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Precalculus
NAME _____________________________________
JUNE 2014
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. Lewis, 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 10, 2014. 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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Precalculus
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)
Write y = -
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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8
3
x + 7 in standard form.
x-
2
5
y-int
____________
_________________
perpendicular to it ____________
5)
8
____________
. Identify the slope of a line:
parallel to it ____________
3
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).
_________________
ìï-2x + y = 4
12) Solve the system using substitution. í
îï7x - 3y = -13
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_________________
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Precalculus
ìï2x + 3y = -6
13) Solve the system using linear combinations. í
ïî3x + 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)
b)
2)
2 7 - 6 - 8 7 - 11 6
_________________
27 - 11 12
_________________
Simplify (if possible).
a)
c)
2 · 10 ______________
æ6 5ö
è
ø
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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)
æ 7 - 2 3ö
è
ø
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:
________________________________
___________________________________________
Shape:
________________________________
___________________________________________
Shape:
________________________________
___________________________________________
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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Precalculus
VII. TRIGONOMETRY
1)
Given the triangle, find the six trigonometric functions for Q .
Q
11
7
2)
Find the value of Q . Round your answer to the nearest tenths.
A)
3)
sinQ = 0.3490
B)
cotQ = 1.1297
Evaluate the following. Round to the nearest ten-thousandths place.
A)
sec 78o
B)
tan 85o
84o
4)
Convert the following angle to radians.
5)
Convert the following angle to degrees.
6)
Find the complement of 52o.
7)
Find the supplement of
8)
Find two coterminal angles (one positive and one negative) for 520o.
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8p
15
-11p
9
.
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Precalculus
9)
Find the missing value. Round to the tenths.
25
x
15
10) Draw an angle with the given measure in standard position and find its reference
angle.
A) 207
B)
-420
C)
9p
6
11) Express the following in terms of its reference angle.
A)
tan 152o
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B)
sec
17p
5
12