Honors Geometry Summer Math Packet Summer 2015
Covering Prerequisite Concepts for Incoming Honors Geometry Students
This summer packet contains exciting math problems designed to ensure your readiness for Honors
Geometry. The topics covered in this packet are concepts that should have been mastered in courses
before entering Honors Geometry.
Show all work that leads you to each solution. Use separate paper, if necessary. You may get help with
this packet from friends, a tutor, the internet, or a teacher; but, please understand that “help” means
having someone explain how to solve the problem, not just simply supplying the answer or copying the
work someone else did. YOU are responsible for understanding the material contained in this packet and
for being able to employ the skills necessary to solve each problem.
All work should be completed and ready to turn in on the first day of school. This packet will count as
part of your first term grade and will be graded on completeness and correctness. You will not be given
credit for problems for which no work is shown. Summer Math Packet test will be given the first full
week of school.
Do a little of your Summer Math Packet each week. You are not expected to do all of it on the first day
or the last week. Your Summer Math Packet will be used to analyze your strengths and weaknesses. If
the work in this packet is too challenging for you, it may be that Honors Geometry will be too
challenging also. Please call the high school Guidance Department if you find yourself needing to switch
out of Honors Geometry.
Students should try to answer all of the questions, if possible. However, a minimum of 97 of the
questions must be answered to receive full credit. So if you really can’t answer certain questions, you
may write the word “pass” on up to 10 of the questions without penalty. (The purpose of this option is
to allow students to show what they know on certain concepts while informing the teacher of concepts
that may need to be reviewed with students after school starts.)
Honor and integrity are at the heart of all Affton Cougars. Smart Cougars never cheat. You are only
hurting yourself by attempting to copy someone else’s work. This packet is to help you be ready for
Honors Geometry, and help your teachers know what you can do. If you should lose your packet, please
email [email protected] for another copy.
Thank you and have a great summer!
Secondary Math Teachers
Affton High School
1
Table of Contents
Page Objective
Suggested
Completion Date
1
Formula Reference Sheet
2
Formula Reference Sheet
3
Formula Reference Sheet
6
Vocabulary ................................................................. June 12
7
Formula Matching ...................................................... June 12
8
Fractions ................................................................. June 19
8
Expressions................................................................. June 19
9
Exponents and Radicals .............................................. June 26
10 Solving Equations ....................................................... June 26
11 Proportions ................................................................... July 3
12 Factoring Quadratic Equations ...................................... July 3
12 Pythagorean Theorem ..................................................July 10
13 Systems of Equations ...................................................July 17
14 Number Line Inequalities .............................................July 17
14 Graphing Functions ......................................................July 24
17 Various Graphs .............................................................July 24
2
Formula Reference Sheet For Geometry Summer Work
Solving Linear Inequalities
 Remember: When you divide both sides by a negative number, flip the inequality symbol.
 Shade the graph greater than or less than when graphing linear inequalities.
Writing Equations of Lines
Slope formula:
(use when given two points.)
Slope-intercept form:
x-intercept: Where the graph crosses the x-axis. (x, 0)
y-intercept: Where the graph crosses the y-axis. (0,y)
Vertical line: slope = undefined; equation is
Horizontal line: slope = 0; equation is
Parallel lines have the same slope.
Perpendicular lines have opposite reciprocal (negative-flip) slopes.
Graphing Lines
Slope-Intercept Form:
; where m = slope and b is the y-intercept.
1) Start by graphing the y-intercept on the y-axis.
2) Next, find more points on the line by using the slope.
Vertical lines are x = ____
Horizontal lines are y = ____
Positive slope = the line will rise to the right.
Negative slope = the line will fall to the right.
Solving Quadratic Equations (Quadratic Equations are equations that include an
term.)
1. Solve by factoring: Completely factor the equation and then set each factor = 0, then solve for x.
2. Solve by using the Quadratic Formula:
(the quadratic formula will always work)
3
4
5
Vocabulary
Word Bank:
coefficient
percentage
slope-intercept form
range
mode
constant
like terms
mean
sum
median
denominator
numerator
linear-standard form
x-intercept
probability
difference
product
quotient
y-intercept
slope
1. ____________________ the bottom number in a fraction
2. ____________________ an amount obtained by addition
3. ____________________ y = mx + b
4. ____________________ Ax + By = C
5. ____________________ mathematical average of all the terms in a data set
6. ____________________ an amount obtained by multiplication
7. ____________________ the point where a line crosses the y-axis
8. ____________________ a value or quantity at the midpoint of a data set
9. ____________________ an amount obtained by division
10. ___________________ the point where a line crosses the x-axis
11. ___________________ the top number in a fraction
12. ___________________ an amount obtained by subtraction
13. ___________________ the number being multiplied by a variable (the number in front of
the variable
14. ___________________ a term that has no variable factor (it is just a number)
15. ___________________ terms with exactly the same variable
16. ___________________ the ratio of a line’s vertical change to its horizontal change
17. ___________________ the most frequently occurring value in a data set
18. ___________________ a rate, number, or amount in each hundred
19. ___________________ the likelihood of a given event’s occurrence
20. ___________________ the difference between the lowest and highest values
6
Formulas
Match the following formulas to their correct descriptions.
y2  y1
x2  x1
21. ________ Slope-Intercept Form
A. m 
22. ________ Standard Form of a Line
B. Ax  By  C
23. ________ Slope
C. a2  b2  c2
24. ________Distance Formula
D. y  mx  b
25. ________Midpoint Formula
E. d  ( x2  x1 )2  ( y2  y1 )2
26. ________Quadratic Formula
 x  x y  y2 
F. M   1 2 , 1

