CHAPTER 2 TEST ACCELERATED
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–4
6
2
16
?
30
?
a. 22, 46
c. 18, 32
b. 12, 26
d. 20, 34
2. Evaluate the expression to find the missing values in the table.
z
z+4•2
9
17
11
?
23
?
a. 3, 15
c. 30, 54
b. 19, 31
d. 28, 40
3. 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
4. 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
5. 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
6. Write the phrase “5 times p” as a numerical or algebraic expression.
a.
c.
b.
d. 5p
7. Write the phrase “z divided by 2” as a numerical or algebraic expression.
a.
c.
b.
d.
8. 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
9. Write two phrases for the expression t  25.
a. the product of t and 25; t times 25
b. t subtracted from 25; t less than 25
c. the quotient of 25 and t; 25 divided by t
d. the quotient of t and 25; t divided by 25
____ 10. Write an expression for the sequence in the table.
1
2
3
4
Position
Value of Term
____
____ 11.
____ 12.
____ 13.
____ 14.
____ 15.
____ 16.
5
n
?
a.
c.
b.
d.
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
.
Solve the equation m + 10 = 53. Check your answer.
a. m = 43
c. m = 63
b. m = 53
d. m = 44
Solve the equation
. Check your answer.
a. s = 48
c. s = 47
b. s = 57
d. s = 61
Write “12 is 8 subtracted from y” as an algebraic equation. Then find the solution.
a.
;
b.
;
c.
;
d.
;
Solve the equation 10m = 200. Check your answer.
a. m = 210
c. m = 20
b. m = 190
d. m = 21
Solve the equation. Check your answer.
a. n = 38
b. n = 8 3
5
c. n = 215
d. n = 48
____ 17. Solve the equation. Check your answer.
a. p = 42
c. p = 88
b. p = 22
d. p = 46
____ 18. 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
d.
–20
–15
–10
–5
0
5
10
15
20
____
19. Solve the inequality m – 2  1. Graph the solutions on a number line.
a. m –1
c. m3
–20
b.
–15
–5
5
10
15
–20
20
d.
–15
–10
–5
0
5
10
15
–15
–5
0
5
10
15
20
–10
–5
0
5
10
15
20
–50
–25
0
25
50
75
–50
–25
0
25
50
75
–50
–25
0
25
50
75
–1
0
m  –1
–20
20
–10
–15
20. Solve the inequality 2y  10. Graph the solutions on a number line.
a. y5
c. y 20
–20 –16 –12 –8
b.
–4
4
8
12
16
–75
20
d.
–4
0
4
8
12
16
y  20
–75
20
 3. Graph the solutions on a number line.
21. Solve the inequality
a.
0

y 5
–20 –16 –12 –8
____
0
m 3
–20
____
–10
c.
3
m  4 
m12
–75
–4
b.
–3
–2
–1
0
1
2
3
4
m 12
–75

d.
–50
–25
0
25
50
m
3
4

75
–4
–3
–2
Numeric Response
22.
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
1
2
3
4
23.
Matching
____
____
____
____
24.
25.
26.
27.
Match each vocabulary term with its definition.
a. algebraic expression
e. variable
b. constant
f. ms. mora
c. solution
g. ms. mora
d. inequality
an expression that contains at least one variable
a value or values that make an equation true
a value that does not change
a symbol used to represent a quantity that can change
Short Answer
28. Write two phrases for the expression 85 – y.
29. Define algebraic expression and give an example
30. Define inequality and give an example
31. When graphing inequalites, how do you decide whether or not to shade to the left or right on the number line?
32. 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
33. Explain the meaning of the statement “Subtraction is the inverse of addition.” Use the equation
to demonstrate.
CHAPTER 2 PRACTICE TEST ACCELERATED
Answer Section
MULTIPLE CHOICE
1. ANS: B
Substitute for x in x – 4.
x = 6; 6 – 4 = 2
x = 16;16 – 4 = 12
x = 30; 30 – 4 = 26
The missing values are 12 and 26.
Feedback
A
B
C
D
To evaluate the expression, use substitution.
Correct!
Substitute the number for the variable.
Substitute the number for the variable and then find the value.
