Algebra 1 Semester Exam Study Guide
Algebra 1 Semester Exam 2015-2016
30 questions
Topics:




Expressions, Equations, and Inequalities
Functions
Linear Function
Systems of Equations and Inequalities
Reporting Category 1: (50% of the Semester Exam)
Algebra and Modeling
Reporting Category 2: (50% of the Semester Exam)
Functions and Modeling
 This Study Guide includes sample problems from the textbook that
students can use to help prepare for the exam.
 They are NOT the test items.
 This is geared towards the DISTRICT semester exam.
 There will not be a study guide that is geared towards any state
assessment (End of Year EOC).
 Answers will not be provided by District Office for the Study Guide.
Algebra 1 Semester Exam Study Guide
BENCHMARK
MAFS.912.A-CED.1.1
MAFS.912.F-IF.1.1
DOK
Skill/Concepts
M
Create an inequality
that represents
context and use to
solve a problem
M
Determine which
domain would not
make a function
(given a range)
Example problem or problems to support studying
a. A full year membership to a gym costs $325 upfront with no
monthly charge. A monthly membership costs $100 upfront
and $30 per month. For what numbers of months is it less
expensive to have a monthly membership?
b. Marcus has accepted a job selling cell phones. He will be
paid $1500 plus 15% of his sales each month. He needs to
earn at least $2430 to pay his bills. For what amount of
sales will Marcus be able to pay his bills?
Give the domain and range of each relation. Tell whether the
relation is a function. Explain.
a.
b.
Find the equation for each of the lines below.
MAFS.912.A-REI.4.10
M
Determine the
equation of a line on
a graph
MAFS.912.F-LE.1.1
L
Justify why a linear
function is a function
MAFS.912.A-CED.1.4
M
Solve for a specific
variable in a surface
area formula
MAFS.912.F-IF.1.2
M
Evaluate the function
for two given values
and find the
difference between
them
MAFS.912.F-IF.2.6
M
Determine the
average rate of
change of a function
a. Ronda wants to justify that 𝑓(𝑥) = 4𝑥 − 9 is a linear
function. If she evaluated 𝑓(𝑥) for consecutive integer
values, write a statement that justifies the claim that 𝑓(𝑥) is
a linear function.
1
b. Cassie wants to justify that 𝑓(𝑥) = 2 𝑥 − 4 is a linear
function. If she evaluated 𝑓(𝑥) for consecutive integer
values, write a statement that justifies the claim that 𝑓(𝑥) is
a linear function.
5
a. Solve for Fahrenheit. 𝐶 = (𝐹 − 32)
1
𝑘𝑥 2
2
9
b. Solve for k. 𝐸 =
c. Solve for w. 𝑆𝐴 = 2(𝑙𝑤 + ℎ𝑤 + ℎ𝑙)
a. The function 𝑓(ℎ) can be used to find the height, ℎ, in feet,
of a tree, 𝑦, years after it was planted. 𝑓(ℎ) = 3𝑦 + 2
What is the difference in height, ℎ, of the tree between
years 4 and 9?
b. The function 𝑓(ℎ) can be used to find the height, ℎ, in feet,
of a tree, 𝑦, years after it was planted. 𝑓(ℎ) = 5𝑦 − 8
What is the difference in height, ℎ, of the tree between
years 3 and 11?
Each day a dolphin trainer receives 150 pounds of fish to
divide equally among 𝑥 dolphins. This function relates the
150
number of pounds, 𝑓, of fish each dolphin gets. 𝑓 = 𝑥 The
number of dolphins has increased from 11 to 15. What is
the average rate of change in the number of pounds of fish
per dolphin?
Algebra 1 Semester Exam Study Guide
a. The table shows the volume of gasoline in a gas tank at
different times. Find the rate of change for each time
interval. During which time interval did the volume
decrease at the greatest rate?
MAFS.912.F-LE.1.1
M
Determine which
interval shows a
constant rate of
change
MAFS.912.A-SSE.1.1
M
Interpret parts of a
function within a
context
MAFS.912.F-IF.1.2
M
Find the value of x
given f(x)
L
Determine the effect
of rate of changes on
a graph
MAFS.912.F-IF.2.6
b. The table shows the length of a baby at different ages. Find
the rate of change for each time interval. Round your
answers to the nearest tenth. During which interval did the
baby have the greatest growth rate?
a. The function 𝑓(𝑥) = 100𝑥 + 75 represents what the
daycare center charges during a time period. If x represents
the number of weeks, what does the 100 represent? What
does the 75 represent?
b. The function 𝑓(𝑥) = 60 − 0.18𝑥 represents the amount of
water within a family swimming pool. If x represents the
number of days, what does the 60m3 represent? What does
the -0.18 represent?
