( 3 + 5) A) 321 - 5
B) 319 + 5 108 - 3
C) 13
D) 13 + 29 3
Answer: D Type: BI Var: 5 Objective: Multiply Radical Expressions Involving Multiple Terms
3)
x+5 -4 A) x - 9
x+5+4 B) x - 11
C) x + 11
Answer: B Var: 50+ Type: BI Objective: Multiply Radical Expressions Involving Multiple Terms
Page 27
D) x + 9
4)
y+6 -7
2
A) y + 14 y + 6 - 55
B) y - 43
C) y - 14 y + 6 + 55
D) y + 55
Answer: C Type: BI Var: 50+ Objective: Multiply Radical Expressions Involving Multiple Terms
0.5 Factoring 0 Concept Connections
Provide the missing information. 1) The binomial a3 + b3 is called a sum of
and factors as
.
Answer: cubes, (a + b)(a2 - ab + b2) Type: SA Var: 1 Objective: Concept Connections
2) The binomial a3 - b3 is called a
of cubes and factors as
.
Answer: difference, (a - b)(a2 + ab + b2) Type: SA Var: 1 Objective: Concept Connections
3) The trinomial a2 + 2ab + b2 is a
square trinomial. Its factored form is
.
Answer: perfect, (a + b)2 Type: SA Var: 1 Objective: Concept Connections
4) The binomial a2 - b2 is called a difference of
and factors as
Answer: squares, (a + b)(a - b) Type: SA Var: 1 Objective: Concept Connections 1 Factor Out the Greatest Common Factor
Factor out the greatest common factor. 1) 12r2s - 24rs2 + 18rs A) 2rs(6r - 12s - 12) C) 6rs(2r - 4s + 3)
B) 3rs(4r - 8s + 6) D) 6r(2rs - 4s2 + 3s)
Answer: C Type: BI Var: 50+ Objective: Factor Out the Greatest Common Factor
Factor out the indicated quantity. 2) -40q4r + 56q3r - 24q2r: Factor out the quantity -8q2r A) -8q2r(5q2 - 7q + 3) B) -8q2r(-5q2 - 7q + 3) C) -8q2r(5q3 - 7q2 + 3) D) -8q2r(-5q2 + 7q - 3) Answer: A Type: BI Var: 50+ Objective: Factor Out the Greatest Common Factor
Page 28
.
Solve the problem. 14) If the slope of a line is
7 10
, how much vertical change will be present for a horizontal change of
63 ft? A) 6.3 ft
B) 90 ft
C) 44.1 ft
D) 441 ft
Answer: C Type: BI Var: 50+ Objective: Determine the Slope of a Line 3 Apply the Slope-Intercept Form of a Line
Write the equation in slope-intercept form and determine the slope and y-intercept. 1) -2x = -3y - 6 2 2 2 2 A) y = x + 6; slope: ; y-intercept: (0, 6) B) y = x + 6; slope: ; y-intercept: (0, 6) 3 3 3 3 2 2 2 2 C) y = x - 2; slope: ; y-intercept: (0, -2) D) y = - x - 2; slope: - ; y-intercept: (0, -2) 3 3 3 3 Answer: C Type: BI Var: 40 Objective: Apply the Slope-Intercept Form of a Line
Determine the slope and the y-intercept of the line. 2) 6 = -6y A) Slope: 0; y-intercept: (-1, 0) C) Slope: undefined; y-intercept: (-1, 0)
B) Slope: 0; y-intercept: (0, -1) D) Slope: 1; y-intercept: (0, -1)
Answer: B Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
3) 6x - 5y = 4 6 A) Slope: -
; y-intercept: 0, -
5
C) Slope: Slope:
4
5
5 6 5
; y-intercept: 0, -
; y-intercept: 0, - 5 4 6
D) Slope: Slope:
6 ; y-intercept: 0, 4 5
4 5
Answer: C Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
Page 55
B) Slope: Slope:
Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept. 4) 3x = 3 - y 5 y 4 3 2 1 -5 -4 -3 -2 -1 -1
1
2
3
5x
4
-2 -3 -4 -5
A) y = 3x + 3
