Algebra 1 Enrichment/Instructional Packet - Mathematics Prince George's County Public Schools - PGCPS

Algebra 1
Enrichment/Instructional Packet

 Mathematics

 Prince George’s County Public Schools
 Division of Academics
 Department of Curriculum and Instruction

 The teacher will not grade this packet.

This Enrichment Packet has been compiled to complement
high school mathematics classroom instruction aligned to the
Maryland College and Career Ready Standards (MCCRS). The
packet is intended to be used for review and practice of
previously taught and new concepts.

We strongly encourage you to work diligently to complete the
activities. You may experience some difficulty with some
activities in this packet, but we encourage you to think
critically and creatively and complete them to the best of your
ability.

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Week 1

Resource: enVision Algebra 1

Lesson: 1-3 Solving Equations with a Variable on Both Sides

Objective: Students will
 ● Use the properties of equality to solve linear equations with a variable on both
 sides.
 ● Identify whether linear equations have one solution, infinitely many solutions, or
 no solution.

Content Standards:
HSA-CED.A.2: Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
HSA-REI.B.3: Solve linear equations and inequalities in one variable, including
equations with coefficients represented by letters.

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Week 1
Problem # 1:

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Problem # 2:
Phil and Matt made cookies for a fundraiser at their high school.

 ● Phil made 25% more cookies than Matt.
 ● The cookies sold for $0.25 each.
 ● After the sale, 20% of the combined total of their cookies remained.
Part A
Create an equation to represent the total amount of money Matt and Phil earned at the
fundraiser based on the number of cookies Matt made. Explain how you determined your
equation.

Part B
Phil and Matt made a total of $72.00, selling the cookies. How many cookies did Phil make and
how many cookies did Matt make? Show your work.

Part C
Next year Phil and Matt may sell the cookies for $.50 each. They plan to make the same total
number of cookies, but they predict that they will only sell 70% of them, given the price
increase. Based on their prediction, should Phil and Matt raise the price of the cookies? Justify
your answer.

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Week 2

Resource: enVision Algebra 1

Lesson: 3 - 2 Linear Functions

Objective: Students will
 ● Write and evaluate linear functions using function notation.
 ● Graph a linear function and relate the domain of a function to its graph.
 ● Interpret functions represented by graphs, tables, verbal descriptions, and function
 notation in terms of a context.

Content Standards:
HSF-IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.
HSF-IF.B.5: Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.

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Week 2

Problem # 1:
Jamie has a plan to save money for a trip. Today, she puts 5 pennies in a jar. Tomorrow, she will put the
initial amount in plus another 5 pennies. Each day she will put 5 pennies more that she put into the jar
the day before, as shown in the table.

 Day 0 1 2 3
 Deposit (pennies) 5 10 15 20
Part A
Let f (d) represent the amount of pennies she puts into the jar on day d. What does f(10) = 55 mean?
 A. Jamie will put 10 pennies in the jar on day 55.
 B. Jamie will put 55 pennies in the jar on day 10.
 C. Jamie will have 10 pennies in the jar on day 55.
 D. Jamie will have 55 pennies in the jar on day 10.

Part B

Let f (d) represent the amount of pennies she puts into the jar on day d. Today is day 0.

Select the statement that is true.

 A. f (d + 1) = f (d)

 B. f (d + 1) = 5(f (d))

 C. f (d + 1) = f (d) + 1

 D. f (d + 1) = f (d) + 5

Problem # 2:
Jerome is constructing a table of values that satisfies the definition of a function.

 Input -13 20 0 -4 11 -1 17
 Output -15 -11 -9 -2 -1 5 5 13

Which number(s) can be placed in the empty cell so that the table of values satisfies the definition of
function?

Select all that apply.
 A. – 5
 B. – 1
 C. 0
 D. 2
 E. 11
 F. 17

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Week 3

Resource: enVision Algebra 1

Lesson: 4 -1 Solving System of Equations by Graphing

Objective: Students will
 ● Graph system of linear equations in two variables to find an approximate solution.
 ● Write a system of linear equations in two variables to represent real-world problems.

Content Standards:
HSA-REI.C.6: Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.

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Week 3
Problem # 1
A small company manufactures a certain item and sells it online. The company has a business model
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where the cost C, in dollars, to make x items is given by the equation = 3 x+50 and the revenue R, in
dollars, made by selling x items given by the equation R = 10x. The break-even point is the point where
the cost and revenue equations intersect.

Part A

 Graph the cost and revenue equations on the xy-coordinate plane provided.

 Part B
How many items must the company sell to break even? -Enter your answer in the box.

