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. Isabel wrote 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. Mike completed 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.
1
2
3
4
5
n
Position
?
Value of Term
a.
b.
c.
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.
–20
–15
–10
–5
0
5
10
15
20
b.
–20
–15
–10
–5
0
5
10
15
20
–20
–15
–10
–5
0
5
10
15
20
–50
–25
0
25
50
75
–50
–25
0
25
50
75
–25
0
25
50
75
–1
0
d.
–20
–15
–10
–5
0
5
10
15
20
____ 15. Solve the inequality 2y  10. Graph the solutions on a number line.
a. y5
c. y 20
–20 –16 –12 –8
–4
0
4
8
12
16
20

b. y 5
d. y  20
–20 –16 –12 –8
–4
____ 16. Solve the inequality
0
4
8
12
16
20
c. m12
–3
–2
–1
–75
0
1
2
3
4
b. m 12
–75
–75
 3. Graph the solutions on a number line.
a. m  3 
4
–4
–75
–50
–25
0
25
50
75
–50

d. m  3 
4
–4
–3
–2
1
2
3
4
____ 17. Solve the equation. Check your answer.
a. p = 33
b. p = 7 3
5
c. p = 43
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.
22.
23.
24.
25.
is a statement that two quantities are not equal
an expression that contains at least one variable
a value or values that make an equation true
a symbol used to represent a quantity that can change
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.
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
Essay
31. Explain the meaning of the statement “Subtraction is the inverse of addition.” Use the equation
demonstrate.
to
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
B
C
D
Correct!
First, substitute the number for the variable. Then, use the order of operations to find the
value.
Use the order of operations.
Substitute the number for the variable and then find the value.
PTS: 1
DIF: Average
REF: Page 54
OBJ: 2-1.1 Evaluating Algebraic Expressions
NAT: 8.5.3.c
TOP: 2-1 Variables and Expressions
KEY: 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
B
C
D
Use the operation that means to put together groups of equal parts.
Correct!
Use the operation that means to put together groups of equal parts.
Use the correct operation.
PTS: 1
DIF: Average
REF: Page 58
OBJ: 2-2.1 Application
NAT: 8.5.2.g
TOP: 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
B
C
D
Use the correct operation.
Use the correct operation.
To put things together, use addition. To find how many more, use subtraction.
Correct!
PTS: 1
DIF: Basic
REF: Page 58
OBJ: 2-2.1 Application
NAT: 8.5.2.g
TOP: 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
B
C
D
Look for keywords in the phrase.
Correct!
Look for keywords in the phrase.
Check the order of the terms.
PTS: 1
DIF: Basic
REF: Page 59
OBJ: 2-2.2 Translating Words into Math
NAT: 8.5.2.b
TOP: 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
B
C
D
Look for keywords in the phrase.
Look for keywords in the phrase.
Correct!
Look for keywords in the phrase.
PTS: 1
DIF: Average
REF: Page 59
OBJ: 2-2.2 Translating Words into Math
NAT: 8.5.2.b
TOP: 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
B
C
D
Look for keywords in the phrase.
Check the order of the terms.
Correct!
Look for keywords in the phrase.
PTS: 1
DIF: Average
REF: Page 59
OBJ: 2-2.2 Translating Words into Math
NAT: 8.5.2.b
TOP: 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
B
C
D
Look for keywords.
Look for keywords.
Correct!
Check the operation.
PTS: 1
DIF: Average
REF: Page 59
OBJ: 2-2.3 Translating Math into Words
NAT: 8.5.2.g
TOP: 2-2 Translate Between Words and Math
KEY: expression | algebraic expression
8. ANS: B
p  7:
p divided by 7;
the quotient of p and 7
Feedback
A
B
C
D
Check the operation.
Correct!
Check the order of the terms.
Check the operation.
PTS: 1
DIF: Average
REF: Page 59
OBJ: 2-2.3 Translating Math into Words
NAT: 8.5.2.g
TOP: 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
the next term in the sequence. This rule works for the entire sequence.