B) y = 3x - 3 5 y
5 y
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 -1
1
2
3
4
5x
-1
-2
-2
-3
-3
-4
-4
-5
-5
C) y = -3x - 3
1
2
3
4
5x
1
2
3
4
5x
D) y = -3x + 3 5 y
5 y
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 -1
1
2
3
4
5x
-5 -4 -3 -2 -1 -1
-2
-2
-3
-3
-4
-4
-5
-5
Answer: D Type: BI Var: 32 Objective: Apply the Slope-Intercept Form of a Line
Page 56
-5 -4 -3 -2 -1
5) -3x + 5y = -15 5 y 4 3 2 1 -5 -4 -3 -2 -1 -1
1
2
3
4
5x
-2 -3 -4 -5
3 A) y = x + 3 5
5 B) y = x - 3 3 5 y
5 y
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 -1
1
2
3
4
5x
-5 -4 -3 -2 -1 -1
-2
-2
-3
-3
-4
-4
-5
3 C) y = -
2
3
4
5x
1
2
3
4
5x
-5
3
x-3
D) y = x - 3 5
5 5 y
5 y
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 -1
1
2
3
4
5x
-5 -4 -3 -2 -1 -1
-2
-2
-3
-3
-4
-4
-5
-5
Answer: D Type: BI Var: 40 Objective: Apply the Slope-Intercept Form of a Line
Page 57
1
6) -5x - 2y = 0 5 y 4 3 2 1 -5 -4 -3 -2 -1 -1
1
2
3
4
5x
-2 -3 -4 -5
5 A) y = - x 2
2 B) y = x 5 5 y
5 y
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 -1
1
2
3
4
5x
-5 -4 -3 -2 -1 -1
-2
-2
-3
-3
-4
-4
-5
2
3
4
5x
1
2
3
4
5x
-5
5
2
C) y = x 2
D) y = - x 5 5 y
5 y
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1 -1
1
2
3
4
5x
-5 -4 -3 -2 -1 -1
-2
-2
-3
-3
-4
-4
-5
-5
Answer: A Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
Page 58
1
Determine if the function is linear, constant, or neither. 5 7) f(x) = 3 A) linear
B) constant
C) neither
Answer: B Type: BI Var: 33 Objective: Apply the Slope-Intercept Form of a Line
Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). 8) (-4, -5); m = 4 A) f(x) = 4x - 4 B) f(x) = 4x + 11 C) f(x) = 4x - 25 D) f(x) = 4x - 5 Answer: B Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
9) (-3, 1); m = -
2
3 2 A) f(x) = - x - 3 3
B) f(x) = -
2
x-1
3
C) f(x) = -
2
x+5
3
D) f(x) =
2
x-1
3
Answer: B Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
Use the slope-intercept form to write an equation of the line that passes through the given points. Use function notation where y = f(x). 10) (2, -3) and (-7, -11) 8 1 9 1 9 8 43 43 A) f(x) = - x B) f(x) = - x C) f(x) = x D) f(x) = x 9 9 8 9 8 9 9 9 Answer: D Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
11) (10, 2) and (8, 10) A) f(x) = 4x + 38
B) f(x) = -4x + 38
Answer: C Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
Page 59
C) f(x) = -4x + 42
D) f(x) = -4x - 42
Use the slope-intercept form to write an equation of the line that passes through the given point and has the given slope. Use function notation where y = f(x). 12) (9, -3); m = 0 A) f(x) = -3 B) f(x) = 9x C) f(x) = 0 D) f(x) = 9 Answer: A Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line
13) (-2.5, 4.3); m = -5.2 A) f(x) = -8.7x - 5.2 C) f(x) = -5.2x - 8.7
B) f(x) = -5.2x + 8.7 D) f(x) = -5.2x + 4.3
Answer: C Type: BI Var: 50+ Objective: Apply the Slope-Intercept Form of a Line 4 Compute Average Rate of Change
Find the slope of the secant line indicated with a dashed line. 1) 16 14
y
12 10 8 6 4 2 -16 -14 -12 -10 -8 -6 -4 -2 -2
