Dear Parents and/or Guardians,
During the summer, I am requiring students who are in 7th grade Algebra, and who will be moving on to
Geometry, 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 on
separate notebook paper.
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 Algebra 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
---------------------------------------------------------------------------------
Student Name (please print)
Student Signature
Date
Parent/Guardian Name (please print)
Parent/Guardian Signature
Date
Name:______________________________________________________________________________________
Period:_______________
Geometry
Frank Black Middle School – Mr. Straube
Summer Review Packet
Geometry Course Description:
This course is a rigorous study of the concepts of geometry requiring analytical thinking in addition to
factual knowledge of the material. Students develop their deductive reasoning skills throughout the
course through informal justifications and arguments as well as formal proofs. Topics include angles,
angle measurement, triangles, congruent triangles, quadrilaterals and other polygons, circles, parallel
lines, solid figures, perimeter, area, volume, geometric probability, loci, coordinate transformations, NonEuclidean Geometry, rules of logic, extensive analytic problem solving, the axiomatic development of
Euclidean geometry, and historical contributions in the development of geometry. Students are expected
to study these topics in greater depth and at a more rapid pace than a traditional geometry course, with a
significant emphasis on analytical reasoning kills, a formal mathematical vocabulary, techniques in
perspective drawing, and formal geometric constructions.
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. Additionally, students are also required
to independently research and deliver a formal presentation on an assigned mathematical topic.
Students will read and write a critical analysis of the novelette Flatland. Students should have a strong
understanding of Algebra. The TI-83 Plus is the recommended graphing 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 Geometry, as the skills that you have learned in Algebra 1 will be used daily throughout
this course. In order to receive full credit, all work must be shown for each problem. The problems
should be attempted satisfactorily on separate paper. 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.
Solving Equations in One Variable
Solve
1.
3𝑦−2(𝑦−1)
6
=
−1
2. 3(𝑥 − 2) − 𝑥 = 2(2𝑥 − 1)
3. 3(180 − 𝑦) = 2(90 − 𝑦)
4. 6𝑥 − 3(6 − 5𝑥 ) + 3𝑥 = 10 − 4(2 − 𝑥)
1
1
1
2
4
2
5. (6 + 4𝑥 ) − (8𝑥 − 12) = (2𝑥 − 4)
6. 5𝑥 − [7 − (2𝑥 − 1)] = 3(𝑥 − 5) + 4(𝑥 + 3)
Solve each system of equations by the substitution method.
7. 𝑦 = 2𝑥 + 5
8. 8𝑥 + 3𝑦 = 26
9. 𝑥 − 8 = 3 + 𝑦
3𝑥 − 𝑦 = 4
2𝑥 = 𝑦 − 4
2𝑥 − 5𝑦 = 8
10. 𝑥 − 7𝑦 = 13
11. 3𝑥 + 2𝑦 = 71
12. 3𝑥 + 𝑦 = 19
3𝑥 − 5𝑦 = 23
𝑦 = 4 + 2𝑥
2𝑥 − 5𝑦 = −10
Solve each system of equations using the elimination method.
13. 3𝑥 + 4𝑦 = 9
−3𝑥 − 2𝑦 = −3
16. 2𝑥 − 8𝑦 = 24
3𝑥 + 5𝑦 = 2
14. 4𝑥 − 6𝑦 = −26
15. 5𝑥 + 3𝑦 = 30
−2𝑥 + 3𝑦 = 13
3𝑥 + 3𝑦 = 18
17. 3𝑥 + 𝑦 = −3
18. 5𝑥 − 9𝑦 = 47
𝑥 + 4𝑦 = 10
6𝑥 + 2𝑦 = 18
The Coordinate Plane
Name the coordinates of each point.
19. M
24. T
20. N
25. U
21. K
26. V
22. R
27. W
23. S
28. Q
29. Name all the points shown that lie on the x-axis.
30. Name all the points shown on the y-axis.
31. What is the x-coordinate of every point that lies on a vertical line through P?
32. Which of the following points lie on a horizontal line through W?
(-2,1)
(2,3)
(1,-3)
(-2,0)
(0,-3)
(2,0)
Name all the points shown that lie in the quadrant indicated. (A point on an axis is not
in any quadrant)
33. Quadrant I
34. Quadrant II
35. Quadrant III 36.Quadrant IV
Plot each point on the graph above.
37. A (2,1)
38. B (5,0)
39. C (0,3)
40. D (-3,1)
41. E (-2,-1)
42. F (1,-2)
43. G (4,-2)
44. H (-4,-3)
Simplify the following fractions
45.
