Name: ________________________
Class: ___________________
Date: __________
ID: A
8th Grade Advanced Topic II Literal Equations and Inequalities, MA.8.A.4.1, MA.8.A.4.2
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1
The formula
is used to calculate the area A of a rectangular surface using the length (l) and the
width (w) of the surface. Which formula could be used to find w in terms of A and l?
A.
B.
C.
D.
2
The equation below is used to find C, the total cost for printing a quantity of books (b).
Which equation is equivalent when solved for b in terms of C?
F.
G.
H.
I.
3
Brittany had 7 rolls of quarters and 4 extra quarters. She used the equation
to find n, the
number of quarters she had altogether. Which equation could she use to find q, the number of quarters in
each roll?
A.
B.
C.
D.
1
Name: ________________________
4
ID: A
The pressure a shoe heel applies to the floor depends on the weight on the heel and the surface area of
the tip of the heel. The equation below can be used to find p, the pressure applied, based on w, the
weight, and a, the surface area of the tip of the heel.
Which equation is equivalent when solved for w in terms of p and a?
F.
G.
H.
I.
5
Margo sells bracelets for $8 each and necklaces for $12 each. The equation below can be used to
calculate E, her total earnings.
If b is the number of bracelets, and n is the number of necklaces she sold, which equation can be used to
find b, when E and n are known?
A.
B.
C.
D.
6
The equation below is used to find b, the total number of books collected by two students during a
book drive. Marcia collected x number of books. Alan collected 5 more than 2 times the number of
books Marcia collected.
Which equation is equivalent when solved for x in terms of b?
F.
G.
H.
I.
2
Name: ________________________
7
ID: A
The weight of an object depends on the mass and force of gravity. The equation below is used to find w,
the weight of an object if m, the mass of the object, and g, the force of gravity, are known.
Which equation could be used to find m in terms of w and g?
A.
B.
C.
D.
8
The equation below is used to find S, the sum of the measures of the interior angles of a polygon with n
sides.
Which equation is equivalent when solved for n in terms of S?
F.
G.
H.
I.
9
In the inequality below, x represents the number of cups of coffee that workers at a company drink
each day.
Which phrase MOST accurately describes the value of x?
A.
B.
C.
D.
at most 52 cups of coffee
exactly 52 cups of coffee
fewer than 52 cups of coffee
more than 52 cups of coffee
3
Name: ________________________
10
ID: A
Hillary will not be charged a service fee if she keeps at least $725 in her bank account. On Monday, her
account balance was $810.90. Hillary wrote the inequality below to find x, the amount she can
withdraw and still avoid paying the service fee.
Which amount of money can she withdraw and NOT be charged with a service fee?
F.
$50
G. $86
H. $90
I. $100
11
Swimmers who are x years of age may enter a swimming competition. Which number line best
represents x if
and
A.
B.
C.
D.
12
A math club bought and printed T-shirts to sell as a fundraiser. The cost of 72 T-shirts was $388.80,
and the print set-up cost was $40. They plan to sell each T-shirt for $7. The inequality below can be
used to find x, the minimum number of T-shirts they need to sell to recover the money spent on initial
costs.
What is the minimum number of T-shirts they must sell to recover the money spent on initial costs?
F.
G.
H.
I.
50
49
61
62
T-shirts
T-shirts
T-shirts
T-shirts
4
Name: ________________________
13
ID: A
Solve for x in the inequality below.
−15x ≤ −25
A. x ≥
B. x ≥
C. x ≤
D. x ≤
14
In the inequality 10x + 18 ≤ 238, x represents the number of days Matt will be able to work during the
summer. Which phrase MOST accurately describes that number of days?
F.
G.
H.
I.
15
exactly 22 days
at most 22 days
less than 22 days
more than 22 days
What are all possible values of x that satisfy the inequality
A.
B.
C.
D.
5
Name: ________________________
16
ID: A
During one week in January, the temperature in Maine was at least
Fahrenheit and less than
Fahrenheit. Which graph represents all the possible values for the temperature during that week?
F.
G.
H.
I.
