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Precalculus
NAME _____________________________________
JUNE 2011
PRECALCULUS SUMMER ASSIGNMENT
To prepare you for the upcoming year, the Mathematics Department has created this
summer assignment as a means of reviewing important skills and concepts that you have
learned. The assignment has been divided into different sections. You are responsible
for completing this packet on your own. Try and complete most of the assignment
without using a calculator.
To supplement your knowledge, Ms. Hinrichsen, Mr. Lynch, and Ms. Rossi will have a PDF
file of website resources on their websites on their PRECALCULUS pages. Feel free to
email any of them with a question. Please consider that it is summer break, and they may
not get back to you the same day.
The packet will be collected on Wednesday, September 7, 2011. An assessment
(quiz/quest) will be given to assess the students’ knowledge of the material. Be sure to
SHOW ALL WORK to receive credit. All answers should be EXACT (simplified fractions
and radicals).
I.
1)
COORDINATE GEOMETRY
Find the slope, midpoint, and length of the line
segment that has the following endpoints (2, -5) and
(6, 1). Simplify all answers.
Slope ____________
Midpoint
_________
Length ___________
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2)
Find the x- and y-intercepts for 4x – 9y = 12.
3)
A line has a slope of
4)
A line has a slope of
5
and contains the points (2, -7)
6
and (x, 4). Find the value of x.
a)
4
7
b)
3
Write y   x  7 in standard form.
8
6)
Write y 
7)
Write the equation of the line with a slope of -11
and a y-intercept of (0, -2).
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3
2
5
y-int
____________
_________________
perpendicular to it ____________
5)
x
____________
. Identify the slope of a line:
parallel to it ____________
8
x-int
in general form.
_________________
_________________
_________________
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Precalculus
8)
Write the equation of a line with a slope of
and
_________________
Write the equation of a line containing points (3, 7)
and (11, -5).
_________________
passing through (-10, 3).
9)
2
5
10) Write the equation of the line with zero slope through
(-12, 5).
_________________
11) Write the equation of the line parallel to the y-axis
passing through (2, 1).
_________________

2x  y  4
12) Solve the system using substitution. 

7x  3y  13
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Precalculus
2x  3y  6
13) Solve the system using linear combinations. 
3x  4y  7
(Elimination)
_________________
14) Graph 3x + 4y = -12.
II.
1)
FACTORING
AND
POLYNOMIALS
Factor each of the following completely.
a)
y2 – 6y – 40
b)
3a2 + 14a + 8
c)
27x3 + 8y3
d)
5a2 – 45
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Precalculus
3uw2 + 24uw + 45u
1)
e)
2)
Solve by factoring.
a)
x2 + 13x = 30
f)
2n3 + 10n2 – 7n - 35
b)
2x3 - 9x2 = 0
3)
Solve by completing the square: x2 + 10x – 7 = 0
_________________
4)
Solve using the Quadratic Formula: 2x2 – 2x – 5 = 0
_________________
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Precalculus
5)
Solve using synthetic division: 2x3 - x2 – 13x – 6 = 0
_________________
III. RADICALS
1)
Simplify (if possible).
a)
2 7  6  8 7  11 6
27  11 12
b)
2)
_________________
_________________
Simplify (if possible).
2  10 ______________
a)
c)
6 5


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2
______________
b)
d)
12  5 3 ______________
14
2
______________
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Precalculus
3)
Simplify (if possible).
a)
b)
IV.
1)
 7  2 3


2
_________________
54 3
_________________
2 3
COMPLEX NUMBERS
Simplify each expression.
a)
d)
36
i 130
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b)
e)
48
(4 – 6i) + (11 + 2i)
c)
i 27
f)
(-12 + 5i) - (2 - 7i)
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Precalculus
2)
Given the complex number 4 – 9i, identify:
Real Part
3)
c)
1)
Conjugate
Simplify each of the following expressions.
a)
V.
Imaginary Part
6  15 ______________
b)
5
2i
______________
2  3i
_________________
5  8i
FUNCTIONS
State the domain of each of the following functions.
a)
f(x) = 4 – 6x – 7x3
b)
g(x) 
c)
h(x)  3x  8
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2x  10
x  7x  30
2
_________________
_________________
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Precalculus
2)
Given the functions below, evaluate each of the following.
f(x) = 2x2 – 3
3)
g(x) = 4x + 7
a)
f(-3) ______________
b)
c)
h(f(g(2))) ______________
h(x) =
6
x3
g(h(-1)) ______________
For each of the following functions, identify the shape of the graph. Also identify
any transformations including shifts and reflections. Be sure to indicate the number
of units and the direction.
a)
f(x) = - |x + 3|
Transformations:
b)
g(x) = (x – 4)2 + 11
Transformations:
c)
h(x) =
x 5
Transformations:
d)
3
k(x) =  x  7  4
Transformations:
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Shape:
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Shape:
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Shape:
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Shape:
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Precalculus
VI.
RATIONAL EXPRESSIONS
Perform the indicated operation and simplify each expression.
1)
2)
3y
4  y2
8
3x  6
3
4)

2y2  y  3


y2  1
5x
x 4
2

2y3  3y2
y2  3y  2
3)
10n
n  3n  4
2

2
n1
4
x2 x
5
7

x  2 6x
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