Feedback
A
B
C
D
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.
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.
Correct!
Check that the expression works for all of the data in the table.
PTS: 1
DIF: Average
REF: Page 63
OBJ: 2-3.2 Writing an Expression for a Sequence
TOP: 2-3 Translating Between Tables and Expressions
NAT: 8.5.2.b
. Check this rule for
10. ANS: C
?
?
Since
Substitute 23 for b.
Add.
, 23 is a solution to
.
Feedback
A
B
C
D
If the value for the variable makes the equation true, then that value is a solution.
Simplify both sides of the equation and compare.
Correct!
Substitute the given value for b in the equation, and see if you get a true statement.
PTS: 1
DIF: Average
REF: Page 70
OBJ: 2-4.1 Determining Solutions of Equations
TOP: 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
B
C
D
Add to both sides of the equation to undo the subtraction.
Substitute the solution in the equation to check your answer.
Add to both sides of the equation to undo the subtraction.
Correct!
PTS: 1
DIF: Average
REF: Page 78
OBJ: 2-6.1 Solving Subtraction Equations
NAT: 8.5.3.c
TOP: 2-6 Subtraction Equations
KEY: 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
B
C
Check the order of the number and the variable.
Use addition to undo the subtraction.
Correct!
D
Check the order of the number and the variable.
PTS: 1
DIF: Advanced
NAT: 8.5.3.c
TOP: 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
B
C
D
Substitute the solution in the equation to check your answer.
Divide to undo the multiplication.
Divide to undo the multiplication.
Correct!
PTS:
OBJ:
TOP:
14. ANS:
–20
1
DIF: Average
REF: Page 81
2-7.1 Solving Multiplication Equations
NAT: 8.5.3.c
2-7 Multiplication Equations
KEY: equation | solving | multiplication
B
–15
–10
–5
0
5
10
15
20
The closed circle on the point 12 shows that 12 is a solution.
Feedback
A
B
C
D
Check the inequality symbol to make sure the arrow on the number line is going in the
correct direction.
Correct!
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.
Check the inequality symbol to make sure the arrow on the number line is going in the
correct direction.
PTS: 1
DIF: Average
TOP: 2-Ext Inequalities
15. ANS: A
y is multiplied by 2.
2y  10
REF: Page 90
OBJ: 2-Ext.1 Graphing Inequalities
KEY: inequality | graph
Divide both sides by 2 to undo the multiplication.
y5
–16 –12 –8
–4
0
4
8
12
16
20
24
The closed circle on the point 5 shows that 5 is a solution.
Feedback
A
B
C
D
Correct!
Check the inequality symbol to make sure the arrow on the number line is going in the
correct direction.
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.
To solve the inequality, divide both sides by the number to undo the multiplication.
PTS:
OBJ:
TOP:
16. ANS:
1
DIF: Average
REF: Page 90
2-Ext.2 Solving and Graphing Inequalities
NAT: 8.5.4.a
2-Ext Inequalities
KEY: inequality | graph | solving
C
3
m is divided by 4.
 3(4)
Multiply both sides by 4 to undo the division.
m12

–75
–50
–25
0
25
50
75
The open circle on the point 12 shows that 12 is not a solution.
Feedback
A
B
C
D
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.
Check the inequality symbol to make sure the arrow on the number line is going in the
correct direction.
Correct!
To solve the inequality, multiply both sides by the number to undo the division.
PTS:
OBJ:
TOP:
17. ANS:
1
DIF: Average
REF: Page 90
2-Ext.2 Solving and Graphing Inequalities
NAT: 8.5.4.a
2-Ext Inequalities
KEY: inequality | graph | solving
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
B
C
D
Substitute the solution in the equation to check your answer.
Multiply to undo the division.
Multiply to undo the division.
Correct!
