Download Unit One Final Test

Chapter 1 Pretest
Name:
Date:
1
Write an algebraic expression for the phrase.
the product of d and 4
2
A
B
4d
C
D
d+4
Write an algebraic expression for the phrase.
the sum of d and twice g
A
B
C
D
d + 2g
g + 2d
d + g2
2(d + g)
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
3
Boxes of nails are stacked on top of each other on a work bench. The table below shows
how the height above the floor of the topmost box depends on the number of boxes. What
is a rule for the height? Give the rule in words and as an algebraic expression.
Number of Boxes
Height (in.)
2
(9 • 2) + 39
3
(9 • 3) + 39
4
(9 • 4) + 39
n
?
A
B
The height above the floor, in inches, of the stack of boxes is the product of 39
and 9 plus the number of boxes, n. An algebraic expression for this rule is 39(9 +
n).
The height above the floor, in inches, of the stack of boxes is the sum of 39 and 9
times the number of boxes, n. An algebraic expression for this rule is 9n + 39.
The height above the floor, in inches, of the stack of boxes is the quotient of 9 and
C
D
39 plus the number of boxes, n. An algebraic expression for this rule is
.
The height above the floor, in inches, of the stack of boxes is the product of 9 and
39 plus the number of boxes, n. An algebraic expression for this rule is 9(n + 39).
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
4
The table shows the costs associated with a ski trip. Write an expression to determine the
cost of 4 children and 2 adults renting equipment for a ski trip that lasts h hours. The
equipment rental fee is for the entire family.
Adult Lift Pass
$35
Child Lift Pass
$15
Family Equipment
Rental
$10 per hour
A
B
C
D
5
[4(15) + 2(35) + 6(10)]h
[4(15) + 2(35) + 10]h
4(15) + 2(35) + 10h
4(15) + 2(35) + 6(10)h
Simplify the expression.
32 + (9 – 8 ÷ 2)
A
B
C
D
6
11
14
Simplify the expression.
9 ÷ (–3) + 4 ÷ (–8)
A
B
C
D
3.5
–3.5
2.5
–2.5
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Chapter 1 Pretest
7
Simplify the expression.
A
B
C
D
8
9
–9
9, –9
40.5
Evaluate the expression for the given values of the variables.
; a = –3, b = –2
A
B
C
D
9
4
–4
7
3.5
Evaluate the expression for the given values of the variables.
2a2 – (4b + c); a = –3, b = –2, and c = 1
A
B
C
D
29
25
9
11
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Chapter 1 Pretest
10
Name the subset(s) of real numbers to which each number belongs. Then order the
numbers from least to greatest.
,
,
A
belongs to the set of rational numbers,
belongs to the set of irrational
numbers, and belongs to the set of integers and irrational numbers. The
numbers ordered from least to greatest are
B
,
, and
12
,
to the nearest integer.
47
24
9
10
What property is shown in the following equation?
17 + 8 + 3 = 17 + 3 + 8
A
B
C
D
, and
.
belongs to the set of rational numbers,
belongs to the set of irrational
numbers, and belongs to the set of whole numbers and integers. The numbers
Estimate
A
B
C
D
,
.
ordered from least to greatest are
11
.
belongs to the set of irrational numbers,
belongs to the set of rational
numbers, and belongs to the set of integers. The numbers ordered from least
to greatest are
D
, and
belongs to the set of irrational numbers,
belongs to the set of rational
numbers, and belongs to the set of integers and rational numbers. The
numbers ordered from least to greatest are
C
,
Associative Property of Addition
Commutative Property of Addition
Identity Property of Zero
Identity Property of 1
Copyright © 2005 - 2006 by Pearson Education
, and
.
Chapter 1 Pretest
13
Use the table below. Find the total cost of 1 salad, 3 sandwiches, and 2 drinks. Use mental
math.
Lunch Menu
Salad
$3.25
Sandwich
$6.75
Drink
$1.50
A
B
C
D
14
What word phrases represent the expressions
expressions equivalent? Explain.
