Dear Parents and/or Guardians,
During the summer, I am requiring students who are in 6th or 7th grade Mathematics and moving on to 7th
or 8th grade Algebra 1 to complete a portfolio of mathematics problems. The purpose of this experience
is for the students to practice the skills and concepts learned in their previous math courses that are
essential to the course that they will be taking in the fall. The completed portfolio will be due on the first
day of school.
I encourage you to work together with your child to devise a plan to meet the completion date and to
closely monitor your child’s progress so that the summer reinforcement work is completed in a timely
fashion. Please ensure that your son or daughter does all work neatly and in an organized fashion in
pencil.
All packets may be accessed on the Frank Black Middle School website under the Mathematics
Department to be printed out if your child loses his or her initial copy. Your child has been encouraged to
use the notes taken from his or her current math class to assist in completing the portfolio. Also available
on the website there will be a copy of this letter should it be lost over the summer and you need to reread
these instructions. All of the problems within this assignment are review problems. I believe that this
summer practice will enhance your child’s performance in his/her selected fall mathematics course.
I will be checking that the portfolio has been completed and will evaluate it based on completeness on the
first day of school. In addition, a brief assessment will be given to evaluate basic understanding and skill
mastery on the core topics the first week of school. This formal in-class assessment will occur after
students have been provided with reasonable opportunity to ask questions. A representative sample of
problems will be chosen for the quiz, modeled after those from the packet. The quiz and the evaluation
will be part of the first cycle grade.
I am asking that your son/daughter present this letter to you upon receipt, and I respectfully request
your signature on the bottom of this letter to acknowledge that you have been informed of this
requirement. Your child should also sign and return the bottom portion of this form to me, Mr. Straube,
in room 102, by Thursday, May 29, 2014. Thank you for your cooperation.
Best wishes for a happy and healthy summer.
Sincerely,
Rob Straube
Algebra 1 & Geometry Teacher
rstraube@houstonisd.org
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Student Name (please print)
Student Signature
Date
Parent/Guardian Name (please print)
Parent/Guardian Signature
Date
Name:______________________________________________________________________________________
Period:_______________
Algebra 1
Frank Black Middle School – Mr. Straube
Summer Review Packet
Algebra 1 Course Description:
This course is designed to provide students with a mathematically sound understanding of the concepts
of Algebra. The student will develop fundamental algebraic skills and concepts based on the structure of
the system of real numbers. Topics will include equations, inequalities, problem solving, polynomials,
factoring, graphs and functions, simultaneous equations, irrational numbers, square roots, relations,
functions, and variation. Challenging problems are assigned and independent work is required.
Students are also required to complete a series of projects throughout the year. Students will receive a
summer project to complete that is due on the first day of school. Students should have received a strong
grade in their Pre-Algebra class, or have scored highly on a qualifying readiness examination. The TI-83
Plus is the recommended graphic calculator for this course.
Summer Packet Expectations:
The problems you will work through in this packet are designed to help you review topics that are critical
to your success in Algebra 1. In order to receive full credit, all work must be shown for each problem.
The problems should be satisfactorily attempted. All work should be completed neatly in pencil. Do not
use pen.
The packet is due the first day of school, and will be checked for completion for your first project grade.
During the first week of school, the concepts in this packet will be reviewed, and an assessment will be
given the first week.
If any help is needed to ensure that the packet is completed successfully before the first day of school,
students may contact me via email at rstraube@houstonisd.org.
Variables & Expressions
General Questions: Answer each question using complete sentences.
1. What is the difference between an expression and an equation?
2. Can you name three words that indicate each operation (+, -, ÷,×)
3. How do you evaluate an expression?
4. What are like terms?
5. How do you combine like terms?
Vocabulary, Equations, & Expressions
1. Circle the constant and underline the coefficient for each expression below.
a. 5x-3
b. 2x+7
c. 2-4x
d. x+3
2. Create an algebraic expression with a coefficient of 7 and a constant of 4.
3. Create an algebraic expression with a coefficient of -1 and a constant of -12.
4. Create an equation that contains a coefficient of 6.
5. Create an equation that contains a coefficient of -13.
6. Which of the following are algebraic expressions? Circle all that apply.
5x-2
8x
w
14+5x
2w-6
Translating between Words and Expressions
Translate the words into an algebraic expression.
7. 4 times x
8. The sum of x and 6
9. The product of 9 and y
10. w less than 8
11. 5 more than x
12. The difference of 6 and x
13. 9 times the sum of x and 4
14. The product of 5 and y divided by 3
4x-8=9
15. The quotient of 300 and the quantity of x times 2
16. x less than 32.
