Chapter 2 Test (Please Do Not Write on This )

CHAPTER 2 TEST (PLEASE DO NOT WRITE ON THIS!!!)

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____1.Evaluate the expression to find the missing values in the table.

x / x + 2 • 4
8 / 16
11 / ?
22 / ?
a. / 19, 30 / c. / 27, 38
b. / 3, 14 / d. / 52, 96

____2.Isabelwrote 11 letters to friends each month for x months in a row. Write an expression to show the total number of letters Isabel wrote.

a. / / c. / 11 + x
b. / 11x / d. / 11 – x

____3.Mikecompleted 19 math problems before dinner for tonight’s homework, and he completed x problems after dinner. Write an expression to determine the total number of problems he completed.

a. / 19x / c. / 19 – x
b. / / d. / 19 + x

____4.Write the phrase “13 added to z” as a numerical or algebraic expression.

a. / 13 z / c. / z • 13
b. / z + 13 / d. / 13 – z

____5.Write the phrase “the product of 12 and 89” as a numerical or algebraic expression.

a. / / c. / (12)(89)
b. / / d. /

____6.Write the phrase “z divided by 2” as a numerical or algebraic expression.

a. / / c. /
b. / / d. /

____7.Write two phrases for the expression 18t.

a. / the quotient of 18 and t; 18 divided by t
b. / t more than 18; t added to 18
c. / 18 groups of t; 18 times t
d. / t subtracted from 18; t less than 18

____8.Write two phrases for the expression p 7.

a. / p subtracted from 7; p less than 7
b. / the quotient of p and 7; p divided by 7
c. / the quotient of 7 and p; 7 divided by p
d. / the product of p and 7; p times 7

____9.Write an expression for the sequence in the table.

Position / 1 / 2 / 3 / 4 / 5 / n
Value of Term / / / / / / ?
a. / / c. /
b. / / d. /

____10.Determine whether is a solution to .

a. / Since , 23 is not a solution to .
b. / Since , 23 is not a solution to .
c. / Since , 23 is a solution to .
d. / Since , 23 is not a solution to .

____11.Solve the equation . Check your answer.

a. / s = 48 / c. / s = 47
b. / s = 57 / d. / s = 61

____12.Write “12 is 8 subtracted from y” as an algebraic equation. Then find the solution.

a. / ;
b. / ;
c. / ;
d. / ;

____13.Solve the equation 7m = 84. Check your answer.

a. / m = 77 / c. / m = 13
b. / m = 91 / d. / m = 12

____14.Graph the solutions to z 12 on a number line.

a. / / c. /
b. / / d. /

____15.Solve the inequality 2y 10. Graph the solutions on a number line.

a. / y5
 / c. / y20

b. / y5
/ d. / y 20

____16.Solve the inequality  3. Graph the solutions on a number line.

a. / m
/ c. / m12

b. / m12
/ d. / m

____17.Solve the equation. Check your answer.

a. / p = 33 / c. / p = 43
b. / p = / d. / p = 190

Multiple Response

Identify one or more choices that best complete the statement or answer the question.

____18.Solve the equation n + 10 = 37. Check your answer.

a. / n = 47 / c. / n = 37
b. / n = 28 / d. / n = 27

Numeric Response

19.(CRT) An expression is shown below.

4n + 7.

What is the value of the expression when n = 2? Show your work.

a. 15

b. 36

c. 42

d. 49

20.

Matching

Match each vocabulary term with its definition.

a. / algebraic expression / e. / variable
b. / constant / f. / ms mora
c. / solution / g. / ms.mora
d. / inequality

____21.is a statement that two quantities are not equal

____22.an expression that contains at least one variable

____23.a value or values that make an equation true

____24.a symbol used to represent a quantity that can change

____25.a value that does not change

Short Answer

26.Write two phrases for the expression 85 – y.

27.Define algebraic expression and give an example

28.Define variable and give an example

29.When graphing inequalites, how do you decide whether or not to shade to the left or right on the number line?

30.Solve the inequality 5 x 1, and graph the solution on a number line. Show your work.