2
a. Given the function 𝑓(𝑥) = 3 𝑥 + 3, what is the value of 𝑥
when 𝑓(𝑥) = 24?
3
b. Given the function 𝑓(𝑥) = 5 𝑥 − 8, what is the value of 𝑥
when 𝑓(𝑥) = 13?
a. A person’s body mass index (BMI) is calculated by dividing
the person’s mass in kilograms by the person’s height in
meters. The table shows the median BMI for U.S. males from
age 2 to age 12. For which intervals is the average rate of
change in the BMI positive?
b. Eleanor is conducting an experiment. She starts with 5
samples of lemonade at different temperatures. Then, she
recorded how long it took each sample to freeze solid. The
graph shows her results. What conclusions can you make
from the graph with regards to rate of change?
Algebra 1 Semester Exam Study Guide
MAFS.912.F-IF.3.7a
M
Determine which
graph has the same
slope as a given line
MAFS.912.A-SSE.1.1
L
Determine what x
represents in an
expression
M
Interpret the key
features of a table
(relative maximum/
minimum)
M
Determine what the
y-intercept is of a
function with the
greater rate of
change (equation/
two points)
MAFS.912.A-CED.1.3
M
Determine which
solution is plausible
in a systems of linear
inequalities
MAFS.912.A-REI.1.1
L
Determine which
step is valid in solving
an equation for x
L
Determine a
reasonable domain
for a function within
a given context
MAFS.912.F-IF.2.4
MAFS.912.F-IF.3.9
MAFS.912.F-IF.2.5
a. Determine a line that has the same slope as 4𝑦 − 8 = 2𝑥.
Graph it on a coordinate plane.
b. Determine a line that has the same slope as 2𝑥 + 3𝑦 = 12.
Graph it on a coordinate plane.
a. This expression describes the cost, in dollars, for Beth to buy
some new clothes. (20 + 18𝑥) ∗ 1.12 If 𝑥 represents the
number of skirts, what would the 18 represent? What
would the 20 represent? What would the 1.12 represent?
b. This expression describes the cost, in dollars, for Bob to buy
some new clothes. (50 + 12𝑥) ∗ 1.16 If 𝑥 represents the
number of pants, what would the 12 represent? What
would the 50 represent? What would the 1.16 represent?
a. The profit produced by an apple orchard increases as more
trees are planted. MaryAnn graphs this continuous
relationship with the domain of 0 ≤ 𝑥 ≤ 40 on a coordinate
plane.
Apples
Profit
10
1410
20
2820
30
4230
40
5640
What is true about the maximum and minimum for the
graph?
a. Given the function 𝑓(𝑥) = 5𝑥 + 4 and the points for
function 𝑔(𝑥) (-1, -6) and (2, 3). Which function has the
greater y-intercept? Which function has the greater rate of
change?
b. Given the function 𝑓(𝑥) = 3𝑥 + 8 and the points for
function 𝑔(𝑥) (-2, -4) and (5, 3). Which function has the
greater y-intercept? Which function has the greater rate of
change?
a. Charlene makes $10 per hour babysitting and $5 per hour
gardening. She wants to make at least $80 a week, but can
work no more than 12 hours a week. Write a system of
linear equations. Graph the solutions of the system.
Describe all possible combination of hours that Charlene
could work at each job if only whole numbers are allowed.
What is the greatest amount Charlene can earn?
b. Zoe plans to knit a scarf. She wants the scarf to be more
than 1 but less than 1.5 feet wide, and more than 6 but less
than 8 feet long. Graph all possible dimensions of Zoe’s
scarf. List two possible combinations.
Solve the following equations. Justify each step.
1
𝑥 + 4𝑥 − 7 = 4𝑥 + 6
2
7
𝑛 = 3𝑛 + 4
2
a. Jerry earns $12 per hour for his after-school job. He never
works more than 14 hours in a week, and he never works a
fraction of an hour. The equation that models this situation
is A=12h where A represents the amount Jerry earns and h
represents the number of hours Jerry works in a week. What
Algebra 1 Semester Exam Study Guide
is the reasonable domain of the function A in the given
context?
b. Joanie earns $16 per hour for his after-school job. She never
works more than 15 hours in a week, and she never works a
fraction of an hour. The equation that models this situation
is A=16h where A represents the amount Joanie earns and h
represents the number of hours Joanie works in a week.
What is the reasonable domain of the function A in the given
context?