17. The quotient of 35 and the quantity of x minus 7.
18. The product of 7 and x minus the quantity of 4 less than y.
19. The quantity of 9 more than x divided by the quantity of 12 less than y.
Tables & Expressions.
Complete the table
20.
n
3n - 1
5
10
15
21.
n
n +7
3
5
7
22.
n
30
50
120
140
n – 70
23.
n
n÷8
-14
-7
8
16
24.
n
4 less than n
1
4
16
14
25.
n
2 more than n
-10
-1
0
5
26. Adult ticket prices are $3 more than child ticket prices. Determine the adult ticket price, given the
child ticket price.
Child Ticket
Price
$5
$7
$10
$12
Adult Ticket
Price
27. Write an expression that represents the adult price, if the child price is “x”
28. For NJASK testing, 25 students are placed in each classroom. Determine the number of classrooms
needed, given the number of students testing.
Number of
Students Testing
Number of
Classrooms
Needed
250
325
400
520
Write an expression that represents the number of classrooms need, if the number of students testing is
“x”
30. Mary has half the amount of money that Jim has. Determine the amount of money that Mary has,
given Jim’s amount of money.
Jim’s amount of
money
$50
Mary’s amount of
money
$100
$175
$220
31. Write an expression that represents the amount of money Mary has, given the amount of Jim’s money
32. Each person running in the race paid $20. Determine the amount of money collected, given the
amount of people running in the race.
Number of
People
Running
150
230
410
520
Amount of
Money Collected
33. Write an expression that represents the amount of money collected, given the number of people
running in the race.
Write an expression for the following situations:
34. Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob’s weight:
35. Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany’s money:
36. Samantha has 12 more stickers than Mike. Mike has S stickers. Samantha’s sticker amount:
37. The recipe calls for twice the amount of sugar than flour. There is F amount of flour in the recipe.
Amount of sugar:
38. Mark’s quiz grade is one more than twice Ted’s quiz grade. Ted’s quiz grade is x. Mark’s quiz grade:
39. Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth’s prom gown
price:
40. David ran the 5k in x minutes. Harry ran the same race in five minute less than double David’s time.
Harry’s time:
41. The beans grew K inches. The tomatoes grew 3 inches more than triple the height of the beans.
Tomato height:
Create a scenario for the following expressions:
42. x + 5
43. 2(x-3)
Evaluating Expressions
Evaluate the expression for the given value.
44.(2𝑛 + 1)2 𝑓𝑜𝑟 𝑛 = 3
45. 2𝑛 + 22 𝑓𝑜𝑟 𝑛 = 3
46. 4𝑥 + 3𝑥 𝑓𝑜𝑟 𝑥 = 5
47. 3(𝑥 − 3) 𝑓𝑜𝑟 𝑥 = 7
48. 8(𝑥 + 5)(𝑥 − 2) 𝑓𝑜𝑟 𝑥 = 4
49. 3𝑥 2 𝑓𝑜𝑟 𝑥 = 2
50. 5𝑥 + 45 𝑓𝑜𝑟 𝑥 = 6
51.
4𝑥
5
𝑓𝑜𝑟 𝑥 = 10
52. 4𝑦 + 𝑥 𝑓𝑜𝑟 𝑥 = 2 𝑎𝑛𝑑 𝑦 = 3
𝑥
1
53. 𝑦 + 17 𝑓𝑜𝑟 𝑥 = 12 𝑎𝑛𝑑 𝑦 = 2
1
54. 6𝑥 + 8𝑦 𝑓𝑜𝑟 𝑥 = 9 𝑎𝑛𝑑 𝑦 = 4
55. 𝑥 + (2𝑥 − 8) 𝑓𝑜𝑟 𝑥 = 10
56. 5(3𝑥) + 8𝑦 𝑓𝑜𝑟 𝑥 = 2 𝑎𝑛𝑑 𝑦 = 10
57. Use the distance formula, d=rt, to find the distance traveled.
a. Rate: 40mph; Time: 2 hours
b. Rate: 60mph; Time: 5 hours
c. Rate: 34mph; Time: ½ hour
Like Terms
58. Create a like term for the given term.
a. 4𝑥
b. 13𝑦
c. 15𝑥 2
d. 16𝑥𝑦
e. 𝑥
Combining Like Terms
Simplify the expression if possible
59. 7𝑥 + 8𝑥
60. 6𝑥 + 8𝑦 + 2𝑥
61. 15𝑥 2 + 5𝑥 2
62. 5𝑥 + 2(𝑥 + 8)
63. −10𝑦 + 4𝑦
64. 9(𝑥 + 5) + 7(𝑥 − 3))
65. 8 + (𝑥 − 4)2
66. 7𝑦 + 8𝑥 + 3𝑦 + 2𝑥
67. 𝑥 + 2𝑥
68. 𝑥 2 + 5𝑥 2
69. 2𝑥 + 4𝑥 + 3
70. 6𝑦 − 3𝑦
71. 9𝑦 + 4𝑦 − 2𝑦 + 𝑦
72. 𝑥 + 5𝑥 + 𝑥 + 12
73. 8𝑥 − 3𝑥 + 2𝑥 + 15
Multiple Choice Section: Determine whether the given terms are like terms. Circle your response.
