Calculus AB − 2008−2009 − Dr. Fred Kral − Bentley School

[Back][bottom][Course Information][syllabus (3 pages)] [College Board description May 2009]

Calculus AB Summer Assignment − Review of Prerequisites to Calculus − Chapter 1.1−1.6

Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF)

HW#

Period 6
Date due    

Period 4
Date Due    

Book

First
Page

CALCULUS
Description

  summer summer     Textbook: See the Syllabus.
  if needed if needed     To get started: Book 1.1 to 1.6 [Answers] [Preface x]
−e Thu 9/4 Fri 9/5     • Please bring a TI−83 or TI−84 graphing calculator to the first class.
0 Thu 9/4 Fri 9/5 Pre−
face
x • You must read the course information, syllabus (hardcopies given on first day), and page x of the Preface: "To Students; How to Learn from this Book."
• You must know:  ° Titles of the three topics (functions/graphs/limits, derivatives, integrals/differential equations);  ° The Rule of Four (graphical, numerical, algebraic, verbal);  ° Four parts of the AP Exam (Multiple Choice without/with calculator, Free Response with/without calculator);  ° TI83/84 skills (graph/window, zeros [2nd][CALC]2, idea of derivative, idea of definite integral, and how to Reset Defaults [2nd][MEM(+)]722.
1 Thu 9/4 Fri 9/5 1.1 7 Questions in textbook: (1), 7, (8), 11, 13, 15, (16), 25, (28), 32, 35, (36), (39).  Functions and change.
()=recommended but not required review.
2 Thu 9/4 Fri 9/5 1.2 14 (1), (4), 6, 11, 16, (17), (18), 19, 21, (22), (23), 31, (34), (37).  Exponential functions.  You need know different forms:  y=A(1+r/100)t, y=A(eBt), y=A(s)t, y=A(1/2)(t/T) and similar forms.
3A Mon 9/8 Mon 9/8 1.3 21 3, 15, 21, 27, (42), 43, (46), 49, (53), 54.  New functions from old: transformations, composites, symmetry, inverses.
3B Tue 9/9 Wed 9/10 1.3 21 1, 7, 913, 29, 50. Transformations.
3C         Sheet #131: Transformations and Slopes [Questions] - [Answers]
4 Mon 9/8 Mon 9/8 1.4 27 1, (4), 7, (10), 13, 16, 19, (22), (32), 39, 41, (42), 43, (44), (46).  Logarithmic functions.
5 Tue 9/9 Wed 9/10 1.5 35 5, (6), 7, (8), 9, 11, 13, (23), 27, (28), 29, 30, (38), 43.  Trigonometric functions.
          Handout: Sheet N120: Trigonometry (formulas).  Formulas to help you remember.
6 Thu 9/11 Fri 9/12 1.6 42 2, 5, 9, 11, 12, 14, 15, (19), (31).  Powers, polynomials and rational functions.
          Handout: Sheet N150: Functions: One−Page Summary.  To help you remember 'everything you need to know' about functions.
8 Mon 9/8 Fri 9/5     Sheet #120: TI−83/84 Skills [Answers].
9         Sheet #009: Sample AP Questions: Multiple Choice (1997) and Free Response (2006−2007). Section I question 82.  Section II question 1d.
  order order     Reminder:  Get the required Barron's guide, 8th edition, ISBN 0764123823.
π2 read
moodle
read
moodle
    Read the initial email in moodle. As of 9/15, I have replies from Lauren, Weiming, Katie, Jacqui, Chloe, Dani, Melinda, Meredith, Trevor, Ryan, Tiffany, Teressa.
201 Q&A:
Mon 9/15
Hand in
at Test
Q&A:
Mon 9/15
Hand in
at Test
    Practice for Calculus #201 [Questions]- [Answers]. Review of prerequisites for calculus.  Give yourself 6090 minutes.  You should not need a calculator for any questions except 9, 18 and 19.   However, the first test may allow you to use a calculator.  *=Challenge: do all problems without a calculator, taking advantage of the multiple choices.
  Mon 9/15 Mon 9/15     Be prepared to ask questions and give answers on the topics of  any of the above work.
  Tue 9/16 Mon 9/15     Quiz #151: take home.  Handed out in class (Fri or Mon).
  Tue 9/16 Wed 9/17     Test 1.  Sections 1.11.6.  Review: Practice for Calculus #210 (very important), homework, quizzes, and worksheets.  Calculator required on some questions.  No notes.

 

Calculus AB Homework Schedule − Chapter 1.6, 1.7, 1.8. Asymptotes, Continuity, Limits

Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF)

HW#

Period 6
Date due   

Period 4
Date due   

Book

First Page

CALCULUS
Description

6

1.6

42

HW #6 questions are also part of this unit.

11

Thu 9/18 Fri 9/19

1.6

42

7, 10, 16, 21, 26 (for 26, read "distinct real zeros" instead of "distinct roots"). Also, find the zeroes without a calculator for A1) y= 7 · (x+3)(x2)(x+7), and  A2) y=x3+7x2+12x.  Powers; Polynomials; Fundamental Theorem of Algebra.