Problem # 2:
In a basketball game, Marlene made 16 field goals. Each of the field goals were worth either 2 points or
3 points, and Malene scored a total of 39 points from field goals.

Part A
Let x represent the number of 2-point field goals and y represent the number of 3-point field
goals. Write a system of equations in terms of x and y to model the situation.

Enter your answer in the space provided. Enter only your system.

{
Part B
How many 3-point field goals did Marlene make in the game?
Enter your answer in the box

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Week 4

Resource: enVision Algebra 1

Lesson: 6 -2 Exponential Functions

Objective: Students will
 ● sketch graphs showing key features of exponential functions.
 ● Write exponential functions using tables and graphs.
 ● Compare linear and exponential functions.

Content Standards:
HSF.IF.B.4: For a function that models a relationship between two quantities, interpret key
features of graphs and tables in terms of the quantities, and sketch graphs showing key features
given a verbal description of the relationship.
HSF.IF.B.5: Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.
HSF.BF.A.1: Distinguish between situations that can be modeled with linear functions and with
exponential functions.

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Week 4
Problem # 1:
 t N(t)

 0 150
 1 450

A certain type of lily plant is growing in a pond in such a way that the number of plants is growing
exponentially. The number of plants, N, in the pond at time t is modeled by the function N(t)= ,
where a and b are constants and t is measured in months. The table shows two values of the function.
 Which equation can be used to find the number of plants in the pond at time t?
 A. N(t)=150(1) 
 B. N(t)=450(1) 
 C. N(t)=150(3) 
 D. N(t)=450 (3) 

Problem # 2:
In a laboratory experiment, a certain plant grows at the rate shown in the table.

 Week Number Height (cm)

 0 2

 2 3.38

 6 9.65

Write an exponential function, h(x), that can be used to model the growth of the plant after x weeks.
Enter your function in the space provided.
 h(x)=

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Problem # 3:
 The graph shows the number of computers that have been infected with a virus in the days
 since the computer virus was first reported.

Let d represent the number of days since the computer viruses was first reported, and let c(d) represent
 the number of computers infected. Which equations model this situation?
Select each correct equation.
 A. c(d)=2d+246
 B. c(d)=96d-224
 C. c(d)=2 +3
 D. c(d)=(8)2 
 E. c(d)= 4 
 F. c(d)=4 −1

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Week 5

Resource: enVision Algebra 1

Lesson: 7-5 Factoring Quadratic Equations in Standard Form

Objective: Students will
 ● Factor a trinomial in the form �2 + �� + �, the factors whose product is equal to the
 trinomial.
 ● Identify and use patterns the signs of the coefficients of the terms of a trinomial
 expressions.

Content Standards:
HSA-SSE.A.1a: Interpret parts of an expression, such as terms, factors, and coefficients.

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Week 5
Problem # 1:
A rectangular garden has a length that is 3 feet longer than its width. Let w represent the width of the
garden, in feet. The entire garden is surrounded by a 2-foot-wide cement walkway. What does the
algebraic expression (w+4)(w+7) represent in this context?

 ● A. the area of the garden only
 ● B. the total area of the garden and walkway
 ● C. the perimeter of the garden only
 ● D. the perimeter of the walkway only

Problem # 2:
Use the information provided to answer Part A and Part B for question 12.
Consider the function f(x) =2 2 + 6 − 8.

 Part A Part B

 What is the Vertex of f(x)? What is the factored form of f(x)?

 A. f(x)=2( − 3)2 -4 A. f(x)= (2x+1)(x-8)
 B. f(x)=2( + 3)2 -4 B. f(x)= (2x-1)(x+8)
 C. f(x)=2( − 1.5)2 -12.5 C. f(x)= 2(x+4)(x-1)
 D. f(x)=2( + 1.5)2 -12.5 D. f(x)= 2(x-4)(x+1)

 Problem # 3:

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Week 6

Resource: enVision Algebra 1

Lesson: 8-1 Key Features of a Quadratic Function

Objective: Students will
 ● Identify key features of the graph of a quadratic function using graphs, tables, and
 equations.
 ● Explain the effect of the value of a on the quadratic parent function.
Content Standards:
HSS-ID.B.6a: Fit a function to the data; use functions fitted to data to solve problems in the
context of the data. Use given functions or choose a function suggested by the context.
Emphasize linear, quadratic, and exponential models.
HSA-CED.A.2: Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
HSF.BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k)
for specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using
technology. Include recognizing even and odd functions from their graphs and algebraic

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expressions for them.

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Week 6
Problem # 1:

Problem # 2:

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