74. 2𝑥 𝑎𝑛𝑑 − 2𝑥
Are Like Terms
Are Unlike Terms
75. 5𝑎 𝑎𝑛𝑑 5𝑏
Are Like Terms
Are Unlike Terms
76. 4𝑦 𝑎𝑛𝑑 5𝑥𝑦
Are Like Terms
Are Unlike Terms
77. 𝑥 2 𝑦 𝑎𝑛𝑑 𝑥𝑦 2
Are Like Terms
Are Unlike Terms
78. 22 𝑎𝑛𝑑 14
Are Like Terms
Are Unlike Terms
79. 𝑥𝑦 𝑎𝑛𝑑 − 𝑥𝑦
Are Like Terms
Are Unlike Terms
80.
81.
82.
83.
84.
85.
86.
87.
Match the expression 3(−4 + 3) with an equivalent expression.
a. 4(3) + 4(3)
b. 3(-4) + 3(3)
c. 4(3) – 4(3)
d. 3(4) + 3(3)
Which algebraic expression represents the number of days in w weeks?
a. w - 7
b. w/7
c. w + 7
d. 7w
Which algebraic expression represents the number of hours in m minutes?
a. w - 60
b. w/60
c. w + 60
d. 60w
In the expression 3𝑥 + 5, the value of 3 best describes:
a. the constant
b. the operations
c. the variable
d. the coefficient.
In the expression 2𝑥 + 16, the value of 16 best describes:
a. the constant
b. the operations
c. the variable
d. the coefficient.
Evaluate the expression 2𝑥, when 𝑥 = 10
a. 20
b. 12
c. 210
d. 5
1
What operation is being performed between the coefficient and variable in the expression
a. addition
b. division
c. subtraction
d. multiplication
20
𝑥
?
A group of 15 parents buys tickets to a fundraiser show and receives a group discount of $2 off the
regular ticket price p. Which expression represents the total cost of the tickets, in dollars?
a. 15 p + 2
b. 15 (p + 2)
c. p -15  2
d. p (15 - 2)
88.
A music store cells CDs for $15 and tapes for $3. Which expression could be used to find the dollar
total of the sales for an hour if the store sold 8 CDs and 5 tapes?
89.
a. (8 + 15)  (5 + 3)
b. (815) + (53)
c. (83) + (515)d
d. (8÷15) + (5÷3)
There were three times as many adults as students attending a school play. If the attendance was
480, how many adults and how many students attended the play?
a. 360 students; 120 adults b. 240 students; 240 adults
c. 120 students; 360 adults d. 160 students, 320 adults
90.
91.
92.
93.
Which of the following is not a variable expression?
a. 4n
b. n + m
c. n - 4
d. 4 + 3
What is the value of the expression 𝑥 + 𝑦, when x = 15 and y = 21?
a. 6
b. 30
c. 36
d. 42
Evaluate 𝑛2 − 𝑚, when m = 7 and n = 8.
a. 9
b. -9
c. 57
d. 71
Claire has had her driver’s license for three years. Bill has had his license for “b” fewer years than
Claire. Which expression shows the number of years Bill has had his driver’s license?
94.
a. 3 + b
b. b + 3
c. 3 – b
d. b < 3
Which situation is best modeled by the expression 25 − 𝑥?
a. George places “x” more video games on a shelf with 25 games
b. Sarah has driven “x” miles of a 25 mile trip
c. Ameilia paid $25 of an “x” dollar lunch she shared with Ariel
d. George has 25 boxes full of “x” baseball cards each
95.
96.
97.
98.
Evaluate −3𝑥 + 5 when x = -2
a. 11
b. -1
c. 1
d. -11
Nine decreased by the quantity eight times a number “x”
a. 8x-9
b. 9-8x
c. 9x-8
d. 8-9x
Four more than the quotient of 25 and y
a.
25
c.
25+4
𝑦
𝑦
+4
b.
d.
𝑦
25
+4
𝑦
25−4
What is the coefficient of x in the expression 4𝑦 + 5 − 𝑥
a. 5
b. 1
c. -1
d. –
Variables & Expressions: Short Constructed Response
99.