2
4 6 8 10 12 14 16 x
(-4,2 -5) -6 -8
(-2, -14)
-10 -12 -14 -16
A) m =
4 9
B) m = -
Answer: C Type: BI Var: 50+ Objective: Compute Average Rate of Change
Page 60
9 4
C) m =
9 4
D) m = -
4 9
Solve the problem. 2) The population of a certain country since 1990 can be approximated by f(t) = 0.008t2 + 2.1t + 175 where f(t) is the population in millions and t represents the number of years since 1990. Find the average rate of change in the country's population between 1990 and 2010. Round to 1 decimal place. A) 2.0 million/yr B) 2.3 million/yr C) 2.9 million/yr D) 2.5 million/yr Answer: B Type: BI Var: 50+ Objective: Compute Average Rate of Change
3) The function given by y = f (x) shows the value of $6,000 invested at 5% interest compounded continuously, x years after the money was originally invested. Find the average amount earned per year between the 25th year and 30th year. y 32000 28000
(30, 26,890)
Value ($)
24000 (25, 20,942)
20000
(20, 16,310)
16000 12000
(15, 12,702)
8000
(10, 9,892) (5, 7,704)
4000
5
10 15 20 Number of Years
A) $1,189.60/year
25
30
x
B) $5,948.00/year
C) $20,942.00/year
D) $26,890.00/year
Answer: A Type: BI Var: 40 Objective: Compute Average Rate of Change
Determine the average rate of change of the function on the given interval. 4) f (x) = x + 1 on [0, 3] 1 3 3 A) B) C) 3 3 3 Answer: D Type: BI Var: 20 Objective: Compute Average Rate of Change
Page 61
D)
1 3
5) f (x) = 3x2 + 3 on [3, 5] A) -24
B)
3
C) 24
D)
2
5 2
Answer: C Type: BI Var: 50+ Objective: Compute Average Rate of Change
6) f (x) = x3 + 3 on [2, 3] A) 19
B) -19
C) -
19 2
D)
19 2
Answer: A Type: BI Var: 40 Objective: Compute Average Rate of Change 5 Solve Equations and Inequalities Graphically
Use the graph to solve the equation and inequality. Write the solution to the inequality in interval notation. 1) a. 3x - 3 = 2x - 1 b. 3x - 3 > 2x - 1 5 y 4 3
(2, 3)
2 1 -5
-4
-3
-2
1
-1
2
3
4
5x
-1 -2 -3 -4 -5
A) a. {2}; b. (-∞, 2) C) a. {3}; b. (3, ∞) Answer: B Type: BI Var: 24 Objective: Solve Equations and Inequalities Graphically
Page 62
B) a. {2}; b. (2, ∞) D) a. {3} b. (-∞, 3}
2)
a. 3x - 1 = 2x - 2 b. 3x - 1 < 2x - 2 5 y 4 3 2 1 -5
-4
-3
-2
1
-1
2
3
4
5x
-1 -2 -3 (-1, -4)
-4 -5
A) a. {-1}; b. (-∞, -1) C) a. {-4} b. (-∞, -4}
B) a. {-4}; b. (-4, ∞) D) a. {-1}; b. (-1, ∞)
Answer: A Type: BI Var: 50+ Objective: Solve Equations and Inequalities Graphically
2.5 Applications of Linear Equations and Modeling 0 Concept Connections
Provide the missing information. 1) Given a point (x1, y1) on a line with slope m, the point-slope formula is given by Answer: y - y1 = m(x - x1) Type: SA Var: 1 Objective: Concept Connections
2) If two nonvertical lines have the same slope but different y-intercepts, then the lines are (parallel/perpendicular). Answer: parallel Type: SA Var: 1 Objective: Concept Connections
3) If m1 and m2 represent the slopes of two nonvertical perpendicular lines, then m1m2 = . Answer: -1 Type: SA Var: 1 Objective: Concept Connections
Page 63
.