A
B
C
D
15
$25.00
$26.50
$25.75
$26.25
and
? Are the two
The first expression is “the product of 2 times a number x and 3 plus 7,” and the
second is “2 times a number x times the sum of 3 and 7.” The two expressions are
equivalent by the Commutative Property of Addition.
The first expression is “the sum of 2 and a number x plus 7,” and the second is “2
times a number x plus 7.” The two expressions are equivalent by the Associative
Property of Addition.
The first expression is “the sum of 2 times a number x and 3 plus 7,” and the
second is “2 times a number x plus the sum of 3 and 7.” The two expressions are
equivalent by the Commutative Property of Addition.
The first expression is “the sum of 2 times a number x and 3 plus 7,” and the
second is “2 times a number x plus the sum of 3 and 7.” The two expressions are
equivalent by the Associative Property of Addition.
Use grouping symbols to make the following equation true.
A
B
C
D
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
16
Choose the term that correctly completes the sentence.
Together, rational numbers and irrational numbers form the set of
A
B
C
D
17
.
real numbers
whole numbers
natural numbers
integers
What set of numbers is reasonable for the temperatures on a winter day?
A
B
C
D
irrational numbers
whole numbers
integers
rational numbers
18
What is the simplified form of
numbers.
19
, when
? Explain using the properties of real
A
; Use the rule for multiplying fractions to rearrange the expression to
then the Identity Property of Multiplication to simplify further.
B
; Use the rule for multiplying fractions to rearrange the expression to
then the Identity Property of Multiplication to simplify further.
C
; Use the rule for multiplying fractions to rearrange the expression to
then the Identity Property of Multiplication to simplify further.
D
; Use the rule for multiplying fractions to rearrange the expression to
then the Identity Property of Multiplication to simplify further.
Simplify 56 · 25 · 4. State a property that you can use.
A
B
C
D
27; Inverse Property of Multiplication
5,600; Associative Property of Multiplication
5,600; Commutative Property of Multiplication
5,600; Identity Property of Multiplication
Copyright © 2005 - 2006 by Pearson Education
, and
, and
, and
, and
Chapter 1 Pretest
20
Simplify 12edf – 13def. State a property that you can use.
A
B
C
D
21
22
Write an algebraic expression for the phrase the sum of g and 3.
A
B
3g
3g + 3
C
D
g
3
g+3
Write a word phrase for -5-4n
A
B
C
D
23
–edf; Inverse Property of Multiplication
–25edf; Associative Property of Multiplication
–edf; Commutative Property of Multiplication
edf; Identity Property of Multiplication
negative 5 minus 4 plus a number n
negative 5 minus 4 times a number n
4 times a number n minus 5
5 minus 4 times a number n
Evaluate the expression 9(a + 2b) + c for a = –3, b = –2, and c = 1.
A
B
C
D
–62
–91
46
64
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
24
Crates of old vinyl records are stacked on top of each other on a desk. The table below
shows how the height above the floor of the topmost crate depends on the number of
crates. What is a rule for the height? Give the rule in words and as an algebraic
expression.
Number of Crates
Height (in.)
2
(10 • 2) + 43
3
(10 • 3) + 43
4
(10 • 4) + 43
n
?
A
B
C
D
25
The height above the floor, in inches, of the stack of crates is the sum of 43 and
10 times the number of crates, n. An algebraic expression for this rule is 43(10 +
n).
The height above the floor, in inches, of the stack of crates is the product of 43
and 10 plus the number of crates, n. An algebraic expression for this rule is 43(10
+ n).
The height above the floor, in inches, of the stack of crates is the sum of 43 and
10 times the number of crates, n. An algebraic expression for this rule is 10n + 43.
The height above the floor, in inches, of the stack of crates is the product of 43
and 10 plus the number of crates, n. An algebraic expression for this rule is 10n +
43.
Simplify the expression.
(10 ÷ 5) · 3
A
B
C
D
1.5
5
6
15
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
26
Simplify the expression.
