Summer Assignment
for new students starting August, 2007 (A)-(D) due first class
A)
Set up a
notebook binder of at least 1.5 inches which will contain 6 labeled
Plastic file folders for:
AP Practice questions,
Tests
Quizzes
Homework
AP guidelines
AP handout sheets.
B)
For your binder,you will also need to
insert a spiral-bounded 5 subject notebook for your reading outlines, questions
and class notes.
C) Assignment
due first day of class in August 2007:Read 1.1-1.4 also read p.421-426,460-462,
Sections 7.1,7.2,7.3 and p.467-468
D)
USUAL CLASS ORGANIZATION:
The Rule of
Three will accompany each class date:
EVERY CLASS WILL HAVE THREE COMPONENTS:RO-CN-DP
1)RO:The reading and outlining done
before (sometimes after) a class referred to as RO.
2) CN:The class
notes on the RO topics and materials.
3) DP:The “Do
Problems” referred to as DP and listed on the Bare Bones Assignment sheet
Required: Each component listed in the top right hand side of the
pages of your notebook must have the
topic written out clearly and detailed: e.g. RO:“Area
between Curves” April 3,2008 or “CN: Area between curves”
April 3,2008
Homework for Fall-Spring 2007-2008
Note well:
These assignments are the BARE BONES of the course.
The letters RO means “Read and outline”. Outlining must be
done thoughtfully and carefully otherwise you are wasting precious time. The
letters DP means, “Do problems”. If for any reason class is
cancelled, (snow, ice, other issues) you
must stay on schedule and complete the homework for the assigned class
day. Be sure your work is properly
organized according to the “Rule of Three” It is your
responsibility to follow the class lectures and organize your work in a timely
fashion.The
three components will be graded at three separate times as they are due.(33-34%
grades at each grading interval)
Throughout the year and possibly daily, there
will be additions
to
the RO and DP and CN assignments either
given in class or posted on
the
web. I will alert you via SHA email every time there is ANY update to
this
website.
Check your SHA email daily.
Secret to Success in AP Calculus:
Be prepared to study, think and understand many of these concepts outside of class. Your success in this class will depend on your willingness to spend time OUTSIDE OF CLASS to comprehend the amazing concepts of Calculus.
There are “Good Question” segments that will be implemented as well as a myriad of practice sheets and practice tests for the AP exam.
~~~~~
Note well: Expect to spend 1-2 hours PER class hour each week. So on a three class week, 4.5 class hours will yield a 4.5-9 hour study week!!
Criteria
for reading and outlining assignments :_(RO)
__________
Only record facts and
information that you think are important. DO NOT
COPY THE BOOK WORD FOR
WORD.
Throughout the next two terms, expect to spend 1-2 hours PER class hour each
week. So on a three class week, 4.5 class hours will yield a 4.5-9 hour study
week!!
Criteria
for doing problems: (DP)__________
As soon as a topic
and section is covered in class, you are responsible for doing the
correlating DP problems THAT NIGHT. The
next class you will be accountable (either quizzed or homework collection or
oral examination) for
the DP component of the grading for that section. Welcome to college.
As soon as a section is covered in class you are responsible for the
correlating class assignment that very night for homework.If
class material is supplemental you are responsible for reviewing the class
notes for homework.
Bare Bones
. .Hand In DP’s and RO’s are underlined:
AP Topics are underlined and bold faced
Chapter I: First
day of class,August,2007 Summer Assignment RO due Assignment due first day of class in
August 2007:Read 1.1-1.4 also read p.421-426,460-462, Sections 7.1,7.2,7.3 and
p.467-468
Section 2.1: The tangent and velocity problems Date:RO: p. 65-67
Section 2.1: Velocity Problem:Review CN for p.65-67. These are 2 of the most
important
pages in this book. Study carefully and:DP problem #1on p.69
2.2: Date: Section 2.2 : The Limit of a Function: RO p.70-79. BE CAREFUL. This theory is the basis of all Calculus. After CN on this section DP. P.79 1-4 all.BE SURE TO DATE AND LIST THE SECTION AS THE LEAD TOPIC FOR THE THREE COMPONENTS: Limit of a function: Section 2.2.
2.2:Limit of a
Function: DP:Hand in DP: 2.2:DP p.80 #5,7,9
2.3: Calculating Limits Using Limit Laws: RO p.82-89
2.3:Limit
Calculations:DP p. 89 1-30 odds and #34 and #55. Hand In p.90
#15,18,20
2.4: Infinite Limits: RO p.99-108.DP p.110 1-3 all.
