Name_ Block_ Due
Date_
AP Calculus
Limits, Continuity, IVT FRQ
*NO Calculator Allowed*
The function f is defined as .
a) Find .
b) Is f(x) guaranteed to have a root on the closed interval [-2, 3]? Justify your answer. If f(x) does have
roots
on [-2, 3], t
AP Calculus AB and BC
Summer Assignment 2014
This is your summer assignment. It covers topics learned in Algebra 2 and Math Analysis/Trig. These
are topics that are prerequisite to being successful in Calculus. Please wait until at least August 1st to
beg
2-5: Implicit Differentiation:
1.
Find using Implicit Differentiation.
2.
3.
4.
Find by implicit differentiation and evaluate the derivative at the given point or x-value.
5.
6. at x = -2
7. Find the equation of the tangent line.
8. Find for
9. Find the e
APCALCULUS,AB
20142015
Teaching Strategies
Students taking AP Calculus are expected to have a strong Algebra and PreCalculus foundation. As a
group we will work extensively on study habits, algebra skills, appropriate use of the graphing
calculators, and
LL}
SOLUTIONS T0 PRACTECE PROBLEM SET 4
54;:3 + 1 6x I
First, expand (4x2 + 1)2 to get 161'4 + 8x2 + 1 . Now, use the Power Rule to take the
derivative of each term. The derivative of 1 6x4 = 1 6(4)(3 ) = 64x3 . The derivative of
8x2 : 8(25) = 1 6x. The d
ll.
12.
13.
14
15
16.
17.
' 18.
19.
23.
24.
25.
x(2x + 7)(x 2)
{QR/ENE)
ax5+bx4+cx3+dx2+ex+f
THE PRODUCT RULE
Now that you lqtow how to find. derivatives of simple polynomials, its time to get more complicated.
What if you had to find the derivative
Name_ Date_ Block_
AP Calculus
Pre-Calc Review
*NO
CALCULATOR*
Part I: Find the exact value.
7p
6
2) sin
7p
4
3) tan
11p
6
4) cot
4p
3
5) csc
p
4
6) sec
2p
3
7) sin
2p
3
8) sec
3p
2
9) cot
5p
6
Par
t1
on
2nd
day
of
sch
ool.
1) cos
Part II: Find the exact
Derivatives Review
1. Calculate
dy
for the following functions. Show the work that leads to your answers. Simplify
dx
Review all of the
derivative
completely. Factor out GCFs, no negative exponents, combine fractions.
5 - 7x
3x - 2
b)
a)
y=
c)
e)
y =e 2 x
AP Calculus (AB) Motion Problems
1) A coin is dropped from a height of 64 ft. if 5 ft is the height ofthe stone t sec after being dropped,
then 5(1) = ~16t2 +64. (a) How long does it take the coin to reach the ground? lb) Find the
instantaneous velocity o
AP Calculus (AB)
Motion FRQ
1) On a recent visit to New York City, Mr. Texler was hit in the head with an egg from the top of the
Empire
State Building. This is another reason Mr. Texler doesnt like the New York Yankees.
a)
If the egg was dropped from res
Name _ Date_
AP Calculus (AB)
Limits Test Review (Ch.1 & 3-5)
Please show work on separate paper.
1.
2.
5.
6.
9.
10.
13.
3.
7.
4.
8.
11.
12.
14.
16.
17. If , find
22.
15.
18.
23.
For what value of a does
What value should be assigned to
exist?
k to make h
AP Calc AB Texler Calendar
September2014
HWDue
9/2/2014
Public
Source:1415R160APCALCULUSAB3177A41415
Category:Appointment
SummerAssignment
HelpSession4:00
9/3/2014
Public
Source:1415R160APCALCULUSAB3177A41415
Category:Appointment
4:004:45CalculusABHelpSes
AP Calculus (AB)
Motion Problems
1) A coin is dropped from a height of 64 ft. If s ft is the height of the stone t sec after being
dropped, then . (a) How long does it take the coin to reach the ground? (b) Find the
instantaneous velocity of the coin when
Name_ Block_ Due
Date_
AP Calculus
Limits, Continuity, IVT FRQ
*NO Calculator Allowed*
The function f is defined as .
a) Find .
b) Is f(x) guaranteed to have a root on the closed interval [-2, 3]? Justify your answer. If f(x) does have
roots
on [-2, 3], t
Derivative Bingo
from John Handley High School
Name_
Directions: Find the first derivative of each function below. Locate the derivative on the Bingo card
below. Circle the answer. Keep working problems in any order until you have five circled in a line-h
Wit/la
,6?
PRODUCT RULE AND QUOHENT RULE 5 7
Differentiate. Use proper notation and simplify your nal answers.
In some cases it might be advantageous to simplify/rewrite rst.
Please work together With
your classmates on this
H!
*F actor out any common f
TurveyforRelatedRates
In 1953, Roger Price invented a minor art form called the Droodle,
which he described as "a borkley-looking sort of drawing that doesn't
make any sense until you know the correct title." In 1985, Games
Magazine took the Droodle one s
Special Cases:
A)
B)
C)
y
y
y
x
x
x
D)
E)
Unbounded
Behavior
y
y
x
Oscillating Behavior
x
Practice:
1)
2)
8
y
7
6
8
5
7
4
y
6
3
5
2
4
1
3
2
8 7
6
5
4
3
2
1
1
1
2
3
4
5
6
7
8 x
1
2
8 7
3
6
5 4
3
2
1
1
1
2
3
4
5
6
7
8 x
2
4
5
3
6
4
7
5
6
8
7
8
The following
Name
Date
._~-
_
Notes: 2-2 Particle Motion - Moving Along a Straight Line
I. Rules:
a.
When velocity is positive the particle is moving to the right.
b.
When velocity is negative the particle is moving to the left .
c.
When velocity is zero you the parti
Please work together with
PRODUCTRULEANDQUOTIENTRULE classmates on this
your
assignment. Help
someone!
1. a) Find f ( x) for f ( x) =5 x sin x
2. a) Find f ( x) for f ( x) =(1 x )( x 3 )
b) Write the equation of the tangent line to f(x) at x =p .
b) Write