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Copyright © 2005 - 2006 by Pearson Education

Chapter 1 Pretest Name:

Date:

1 Write an algebraic expression for the phrase.

the product of d and 4

A B 4d

C D d + 4

2 Write an algebraic expression for the phrase.

the sum of d and twice g

A d + 2g B g + 2d C d + g2

D 2(d + g)

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. Whatis a rule for the height? Give the rule in words and as an algebraic expression.

Number of BoxesHeight (in.)

2 (9 • 2) + 39

3 (9 • 3) + 39

4 (9 • 4) + 39

n ?

The height above the floor, in inches, of the stack of boxes is the product of 39A and 9 plus the number of boxes, n. An algebraic expression for this rule is 39(9 +

n).

B 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

C39 plus the number of boxes, n. An algebraic expression for this rule is .

D The height above the floor, in inches, of the stack of boxes is the product of 9 and39 plus the number of boxes, n. An algebraic expression for this rule is 9(n + 39).

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. Theequipment rental fee is for the entire family.

Adult Lift Pass $35

Child Lift Pass $15

Family EquipmentRental

$10 per hour

A [4(15) + 2(35) + 6(10)]hB [4(15) + 2(35) + 10]hC 4(15) + 2(35) + 10hD 4(15) + 2(35) + 6(10)h

5 Simplify the expression.32 + (9 – 8 ÷ 2)

A

B

C 11D 14

6 Simplify the expression.9 ÷ (–3) + 4 ÷ (–8)

A 3.5B –3.5C 2.5D –2.5

Chapter 1 Pretest


7 Simplify the expression.

A 9B –9C 9, –9D 40.5

8 Evaluate the expression for the given values of the variables.

; a = –3, b = –2

A 4B –4C 7D 3.5

9 Evaluate the expression for the given values of the variables.

2a2 – (4b + c); a = –3, b = –2, and c = 1

A 29B 25C 9D 11

Chapter 1 Pretest


10 Name the subset(s) of real numbers to which each number belongs. Then order the numbers from least to greatest.

, ,

belongs to the set of rational numbers, belongs to the set of irrationalA numbers, and belongs to the set of integers and irrational numbers. The

numbers ordered from least to greatest are , , and .

belongs to the set of irrational numbers, belongs to the set of rationalB numbers, and belongs to the set of integers and rational numbers. The

numbers ordered from least to greatest are , , and .

belongs to the set of irrational numbers, belongs to the set of rationalC numbers, and belongs to the set of integers. The numbers ordered from least

to greatest are , , and .

belongs to the set of rational numbers, belongs to the set of irrationalD numbers, and belongs to the set of whole numbers and integers. The numbers

ordered from least to greatest are , , and .

11 Estimate to the nearest integer.

A 47B 24C 9D 10

12 What property is shown in the following equation?

17 + 8 + 3 = 17 + 3 + 8

A Associative Property of AdditionB Commutative Property of AdditionC Identity Property of ZeroD Identity Property of 1

Chapter 1 Pretest


13 Use the table below. Find the total cost of 1 salad, 3 sandwiches, and 2 drinks. Use mentalmath.

Lunch Menu

Salad $3.25

Sandwich $6.75

Drink $1.50

A $25.00B $26.50C $25.75D $26.25

14 What word phrases represent the expressions and ? Are the two expressions equivalent? Explain.

The first expression is “the product of 2 times a number x and 3 plus 7,” and theA 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

B times a number x plus 7.” The two expressions are equivalent by the AssociativeProperty of Addition.The first expression is “the sum of 2 times a number x and 3 plus 7,” and the

C 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

D 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.

15 Use grouping symbols to make the following equation true.

A B C D

Chapter 1 Pretest


16 Choose the term that correctly completes the sentence.Together, rational numbers and irrational numbers form the set of .

A real numbersB whole numbers C natural numbers D integers

17 What set of numbers is reasonable for the temperatures on a winter day?

A irrational numbersB whole numbersC integersD rational numbers

18

What is the simplified form of , when ? Explain using the properties of real numbers.

A ; Use the rule for multiplying fractions to rearrange the expression to , and then the Identity Property of Multiplication to simplify further.

B ; Use the rule for multiplying fractions to rearrange the expression to , and then the Identity Property of Multiplication to simplify further.

C ; Use the rule for multiplying fractions to rearrange the expression to , and then the Identity Property of Multiplication to simplify further.

