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Name _________________
YOG ___
Date ______
SUMMER MATH PACKET FOR
GEOMETRY STUDENTS
2006-2007
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1. Signed Number Problems
Directions: Simplify the following problems.
Work
a. (-7) + (-2)
Answer Work
b. 9 – (-3)
Answer Work
c. 3 + (-8)
d. (-3)(4)
e. (-5)(-5)
f. (-8)(-½)
g. -9
3
h. -6
-4
i. -8
(½)
Answer
2. Order of Operations
Directions: Simplify the following problems using the order of operations.
Work
Answer
a) 4 – (2.9 – 17)
b) [8 – 3(2)] – 6
c) 12 + [16  (3 + 1)]
d) 18  [(8)(2) – 7]
e)
(9.9)  (3.3) + [(4.3)(16.1) – 17]
2
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3. Solving Linear Equations
Directions: Solve for x.
Work
Answers
a) 3x  7  23
b)
1
x  1  1
2
c)
4 
4
x  6
5
d) 16  2 
2x
5
e) x  5 x  5  6  3x
1
2
f) 10  x  x
g) 19  x  2( x  1)
h)
55x  3(9 x  12)  64
i)
9
1
( x  3)  27  x
2
2
j)
4
(2 x  4)  4(4 x  6)
9
3
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4. Graphing Linear Equations Using Slope and y-intercepts
4a. Directions: Use the slope and the given points to find the y-intercept. (Hint:
y=mx+b)
Work
a.) slope = ½;
(3,2)
b.) slope = 3;
(-5,4)
Answer
c.) slope = -½; (½,2)
4b. Directions: Find the slope and y-intercept of each equation or set of coordinates and
graph it.
Problem/Work
a)
Answer
y  2x  7
Graph
10
y
slope: ____
y-intercept:____
x
-10
-10
10
4
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b)
3 x  4 y  12
10
y
slope: ____
y-intercept:____
x
-10
-10
c)
(-6,-1) (-6,4)
10
10
y
slope: ____
y-intercept:____
x
-10
-10
d)
(2,2) (-3,5)
10
10
y
slope: ____
y-intercept:____
x
-10
-10
10
5
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e)
4 y  4 x  16
slope: ____
10
y
y-intercept:____
x
-10
-10
f)
(0,-6) (8,0)
slope: ____
10
10
y
y-intercept:____
x
-10
-10
g)
(1,-2) (-2,-2)
slope: ____
10
10
y
y-intercept:____
x
-10
-10
10
6
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5. Substituting into Formulas
Substitute the given numbers to solve for the variables in the following equations.
Work
a)
A  r 2
r = 3.5 cm
b)
A  r 2
A = 25 
c)
C = 2 r
r=½
d)
C = 2 r
C = 84 
e)
p  2(l  w)
Answer
p = 16; l = 5
6. Combining Like Terms and the Distribute Property
Simplify the following expressions.
Work
a)
3n + 5 – n
b)
4x + 3y – 7 + 2y + x
c)
4(3p – 8)
d)
5n(8 + 2n)
e)
9(n – 1) – (7n+2n)
Answer
7
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7. Factoring
Factor the following.
Work
a)
x2 + 5x + 6
b)
x2 + 9x – 22
c)
6x2 + 13x – 28
d)
6x2 – 5x – 21
e)
x2 – 16
f)
x2 + 6x + 9
Answer
8. Word Problems
a.) Alaska is the largest state in the United States, with an area of 570,374 mi2. It
accounts for about 15% of the country’s area. Estimate the area of the United States.
b.) Suppose Kayla buys ¾ of a yard of fabric for $2.50. What is the price of the fabric
per yard?
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c.) Tina is a sales associate in a clothing store. Each week she earns $250 plus a
commission equal to 3% of her sales. This week she would like to earn no less than
$460. What dollar amount of clothes must she sell?
d.) Jackie has been offered two jobs. The first job will give her a starting annual salary
of $26,000, plus annual increases of $1500. The second will give her a starting annual
salary of $29,000, plus annual increases of $900.
1. For each offer, write the annual salary as a linear equation
2. Graph both functions and find the point of intersection.
$
Years
3. Which job should Jackie choose if she plans on staying at her job for at least 6
years? Explain
6/30/2005
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