49.
53.
57.
61.
14
70
𝑥
46.
50.
3𝑥
3𝑎𝑏2
6𝑏𝑐
𝑥+2
3𝑥+6
𝑏2 −25
𝑏2 −12𝑏+35
54.
58.
62.
75
47.
15
5𝑏𝑐
10𝑏2
6𝑎+12
6
2𝑐−2𝑑
2𝑐+2𝑑
𝑎2 +8𝑎+16
𝑎2 −16
Solve each equation by factoring
64. 𝑥 2 + 5𝑥 − 6 = 0
65. 𝑥 2 − 7𝑥 − 18 = 0
66. 𝑥 2 = 20𝑥 − 36
67. 𝑥 2 + 8𝑥 = 20
68. 4𝑥 2 + 15 = 17𝑥
69. 3𝑥 2 − 13𝑥 − 10 = 0
70. 6𝑥 2 + 11𝑥 − 10 = 0
71. 8𝑥 2 + 10𝑥 − 25 = 0
51.
55.
59.
63.
18𝑎
36
−8𝑦 3
2𝑦
9𝑥−6𝑦
3
𝑡 2 −1
𝑡−1
3𝑥 2 −6𝑥−24
3𝑥 2 +2𝑥−8
48.
52.
56.
60.
3𝑥
𝑥
−18𝑟 3 𝑡
12𝑟𝑡
33𝑎𝑏−22𝑏
11𝑏
5𝑎+5𝑏
𝑎2 −𝑏2
Solve the following proportions
72.
75.
78.
7
2
=
10
6𝑥+7
2−4𝑥
−6
𝑦
73.
3
=
=
6
2𝑥+9
6𝑥−8
10
76.
79.
7
=
3
4
𝑥−3
𝑥+2
5
21
74.
𝑥
=
=
6
77.
𝑥+3
4
80.
𝑥+1
5
25
=
3𝑥−5
2
2
𝑥−3
10
𝑥
=
=
𝑥−15
4
𝑥−2
6
The Slope of a Line
Given two points, find the slope
81.(3, −4) 𝑎𝑛𝑑 (3, −2)
Graphs of Linear Equations in Two Variables
Graph the following
83. 2𝑥 + 5𝑦 = 15
3
1
2
2
82. ( , −3) 𝑎𝑛𝑑 ( , −7)
Finding the Equation of a Line
Write the equation of the line in both standard form and point-slope form that
has the given conditions.
1
84. Contains the point (-4,-2) and has slope =
2
85. Contains the points (3,-2) and (2,-3)
86. Perpendicular to the line 4𝑥 − 𝑦 = −3 and passes through the point (−8,3)
87. Contains the points (-3,0) and (0,-1)
Algebraic Solving of Systems of Linear Equations in Two Variables
Solve the system of equations algebraically.
88. 8𝑥 − 3𝑦 = 3
89. 6𝑥 = 4𝑦 + 5
3𝑥 − 2𝑦 + 5 = 0
6𝑦 = 9𝑥 − 5
Products and Quotients of Rational Expressions
Simplify
90.
𝑥𝑦 2
6
÷
𝑥 2 𝑦−1
91.
9
𝑥 2𝑦
𝑥 2 −𝑦
2 ×
2𝑥+2𝑦
92.
𝑥𝑦
𝑥 2 +5𝑥−6
3𝑥−3
÷
3𝑥+18
𝑥 2 −𝑥
Factor Completely
93. 100𝑎2 − 36𝑏 2
94. 16𝑥 2 + 40𝑥𝑦 + 25𝑦 2
95. 8𝑛𝑚 − 10𝑛𝑚 + 12𝑛𝑚 − 15
96. 6𝑥 2 − 7𝑥 − 3
97. 𝑥 4 − 2𝑥 2 + 1
98. 16𝑥 3 − 64𝑥 2
99. 16𝑥 4 − 𝑦12
100. 14𝑥 5 𝑦 3 𝑧 + 10𝑥 2 𝑦 − 2𝑥 3 𝑦𝑧 2
101. 𝑐 2 − 4𝑑 2
102. 36𝑎2 − 49𝑏2
103. 4𝑘 2 + 20𝑘 + 25
104. 25𝑗 2 − 80𝑗 + 64
105. 5𝑥 2 + 13𝑥 + 6
106.𝑥 2 − 10𝑥𝑦 + 24𝑦 2
107. 𝑥 3 + 5𝑥 2 − 9𝑥 − 25
108. 8𝑛𝑚 − 10𝑛 + 12𝑚 − 15