Essay

31.Explain the meaning of the statement “Subtraction is the inverse of addition.” Use the equation to demonstrate.

CHAPTER 2 PRACTICE TEST

Answer Section

MULTIPLE CHOICE

1.ANS:A

Substitute for x in x + 2 • 4. Use the order of operations.

x = 8; 8 + 2 • 4 = 16

x = 11;11 + 2 • 4 = 19

x = 22; 22 + 2 • 4 = 30

The missing values are 19 and 30.

Feedback
A / Correct!
B / First, substitute the number for the variable. Then, use the order of operations to find the value.
C / Use the order of operations.
D / Substitute the number for the variable and then find the value.

PTS:1DIF:AverageREF:Page 54

OBJ:2-1.1 Evaluating Algebraic ExpressionsNAT:8.5.3.c

TOP:2-1 Variables and ExpressionsKEY:expression | algebraic expression | evaluate

2.ANS:B

To find the total number of letters Isabel wrote, multiply the number of letters by the number of months.

11x

Feedback
A / Use the operation that means to put together groups of equal parts.
B / Correct!
C / Use the operation that means to put together groups of equal parts.
D / Use the correct operation.

PTS:1DIF:AverageREF:Page 58OBJ:2-2.1 Application

NAT:8.5.2.gTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

3.ANS:D

To find the total number of problems Mike completed, add the number of problems completed after dinner to the number of problems completed before dinner.

19 + x

Feedback
A / Use the correct operation.
B / Use the correct operation.
C / To put things together, use addition. To find how many more, use subtraction.
D / Correct!

PTS:1DIF:BasicREF:Page 58OBJ:2-2.1 Application

NAT:8.5.2.gTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

4.ANS:B

Use “+” when you see these keywords:

added to

plus

the sum

more than

Use “” when you see these keywords:

subtracted from

minus

the difference

take away

Feedback
A / Look for keywords in the phrase.
B / Correct!
C / Look for keywords in the phrase.
D / Check the order of the terms.

PTS:1DIF:BasicREF:Page 59OBJ:2-2.2 Translating Words into Math

NAT:8.5.2.bTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

5.ANS:C

Use multiplication when you see these keywords:

times

multiplied by

the product

groups of

Feedback
A / Look for keywords in the phrase.
B / Look for keywords in the phrase.
C / Correct!
D / Look for keywords in the phrase.

PTS:1DIF:AverageREF:Page 59OBJ:2-2.2 Translating Words into Math

NAT:8.5.2.bTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

6.ANS:C

Use “” when you see these keywords:

divided by

the quotient

Feedback
A / Look for keywords in the phrase.
B / Check the order of the terms.
C / Correct!
D / Look for keywords in the phrase.

PTS:1DIF:AverageREF:Page 59OBJ:2-2.2 Translating Words into Math

NAT:8.5.2.bTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

7.ANS:C

18t:

18 times t;

t multiplied by 18;

the product of 18 and t;

18 groups of t

Feedback
A / Look for keywords.
B / Look for keywords.
C / Correct!
D / Check the operation.

PTS:1DIF:AverageREF:Page 59OBJ:2-2.3 Translating Math into Words

NAT:8.5.2.gTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

8.ANS:B

p 7:

pdivided by 7;

the quotient of p and 7

Feedback
A / Check the operation.
B / Correct!
C / Check the order of the terms.
D / Check the operation.

PTS:1DIF:AverageREF:Page 59OBJ:2-2.3 Translating Math into Words

NAT:8.5.2.gTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

9.ANS:C

Look for a relationship between the positions and the values of the terms in the sequence.

Think: How do I go from position 1 to the value of its term, ? Try the expression . Check this rule for the next term in the sequence. This rule works for the entire sequence.

Feedback
A / Look for a relationship between the positions and the values of the terms in the sequence. Check that the expression works for all of the data in the table.
B / Look for a relationship between the positions and the values of the terms in the sequence. Check that the expression works for all of the data in the table.
C / Correct!
D / Check that the expression works for all of the data in the table.