2 
 2
27. ________ Pythagorean Theorem
b  b2  4ac
G. x 
2a
7
Fractions
Perform the indicated operation and simplify, if necessary.
28.
5 3
 
4 4
29.
7 1
 
8 2
30.
31.
1 7
 
9 8
32.
15 12


3 5
33. 
34.
2 5
 
3 8
35.  
5 2

3 5
36.
6 3
 
7 2
3 2
 
5 7
1 5
 
3 2
Expressions
Evaluate each of the following expressions. Let x = 4, y = –2, and z = 7
37. 2 x  3 y 2
38. 5( x  y)
40. x3  y 2
41. 3xz  z 2 y
39.
y
x
8
Evaluate each expression:
42. 3  7  5  2
43. 24  22  7  5
44. 2(5  3)  5  4
45. 3(12  7)  33
46. (3  5)3  2(4  3)
47. 49  (5  2) 2  14
48.

(2  4) 2
3
49. (7  92 )  (5  4)2
Exponents and Radicals
Simplify the following expressions completely.
50.
15a 4 b 2 c3
5ac5
51. ( x 4 )2
52. (2 x3 )2
9
Simplify. Leave answers in radical form (no decimals).
53.
18
54. 5 80
56.
1
2
57.
55. 3 2 5 10
12
5
58.
2 2
3
Solving Equations
Solve the following equations.
59.
r 8
 2
3
61. 2  10 x  8x  1
63. 3 
2
2
y  11  y
5
5
65. 1.03t  4  2.15 t  8.72
60. 3( x  2)  18
62. 2(a  3)  5  3(a  1)
64. 2  x  3( x  1)  18
66. 3( x  5)  8x  18
10
Proportions
Solve each proportion for the indicated variable.
67.
2
x

3 12
68.
5 10

y 14
69.
15
9

5  3n n
70.
x  2 4 x  13

2
3
Solve for each problem below by using proportions.
71. Sue was paid $384 for working 32 hours. How many hours will she have to work to earn $672?
72. Tommy drove 238 miles in 5 hours. How long will it take him to travel the next 72 miles, if he
continues at the same speed? (Give your answer in minutes.)
73. Matt paid $33.41 for 13 gallons of gasoline. How many gallons can he buy if he only has $14?
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Factoring Quadratic Equations
Factor the following expressions.
74. x2  9 x  20
75. x2  3x  28
76. x2  4 x  32
77. x 2  64
78. 4 x 2  25
79. 3x2  3x  6
Pythagorean Theorem
Find the missing side length. If needed, round to the nearest tenth.
6.25
80.
81.
9
x
x
2.3
5
83.
x
8
x
82.
15
3
3x
84.
x+2
x–2
x
12
Systems of Equations
Find the value of x, and y that satisfy each system of equations below.
85.
2x  3 y  5
86.
x  5y  9
3x  y  2
8 x  15 y  7
Number Line Inequalities
Graph each inequality on a number line.
87. 18  4 x  50
88. 7  2t  21
89. 2 x  6  6 x  2
90. 3x  12 or 4 x  10
13
Graphing Functions
91. y  2
92. 2 y  4 x  6
y
y
x
x
1
93. y   x  4
2
94. x  1
y
y
x
x
95. y  x 2
96.
y x
y
y
x
x
14
97. 2 x  y  5
98. 6 x  5 y  30
y
y
x
x
99. Write the equation of a line that passes through (–3, 2) and is parallel to x  y  7 . Then
graph.
y
x
100. Write the equation of the line that passes through (–5, 9) and (–4, 7) in slope-intercept
form. Then graph.
y
x
15
101. Sketch a line with the appropriate slope.
y
y
x
x
Positive
Negative
y
y
x
x
Zero
Undefined
16
Various Graphs
Write the equations or inequalities for the following graphs.
102. __________________
105. __________________
103. __________________
106. __________________
104. _________________
107. _________________
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