A
B
C
D
27
Simplify the expression.
,
A
B
C
D
28
Simplify the expression.
|
|
A
B
C
D
29
6
5.7
Simplify the expression.
A
B
C
D
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
30
Is the statement true or false? If false, give a counterexample.
For all real numbers a, b and c, a(b+c)=ab+bc
A
B
C
D
31
Is the ordered pair (6, 5) a solution to the equation 3x-4y=-2? Explain.
A
B
C
D
32
true
false; a(b + c) = ab – ac
false; if a = b = c = 1, then 1(1 + 1) 1(1) + 1(1)
false; if a = 1, b = 2, and c = 3, then 1(2 + 3) 1(2) + 2(3)
yes;
yes;
no;
no;
Which group of numbers is ordered from least to greatest?
A
4/5, –0.9, –3
B
–3, –0.9,5
C
–0.9,
D
4
, –3
, –3, –0.9
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
33
Ms. Hader split her class up into n debate teams. Each team has 4 students. Choose the
graph that describes the total number of students, s, in Ms. Hader’s class. If there are 9
teams, how many students are in the class?
A
There are 40 students in the class.
B
There are 22 students in the class.
C
There are 36 students in the class.
D
There are 18 students in the class.
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
34
Simplify the expression.
–(–x)3 – x3
A
B
C
D
35
–4x3
–2x3
2x3
0
Simplify the expression.
A
B
C
D
36
Simplify the expression.
–(–5 + 4m)
A
B
C
D
37
5 – 4m
5 + 4m
–5 – 4m
–5 + 4m
Simplify the expression.
–9(4 – 3j)
A
B
C
D
36 – 27j
36 + 27j
–36 + 27j
36 + j
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
38
Name the subset(s) of real numbers to which the number belongs.
–1.57
A
B
C
D
39
Name the subset(s) of real numbers to which the number belongs.
A
B
C
D
40
rational only
rational and irrational
irrational only
rational and integer
Which property does 3(17) = 3(20) – 3(3) illustrate?
A
B
C
D
41
integer only
rational only
irrational and rational
rational and integer
Associative Property of Multiplication
Commutative Property of Multiplication
Distributive Property
Identity Property of Multiplication
Is the set of whole numbers the same as the set of positive integers? Explain.
A
B
C
D
No; the set of positive integers includes 0 but the set of whole numbers does not.
Yes; both sets start at 1 and continue into infinity.
No; the set of whole numbers includes 0 but the set of positive integers does not.
Yes; both sets start at 0 and continue into infinity.
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
42
Find and correct the error in the work shown below.
A
The student multiplied 3 by 8 before adding 7. The correct answer should be 23.
B
The student subtracted 8 and 4 before dividing by 2. The correct answer should
be 27.
The student added 8 and 4 before dividing by 2. The correct answer should be
27.
The student added 7 and 3 before multiplying by 8. The correct answer should be
23.
C
D
43
Which of the following expressions simplifies to -abcd, where a, b, c and d are real
numbers?
A
B
C
D
44
Determine whether the following is an example of inductive or deductive reasoning.
Explain.
Consider the statement: For all real numbers a and b,
.
This statement is false, because for a = 3 and b = 5,
, whereas
. Since
,
for all real numbers a and b.
A
B
C
D
45
Deductive reasoning; the conclusion was found logically from the given facts.
Inductive reasoning; the conclusion was found logically from the given facts.
Deductive reasoning; the conclusion was found by generalizing observations.
Inductive reasoning; the conclusion was found by generalizing observations.
Is the statement “The absolute value of a number is always greater than its opposite” true?
A
B
C
D
Yes; absolute value is always positive.
Yes; all positive numbers are greater than their opposites.
No; the absolute value of a negative number is equal to its opposite.
No; all negative numbers are greater than their opposites.
Copyright © 2005 - 2006 by Pearson Education
Chapter 1 Pretest
Copyright © 2005 - 2006 by Pearson Education