PTS: 1
NAT: 8.5.3.c
DIF: Average
REF: Page 85
TOP: 2-8 Division Equations
OBJ: 2-8.1 Solving Division Equations
KEY: equation | solving | division
MULTIPLE RESPONSE
18. ANS: D
n + 10 = 37
n + 10 10 = 37
n = 27
10
10 is added to n.
Subtract 10 from both sides to undo the addition.
Check
n + 10 = 37
?
?
PTS: 1
NAT: 8.5.3.c
Substitute 27 for n in the equation.
Add.
27 is the solution.
DIF: Basic
REF: Page 75
TOP: 2-5 Addition Equations
OBJ: 2-5.1 Solving Addition Equations
KEY: equation | solving | addition
DIF: Average
NAT: 8.5.3.c
TOP: 2-1 Variables and Expressions
DIF: Advanced
NAT: 8.5.3.b
TOP: 2-7 Multiplication Equations
NUMERIC RESPONSE
19. ANS: a. 15
PTS: 1
20. ANS: a. n < 3
PTS: 1
MATCHING
21. ANS:
NAT:
22. ANS:
NAT:
KEY:
23. ANS:
D
PTS: 1
DIF: Basic
8.5.4.b
TOP: 2-4 Equations and Their Solutions
A
PTS: 1
DIF: Basic
8.5.3.b
TOP: 2-1 Variables and Expressions
expression | algebraic expression | evaluate
C
PTS: 1
DIF: Basic
REF: Page 70
KEY: equation | solving
REF: Page 54
REF: Page 70
NAT:
24. ANS:
NAT:
KEY:
25. ANS:
NAT:
KEY:
8.5.4.b
TOP: 2-4 Equations and Their Solutions
e
PTS:
1
DIF:
8.5.3.b
TOP: 2-1 Variables and Expressions
expression | algebraic expression | evaluate
b
PTS: 1
DIF: Basic
8.5.3.b
TOP: 2-1 Variables and Expressions
expression | algebraic expression | evaluate
KEY: equation | solving
Basic REF: Page 54
REF: Page 54
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: 1
DIF: Average
OBJ: 2-2.PA02 Translate Between Words and Math
NAT: 8.5.2.a
TOP: 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: 1
NAT: 8.2.2.b
28. ANS:
DIF: Average
OBJ: 2-4.PA04 Equations and Their Solutions
TOP: 2-4 Equations and Their Solutions KEY: equation | solving
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: 1
DIF: Average
OBJ: 2-5.PA05 Solving Addition Equations
NAT: 8.5.3.a
TOP: 2-5 Addition Equations
KEY: 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: 1
DIF: Average
OBJ: 2-6.PA06 Solving Subtraction Equations
NAT: 8.5.4.a
TOP: 2-6 Subtraction Equations
KEY: 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: 1
DIF: Average
OBJ: 2-7.PA07 Solving Multiplication Equations
NAT: 8.5.3.a
TOP: 2-7 Multiplication Equations
KEY: equation | solving | multiplication
31. ANS:
The solution is y = 63.
y = 63
Check
9 = 9?
Yes, so 63 is the solution.
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: 1
DIF: Average
OBJ: 2-8.PA08 Solving Division Equations
NAT: 8.5.4.a
TOP: 2-8 Division Equations
KEY: equation | solving | division
32. ANS:
The solution is 4  x (or x  4).
5 x  1
– 1 – 1
4 x
–6
–5
–4
1 is added to x.
Subtract 1 from both sides to undo the addition.
(or x  4)
–3
–2
–1
0
1
2
3
4
5
6
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: 1
NAT: 8.1.1.b
DIF: Average
OBJ: 2-Ext.PA09 Inequalities
TOP: 2-Ext Inequalities
KEY: 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
–9=–9
x= 8
9 is added to x.
Subtract 9 from both sides to undo the addition.
PTS: 1
DIF: Basic
OBJ: 2-5.PA12 Addition Equations
NAT: 8.5.4.a
TOP: 2-5 Addition Equations
KEY: 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.