2.5: RO p. 109 (The Intermediate Value Theorem) all the way up to P.119.
Hand
In DP p.111 #45-48
odds.
2.5: Continuity: Hand In DP: p.111 #1-6 all; #9,#12.
Date for In-Class Test #1:____________________
TEST NUMBER 1:Pretest book problems for review and hand-in grade:
Prepare for TEST : Chapter 1 and Chapter
2.1-2.5:Practice Problems due the class before the test:p.121 #1-7 all;
p.122 True-False: 1-14 all and on bottom of page #1-7 allp. Also,p.261 9-32 evens.
2.6: Tangents,
velocities and other rates of change Section
2.6:RO p.112-119
2.6 Tangents,
velocities and rates of change DP p.119 1-21 odds. HAND IN DP:p.121
#2,#5,#7,#8, #26,#27,#36. Make sure all the questions below are addressed:
2.6: Take Home Quiz: due_date:_________________
WRITING
MATHEMATICS:_______________________
Goal for above assignment: Learning how to write out explanations for :
a) Describe several
ways a limit fails to exist.
b)What does the Squeeze Theorem say?
c)
What does the Intermediate Value Theorem say?
d)Write expressions for tangent lines using slope-point
formula and
the concept of the slope as the rate of change.
e)
Is there a way to write how a function is continuous using limit
notation
only?
3.1 : Derivatives Take Home Test: Hand in RO for
Chapter 3.1 according to the following questions. Make two copies of the
following. Staple one in your notebook for the RO component for Chapter 3.1 and
pass the other copy in for a take-home test grade.
Take Home Test: WRITING ABOUT MATHEMATICS:
Date Due:_________________________ Name:_______________
Answer the following 17 questions in complete sentences:
1) What is the study of
differential calculus concerned with?
2) What is
the central concept of differential calculus?
3) Once you
master how to calculate derivatives, how can you use them?
4) Define the
analytical representation of a derivative of a function f at a number
“a”. Explain what each part of the definition means.
5) Draw a
Cartesian co-ordinate system
graph that is properly labeled and marked to showcase exactly
what the geometric interpretation of a derivative means graphically. Justify
your answer.
6) How is the
derivative interpreted as the slope of a tangent line? Explain.
7) How is a
derivative interpreted as a Rate of Change?
8) What
exactly is instantaneous velocity?
9)What happens to the y-values of a function when the
derivative of a function is a large number?
10) What
happens to the y-values of a function when the derivative of a function is a
small number?
11) What
happens if the theory of derivatives is applied to a particular function say s=
f(t) called the position function which models the
position of a particle along a straight
line at any time t. NOTE: We are simply APPLYING the derivative theory to a
PARTICULAR function and asking: what does the derivative mean IN THIS CASE. If
t=a, what exactly does f’(a) mean? Be specific
and thorough in your explanation.
12) What is
the definition of speed of a particle?
13) What is
the difference between average rate of change and instantaneous rate of change,
and rate of change? How does the derivative relate to these terms?
14) Define a
tabular function.
15) List the
two different ways you could use to estimate the derivative of a tabular
function? Refer to p.118 Example 5 and p.131 ex 6. Discuss in detail exactly
how each method could be used, given a tabular function. Make sure you
emphasize the importance of the word “Estimation” versus
“Actual” result.
16) What are
the units for an average rate of change defined by a change in x divided by a
change in y?
17) Who was
the first person to formulate explicitly the ideas of limits and derivatives?
3.1:Derivatives:DP
p.132 # 1-33 odds and HAND-IN # 34
3.2: Derivative as a function:RO
p.134-142 . Hand In: “How can a function fail to be differentiable?
Draw graphs to explain your answer.”
3.2:The graphs of f and f’ :Study
p.134 Example #1 very carefully then do
DP p.142 # 1,3,5,6,7,13,14 HANDIN:p.143
#2,#15.
In Class Test #2 will cover 2.6-3.2(p.112 - p.145) Make sure you understand that when a derivative is large , the y-values are changing rapidly and when the derivative is small, the curve is relatively flat and the y-values change slowly.