PTS: 1
DIF: Basic
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
Substitute for z in z + 4 • 2. Use the order of operations.
z = 9; 9 + 4 • 2 = 17
z = 11;11 + 4 • 2 = 19
z = 23; 23 + 4 • 2 = 31
The missing values are 19 and 31.
Feedback
A
B
C
D
First, substitute the number for the variable. Then, use the order of operations to find the
value.
Correct!
Substitute the number for the variable and then find the value.
Use the order of operations.
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
3. 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
4. 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
5. 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
6. ANS: D
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.
Look for keywords in the phrase.
Correct!
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
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
8. 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
9. ANS: D
t  25:
t divided by 25;
the quotient of t and 25
Feedback
A
B
C
D
Check the operation.
Check the operation.
Check the order of the terms.
Correct!
PTS:
NAT:
KEY:
10. ANS:
1
DIF: Average
REF: Page 59
OBJ: 2-2.3 Translating Math into Words
8.5.2.g
TOP: 2-2 Translate Between Words and Math
expression | algebraic expression
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.
. Check this rule for
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:
OBJ:
TOP:
11. ANS:
1
DIF: Average
REF: Page 63
2-3.2 Writing an Expression for a Sequence
2-3 Translating Between Tables and Expressions
C
?
?
Since
NAT: 8.5.2.b
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
12. ANS: A
m + 10 = 53
10 is added to m.
m + 10 10 = 53 10
Subtract 10 from both sides to undo the addition.
m = 43
Check
m + 10 = 53
?
?
Substitute 43 for m in the equation.
Add.
43 is the solution.
Feedback
A
B
C
D
Correct!
Substitute the solution in the equation to check your answer.
Subtract from both sides of the equation to undo the addition.
Subtract from both sides of the equation to undo the addition.
PTS: 1
DIF: Basic
REF: Page 75
OBJ: 2-5.1 Solving Addition Equations
NAT: 8.5.3.c
13. ANS: D
TOP: 2-5 Addition Equations
KEY: equation | solving | addition
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
14. 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
D
Check the order of the number and the variable.
Use addition to undo the subtraction.
Correct!
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
15. ANS: C
10m = 200
m is multiplied by 10.
Divide both sides by 10 undo the multiplication..
m = 20
Check
10m = 200
10(20) = 200 ?
?
Substitute 20 for m in the equation.
Multiply.
20 is the solution.
Feedback
A
B
C
D
Divide to undo the multiplication.
Substitute the solution in the equation to check your answer.
Correct!
Divide to undo the multiplication.
PTS:
OBJ:
TOP:
16. ANS:
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
C
n is divided by 5.
Multiply both sides by 5 to undo the division.
n = 215
Check
?
?
Substitute 215 for n in the equation.
Divide.
215 is the solution.
Feedback
A
B
C
D
Substitute the solution in the equation to check your answer.
Multiply to undo the division.
Correct!
Multiply to undo the division.
PTS: 1
NAT: 8.5.3.c
17. ANS: C
DIF: Average
REF: Page 85
TOP: 2-8 Division Equations
OBJ: 2-8.1 Solving Division Equations
KEY: equation | solving | division
p is divided by 2.
Multiply both sides by 2 to undo the division.
p = 88
Check
?
Substitute 88 for p in the equation.
?
Divide.
88 is the solution.
Feedback
A
B
C
D
Substitute the solution in the equation to check your answer.
Multiply to undo the division.
Correct!
Multiply to undo the division.
PTS: 1
NAT: 8.5.3.c
18. ANS: B
–20
–15
–10
DIF: Average
REF: Page 85
TOP: 2-8 Division Equations
–5
0
5
10
15
OBJ: 2-8.1 Solving Division Equations
KEY: equation | solving | division
20
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.
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.
B
C
D
PTS: 1
DIF: Average
REF: Page 90
OBJ: 2-Ext.1 Graphing Inequalities
TOP: 2-Ext Inequalities
KEY: inequality | graph
19. ANS: C
2 is subtracted from m.
m–21
Add 2 to both sides to undo the addition.
m – 2 + 2 1 + 2
m3
–20
–15
–10
–5
0
5
10
15
20
The open circle on the point 3 shows that 3 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!
Solve the inequality the same way you solve an equation.