PTS:1DIF:AverageREF:Page 63

OBJ:2-3.2 Writing an Expression for a SequenceNAT:8.5.2.b

TOP:2-3 Translating Between Tables and Expressions

10.ANS:C

? / Substitute 23 for b.
? / Add.

Since , 23 is a solution to .

Feedback
A / If the value for the variable makes the equation true, then that value is a solution.
B / Simplify both sides of the equation and compare.
C / Correct!
D / Substitute the given value for b in the equation, and see if you get a true statement.

PTS:1DIF:AverageREF:Page 70

OBJ:2-4.1 Determining Solutions of EquationsTOP:2-4 Equations and Their Solutions

11.ANS:D

/ 7 is subtracted from s.
/ Add 7 to both sides to undo the subtraction.
s = 61

Check

? / Substitute 61 for s in the equation.
? / Subtract.
/ 61 is the solution.
Feedback
A / Add to both sides of the equation to undo the subtraction.
B / Substitute the solution in the equation to check your answer.
C / Add to both sides of the equation to undo the subtraction.
D / Correct!

PTS:1DIF:AverageREF:Page 78

OBJ:2-6.1 Solving Subtraction EquationsNAT:8.5.3.c

TOP:2-6 Subtraction EquationsKEY:equation | solving | subtraction

12.ANS:C

The symbol “” represents “is equal to” and the algebraic expression “” represents “8 subtracted from y.”

/ 8 is subtracted from y.
Add 8 to both sides to undo the subtraction.
Feedback
A / Check the order of the number and the variable.
B / Use addition to undo the subtraction.
C / Correct!
D / Check the order of the number and the variable.

PTS:1DIF:AdvancedNAT:8.5.3.cTOP:2-6 Subtraction Equations

KEY:algebraic equation | subtraction equation | solving algebraic equations | solving subtraction equations

13.ANS:D

7m = 84 / m is multiplied by 7.
/ Divide both sides by 7 undo the multiplication..
m = 12

Check

7m = 84
7(12) = 84 ? / Substitute 12 for m in the equation.
? / Multiply.
/ 12 is the solution.
Feedback
A / Substitute the solution in the equation to check your answer.
B / Divide to undo the multiplication.
C / Divide to undo the multiplication.
D / Correct!

PTS:1DIF:AverageREF:Page 81

OBJ:2-7.1 Solving Multiplication EquationsNAT:8.5.3.c

TOP:2-7 Multiplication EquationsKEY:equation | solving | multiplication

14.ANS:B

The closed circle on the point 12 shows that 12 is a solution.

Feedback
A / Check the inequality symbol to make sure the arrow on the number line is going in the correct direction.
B / Correct!
C / A closed circle on the point shows that the point is a solution. An open circle on the point shows that the point is not a solution.
D / Check the inequality symbol to make sure the arrow on the number line is going in the correct direction.

PTS:1DIF:AverageREF:Page 90OBJ:2-Ext.1 Graphing Inequalities

TOP:2-Ext InequalitiesKEY:inequality | graph

15.ANS:A

2y 10 / y is multiplied by 2.
/ Divide both sides by 2 to undo the multiplication.
y5

The closed circle on the point 5 shows that 5 is a solution.

Feedback
A / Correct!
B / Check the inequality symbol to make sure the arrow on the number line is going in the correct direction.
C / For "less than" or "greater than", use an open circle. For "greater than or equal to" or "less than or equal to", use a closed circle.
D / To solve the inequality, divide both sides by the number to undo the multiplication.

PTS:1DIF:AverageREF:Page 90

OBJ:2-Ext.2 Solving and Graphing InequalitiesNAT:8.5.4.a

TOP:2-Ext InequalitiesKEY:inequality | graph | solving

16.ANS:C

 3 / m is divided by 4.
 3(4) / Multiply both sides by 4 to undo the division.
m12

The open circle on the point 12 shows that 12 is not a solution.