4) Suppose that y = C (x) represents the cost to produce x items, and that y = R (x) represents the revenue for selling x items. The profit P (x) of producing and selling x items is defined by P (x) = . Answer: R (x) - C (x) Type: SA Var: 1 Objective: Concept Connections 1 Apply the Point-Slope Formula
Use the point-slope formula to write an equation of the line that passes through the given points. Write the answer in slope-intercept form (if possible). 1) (3, -3) and (-4, -5) 7 3 2 3 2 27 7 27 D) y = - x A) y = x B) y = - x C) y = x 7 7 2 7 2 7 7 7 Answer: A Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
2) Passes through (4, 1) and the slope is undefined. A) y = 1 B) y = x + 1
C) y = x + 4
D) x = 4
Answer: D Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
Write an equation of the line satisfying the given conditions. Write the answer in standard form. 6 3) The line has a slope of - and contains the point (-5, -8). 7 6 6 86 83 B) y = - x C) x + y = A) 6x + 7y = 86 D) 6x + 7y = -86 7 7 7 7 Answer: D Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. 2 4) The line passes through the point (15, -2) and has a slope of . 5 2 2 2 2 B) y = x + 15 C) y = x - 8 D) y = x + 22 A) y = - x - 8 5 5 5 5 Answer: C Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
Page 64
5) The line passes through the point (2, 13) and has a slope of 4. A) y = 4x + 2 B) y = -4x + 13 C) y = 4x + 13
D) y = 4x + 5
Answer: D Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
3 6) The line passes through the point (-4, 1) and has a slope of . 2 3 3 3 B) y = x + 7 C) y = x - 5 A) y = - x + 7 2 2 2
D) y =
3
x-4
2
Answer: B Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
7) The line passes through (12, 9) and (9, 9). 1 21 A) y = - x + B) y = 9 6 2
1 21 x6 2
C) x = 9
D) y = -
C) y = -12
D) y = -12x
Answer: B Type: BI Var: 50+ Objective: Apply the Point-Slope Formula
8) The line passes through (-12, -12) and (-12, -4). A) y = 12 B) x = -12 Answer: B Type: BI Var: 50+ Objective: Apply the Point-Slope Formula 2 Determine the Slopes of Parallel and Perpendicular Lines
The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. 8 1) m = 5 8 5 8 B) a. m = 0; b. m = A) a. m = ; b. m = 5 8 5 5 8 5 C) a. m = 0; b. m = D) a. m = ; b. m = 8 5 8 Answer: D Type: BI Var: 44 Objective: Determine the Slopes of Parallel and Perpendicular Lines
Page 65
The slope of a line is given. Find the slope of a line parallel to the given line. 11 2) m = 10 11 10 10 A) B) C) 10 11 11
D) -
11 10
Answer: A Type: BI Var: 50+ Objective: Determine the Slopes of Parallel and Perpendicular Lines
The slope of a line is given. Find the slope of a line perpendicular to the given line. 14 3) m = 5 5 14 5 A) B) C) 14 5 14
D) -
14 5
Answer: C Type: BI Var: 50+ Objective: Determine the Slopes of Parallel and Perpendicular Lines
The slope of a line is given. a. Determine the slope of a line parallel to the given line, if possible. b. Determine the slope of a line perpendicular to the given line, if possible. 4) m is undefined A) a. m is undefined; b. m = 0 B) a. m = 0; b. m = -1 C) a. m = 0; b. m is undefined D) a. m = 0; b. m = 1 Answer: A Type: BI Var: 2 Objective: Determine the Slopes of Parallel and Perpendicular Lines
Determine if the lines defined by the given equations are parallel, perpendicular, or neither. 7 5) y= x- 2 5 7 y=- x-4 5 A) perpendicular
B) neither
C) parallel
Answer: B Type: BI Var: 50+ Objective: Determine the Slopes of Parallel and Perpendicular Lines
6) -4y = 2x + 5 -4x = 8y + 3 A) perpendicular Answer: B
B) parallel
Type: BI Var: 50+ Objective: Determine the Slopes of Parallel and Perpendicular Lines
Page 66
C) neither