AP Calculus AB - Summer Packet
Date:
Name:
1.
The expression 23 42 is equivalent to
A.
2.
2w5
1
25
5.
5w
2w8
2
B.
1
Evaluate:
B.
2
85
D. 86
is equivalent to
C.
20w5
7.
4
3
C.
3
4
10
D.
25
1
9
1
9
B.
2?
C.
9
D.
The expression 8
4
86 is equivalent to
24
8
2
A.
D. 20w8
8.
1
25
What is the value of 3
A.
is
What is the value of
A.
C.
10w3
B.
The value of 5
A.
4.
212
B.
The expression
A.
3.
27
6.
8
B.
C.
82
9
D. 810
Which expression is equivalent to (3x2 ) 1 ?
A.
1
3x2
B.
3x2
C.
1
9x2
D.
9x2
2 0
3 ?
C.
3
4
D.
6
12
9.
10x0
page 1
2x2
Expressed in simplest form,
4x
to
32
is equivalent
16
A.
x+4
2
B.
C.
x + 16
4
D. x + 4
x
2
16
10.
Expressed in simplest form,
is equivalent to
A.
11.
1
B.
1
C.
x2
16.
x2 64
, x 6= 8,
16x + 64
x 8
x+8
D.
A.
B.
C.
D.
x+8
x 8
The y-intercept of the graph of the equation
y = 2x 3 is
A.
2
B.
2
C.
3
D.
3
17.
12.
Which graph represents the equation x = 3?
What is the slope of the line that passes through
the points (4; 5) and (7; 3)?
Which equation is represented by this graph of
line ` ?
A.
x=y+4
B.
y=x+4
C.
x=4
D. y = 4
13.
What is the slope of the line which passes through
the points (3; 8) and ( 1; 0)?
14.
Two points whose coordinates are (4; 17) and (2; a)
determine a line whose slope is 6. Find the value
of a.
15.
The line that passes through points (1; 3) and
(2; y) has a slope of 2. What is the value of y ?
page 2
18.
Factor: 9x2
19.
What is the volume, in cubic centimeters, of a
cube whose edge measures 2 centimeters?
1
AP Calculus AB - Summer Packet
20.
21.
22.
23.
In the accompanying diagram, a rectangular
container with the dimensions 10 inches by
15 inches by 20 inches is to be lled with water,
using a cylindrical cup whose radius is 2 inches
and whose height is 5 inches. What is the
maximum number of full cups of water that can
be placed into the container without the water
over owing the container?
24.
The area of a triangle is 24 square centimeters. If
the base of this triangle is 8 centimeters, nd the
number of centimeters in the altitude.
Find the area of a right triangle whose legs have
lengths 6 and 8.
What is the inverse of the function y
2 x
7
A.
y=
C.
y = 7x
B.
2
y=
D. y =
The inverse of the function y = 2x
5 is
y = 12 (x
A.
y = 12 (x + 5)
B.
C.
y = 2x + 5
D. y = 5
5)
2x
25.
Express 160 in radian measure.
26.
Express 300 in radian measure.
27.
Express 210 in radian measure.
28.
Express sin( 215 ) as a function of a positive
acute angle.
2 = 7x?
2x
7
x 2
7
page 3
AP Calculus AB - Summer Packet
29.
In right triangle BCD, BD = 12, mO C = 90, and
mODBC = 47. Find DC to the nearest tenth.
32.
7
, determine all c in the interval
x
f (7) f (1)
.
(1; 7) such that f 0 (c) =
7 1
Given f (x) = 8
A.
33.
30.
34.
31.
14
, nd all c in the interval
x
f (7) f (2)
(2; 7) such that f 0 (c) =
.
7 2
Given f (x) = 9
A.
9
2
B.
p
14
C.
p
14
D.
35.
p
2 14
3
page 4
7
p
7
B.
C.
7
8
D. 3
16
, nd all c in the interval
x
f (8) f (2)
.
(2; 8) such that f 0 (c) =
8 2
Given f (x) = 10
A.
In the accompanying diagram of right triangle
ABC, a right angle is at C, AB = 26, and
mOA = 27. Find the length of BC to the nearest
tenth.
p
4
B.
8
5
C.
4
Find the vertical asymptote(s) of y =
A.
x= 3
B.
C.
y=3
D. x = 0
D. 7
3x2
x2
9
.
y=x
What is the equation of the line that passes
through the point (3; 7) and has a slope of
A.
y=
C.
y=
4
3x
37
3x
+3
4
3
B.
y=
D. y =
4
3x
59
9 x
4
3?
3
4
3
AP Calculus AB - Summer Packet
36.
37.
38.
39.
Which is an equation of the line that passes
through the point (1; 4) and has a slope of 3?
40.
Which equation represents a line that has a slope
of 34 and passes through the point (2; 1)?
A.
y = 3x + 4
B.
y = 13 x + 4
A.
3y = 4x
5
B.
C.
y = 3x
D. y = 3x + 1
C.
4y = 3x
2
D. 4y = 3x + 5
1
3y = 4x + 2
What is an equation of the line that passes through
the point ( 2; 8) and has a slope of 3?
A.
y = 3x
2
C.
y = 3x + 2
B.
y = 3x
22
y = 2x
1
C.
y= x+2
If point (k; 3k) lies on the graph of the equation
3x + y = 12, what is the value of k?
42.
If point (k; 5) is on the graph of the equation
3x 4 = y, what is the value of k ?
43.
If f (b) = b0 + b
D. y = 3x + 22
An equation of the line that passes through the
point (0; 1) and whose slope is 2 is
A.
41.
B.
y = 2x + 2
D. y = 2x
1
Write an equation of the straight line whose slope
is 2 and whose y-intercept is the same as that of
the line represented by the equation y = 4x 2.
page 5
1
+ b 2 , nd f (2).
AP Calculus AB - Summer Packet
44. Which graph represents an exponential equation?
A.
B.
C.
D.
page 6
AP Calculus AB - Summer Packet
45.
In the diagram
below of a unit circle, the ordered
p
p
2
2
pair ( 2 ,
2 ) represents the point where the
terminal side of intersects the unit circle.
46.
In the unit circle shown in the accompanying
diagram, what are the coordinates of (x; y)?
A.
C.
p
3
; 0:5
2
( 30; 210)
B.
p
3
0:5;
2
D.
p
p
2
2
;
2
2
What is mO ?
A.
45
B.
135
C.
225
D. 240
page 7
AP Calculus AB - Summer Packet
47.
Find the value of the following functions:
49.
sin(0) =
lim f is
x! 6
A.
cos(0) =
1
B.
1
C.
6
4
D. no limit
sin (pi/2) =
cos (pi/2) =
sin (pi) =
cos (pi) =
50.
sin (3pi/2) =
lim f is
x!5
cos (3pi/2) =
A.
sin (2pi) =
D. no limit
1
B.
2
C.
B.
2
C.
B.
0
C.
B.
3
C.
cos(2pi) =
sin (4pi) =
cos (13pi) =
51.
sin (100pi) =
cos (21pi) =
A.
sin (4pi/8) =
1
1
D. 0
cos (10pi/20) =
52.
48.
lim f is
x!0+
The gure below shows the graph of f . Use the
gure to answer the following question(s).
lim f is
x!0
A.
2
4
D. no limit
53.
lim f is
lim f is
x!3
x!10
A.
2
B.
3
C.
4
D.
A.
1
1
1
D. no limit
page 8
AP Calculus AB - Summer Packet