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Calculus
NAME _____________________________________
JUNE 2011
CALCULUS 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 two parts: No Calculator and With
Calculator. You are responsible for completing this packet on your own.
To supplement your knowledge, Mr. Lynch and Mrs. Ricca will have a PDF file of website
resources on both of their websites on their CALCULUS pages. Along with the resources
file will be a PDF file of selected answers so that you can check your work and monitor
your progress.
Feel free to email either of them with a question. Please consider that it is summer
break, and they may not get back to you the same day. If you send the email to both, it
may get you a faster response (one may be on vacation and the other may be available).
The packet will be collected on Tuesday, September 6, 2011. An assessment (quiz/quest)
will be given to assess the student’s knowledge of the material. Be sure to SHOW ALL
WORK to receive credit.
PART I - NO CALCULATOR
I.
COORDINATE GEOMETRY
1)
Identify the x- and y-intercepts for 3x – 8y = 12.
2)
Rewrite 10x + 6y = 20 in slope-intercept form.
Identify the slope and y-intercept.
MPH/NPR 6/10
x-int
____________
y-int
____________
slope ____________
y-int
____________
1
Calculus
3)
A line has a slope of -3/5 and contains the points
(-2, 6) and (x, 1). Find the value of x.
4)
Write y  
5)
Write y 
6)
Find the equation of the line with a slope of 5/6
and a y-intercept of (0, -8).
_________________
7)
Find the equation of a line with a slope of 2/3 and
passing through (-15, 4).
_________________
8)
Find the equation of a line through the points
(-7, 12) and (2, 6).
_________________
9)
Write the equation of the line through the point
(16, -9) with zero slope.
_________________
MPH/NPR 6/10
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3
2
5
x  3 in standard form.
x
1
4
in general form.
_________________
_________________
_________________
2
Calculus
10) Write the equation of the line parallel to the y-axis
and through (8, -14).
_________________
11) Write the equation of the line perpendicular to
3x + 2y = -4 and through the point (-6, 1).
_________________
2x  3y  27
12) Solve the system 
5x  2y  40
II.
1)
FACTORING
AND
_________________
POLYNOMIALS
Factor each of the following completely.
a)
y2 – 14y – 32
b)
3a2 + 11a + 6
c)
5n2 – 45
d)
27x3 + 8y3
e)
2m2n2 – 18m2n + 36m2
MPH/NPR 6/10
3
Calculus
2)
Solve each of the following equations using factoring or the Quadratic Formula.
a)
x2 - 7x = 18
b)
2x2 - 4x + 3 = 0
c)
3x3 + 2x2 - 27x - 18 = 0
d)
4x2 - 23x – 6 = 0
III. FUNCTIONS
1)
Evaluate each of the following given:
f(x) = x2 - 7
a)
f(-6)
d)
h(g(f(2)))
MPH/NPR 6/10
g(x) = 4x + 3
b)
h(x) =
h(-8)
c)
e)
3x
x8
f(g(1))
f(4 + a)
4
Calculus
2)
State the domain of each of the following functions.
a)
f(x) = 3x – 11
b)
D: _____________
d)
f(x) = | 8 – 2x |
D: _____________
3)
2
(x  5)(x  1)
c)
D: _____________
e)
g(x) =
3
2x  1
D: _____________
h(x) =
x6
D: _____________
f)
h(x) = 4x2 – 7x + 1
D: _____________
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 - 2| + 1
Transformations:
b)
g(x) = -(x + 7)2 - 5
Transformations:
c)
h(x) = (x - 3)2
Transformations:
d)
k(x) = -|x| - 4
Transformations:
4)
g(x) =
Shape:
________________________________
___________________________________________
Shape:
________________________________
___________________________________________
Shape:
________________________________
___________________________________________
Shape:
________________________________
___________________________________________
Determine the inverse of f(x) = 3x – 2.
MPH/NPR 6/10
5
Calculus
IV.
RATIONAL EXPRESSIONS
1)
Simplify:
2)
Simplify:
3)
Simplify:
2x2  6x
Simplify:
2
x4
x2
x 1
2

2x  6
7

4x  12
3
3x  20
x2  4x

x2  9
MPH/NPR 6/10
4x2  1
2x2  9x  5 3x  3x2
5
4)

5
x1


2
x3
2
x3
6
Calculus
V.
LOGARITHMIC FUNCTIONS
1)
Evaluate each of the following.
a)
log 2 8 ___________
b)
log 17 174 __________
c)
log 9 9 ___________
d)
log 15 1 ___________
e)
log 36 6 ___________
f)
log 3
x5 y
9
___________
2)
Expand the expression: log
3)
Condense the expression: 2 log 5 – 4 log w – 3 log y ______________________
4)
Solve each of the following equations.
a)
VI.
z4
.
1
__________________________________
23x = 82x + 4
b)
1 + 2 log 3 (x – 1) = 5
TRIGONOMETRIC FUNCTIONS
Evaluate each of the following expressions.
5
1)
sin
4)
csc - ___________
7)

1
cot  Sin1  ___________
2

4
MPH/NPR 6/10
___________
2)
cos
5)
tan
11
6
3
4
__________
__________
8)

3)
sec
6)
Tan1
3
__________
3 __________

3 
sec  Cos 1
 ___________
5

7
Calculus
PART II - WITH CALCULATOR
I.
COORDINATE GEOMETRY
1)

 x2  y  27
Solve the system: 

3x  y  23
2)

 2x  y  1
Solve the system:  2
2
 x  3y  8x  4y  16

II.
LOGARITHMIC FUNCTIONS
Solve each of the following equations. Round your final answers to thousandths.
1)
2 – 4 log (3x + 1) = -7
MPH/NPR 6/10
2)
32x – 3 + 5 = 10
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Calculus
III. TRIGONOMETRIC FUNCTIONS
1)
In ABC, mA = 90, a = 29, and b = 21. Solve
the triangle.
mB
____________
mC
____________
c _______________
2)
A surveyor is standing 50 feet from the base of a large tree. The surveyor
measures the angle of elevation to the top of the tree as 71.5. How tall is the
tree? Round your final answer to thousandths.
3)
A zip-line steel cable is being constructed for a reality television competition show.
The high end of the zip-line is attached to the top of a 50-foot pole while the lower
end is anchored at ground level to a stake 50 feet from the base of the pole. Find
the angle of elevation of the zip-line. Round your final answer to thousandths.
4)
A triangle has sides of length 5, 8, and 10. What is the measure of its largest
angle? Round your final answer to thousandths.
MPH/NPR 6/10
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