Feedback
A / For "less than" or "greater than", use an open circle. For "greater than or equal to" or "less than or equal to", use a closed circle.
B / Check the inequality symbol to make sure the arrow on the number line is going in the correct direction.
C / Correct!
D / To solve the inequality, multiply both sides by the number to undo the division.

PTS:1DIF:AverageREF:Page 90

OBJ:2-Ext.2 Solving and Graphing InequalitiesNAT:8.5.4.a

TOP:2-Ext InequalitiesKEY:inequality | graph | solving

17.ANS:D

/ p is divided by 5.
/ Multiply both sides by 5 to undo the division.
p = 190

Check

? / Substitute 190 for p in the equation.
? / Divide.
/ 190 is the solution.
Feedback
A / Substitute the solution in the equation to check your answer.
B / Multiply to undo the division.
C / Multiply to undo the division.
D / Correct!

PTS:1DIF:AverageREF:Page 85OBJ:2-8.1 Solving Division Equations

NAT:8.5.3.cTOP:2-8 Division EquationsKEY:equation | solving | division

MULTIPLE RESPONSE

18.ANS:D

n + 10 = 37 / 10 is added to n.
n + 10 10 = 37 10 / Subtract 10 from both sides to undo the addition.
n = 27

Check

n + 10 = 37
? / Substitute 27 for n in the equation.
? / Add.
/ 27 is the solution.

PTS:1DIF:BasicREF:Page 75OBJ:2-5.1 Solving Addition Equations

NAT:8.5.3.cTOP:2-5 Addition EquationsKEY:equation | solving | addition

NUMERIC RESPONSE

19.ANS:a. 15

PTS:1DIF:AverageNAT:8.5.3.cTOP:2-1 Variables and Expressions

20.ANS:a. n < 3

PTS:1DIF:AdvancedNAT:8.5.3.bTOP:2-7 Multiplication Equations

MATCHING

21.ANS:DPTS:1DIF:BasicREF:Page 70

NAT:8.5.4.bTOP:2-4 Equations and Their SolutionsKEY:equation | solving

22.ANS:APTS:1DIF:BasicREF:Page 54

NAT:8.5.3.bTOP:2-1 Variables and Expressions

KEY:expression | algebraic expression | evaluate

23.ANS:CPTS:1DIF:BasicREF:Page 70

NAT:8.5.4.bTOP:2-4 Equations and Their SolutionsKEY:equation | solving

24.ANS: e PTS:1DIF:BasicREF:Page 54

NAT:8.5.3.bTOP:2-1 Variables and Expressions

KEY:expression | algebraic expression | evaluate

25.ANS:bPTS:1DIF:BasicREF:Page 54

NAT:8.5.3.bTOP:2-1 Variables and Expressions

KEY:expression | algebraic expression | evaluate

SHORT ANSWER

26.ANS:

Answers could include any two of the following (the order in which y and 85 appear in each phrase is important):

y subtracted from 85

85 minus y

the difference of 85 and y

y less than 85

take away y from 85

Scoring Rubric:
4 / Two of the example phrases are given with the operands in the correct order.
3 / Two of the example phrases are given; however, the operands are not in the correct order.
2 / The answer includes only one example phrase that shows understanding of the concept.
1 / The answer includes none of the example phrases and shows no understanding of the concept.

PTS:1DIF:AverageOBJ:2-2.PA02 Translate Between Words and Math

NAT:8.5.2.aTOP:2-2 Translate Between Words and Math

KEY:expression | algebraic expression

27.ANS:

Scoring Rubric:
4 / The solution is correct, and all of the work is shown as above.
or
A different logical method is used to find the correct solution.
3 / Both solutions are correct, but not all of the work is shown.
2 / The solution for part a is correct, but the solution for part b is incorrect.
or
The solution for part a is incorrect, but the work for part b is correct.
1 / Both solutions are incorrect, and the work shows no understanding of the concept.