PTS:
OBJ:
TOP:
20. ANS:
1
DIF: Basic
REF: Page 90
2-Ext.2 Solving and Graphing Inequalities
NAT: 8.5.4.a
2-Ext Inequalities
KEY: inequality | graph | solving
A
2y  10
y is multiplied by 2.
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:
21. 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: 1
DIF: Average
REF: Page 90
OBJ: 2-Ext.2 Solving and Graphing Inequalities
NAT: 8.5.4.a
TOP: 2-Ext Inequalities
KEY: inequality | graph | solving
NUMERIC RESPONSE
22. ANS: A. 15
PTS: 1
23. ANS: A. n<3
DIF: Advanced
NAT: 8.5.3.b
TOP: 2-7 Multiplication Equations
PTS: 1
DIF: Advanced
NAT: 8.5.3.b
TOP: 2-7 Multiplication Equations
MATCHING
24. ANS:
NAT:
25. ANS:
NAT:
KEY:
26. ANS:
NAT:
27. ANS:
NAT:
KEY:
28. ANS:
NAT:
KEY:
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
8.5.4.b
TOP: 2-4 Equations and Their Solutions
B
PTS: 1
DIF: Basic
8.5.3.b
TOP: 2-1 Variables and Expressions
expression | algebraic expression | evaluate
E
PTS: 1
DIF: Basic
8.5.3.b
TOP: 2-1 Variables and Expressions
expression | algebraic expression | evaluate
REF: Page 70
KEY: equation | solving
REF: Page 54
REF: Page 70
KEY: equation | solving
REF: Page 54
REF: Page 54
SHORT ANSWER
29. ANS:
x
3
7
10
x+7
10
14
17
Substitute for x in x + 7.
x = 7; 7 + 7 = 14
x = 10; 10 + 7 = 17
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: 2-1.PA01 Variables and Expressions
NAT: 8.5.3.b
TOP: 2-1 Variables and Expressions
KEY: expression | algebraic expression | variable
30. 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
31. ANS:
35d sit-ups
Day
1
2
3
d
Number of Situps
1 • 35 = 35
2 • 35 = 70
3 • 35 = 105
d • 35 = 35d
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
NAT: 8.5.1.a
TOP: 2-3 Translating Between Tables and Expressions
KEY: patterns | Performance Assessment | sequence
32. ANS:
m = 15 is a solution.
m + 4 = 19
23 + 4 = 19 ?
27 = 19 ?
27 19
m = 23 is not a solution.
m + 4 = 19
15 + 4 = 19 ?
19 = 19 ?
Substitute 23 for m.
Add.
Substitute 15 for m.
Add.
19 = 19
m = 15 is a solution.
m + 4 = 19
16 + 4 = 19 ?
20 = 19 ?
20 19
m = 16 is not a solution.
Substitute 16 for m.
Add.
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: 2-4.PA03 Equations and Their Solutions
NAT: 8.5.4.b
TOP: 2-4 Equations and Their Solutions KEY: equation | solving
33. ANS:
a. The variable f represents the number of feet, and the variable n represents the number
of inches. So 12f = n shows the relationship between feet and inches.
b.
The two measurements are not equal.
12f = n
12(3) = 42 ?
36 = 42 ?
36 42
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: 2-4.PA04 Equations and Their Solutions
NAT: 8.2.2.b
TOP: 2-4 Equations and Their Solutions KEY: equation | solving
34. 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
35. 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)
–6
–5
–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
36. ANS:
a. The number of carrot sticks served in the cafeteria is a variable because the amount can change.
b. The size of the school building is a constant because it does not change.
c. The number of students absent on any given day is a variable because the number can change.
(The student should associate a variable with amounts that can change and a constant with amounts that are
specific or do not change.)
Scoring Rubric:
4
All items are identified correctly, and the explanations reflect understanding of the
concept.
3
All items are identified correctly, but the explanations are missing or show
incomplete understanding of the concept.
2
1
Not all items are identified correctly, but the explanations show some understanding
of the concept.
None of the items are identified correctly, and the explanations are missing or show
no understanding of the concept.
PTS: 1
DIF: Average
TOP: 2-1 Variables and Expressions
OBJ: 2-1.PA10 Variables and Expressions
KEY: expression | algebraic expression | variable