2017_18 AP Calculus BC – Summer Packet
Welcome to AP Calculus BC at Boca Ciega High School. I’m Mr Lynch - all of you know me already. You should
feel free to reach me at [email protected]. I will check my email most days.
Whether or not you passed the AP Calculus AB exam in May, you can be successful in AP Calculus BC.
We will spend a fair amount of time reviewing the math we learned this last year in AB. The following pages
include a review of most of the key concepts we learned. You should spend 1-2 hours on each of these 5 pages. For the
FRQs on the last two pages, you can obviously find the answers posted online. However, you should seriously attempt
these problems PRIOR to checking your answers.
2017_18 AP Calculus BC – Summer Packet
Focus 1: Log and Exponential Functions
Brief Notes:
If = then = log rewrite as logs to solve exp equations
rewrite as exp to solve log equations
1) Rewrite = ln2 as an exponential equation
2) Rewrite = as a logarithmic equation
3) Rewrite = 2 as a logarithmic equation
4) Without a calculator, solve for the unknown:
3 ∙ 2 + 4 = 28
5) Use a calculator to solve for the unknown:
5 − 3 = 27
6) Without a calculator, solve for the unknown:
5 + log − 3 = 21
7) Use a calculator to solve for the unknown:
3 + ln4 = 16
8) Rewrite using properties of logarithms:
ln ∙ "!#
9) Rewrite using properties of logarithms:
log$'()*
10) Rewrite using properties of logarithms:
ln$
11) Rewrite using properties of logarithms:
ln5 / 12) Rewrite using properties of logarithms:
ln - /5 2 #
13) Condense using properties of logarithms:
ln − ln - + 1
14) Condense using properties of logarithms:
ln − ln − ln3
15) Condense using properties of logarithms:
ln − ln + ln3
16) Condense using properties of logarithms:
3 ln − 0.25ln + 1
17) Find the derivative 6’:
6 = 89 $:;'*
18) Find the derivative 6’:
6 = 89 $
19) Find the derivative 6’:
6 = log 5 % + 2
% &
& +,)
- . /0
*
"
"
% .
+,)
*
-
Focus 2: Derivatives
Some rules:
constant, power, product, quotient
trig fns, , ln(x), implicit
<=
1) Find < given = 3 + − cos
2) Find ’ given = <@
3) Find < given ℎ =
. /%#
. B%
"
-
4) Given functions C and D, with C2 = 4, CE 2 = −1, D2 = −2, and D′2 = 5, find at = 2 :
a.
b.
<
CD
<
$ *
<
c.
H
d.
< G
<
$ *
G
<
3C − 2CD
< H
<
5) Given ℎ = , find ℎ′′
6) Given 3 − − IJK = 2, find
<=
<
7) Find the slope of the “Witch of Agnesi”, given by =
L
M/ .
at the point 2,1
8) Given = !sin % − 2 , find ′
9) Given ln + M + = 2, find the slope at point (1,1)
10) Given functions C and D and values shown in the table, determine the following quantities :
P
2
5
8
C
-1
3
6
a. Average RoC of C on 2,8
b.
<
<
CD2
D
5
-6
3
C’
-4
7
4
D’
-3
11
2
c. Instantaneous RoC of D at P = 5
d.
<
<
C2 ∙ CD2
11) Find any horizontal tangents to the curve = % − 9 − 21 + 5
12) Determine the point at which the function = - is perpendicular to the line 2 + 8 = 11
13) Find
<
<
TU
given S = . /0
14) Given 6 = tan , find 6′′
Focus 3: Integrals
Brief Notes:
1) Find W3 sin + 4 X
Do you need u-substitution ?
(probably)
PATTERN RECOGNITION
%
2) Without a calculator, determine WY XP
3) Find W
M/Z
. /%
X
\/M
4) Without a calculator, determine WY
tanP s[cP XP
^ ] B/0
5) Without a calculator, determine W $
_
* X
.
_
6) Given W 6X = −7 and W^ 6X = 3 , determine W^ 6X
7) Given 6 = W% − -PXP , find 6′
%
8) Without a calculator, determine WY 3 .
. /0
X
a
9) Given ` = W% - X , find `′′
"
10) Determine the average value of = - + 2 on the interval 6,25
L
11) Without a calculator, determine WBM bbX
0
12) Without a calculator, determine WY B% X
13) Determine W
f
U
cde$ *
.
X
14) Each labeled region (A, B, and C) in the graph of 6 (shown to the
Z
right) has an area of 3 square units. Determine WY 6 + 2X.
_
15) Use a calculator to determine W
TU
. /0
%\/M
X accurate to 3 decimal places.
16) Use a calculator to determine W\/Z 5sin $
] /
* X accurate to 3 decimal places.
-/0
17) The graph of `′ is shown to the right. If `3 = 6, determine `0.
Focus 4: Net Accumulation
1) 2009 B - Calculator Required
2) 2008 A – Calculator Required
3) 2004 A – Calculator Required
j
Wjk ghPi9 − ghPJCPXP = li9h8mSP − n9iPih8mSP
Focus 5: Volume
1) 2008 B – Calculator Required
2) 2008 A – Calculator Required
3) 2007 – B – Calculator Required
=
oJ8 = W=h
gp9XiIC8hgqgJKKrIPiJ9h8mgh#X