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Algebra 1 – Unit 2 Sample Items
This document contains sample items aligned to the skills listed in the corresponding “Skills”
document. As Paul Bambrick-Santoyo states in Driven by Data (2010), “In data-driven
instruction, the rigor of the actual assessment items drives the rigor of the material taught in
class.” In order to best prepare our students for the Algebra 1 EOC assessment, we must expose
them to the expectations of this exam. The sample items included are examples of the content,
rigor, and format that our students will be expected to demonstrate on the EOC. Some of the
sample items are easy (and won’t be asked in the exact same way on the EOC), but it is
important to include items aligned to the foundational skills for a given benchmark so that
teachers and coaches can scaffold instruction and identify misunderstanding.
Teachers should use these items as a guide to their instruction, but they are NOT an exhaustive
list of problems, nor do they represent all of the contexts/circumstances in which the skills will
be assessed. Most of the items below show the question stems for multiple-choice and fill-in
response item types. Due to space, most of the multiple-choice items do not have the answer
choices listed, but teachers should get an understanding of the rigor of the item. Additionally, as
a best practice, teachers and coaches should backwards-plan using the Algebra 1 EOC Item
Specifications document published by the Florida Department of Education.
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A.3.1 – Solve linear equations in one variable that includes simplifying
algebraic expressions.
•
Also Assesses: A.3.2 – Identify and apply the distributive, associative, and
commutative properties of real number and the properties of equality.
1. Solve the equation for x. −11 = x − 7
2. Solve the equation for x. x + 2.5 = 16
1
3. What value of x makes the equation true? − x = 9
3
4. What value of x makes the equation true? −5 = −25x
5. What value of x makes the equation true? −4x − 7 = 25
6. Solve the equation for x. − x + 7 = 2 x − 8
6. Solve the equation for x. 7 x + 2 = 9 x − 3 + 4 x
6. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie
is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each
movie. The equation below represents this situation where m is the number of movies rented
each month.
7.50 + 1.00m = 2.50m
What is the number of movies that needs to be rented each month for the total fees to be the same
from either store?
6. In 1492, Christopher Columbus journeyed to the New
World, where he explored portions of the coast of two large
Caribbean islands, Cuba and Hispaniola. Cuba is the larger
of the two islands. Cuba is 10,000 square miles larger than
Hispaniola. Hispaniola is only ¾ as large as Cuba. The
equation below expresses this relationship, where x is the
area of Cuba in square miles.
x − 10,000 =
3
x
4
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What is the area of Cuba, in square miles?
7. Mount Whitney is the highest peak in California, but Mount
Everest, the highest peak in the world, is twice the sum of the
height of Mount Whitney and 3 meters. Overall, Mount Everest
is 4,427 meters higher than Mount Whitney. The comparison is
expressed in the equation below, where x is the height of Mount
Whitney in meters.
2( x + 3) = x + 4427
How high, in meters, is Mount Whitney?
7. Solve the following equation for x. − 4( x + 10) − 6 = −3( x − 2)
8. Mario needs to cut three book shelves from a board that is 1.8 meters long. The second shelf
is 15 centimeters longer than twice the length of the first shelf. The remaining shelf is 5
centimeters longer than the first shelf. The equation below represents this situation, where x is
the length of the first shelf in meters.
x + (2 x + 0.15) + ( x + 0.05) = 1.8
What is the length, in meters, of the first shelf?
8. Leah scored p points in the first half of the basketball game. In the second half, she scored 3
more than ½ the number of points she scored in the first half of the game. Altogether, she scored
21 points in the game. The following equation represents this situation where p represents the
number of points Leah scored in the first half.
1

p +  p + 3  = 21
2

How many points did Leah score in the first half?
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8. At Genesee High School, there are a total of 1,424 students. The sophomore class has 60
more students than the freshman class. The junior class has 50 fewer students than twice the
students in the freshman class. The senior class is three times as large as the freshman class. The
equation below represents this situation, where f is the number of students in the freshman class.
f + ( f + 60) + (2 f − 50) + 3 f = 1424
How many students are in the freshman class?
9. Bill is planning to drive from his house to a baseball stadium and arrive in time for the
beginning of the championship game. His arrival time depends on the traffic. If traffic is light,
he will travel at an average speed of 50 miles per hour and arrive 1 hour early. If traffic is heavy,
he will travel at an average speed of 30 miles per hour and arrive on time. The equation below
can be used to model this situation, where t represents Bill’s driving time, in hours.
50(t − 1) = 30t
What is the distance, in miles, from Bill’s house to the baseball stadium?
9. Shades R Us charges $20 per day to rent a lounge chair and $15 per day to rent an umbrella.
Dan and Lisa paid a total of $245 to rent a lounge chair and an umbrella each during their
vacation. Lisa rented the chair and umbrella for 1 day less than Dan. The following equation
represents this situation, where x represents the number of days Dan rented the lounge chair and
umbrella.
20x +15x + 20(x −1) +15(x −1) = 245
What is the total amount Dan paid to rent the lounge chair and umbrella during his vacation?
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10. Shane wrote the following steps when solving an equation.
Which property justifies Step 1?
A.
B.
C.