A rectangle is 6 inches longer than it is wide. Write and simplify an expression for the perimeter of
the rectangle in terms of the width w.
100. You and a friend worked in the school store last week. You worked 4 hours less than your friend.
Let h be the number of hours your friend worked. Write an expression in simplest form that
represents the total number of hours you both worked.
100. A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is three times
the amount of M&Ms, and the amount of raisins is two times the amount of M&Ms. Let m represent
the amount of M&Ms. Write and simplify an expression for the total number of pieces of food in the
trail mix.
102.
Write an expression containing three terms that is in simplest form. One of the terms should be a
constant.
103.
Simplify: 5 − 2(3𝑥 − 4) + 𝑥
104. Shelly lives 500 miles away. Paul drove 65mph for 4 hours. How many more miles will it take for
him to arrive at Shelly’s house?
5
105. Evaluate the expression 9 (𝐹 − 32) 𝑤ℎ𝑒𝑛 𝐹 = 41
Variables & Expressions: Extended Constructed Response
106. At the video arcade, Jenny buys 25 tokens. She uses two tokens for each game she plays.
a. Write an expression for the number of tokens Jenny has left after playing g games.
b. Find the number of tokens Jenny has left after playing 1, 4, 6, 10 and 12 games.
107. Write an expression that has four terms and simplifies to 16𝑥 + 5
108.
a.
Identify the like terms.
b.
Identify the coefficients
c.
Identify the constant terms
Mary is 5 years older than Bob. If Bob lives to be 65, 70, and 74 years of age, what will Mary’s age
be at the same time? Complete the chart with an expression containing a variable to explain your
answer.
Bob
Mary
109.
A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus
an additional cost per minute.
Plan A:
$40 fee plus $0.45 per minute
Plan B:
$70 fee plus $0.35 per minute
a.
Write an expression to represent the cost of Plan A
b.
Write an expression to represent the cost of Plan B
c.
Which plan would be least expensive for a total of 100 minutes?
Solving Linear Equations
General Questions: Answer each question using complete sentences.
110.
What are inverse operations? Name them.
111.
How do you solve equations?
Inverse Operations
112.
Name the inverse operation needed to solve for the variable.
a. 𝑥 + 9 = 17
b. 𝑦 − 8 = 5
c. 𝑚 + 5 = 21
d.
𝑤
6
= 12
e. 9𝑣 = 108
One Step Equations
Solve
113.
𝑛 + 7 = 20
116. 𝑦 − 21 = −15
119.
𝑚
9
1
= 16
122. 6 𝑡 = 12
114. 𝑥 + 9 = −2
115. 𝑎 − 15 = 27
117. 50 + 𝑤 = 92
118. −4 + 𝑚 = 18
120. 30 = 12𝑚
121. −5𝑚 = 25
123. = −10𝑐 = −80
124. 𝑛 − (−6) = 12
125. −82 + 𝑥 = −20
126.
−𝑟
2
=5
Two Step Functions
Solve
1
127. 7𝑥 − 2 = 26
128. 2 (𝑚 − 3) = 12
129. −6ℎ − 6 = 30
130. 5𝑥 + 20 = −20
131. 3 = −3𝑦 − 15
132. −24 + 14𝑦 − 5
133. 7𝑡 − 5 = 10
134. 9 = 16𝑦 + 51
135. −4 + 11 = 5
𝑥
Extended Constructed Response Questions
136.
The clerk at the bank desk says there is an initial charge of $50.00 to open up a bank account at
the Sunny Farms Bank. He then explains that after, every account added on will cost an additional
$15.50 each. The Smith Family is thinking of opening an account for the family.
a.
Write an equation that represents the cost to open accounts for the family members.
b.
What is the greatest amount of family members that could open a bank account without
exceeding a fee of $500?
c.
How much money would it cost if Mom Smith, Dad Smith, Sister Smith, and Brother Smith
want top open an account, and Mom Smith has a special discount coupon of 15% off the
final price?
137.
The Rainbow Phone Service Company has a monthly fee of $100 and an additional charge of $6.00
for every data one goes over a month. The Cellular Phone Service Company has a monthly fee of
$80 and an additional charge of $10.00 for every data one goes over. The Gomez family is deciding
which of these two phone providers to subscribe to.
a. Write an equation that represents the cost of each phone company’s monthly fee. Let p =
cost.
b. For what number of data over will the total monthly fee for both companies be the
same?
c. The Gomez family’s daughter went over 6 data last month. Which phone service will
save the Gomez family the more if the daughter repeats this bad habit next month?