PTS:1DIF:AverageOBJ:2-4.PA04 Equations and Their Solutions

NAT:8.2.2.bTOP:2-4 Equations and Their SolutionsKEY:equation | solving

28.ANS:

a. / The equation 38 = 25 + x can be used to solve the problem.
38 = 25 + x
– 25 = – 25
13 = x
So the unknown weight is 13 grams.
b. / There must be 49 grams of weight on the left.
y = 25 + 24
y = 49
Scoring Rubric:
4 / The solution is correct, and all of the work is shown as above.
or
A different logical method is used to find the correct solution.
3 / Both solutions are correct, but not all of the work is shown.
2 / The solution for part a is correct, but the solution for part b is incorrect.
or
The solution for part a is incorrect, but the work for part b is correct.
1 / Both solutions are incorrect, and the work shows no understanding of the concept.

PTS:1DIF:AverageOBJ:2-5.PA05 Solving Addition Equations

NAT:8.5.3.aTOP:2-5 Addition EquationsKEY:equation | solving | addition

29.ANS:

The solution is q = 72.

58 = q – 14

+ 14 = + 14

72 = q

Check

58 = 72 – 14 ?

58 = 58 ?

Yes

Scoring Rubric:
4 / The solution is correct, and all of the work is shown as above.
or
A different logical method is used to find the correct solution.
3 / The solution is correct, but not all of the work is shown.
2 / The solution is incorrect, but the work shows understanding of the concept.
1 / The solution is incorrect, and the work shows no understanding of the concept.

PTS:1DIF:AverageOBJ:2-6.PA06 Solving Subtraction Equations

NAT:8.5.4.aTOP:2-6 Subtraction EquationsKEY:equation | solving | subtraction

30.ANS:

a. / The width of the base of the cage is 1 foot.
area = length • width

3 = 3 • w

1 = w

b. / Yes, Oscar would have more room.
Since each side of the base is 2 feet long, it is a square. So l = 2 and w = 2.
area = length • width
A = l • w
A = 2 • 2
A = 4 square feet
Since 4 square feet is greater than 3 square feet, Oscar would have more room.
Scoring Rubric:
4 / The solution is correct, and all of the work is shown as above.
or
A different logical method is used to find the correct solution.
3 / Both solutions are correct, but not all of the work is shown.
2 / The solution for part a is correct, but the solution for part b is incorrect.
or
The solution for part a is incorrect, but the work for part b is correct.
1 / Both solutions are incorrect, and the work shows no understanding of the concept.

PTS:1DIF:AverageOBJ:2-7.PA07 Solving Multiplication Equations

NAT:8.5.3.aTOP:2-7 Multiplication EquationsKEY:equation | solving | multiplication

31.ANS:

The solution is y = 63.

y = 63

Check

9 = 9?

Yes, so 63 is the solution.

PTS:1DIF:AverageOBJ:2-8.PA08 Solving Division Equations

NAT:8.5.4.aTOP:2-8 Division EquationsKEY:equation | solving | division

32.ANS:

The solution is 4 x (or x 4).

5 x 1 1 is added to x.

– 1– 1 Subtract 1 from both sides to undo the addition.

4 x (or x 4)

PTS:1DIF:AverageOBJ:2-Ext.PA09 Inequalities

NAT:8.1.1.bTOP:2-Ext InequalitiesKEY:inequality | graph | solving

ESSAY

33.ANS:

“Subtraction is the inverse of addition” means that subtraction is the opposite of addition, or that it can be used to “undo” addition in an equation.

(The explanation does not require both of the italicized phrases used above.)

x + 9 = 17 / 9is added to x.
– 9 = – 9 / Subtract 9 from both sides to undo the addition.
x = 8

PTS:1DIF:BasicOBJ:2-5.PA12 Addition Equations

NAT:8.5.4.aTOP:2-5 Addition EquationsKEY:equation | solving | addition

Scoring Rubric:
4 / The explanation is correct, and the demonstration is complete as above.
or
A different logical explanation is given, and the demonstration is complete as above.
3 / The explanation is correct, but the demonstration is incomplete or incorrect.
2 / The explanation is incomplete or incorrect, but the demonstration shows some understanding of the concept.
1 / The explanation is incorrect, and the demonstration is missing or shows no understanding of the concept.