D.
Associative property of addition
Commutative property of addition
Distributive property
Additive identity property
10. Which equation is an example of the associative property?
A.
B.
C.
D.
x+y+z = x+ y+z
x(y + z) = xy + xz
x+y+z = z+ y+ x
(x + y)+ z = x + (y + z)
11. When solving the equation, what property was used to go from Step 2 to Step 3?
Step 1: -(2x + 3) = x - 18
Step 2: -2x - 3 = x - 18
Step 3: -3 = 3x – 18
A.
B.
C.
D.
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
MDCPS Education Transformation Office
A.3.3 – Solve literal equations for a specified variable.
1. Shaniqua is constructing an isosceles triangle to use as a model in her algebra class. The
perimeter of her triangle is 24 inches. Shaniqua uses the equation b = 24 − 2s to find b, the
length of the triangle’s third side, in terms of s, the length of each of its two congruent sides.
What is her equation written in terms of s?
A. s = 2(b + 24)
24 + b
B. s =
2
C. s = 2(b − 24)
24 − b
D. s =
2
1. The formula for the lateral area of a pyramid is A =
A. p =
1
pl . What is p in terms of A and l?
2
2A
l
1
B. p = A − l
2
C. p = 2A − l
1
D. p = Al
2
1. There were T people waiting for buses at the station. When the first bus arrived, n people
boarded it. The remaining p people waited for buses to other places.
Use the equation T – n = p, to find n, the number of people who boarded the first bus.
A. n = p −T
T
B. n =
p
n
=
T
−p
C.
D. n = T + p
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1. The formula below illustrates how to calculate body mass index (B), using weight (w) and
height (h).
B=
703w
h2
Which of the following shows this equation correctly solved for w?
A. w = Bh 2 − 703
B. w = B + h 2 − 703
Bh 2
C. w =
703
703B
D. w = 2
h
2. If s =
2x + t
, which of the following shows this equation solved for x?
r
rs − t
2
rs + t
B. x =
2
C. x = 2rs − t
D. x = rs − 2t
A. x =
2. If
ey
+ k = t , what is y in terms of e, n, k, and t?
n
tn + k
e
tn − k
B. y =
e
n(t + k)
C. y =
e
n(t − k)
D. y =
e
A. y =
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2. The Gross Domestic Product of a country for a given year is the sum of the market values of
all goods and services produced within the country during that year. The Gross Domestic
Product per capita is found by using the following formula.
S=
C + I +G + N
P
where:
S = Gross Domestic Product per capita
C = consumer spending
I = investment
G = government purchases
N = net exports
P = population
Which of the following shows the Gross Domestic Product per capita formula solved for C?
PS
I −G − N
PS
B. C =
I +G + N
C. C = PS − I − G − N
D. C = PS − I + G + N
A. C =
* NOTE:
The following problem is an example of an A.3.3 item that requires the student to use
factoring when solving for a certain variable. Because factoring will be covered later in the
year, items that require factoring will NOT be assessed on the Unit 2 Test.
If a + ar = b + r , what is the value of a in terms of b and r?
b
+1
r
1+ b
B. a =
r
b+r
C. a =
1+ r
1+ b
D. a =
r+b
A. a =
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A.4.2 – Add, subtract, and multiply polynomials.
•
Note: Only adding and subtracting polynomials are covered during Unit 2. Multiplying
polynomials will be covered later in the year.
1. Simplify the following expression. −2x 2 + 7x 2
2. Simplify the following expression. (2x 2 − 7)+ (7x 2 + 3)
2. Tammy drew a floor plan for her kitchen, as shown below.
Which expression represents the perimeter, in units, of Tammy’s kitchen floor?
3. What is the sum of −3x 2 − 7x + 9 and −5x 2 + 6x − 4 ?
4. Which expression is equivalent to the perimeter of the shaded portion of the rectangle?
A.
B.
C.
D.
2x +10
2x +12
4x +14
8x + 28
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4. What expression represents the perimeter of the figure shown below?
5. Simplify the following expression. 2x 2 −10x 2
6. Simplify the following expression. (6a 2 + 3a) − (4a 2 + 2a)
6. The sum of two binomials is 5x 2 − 6x . If one of the binomials is 3x 2 − 2x , what is the other
binomial?
7. What is the result when 2x 2 + 3xy − 6 is subtracted from x 2 − 7xy + 2 ?
7. Simplify the following expression. (7x 2 + 5x −1) − (3x 2 − 4x + 2)
8. The perimeter of a rectangle is represented by the expression 6x +16 . If the width of the
rectangle can be represented by the expression 2x , which expression represents the length of the
rectangle?
8. Simplify the following expression. (3x 2 − 2x +1) − (x 2 − 2x − 3) + (4x 2 − x + 2)
9. Simplify the following expression.
5x 3 +10x 3
What is the value of the exponent for the simplified form?
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10. Simplify the following expression.
(−7x 2 + 5x −1) − (3x 2 − 4x + 2)
What is the coefficient of the x2 term?
10. Simplify the following expression.
(4x 3 + 6x 2 + 2x − 3) + (3x 3 + 3x 2 − 5x − 5)
What is the coefficient of the x term?