Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
Part I Matching (4 Points Each)
DIRECTIONS
Write the correct letter in the blank next to each term. Answer choices will
only be used once and some choices will not be used.
1 _C_ Algebraic Equations
2 _F_ Equivalent Equations
3 _G_ Function
4 _A_ Like Terms
5 _B_ Solution
6 _E_ Variable
TEKS 111.32 (6) Underlying
mathematical processes. Many
processes underlie all content areas in
mathematics. As they do mathematics,
students continually use problemsolving, language and communication,
and reasoning (justification and proof)
to make connections within and
outside mathematics. Students also
use multiple representations,
technology, applications and modeling,
and numerical fluency in problemsolving contexts.
Rationale: These vocabulary terms are
essential for the students to know
when attempting to solve a linear
equation. D and H have no match in
this exercise. D describes a ratio and
H describes an identity. The other six
terms have a matching definition.
A Items that contain the same
variable raised to the same power
B Any value that satisfies an
equation
C Equations which can include real
and complex numbers and variables
D A comparison of two numbers by
division
E An expression with no fixed
numerical value
F Describes equations that share a
common solution or solutions
G A relationship between two
mathematical sets, in which each
member of one set corresponds
uniquely to a member of the other
set
H An equation that is true for every
value of the variable
Page 1
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
Part II Multiple Choice (6.5 Points Each)
DIRECTIONS
Read each problem and solve for and circle the correct answer.
1 Solve for 𝑦 in the equation.
3𝑦 + 12 = 6.
A −6
B −2
C 2
D 6
TEKS 111.32 4 (A) find specific
function values, simplify polynomial
expressions, transform and solve
equations, and factor as necessary in
problem situations; (B) use the
commutative, associative, and
distributive properties to simplify
algebraic expressions; and
Rationale: Students should be able to
solve a simple equation with one
variable. The answer choices (A, C, D)
are good distracters because they are
the results you get if you change the
sign at any given step in the equation.
2 Solve for 𝑥 in the equation.
(5 − 9)𝑥 − 5 = 3𝑥 − 26
F −21
G −3
H 3
J 21
TEKS 111.32 4 (A) find specific
function values, simplify polynomial
expressions, transform and solve
equations, and factor as necessary in
problem situations; (B) use the
commutative, associative, and
distributive properties to simplify
algebraic expressions.
Rationale: Students should use the
order of operations in order to first
expand, then simplify the like terms.
If students get the wrong sign at the
first step, students will obtain -21 (F)
or 21 (J) as their answer. We chose -3
(G) to be a distracter for the students
because it will cause the students to
check their work to ensure they find
the correct answer.
3 Sara leaves her house driving 35
miles per hour. Brad leaves the same
house driving in the same direction
15 minutes later driving 50 miles per
hour. How long does it take for Brad
to catch up with Sara?
A 1 hour
B 1 hour and 30 minutes
Page 2
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
C 2 hours
G $75.65
D 2 hours and 30 minutes
H $80.00
TEKS 111.32 3 (A) use symbols to
represent unknowns and variables 4
(A) find specific function values,
simplify polynomial expressions,
transform and solve equations, and
factor as necessary in problem
situations; (B) use the commutative,
associative, and distributive
properties to simplify algebraic
expressions. 7 (A) analyze situations
involving linear functions and
formulate linear equations or
inequalities to solve problems.
Rationale: This problem requires
students to create an equation
involving one variable. Students
should create an equation that
resembles 35𝑡 + 15 = 50𝑡. The answer
choices (B, C, D) are all logical choices
because these are answers a student
might come up with if they were to
simply give estimate rather than do
the math needed for the problem. The
distances are all reasonable options
for the small difference in speed and
the small head start of Sara.
4 Mr. Jones needs a new pair of jeans.
The jeans he wants cost $89.00. They
are on sale for 15% off. How much
will Mr. Jones pay for his new jeans?
J $87.67
TEKS 111.32 3 (A) use symbols to
represent unknowns and variables 4
(A) find specific function values,
simplify polynomial expressions,
transform and solve equations, and
factor as necessary in problem
situations; (B) use the commutative,
associative, and distributive
properties to simplify algebraic
expressions. 7 (A) analyze situations
involving linear functions and
formulate linear equations or
inequalities to solve problems.
Rationale: Students must create an
equation from these clues. If the
student fails to convert the percentage
correctly, the other answers ( G, H, J)
may be found.
5 Solve for 𝑧 in the following
equation.
50𝑧 + 26𝑦 = 12𝑧 + 38
F
19−13𝑦
G
19−7𝑦
19
25
H 1 − 13𝑦
J 38𝑧 + 26𝑦 − 38
F $70.00
Page 3
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
TEKS 111.32 4 (A) find specific
function values, simplify polynomial
expressions, transform and solve
equations, and factor as necessary in
problem situations; (B) use the
commutative, associative, and
distributive properties to simplify
algebraic expressions.
Rationale: Students must first decide
what they are looking for. Answer
choice J has the same value as the
original equation, however, the
student is asked to solve for z. Answer
choices G and H are answers a student
would choose if the student incorrectly
simplified the equation after isolating
the variable.
situations; (B) use the commutative,
associative, and distributive
properties to simplify algebraic
expressions.
Rationale: This question tests the
student’s ability to critically read a
math problem and translate it into an
equation. Each answer choice involves
just one mistake in the reading of the
problem. If students know the
equation for the total surface area of a
cylinder, they will have an advantage.