D ; Use the rule for multiplying fractions to rearrange the expression to , and then the Identity Property of Multiplication to simplify further.

19 Simplify 56 · 25 · 4. State a property that you can use.

A 27; Inverse Property of MultiplicationB 5,600; Associative Property of MultiplicationC 5,600; Commutative Property of MultiplicationD 5,600; Identity Property of Multiplication


Chapter 1 Pretest

20 Simplify 12edf – 13def. State a property that you can use.

A –edf; Inverse Property of MultiplicationB –25edf; Associative Property of Multiplication C –edf; Commutative Property of Multiplication D edf; Identity Property of Multiplication

21 Write an algebraic expression for the phrase the sum of g and 3.

A 3gB 3g + 3C g 3D g + 3

22 Write a word phrase for -5-4n

A negative 5 minus 4 plus a number nB negative 5 minus 4 times a number nC 4 times a number n minus 5D 5 minus 4 times a number n

23 Evaluate the expression 9(a + 2b) + c for a = –3, b = –2, and c = 1.

A –62B –91C 46D 64

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 algebraicexpression.

Number of Crates Height (in.)

2 (10 • 2) + 43

3 (10 • 3) + 43

4 (10 • 4) + 43

n ?

The height above the floor, in inches, of the stack of crates is the sum of 43 andA 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

B and 10 plus the number of crates, n. An algebraic expression for this rule is 43(10+ n).

C The height above the floor, in inches, of the stack of crates is the sum of 43 and10 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

D and 10 plus the number of crates, n. An algebraic expression for this rule is 10n +43.

25 Simplify the expression. (10 ÷ 5) · 3

A 1.5B 5C 6D 15

Chapter 1 Pretest



A

B

C

D


,

A

B

CD


| |

A 6B CD 5.7


A

B

C

D

A trueB false; a(b + c) = ab – acC false; if a = b = c = 1, then 1(1 + 1) 1(1) + 1(1)

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

D false; if a = 1, b = 2, and c = 3, then 1(2 + 3) 1(2) + 2(3)

31 Is the ordered pair (6, 5) a solution to the equation 3x-4y=-2? Explain.

A yes; B yes; C no; D no;

32 Which group of numbers is ordered from least to greatest?

A 4/5, –0.9, –3

B –3, –0.9,45

C –0.9, , –3

D , –3, –0.9

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


C


D


Chapter 1 Pretest


34 Simplify the expression.–(–x)3 – x3

A –4x3

B –2x3

C 2x3

D 0


A

B

C

D

36 Simplify the expression.–(–5 + 4m)

A 5 – 4mB 5 + 4m C –5 – 4m D –5 + 4m

37 Simplify the expression.–9(4 – 3j)

A 36 – 27jB 36 + 27jC –36 + 27jD 36 + j

Chapter 1 Pretest


38 Name the subset(s) of real numbers to which the number belongs.–1.57

A integer onlyB rational onlyC irrational and rationalD rational and integer

39 Name the subset(s) of real numbers to which the number belongs.

A rational onlyB rational and irrationalC irrational onlyD rational and integer

40 Which property does 3(17) = 3(20) – 3(3) illustrate?

A Associative Property of MultiplicationB Commutative Property of MultiplicationC Distributive PropertyD Identity Property of Multiplication

41 Is the set of whole numbers the same as the set of positive integers? Explain.

A No; the set of positive integers includes 0 but the set of whole numbers does not. B Yes; both sets start at 1 and continue into infinity.C No; the set of whole numbers includes 0 but the set of positive integers does not. D Yes; both sets start at 0 and continue into infinity.

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 shouldbe 27.

C The student added 8 and 4 before dividing by 2. The correct answer should be27.

D The student added 7 and 3 before multiplying by 8. The correct answer should be23.

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 Deductive reasoning; the conclusion was found logically from the given facts. B Inductive reasoning; the conclusion was found logically from the given facts.C Deductive reasoning; the conclusion was found by generalizing observations. D Inductive reasoning; the conclusion was found by generalizing observations.

45 Is the statement “The absolute value of a number is always greater than its opposite” true?

A Yes; absolute value is always positive.B Yes; all positive numbers are greater than their opposites.C No; the absolute value of a negative number is equal to its opposite. D No; all negative numbers are greater than their opposites.

Chapter 1 Pretest


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