MAFS.912.A-REI.3.6
M
Determine the
relationship between
two equations
(parallel or
perpendicular)
MAFS.912.A-CED.1.2
M
Real world situation
with systems of
linear equations (2
variables) Create
equations and solve
MAFS.912.A-REI.2.3
M
Solve an equation for
x (variables are
included)
MAFS.912.A-REI.1.1
H
Determine the
reason in an
algebraic proof
M
Determine the
increase of rate of
change in two
equations
MAFS.912.F-LE.2.5
a. Last month Stephanie spent $57 on 4 allergy shots and 1
office visit. This month she spent $9 after 1 office visit and a
refund for 2 allergy shots from her insurance company. How
much does an office visit cost? an allergy shot?
b. The Lees spent $31 on movie tickets for 2 adults and 3
children. The Macias spent $26 on movie tickets for 2 adults
and 2 children. What are the prices for adult and child movie
tickets?
1
a. Look at this equation. (2𝑥 + 𝑏) = 5 Which expression
3
represents the value of x for the equation?
3
b. Look at this equation. (6𝑥 + 𝑏) = 15 Which expression
4
represents the value of x for the equation?
a. What two properties are used in the following solution to
4𝑏 − 3 = 17?
b. What two properties are used in the following solution to
7
𝑏 = 3𝑛 + 4 ?
2
a. The function 𝐴(𝑑) = 0.45𝑑 + 180 models the amount A,
in dollars, that Terry’s company pays him based on the
roundtrip distance d, in miles, that Terry travels to a job site.
The company is modifying its pay structure so that Terry will
get paid a total of $350 for traveling 165 miles round trip
and $450 for traveling ? By how much will the price per mile
increase for the roundtrip distance?
Algebra 1 Semester Exam Study Guide
a. What does the c intercept mean in the graph below?
MAFS.912.F-IF.2.4
M
Interpret the
meaning of the
intercept within
context
MAFS.912.A-REI.4.11
M
Determine the
solution of the
equation 𝑓(𝑥) =
𝑔(𝑥)
MAFS.912.A-CED.1.2
M
Determine which
equation represents
the context
MAFS.912.F-BF.1.1
M
Determine which
equation represents
the context
MAFS.912.A-CED.1.1
M
Create the equation
to represent the
situation
a. Some values for two different linear functions, 𝑓(𝑥) and
𝑔(𝑥), are shown in this table.
𝑓(𝑥)
𝑔(𝑥)
𝑥
5
28
24
7
36
38
What is the solution of the equation 𝑓(𝑥) = 𝑔(𝑥)?
b. Some values for two different linear functions, 𝑓(𝑥) and
𝑔(𝑥), are shown in this table.
𝑓(𝑥)
𝑔(𝑥)
𝑥
0
4
7
-2
0
9
What is the solution of the equation 𝑓(𝑥) = 𝑔(𝑥)?
a. Binh brought $23 with her to the county fair. She purchased
a $5 T-shirt and now wants to buy some locally grown plants
for $2.50 each. What are the numbers of plants that she can
purchase with her remaining money? Write an equation to
represent this situation.
b. A 15-foot-tall cedar tree is growing at a rate of 2 feet per
year beneath power lines that are 58 feet above the ground.
The power company will have to prune or remove the tree
before it reaches the lines. How many years can the power
company wait before taking action? Write an equation to
represent this situation.
a. A small swimming pool initially contains 400 gallons of
water, and water is being added at a rate of 10 gallons per
minute. Write an expression that represents the volume of
the pool after t minutes.
b. Miguel has $250 dollars saved, and he adds $5 to his savings
every week. Write a function that describes the amount A,
in dollars, that Miguel has saved after t weeks.
a. A landscaper is planting a row of 10 shrubs along the
walkway shown below. There must be one shrub at the very
beginning and one shrub at the very end, and the shrubs in
between will be equally spaced along the length of the
walkway. Write an equation can the landscaper use to find
the distance d in feet to leave between the shrubs?
Algebra 1 Semester Exam Study Guide
a. The amount of money that Theresa earns in a week is a
function of h, the number of hours she works, as shown in
the table below. Write a function that represents this
situation.
MAFS.912.F-IF.1.2
M
Determine the
correct function for
the table
h
f(h)
1
22
2
44
3
66
4
88
b. Write a function that represents this situation.
h
f(h)
-2
2
-1
6
1
14
2
18
a. Claire purchased just enough fencing to border either a
rectangular or tirangular garden, as shown, whose
perimeters are the same.
How many feet of fencing did she buy?
b. The table shows the membership fees of three different
gyms.
MAFS.912.A-CED.1.1
M
Solve an equation to
find the total amount
within the context of
the problem