The topics covered will be Limits, all limit laws, continuity, Intermediate Value theorem, derivatives and derivatives as functions (3.2), finding equations for tangent lines, and straight line motion of particles on p.130
Date of Chapter 2.6-3.2 Test:_______________
3.3: Differentiation formulae:RO p.145-154
3.3: Differentiation formulae HAND IN DP p.154-155 #1-42 odds,
#44
3.4: Rates of Change in Natural and Social Sciences RO p.157-166. Hand In HW :
WRITING
ABOUT MATHEMATICS
Answer the following
questions:
1) What is the connection between the difference quotient and the average rate of change of y with respect to x for a given function y=f(x)?
2) Write Leibnitz notation for dy/dx.
3)Study Example #3 on p.158.Answer #1 on p.166
4) In your own words how can the derivative be applied to Chemistry as far as measuring the instantaneous rate of a reaction?(p.160)
5) Discuss the significance of a minus sign in front of a derivative and its application to physics and the theory of compressibility in thermodynamics.(p.161 #5)
6)Considering the facts of biology, would you be able to model the actual graph of a population function as a growth function that is continuous? Why or why not?
7) To actually determine the rate of growth of most bacteria populations,
you would have to be able to compute the derivative of what kind of
function?
End of HW for 3.4
3.4: Rates of Change in the Natural
and Social Sciences. MAKE SURE YOU CHECK THE ANSWER BOOK: DP:
Write out the solutions to
p.166 1-21 odds.
Make a list of any questions you may have as you do this assignment.
3.5 Derivatives of Trigonometric Functions: RO p.169-174.Pay particular attention to #3 on p.173.
3.5: Derivatives of Trigonometric Functions: Study Problem #3 on p. 173.DP
p.174 1-16 odds. HAND IN:p.174 #2,12,16,21,35-42
evens
3.6: The Chain Rule: RO p.175 -181.Pay attention to the mechanical reasoning
behind this Rule.
Take Home Test
Problem Set due date:__________
Test: DP p.181 # 1-42 evens.Show
all work
3.6: Applications of Chain Rule to Trigonometry:
Take Home Quiz Grade: “A blast from the past:
Honors PreCalc mysteries solved:p.183 #68; #71, #75
3.7: Implicit Differentiation RO p.184-188. DP p.188-189 5-20 odds.
HAND-IN: p.188 6,12,14,and
p.190 # 53
3.8: Higher Derivatives: RO p.190-195. DP p195 1-20 odd
3.8: Related Rates RO p.198-202. DP p.202 # 1-6 all
3.9 Related Rates 10 Problems: Take Home Test: DP p.203 8-23 odds, #36 and #38.
Due date:____________________________
Chapter 3: Study for Test Hand In Take Home Quiz: p.213 1-6 all under Concept
Check
4.1 Applications of Differentiation .Section 4.1 RO p.223-229 . Hand In Concept Test Based on 4.1 RO p.223-229:Remember: Make 2 copies and staple your answers to your notebook for Component RO 4.1
Writing About
Mathematics: HAND IN CONCEPT CHECK FOR 4.1p.223-229
Applications
of Differentiation
Write all answers in complete sentences.
1) In your own words, how do derivatives affect the shape of a graph of a function?
2) How do derivatives help us locate the maximum and minimum values of a function?
3) What is an optimization problem?
4) What is an absolute maximum for a function and what is an alternative name for it?
5) Can there be an absolute maximum or absolute minimum at a point of discontinuity?
Justify your answer.
6) If you are asked to find the extreme values for a function, what are you really being asked to do?
7) True or false: local max’s and min’s need to originate from open intervals.
8) What is the difference between a local maximum value for a function and an absolute value for a function?
9) Answer #8 for absolute minimums and absolute maximums.
10) State the Extreme Value Theorem formally and then in your own words.
11) Can you apply the Extreme Value Theorem on a function that has only continuity on an open interval?Give an example to support your answer.
12) Sketch the graph of a function on [-1,2] that is discontinuous but has both an absolute maximum and an absolute minimum.
13) True or false:The Extreme Value Theorem tells us how to find the extremum for a function.
14) When would an absolute maximum not be a local maximum?
15) True or false: All functions have extreme values.
16) State Fermat’s Theorem
17) Give an example from Honors PreCalc library of functions of a function that has
f’(0)=0 BUT the function has no max or min value at x=0.
18) True or false: Can you find extreme values simply by setting f’(x)=0 and solving for x?
19) What is a critical number?
20) If you have a continuous function on a closed interval, where are the only two places an absolute max or absolute min can occur?