6
GR 8 Advanced - Topic II Assessment
TEACHER ANSWER KEY
ID: A
8th Grade Advanced Topic II Literal Equations and Inequalities, MA.8.A.4.1, MA.8.A.4.2
Answer Section
MULTIPLE CHOICE
1
ANS: B
Feedback
A
B
C
D
2
Divided length by area instead of area by length
Correct
Multiplied instead of dividing
Subtracted instead of dividing
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: L
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF222470
I
Feedback
F
G
H
I
3
Divided only C by 5
Divided only 200 by 5
Inverted the dividend and the divisor
Correct
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: M
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Moderate | Grade 08
ItemCode: MF222472
C
Feedback
A
B
C
D
Swapped the position of the variables
Swapped the position of the variables and replaced addition with subtraction
Correct
Inverted the dividend and the divisor
PTS:
OBJ:
STA:
MSC:
1
DIF: L
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF222473
1
ID: A
4
ANS: F
Feedback
F
G
H
I
5
Correct
Swapped w and p
Rotated variables counterclockwise
Added instead of multiplying
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: M
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Moderate | Grade 08
ItemCode: MF222475
A
Feedback
A
B
C
D
6
Correct
Subtracted 8 first, then divided by 12n
Multiplied by 8 instead of dividing
Subtracted 8 first, then multiplied by 12n
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: M
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF222696
F
Feedback
F
G
H
I
Correct
Solved for
Swapped variables
Multiplied by 3 instead of dividing
PTS:
OBJ:
STA:
MSC:
1
DIF: H
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF222944
2
ID: A
7
ANS: A
Feedback
A
B
C
D
8
Correct
Inverted the dividend and the divisor
Chose the multiplicative inverse
Swapped variables
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: L
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF222945
I
Feedback
F
G
H
I
9
Multiplied S by 180 instead of dividing
Added 2 first and multiplied by 180
Added 2 first then divided by 180
Correct
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: H
REF: Math
MA.8.A.4.1 Solve literal equations for a specified variable.
MA.8.A.4.1 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF223109
A
Feedback
A
B
C
D
Correct
Disregarded the inequality sign
Disregarded the “equal to”
Confused “less than” with “greater than”
PTS:
OBJ:
STA:
MSC:
1
DIF: M
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Moderate | Grade 08
ItemCode: MF201655-C6
3
ID: A
10
ANS: F
Feedback
F
G
H
I
11
Correct
Subtracted 725 from 811
Misread relational sign and chose a number greater than 85.28
Subtracted 700 from 800
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: H
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Moderate | Grade 08
ItemCode: MF211089
B
Feedback
A
B
C
D
12
Does not include 17 and 25
Correct
Includes more than age 25
Does not include age 25
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: L
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MF212216
I
Feedback
F
G
H
I
Subtracted 40 instead of adding
Subtracted 40 instead of adding; truncated instead of rounding up to a complete
T-shirt
Truncated, instead of rounding up to a complete T-shirt; does not meet the
inequality
Correct
PTS:
OBJ:
STA:
MSC:
1
DIF: M
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Moderate | Grade 08
ItemCode: MF213342
4
ID: A
13
ANS: B
Feedback
A
B
C
D
14
Sign error in division
Correct
Did not reverse inequality sign
Did not reverse inequality sign, sign error in division
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: M
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MFIBA11521
G
Feedback
F
G
H
I
15
Solved the inequality as if it was an equation
Correct
Did not include the equal part in the inequality
Switched the inequality and did not include the equal part in the inequality
PTS:
OBJ:
STA:
MSC:
ANS:
1
DIF: M
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MFIBM15099
B
Feedback
A
B
C
D
Did not reverse inequality
Correct
Added 12 and 18, then reversed the inequality
Added 12 and 18, then divided by 3
PTS:
OBJ:
STA:
MSC:
1
DIF: L
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Low | Grade 08
ItemCode: MFIBM20413
5
ID: A
16
ANS: G
Feedback
F
G
H
I
This only shows y < 4 part of the inequality
Correct
This does not include
This is the graph for
or
PTS:
OBJ:
STA:
MSC:
1
DIF: M
REF: Math
MA.8.A.4.2 Solve and graph one- and two-step inequalities in one variable.
MA.8.A.4.2 TOP: MA.8.A.4 Algebra
KEY: Webb: Moderate | Grade 08
ItemCode: MF211115
6