However, not many students
memorize their formula chart.
7 Simplify the following equation.
3(𝑥 − 2) − 4(𝑦 − 6) = −27
6 The total surface area of a cylinder
is described as being “two times Pi
times the radius, all multiplied by
the sum of the height and the
radius.” Which is the equivalent
equation?
A 2𝜋𝑟ℎ + 𝑟
B 2𝜋𝑟 2 + ℎ
C 2𝜋𝑟 2 ℎ
D 2𝜋𝑟(ℎ + 𝑟)
TEKS 111.32 3 (A) use symbols to
represent unknowns and variables 4
(A) find specific function values,
simplify polynomial expressions,
transform and solve equations, and
factor as necessary in problem
A 3𝑥 + 4𝑦 = −3
B 3𝑥 + 4𝑦 = −45
C 3𝑥 − 4𝑦 = 3
D 3𝑥 − 4𝑦 = −45
TEKS 111.32 4 (A) find specific
function values, simplify polynomial
expressions, transform and solve
equations, and factor as necessary in
problem situations (B) use the
commutative, associative, and
distributive properties to simplify
algebraic expressions.
Rationale: This question tests the
knowledge of the order of operations.
While D is the correct answer, the
Page 4
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
other answers (A, B, C) are answers
that students will arrive at if they
change the sign or forget to change a
sign when simplifying the equation.
8 The area of a rectangle is 127.365.
The width of the rectangle is 5.0946.
What is the length of the rectangle?
F 5
G 11.286
H 25
J 58.5879
TEKS 111.32 3 (A) use symbols to
represent unknowns and variables 4
(A) find specific function values,
simplify polynomial expressions,
transform and solve equations, and
factor as necessary in problem
situations (B) use the commutative,
associative, and distributive
properties to simplify algebraic
expressions.
Rationale: Students should know the
equation to find the area of a
rectangle. If they know that the width
is always smaller than the length, the
student should be able to rule out F
automatically. If the student uses the
square root of 127.365 the student will
find G as the answer. Answer choice J
is the answer a student will find if the
perimeter rather than the area is used
to find the length of the rectangle.
Page 5
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
Part III Short Answer (7 Points Each)
DIRECTIONS
Answer the following word problems. Make sure to show every step and
simplify to the simplest form.
9 Mrs. Clark is buying a new TV. The
TV costs $499.00 but is getting
$100.00 off for paying cash. After
$100.00 is subtracted, the tax is 8%.
How much is Mrs. Clark paying for
her new TV?
TEKS 111.32 4 (A) find specific
function values, simplify polynomial
expressions, transform and solve
equations, and factor as necessary in
problem situations (B) use the
commutative, associative, and
distributive properties to simplify
algebraic expressions.
[($499.00 − $100.00) −
10 Suzy, Tommy, and John all have a
set number of folders. The three
have a total of 34 folders. Tommy
has twice as many folders as John
and Suzy has two less than three
times as many folders as John. How
many folders does Tommy have?
TEKS 111.32 3 (A) use symbols to
represent unknowns and variables 4
(A) find specific function values,
simplify polynomial expressions,
transform and solve equations, and
factor as necessary in problem
situations (B) use the commutative,
associative, and distributive
properties to simplify algebraic
expressions.
($499.00 − $100.00) ∗ 8%]
$399.00 − ($399.00 ∗ .08)
$399.00 − $31.92
$367.08
𝑥 + 2𝑥 + (3𝑥 − 2) = 34
6𝑥 − 2 = 34
6𝑥 = 36
𝑥=6
Page 6
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
But x is how many John has.
Tommy has 2x folders so we have to
substitute 6 for x. So Tommy has 12
folders.
Page 7
Name ____________________
Date _______________
Subject ________
Chapter Exam
Solving Linear Equations
Part IV Essay (10 Points)
DIRECTIONS
Answer the following essay question. Your response should be at least a
paragraph.
11 Why is it important to know the order of operations when solving linear
equations? Be sure to include the order of operations and an example of when the
order of operations must be used to obtain the correct answer.
TEKS 111.32 (1) Foundation concepts for high school mathematics. As presented in
Grades K-8, the basic understandings of number, operation, and quantitative
reasoning; patterns, relationships, and algebraic thinking; geometry; measurement;
and probability and statistics are essential foundations for all work in high school
mathematics. Students will continue to build on this foundation as they expand
their understanding through other mathematical experiences. (2) Algebraic
thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra;
symbols provide powerful ways to represent mathematical situations and to express
generalizations. Students use symbols in a variety of ways to study relationships
among quantities. (6) Underlying mathematical processes. Many processes underlie
all content areas in mathematics. As they do mathematics, students continually use
problem-solving, language and communication, and reasoning (justification and
proof) to make connections within and outside mathematics. Students also use
multiple representations, technology, applications and modeling, and numerical
fluency in problem-solving contexts.
Example Response: First in the order of operation is parenthesis and exponents.
Next, is multiplication and division followed by addition and subtraction. If you do
not know the order of operations, you will not get the correct answer. For instance,
if you have a parenthesis and you do not perform the operation inside first and do
not use the Distributive Property, you will combine numbers or terms that should
not be combined. This does change the outcome. One example would be (5 − 4) ∗ 2.
When done correctly the student gets 2 as an answer. If doing multiplication first,
the student may get 5 − 8 and therefore have −3 as the answer. In the end, we see
that knowing the order of operations is imperative when solving a linear equation.
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