21) State the Closed Interval Method
22) Study example 8 on page 228 and then do problem #46 on page 231
End of Test
4.1.Maximum and Minimum Values DP p.229, #1-6 all, #31-43 odds;47-53 odd
4.2
The Mean
Value Theorem RO p.234-238.
Hand In: Due Date_________________
A)Write out the Mean
Value Theorem and explain it in your own words.
B)Where is the limit
notation?
C)How does the MVT
relate average rate of change with instantaneous rate of change?
D) Do problem #11-14 all
on p.239
4.3
How Derivatives Affect the Shape of Graphs? RO
p.240- 247 HAND IN QUIZ: p.247 1-18 odds
4.4 Limits at infinity:RO p.249-257 and skip to p.260. Make sure you
know L’Hopital’s rule.Hand In Quiz:DP #9-32
odds on p.261
4.5-4.6 Graphing with Calculus and Calculators.Read study and review (RO) p.263-p.276 for a good prep for no-calculator section of AP exam. Practice on p.277 1-8 odds
p.278-283.
4.8 Derivative Applications to Business and Economics RO p.289-292. DP p. 293 1,5,19,20
Antiderivatives:RO 4.10. RO p.300-305 (oral quiz next class)
Antidrivatives 4.10(PASS IN HW GRADE Due_______) DP p.305 First odds 1,11,17,31,39-42 with explanation and justification.
SECOND SEMESTER SPRING TERM OF YOUR SENIOR YEAR!!!!Remember: You must take a final exam in this class
in May to earn the last 4 of your 8 college credits.
Starting January
,2008 :
Review Optimization
Antiderivatives:RO 4.10. RO p.300-305 (oral quiz next class)
Antidrivatives 4.10(PASS IN HW GRADE Due_______) DP p.305 First odds 1,11,17,31,39-42 with explanation and justification.
Slope Fields :NOTE WELL:QUIZ ALERT Due Date_________________
You are finding sites:CITING THEM and cutting and pasting them into a packet and then writing a BRIEF<CONCISE<paragraph (Entitled : “The Geometry of Antiderivatives”)describing what answers you found to the following four questions from your searching.
Look on line for any info you can find on slope fields. Answer the following questions:
1)what are they?
2)How do you find them?
3)How do you draw them?
4) Print out at least two sites and a paragraph describing the info you found on each.
Slope Fields 4.10 Do p.306 #47,48
PASS IN
Section 10.1 Modeling with
Differential Equations:
TEST ALERT: Due _______________
PASS IN EXPLORATORYASSIGNMENT worth one test grade:
WRITING ABOUT MATHEMATICS:Self-Directed Learning
A) Read p.623-627. Cut , copy and print these questions in WORD, edit by leaving spaces, copy it and pass in these questions along with the answers:
1)
Define
Differential equations
2) What is the mathematical assumption concerning models of population growth?
3) What makes this assumption reasonable?
4) How can we use calculus to represent the rate of growth of a population?
5) Why is the mathematical model for population growth a differential equation?
6) Stare at the differential equation for population growth and decide what happens as P(t) increases?
7) What famous function has a derivative that is ALWAYS a constant multiple of itself?
8) True or false? Population values vary throughout the entire real number system.
9) Define “carrying capacity” and how it affects the math model that needs to account for limited resources as well as ideal conditions.
10) Write out the model for world population growth. What is its formal name and what do all the variables represent?
11) Consider Equation (2) on p624 and deduce qualitative characteristics of the parent function P(t) directly from the eq.#2.
12) Describe in detail what an equilibrium solution is?
13) Look at the figure #3 graph on p.624 . Describe in your own words what you think the graph represents and why.
14) Why does the model for the motion of a spring has solutions that involve combinations of certain sine and cosine functions?
15) What is the order of a differential equation?
16) A function is a solution of a differential equation. When you solve diff.eqs you are actually finding what?
17) How do you find the solution to a differential equation?
18)
Study example 1 on p.626. Use the steps to work out p.627 #1, #2.Do not attempt this without
careful studying of example 1 and 2 on p.626 and p.627. List the page and
problem and show all your work.
19)
Define
initial condition and initial-value problem. Why would we bother to use the
solution of an initial-value problem?
20)
Do #2 Show
all your work.
21)
Do #10
THIS IS THE END OF THE TEST .
In Class Test on Chapter 4 only:
Date___________________
Section 5.1: INTEGRATION!!!!!This segment of assignments begins Integration.
