Precalculus
NAME _____________________________________
JUNE 2015
PRECALCULUS AND FST
OPTIONAL SUMMER WORK
I.
COORDINATE GEOMETRY
1)
Find the slope, midpoint, and length of the line
segment that has the following endpoints (2, -5) and
(6, 1). Simplify all answers.
2)
Find the x- and y-intercepts for 4x – 9y = 12.
3)
A line has a slope of
-5
and contains the points (2, -7)
6
and (x, 4). Find the value of x.
4) Write the equation of the line with a slope of -11
and a y-intercept of (0, -2).
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Precalculus
5)
Write the equation of a line containing points (3, 7)
and (11, -5).
6)
Write the equation of the line with zero slope through
(-12, 5).
7)
Write the equation of the line parallel to the y-axis
passing through (2, 1).
8)
ïì-2x + y = 4
Solve the system graphically. í
ïî7x - 3y = -13
9)
ìï2x + 3y = -6
Solve the system algebraically. í
îï3x + 4y = -7
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Precalculus
II.
1)
2)
FACTORING
POLYNOMIALS
Factor each of the following completely.
a)
y2 – 6y – 40
b)
3a2 + 14a + 8
c)
27x3 + 8y3
d)
5a2 – 45
e)
3uw2 + 24uw + 45u
f)
2n3 + 10n2 – 7n - 35
b)
2x3 - 9x2 = 0
Solve by factoring.
a)
3)
AND
x2 + 13x = 30
Solve by completing the square: x2 + 10x – 7 = 0
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Precalculus
4)
Solve using the Quadratic Formula: 2x2 – 2x – 5 = 0
5)
Solve using synthetic division: 2x3 - x2 – 13x – 6 = 0
III. RADICALS - Simplify (if possible).
1)
2 7 - 6 - 8 7 - 11 6
2)
27 - 11 12
3)
12 · 5 3
4)
æ 7 - 2 3ö
è
ø
5)
2
5-4 3
2+ 3
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Precalculus
IV.
COMPLEX NUMBERS
Simplify each expression.
a)
d)
b)
-36
i 130
g)
-48
e)
-6 · -15
h)
(4 – 6i) + (11 + 2i)
5
2i
V.
FUNCTIONS
1)
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
c)
i 27
f)
(-12 + 5i) - (2 - 7i)
i)
2 - 3i
5 + 8i
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Precalculus
2)
For each of the following functions, identify the shape of the graph. Also identify
any transformations including shifts and reflections.
a)
f(x) = - |x + 3|
Transformations:
b)
h(x) =
d)
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___________________________________________
Shape:
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3
k(x) = - x + 7 - 4
Transformations:
3)
Shape:
x -5
Transformations:
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g(x) = (x – 4)2 + 11
Transformations:
c)
Shape:
Shape:
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Given the functions below, evaluate each of the following.
f(x) = 2x2 – 3
g(x) = 4x + 7
a)
f(-3) ______________
c)
h(f(g(2))) ______________
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b)
h(x) =
6
x+3
g(h(-1)) ______________
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Precalculus
VI.
1)
3)
RATIONAL EXPRESSIONS
Perform the indicated operation and simplify each expression.
3y
4- y
2
·
2y2 + y - 3
10n
n - 3n - 4
2
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y -1
2
-
2
n+1
¸
2y3 + 3y2
y - 3y + 2
2
2)
8
3x + 6
3
4)
+
+
5x
x -4
2
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 .
11
7
2)
Convert the following angle to radians.
84o
3)
Convert the following angle to degrees.
-11p
9
4)
Find two coterminal angles (one positive and one negative) for 520o.
5)
Find the missing value. Round to the nearest tenth.
25
x
15
6)
Draw an angle with the given measure in standard position and find its reference
angle.
A) 207
B) -420
9p
C)
6
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Precalculus
7)
Evaluate each of the following and provide an EXACT answer.
a)
sin 60
b)
cos 240
e)
sec10p
f)
tan
i)
tan
j)
cot
-7p
3
21p
2
17p
6
c)
tan -150
g)
cs c
k)
sec
11p
6
-5p
2
d)
cot 315
h)
c os
l)
csc
11p
4
-5p
3
8)
Write the equation of the curve described.
A reflected cosine curve with a maximum value of 3 and a minimum value of -7. The
horizontal between two consecutive intercepts is 5.
9)
Graph two periods of the following function. Be sure to keep scale and identify key
values.
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f(x) = - 2 sin
p
2
x+3
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