TO: All students planning to take AP Calculus BC next year
FROM: Ms. Lawson
RE: Your Summer Assignment
Attached you will find your summer assignment. It is a set of practice problems from the
precalculus chapter of an old AP test prep book. If you find them difficult, I recommend
investing in a prep book for the SAT Subject Test: Mathematics Test 2. It should be helpful.
Additionally, there are many resources available on-line to help you review topics that you need
help with.
I recommend procrastinating. This assignment will be of the most use to you if you wait until
August and use it as a way to refresh your memory of math before you come back to school. But
don’t procrastinate too long! I will expect you to turn in your completed assignment on the first
day of class in August.
What to do in August:
 Use the attached problem set as an answer sheet and circle your final answers.
 Complete all 30 problems on binder paper or graph paper to show your work.
 Staple your work to this packet and write your name at the top of this page.
What to do the first day of class:
 Bring your completed assignment to class.
 Be prepared to discuss your solutions with the class.
 Turn in your completed assignment when I ask for it.
If you have any questions, please visit me in Room 50 before the end of school or e-mail me at
wlawson@cuhsd.org during the summer.
1. A neighborhood of - 4 with radius 2 is
described by
a. | x – 4 |  2
b. | x – 4 | < 2
c. | x – 2 | < 4
d. | x | < 2
e. | x + 4 | < 2
2. If f ( x)  2 x  8 then f 1 (t ) 
1
a.
2t  8
t 8
b.
2
t
8
c.
2
d. 2t + 8
1
t 8
e.
2
3. If c( x)  cos(sin 1 x) , what is the range of
c?

a. [ 0, ]
2
 
b. [  ,
]
2 2
c. [ - 1, 1 ]
d. [ 0, 1 ]
e. [ - 1, 0 ]
4. If 6 x 7  ax5  bx 3  cx  15  0 , where a, b,
and c are integers, which of the following
could not be a root of the polynomial
equation?
a. 3/2
b. ¾
c. 1/6
d. 5/3
e. – 15
5.
1
1


1  sin x 1  sin x
1
a.
1  sin x
b. 2sec 2 x
c. cos x
d. tan 2 x
e. csc 2 x
6. The graph of | y | = | x | is
a. a circle
b. a line
c. two intersecting lines
d. a hyperbola
e. a single point
7. If f ( x)  x5  3x 2  2 x  7 and g ( x)  3x ,
then g ( f ( x)) 
a. x 6  9 x3  2 x 2  7 x
b. 3x 5  9 x 2  6 x  21
c. 3x
d. 243x5  27 x3  6 x  21
e. 3x 6  9 x3  6 x 2  21x
8. How many of the following functions have
the property f ( x)  f ( x) ?
I. f ( x)  x 4  x 2
II. f ( x)  cos x
a. 0
III. f ( x)  4 x
IV. f ( x)  17
b. 1 c. 2 d. 3
9. sin 2 x  cos 2 x 
a. 1
b. 2sin 2 x  1
c.
 sin x  cos x 
d. 2 cos 2 x  1
e. tan 2 x
2
e. 4
10. Solve for x: 2 x  71log7 4
a. 3 b. 6 c. 7 d. 10
11. What is the period of the function
 x 1
y  2 cos    ?
3 2
a. 2 b. π/3 c. 3 d. 6π
e. 14
e. π
12. If f ( x)  x 2  1 and g ( x)  x  1 , then the
solution set of f ( g ( x))  g ( f ( x)) is
a. { 0, 1 }
b. { 0 }
c. all real numbers
d. { x : x ≥ 0 }
e. {  }
13. Which graph represents the solution set of
x  1  x 1  2x ?
16. Which one of the graphs represents
y  sin(2 x   ) ?
a.
b.
c.
d.
e.
14. If f ( x)  x5  x3  1 and f (a )  10 , then
f (a) 
a. - 7 b. 10 c. - 10 d. 8 e. –
8
( x  2)( x  7)
15. An asymptote for y 
is
x 5
a. x = 0
b. x = - 2
c. x = 5
d. x = - 5
e. x = - 2
17. log 1 x 
b
a.  logb x
b. log x b
c.  log x b
d. b x
e. none of the above
18. Which of the following is a factor of
x17  4 x15  x 3  4 ?
a. x + 2
b. x – 2
c. x + 1
d. x – 1
e. x – 3
19. If f and g are odd and even functions,
respectively, such that f (a )  b and
g (c )  b ,
f (a)
b ≠ 0, then
 f (  a )  g ( c ) 
g ( c )
25. If w( x)  5 x  10 and z ( x)   x 2  6 , then
w( z ( w1 (0))) 
a. 20
b. – 10
c. 15
d. 6
e. 12
26. The graph described by x  4cos t ,
y  4sin t is
a. – 1 b. – 1 – 2b c. – 1 + 2b d. 1 – 2b e. 1 + 2b
a. a line
b. a parabola
20. The set of all points 10t , t  is described
c. a circle
d. an ellipse
by the equation
x
e. none of the above
a. y  10


b. x  10 y
c. x  log10 y
d. y  log10 x
e. log10 x  log10 y
21. Which of the following functions is
periodic with period π?
a. y  sin x
b. y   x
y  cos x
d. y  
e. y  sin  x
22. If f ( x)  logb x and g ( x)  b x , then
f ( g ( x)) 
a. 1
b. x
c. x b
d. b x e. log x b
23. f (a  b)  f (a)  f (b) is true if f ( x) =
a. x
b. log c x
c. sin x
1
d.
x
e. 3x
24. How many of the following functions are
symmetric about the y-axis?
I. y  x 2
c.
II. y  4  x 2
III. y  x
IV. y  cos x
a. 0
b. 1
c. 2
d. 3
e. 4
27. A parametric representation for the line
containing ( - 3, 6 ) and ( 2, 10 ) is
a.
x  3  4t
x  4t
x  3  2t
b.
c.
y  6  5t
y  5t
y  6  3t
x  2  5t
x  1  3t
d.
e.
y  10  4t
y  1  6t


28. The polar coordinates of P are  5,  .
2

What are the rectangular coordinates of P ?
a. ( 0, 5 ) b. ( 5, 0 ) c. ( 2, 2 )
d. ( 0, - 5 ) e. ( - 5, 0 )
29. If r  4sin  is converted to rectangular
coordinates, then
a. x 2  ( y  2)2  4
b. ( x  2)2  y 2  4
c. x 2  y 2  16
d. x 2  4 y 2  4
e. ( x  2)2  ( y  2)2  4
30. Which of the following shows the shape of
the graph of the polar equation r = 2?