5.1 Areas and Distances Section 5.1 RO p. 315-322.
5.1 Areas and Distances DP:Problems on p.324 #1,#3#,15,#16
5.1 The Distance Problem RO p.322-324. DP p.325 11,13,17,#22 part a and #23 part a
5.2 The Definite Integral RO p.326- 332. Hand-In:What is the difference between the area under a curve and the net area?
5.2The Midpoint Rule:RO p.332-336. HAND IN:DP
336 1,3,5,7
5.2 Geometric Interpretation of an Integral DP p.338 35-49 odds, 55-60 odds.
5.3 Fundamental Theorem of Calculus
(Counts as a test grade) This can not be done in a group. Due Date:____________
A)
Discuss the difference between them and the purpose
each serves.
B)
Cite at least one graphical, one numerical and one
physical applications
of the two theorems. (Use typed
MLA
format with references cited)
.
5.3:
FTC: Quiz Alert: DP
p.347 1, 3,5,6,7,11,17,25,27,39,48 For a
pass-in quiz grade due
date_______________
5.4: Indefinite Integrals and the Net Change Theorem
Take Home QUIZ
PROBLEMS Due Date:_____________
DO p.356-358 problems 2, 6,8,9,12,13,14,22,24,27,30,32,34,39,40 . Write out the original problem, the work and then box the answer
6.2: RO p.382-390 DO THIS HW FOR THE NEXT 4 HW evenings. Read and reread this material until it starts to make sense. Make sure you are very diligent about every sentence the author uses. For instance:A cylinder solid does not imply that the base HAS to be a circle. Only right circular cylinders have cylindrical bases. ALL A RIGHT CYLINDER SOLID NEEDS TO BE A RIGHT CYLINDER SOLID is to be a solid bounded by a plane region as a base and a CONGRUENT plane region in a parallel plane. That is why the big slabs of ham on p.383 are actually right cylindrical cross sections. And remember : B means the AREA of the base!!!! Whatever that base shape is!Mr Stewart needs to clarify p.384: “ Notice that….He should say , “Notice that for a RIGHT CIRCULAR CYLINDER, the cross-sectional areas are constant”
Section 6.2: Volumes of Solids of Revolution
DUE
DATE:___________TAKE HOME TEST:VERY IMPORTANT:DP p.391 #3,#13,#15,#17,#5You
need to do at least one problem about x
axis, one problem about the y axis, one problem about x=2 and one about the axis y=4
**************Grade Booster: Extra Credit: Pass in due date________
**************Problem #7 on p.409
Test topics for next
class TEST:Date_________________
All of Chapter 6 and the derivative of inverse functions, Plus, some topics from last test in differentiation and integration. Plus any problems from class handouts and notes.
7.3 Logarithmic Functions and their Derivatives
p.439 # 29,31,33.35 and p.449 #2-11 oddsPASS
IN
7.2 Revisit: The Natural logarithmic Function as defined by a definite
integral p.451
Do problems on p. 458 13-20
7.4: Derivatives of Exponential Functions p.467-474. Hand-In p.475 23-30 odd
10.4: Exponential Growth and Decay:
Hand In p.656 #4,#16
7.5 Derivatives of Inverse Trigonometric Functions p.477-483 Hand in: p.484 #23,25,32,36.
Review of formulas and integration:P.481-483
and p.510 all formula excluding hyperbolic functions
8.1: Integration by Parts RO p.511-516. Hand In: p.516 #3,7,15,25
8.2-8.3 Trig
Integrals p.524 #1 only
8.4 Integration of Rational Functions Using Partial Fractions
ALL OF APRIL UNTIL BREAK WILL BE INTENSIVE AND EXTENSIVE IN-CLASS TIMED TESTING AND REVIEW.
APRIL BREAK:
This is very important: Over April break: Do every problem in the Calculus workbooks
we purchased as a class. Hopefully, you have been doing the problems as we
covered the material in class and you have kept a record of the problems. If
not, just get to work. You have the solution manual so you should be able to
handle any difficulties. Keep a record of what you still do not understand and
we will clear them up the last week before the exam.
At home: Problems in Gray calc workbook
Big AP In Class Test
(55 minutes multiple choice) 25 minutes:class
work from Chapter 7 gray pages:
Wrap-up
Exam review and reflection
sheet.
AP Test in class for in
class quarter grade.
In class group test and individual quiz
In class Individual Board Wars
Wrap-up: College study tips for mathematics.