12 Thu 9/18 Fri 9/19 1.6 42 1, 3, 4, 29[Sketch before looking at choices IIV).  Asymptotes.  Long-range behavior.
161 Mon 9/22 Mon 9/22 Sheet #161: Rational Function Graphs [Questions] - [Solutions]. Done in class.  Period 6: on whiteboard.  Period 4: Handout (corrected).
Sheet #162: Rational Functions: 3 Cases Of End Behavior.  Notes for study.
220 in class Sheet #220: Finding a Zero Without a Calculator [Questions][Solutions].
13 Mon 9/22 Mon 9/22 1.7 47 1, 2, 5, 6, 7, 9, 11, 13[11&13: No TI−83]. Continuity existence. Intermediate Value Theorem.  Recommended: 12, 14*.
171 Tue 9/23 Wed 9/24 (1.7) Sheet #171: Intermediate Value Theorem [Questions] - [Solutions]. Same as textbook 1.7,p.47 questions 12 and 14.
14 Mon 9/22 Mon 9/22 1.7 47 16; 17, 18[Graph it], 19; 20. Continuity and making a function continuous.
15 Mon 9/29 Fri 9/26 1.8 55 1, 2, 3, 4, 5, 6.  Limits: graphs, tables, formulas to graphs, expressions.
16A Mon 9/29 Fri 9/26 1.8 55 11, 13, 15, 19, 21, 22, 28, 29.  Limits.  Piecewise functions, tables, numerical estimates.  For tables, can use Y1(x) using [VARS] button.  Recommended: 12, 16.
181 in class in class (1.8) Sheet #181: Using Tables To Find Limits [Questions] - [Solutions].  Textbook 1.8,p.55 questions 11 and 16 with part e (algebraic) added.
1.8 Limits Lesson plan Tue 9/23, Wed 9/24 + Answers (even #s)
16B Mon 9/29 Fri 9/26 2.1 71 2.1 (not 1.8): 710. Added instructions: round to 5 decimals AND find exact answers using answers from HW#16A and algebra.  Numerical estimates and change of variables.
17 Mon 9/29 Fri 9/26 1.8 56 30, 31, 32, 34, 36.  Limits of polynomials with ± ∞.  No need to "manipulate."
18 Mon 9/29 Mon 9/29 1.8 56 37, 38, 39, 40, 41, 43, 44. Make limits exist.  Includes making holes.

19A

Tue 9/30
Collected

Wed 10/1
Collected

Test 2 Review Packet. Sheet #182: Review of 1.6, 1.7 and 1.8 (includes answers). Required: 2, 5, 6, 7, 8, 15−20, 21−24, 25, 27, 28, 29, 31, 37, 39, 40, 41, 42, 52. Recommended: 11, 12, 13, 14, 26, 30, 33−35.  Hand it in at the test.

201 1.1-
1.6
Review Chapter 1.11.6: Practice for Calculus #201 [Questions]- [Answers].  Pay attention to questions that were not suitable for the first test with a TI−83.

19B

Not
Collected
Not
collected

1.6-
1.8

Review Chapter 1.61.8 (the best way to practice for this test): Self Test: B Set 2, 8th Edition, p.B35: 1−7(rational), 9−10(exponential), 12, 15 (asymptotes), 16(factor), 17(absolute value), 20−22(piecewise), 23−24(asymptotes), 25(piecewise), 30−34(graph), 35(piecewise). Take as a timed self test at home without a calculator.  Time: 60−75 minutes.

Review Chapter 1: recent homework, in-class work, and quizzes.
Thu 10/2 Fri 10/3 Test 2.  Covers all of Chapter 1 and handouts.  Emphasis on 1.6, 1.7, 1.8  No calculator.  No notes.  Timed test: use your 75 minutes wisely.

 

Calculus AB Homework Schedule - Chapter 2: Concept of the Derivative

Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF)

HW#

Period 6
Date due   

Period 4
Date due   

Book

First Page

CALCULUS
Description

3C Mon 10/6 Mon 10/6 1.3   Sheet #131: Transformations and Slopes [Questions] - [Answers]
Barron's reading list for Chapter 2.  For HW#31: 3A, 3E, 4A+4B.  For HW#33: 3E (Note: x=0.5 missing below Fig. N3-5).  For HW#35: 4C, 4D, 4E. For HW#37&38: 3D.
Sheet #211: Definitions and Notation for Derivatives and Motion - [fill in the blanks].  Notes for study.
Sheet #212: Answers to some Chapter 2 even-numbered questions
30 Tue 10/7 Wed 10/8 2.1 71 CSV Textbook: 1, 2, 5, 6, 11, 12, 13, 14.  Rates of change, motion. [Answers]
Sheet #221: Methods for Finding Derivatives. Notes for study.

31

Thu 10/9 Fri 10/10

2.2

78 1, 2[2c: use table, not TI or formula], 13, 19, 25, 33, 37, 39.  Rates of change at a point: tables, graphs, algebra (limit definition).  [Answers]
32A Tue 10/14 Wed 10/15 2.3 86 Textbook: 11, 13, 15, 19, 22, 42[graph is of f ', not f]. Derivative functions: tables, limit definition. [Answers]
32B Thu 10/16 Fri 10/17 2.3 86 Textbook: 1, 3, 5, 25, 27, 29, 31.  Sketch  f ' from graph of  f.
231 Thu 10/16 Fri 10/17 Sheet #231: Sketch  f ' from  f (for 8 functions) - [Answers]
232 Mon 10/20 Fri 10/17 Sheet #232: Sketch f ' from f for 3 Similar Functions - [Answers]
236 Mon 10/20 Mon 10/20 (2.3,
3.1)
Sheet #236: Tangent to a Curve [Questions] - [Solutions].  Power rule (xn) and tangent lines.
33 Mon 10/20 Mon 10/20 (2.3) B74 etc. BSet 3 Multiple Choice. p. B7466. B75: 72.  B77: 8788. B78: 89[Hint: try x2 in the formula], (optional: 90−91 needs TI−83), 92. B90: 100.  Estimating f ' from tables and graphs.  Scanned PDFs:  B Sets.
35 Thu 10/23 Fri 10/24 2.5 97 Textbook: 1, 2[f '=dy/dx and f "=d2y/dx2], 3, 8, 10.  Intro to concavity,  f ''.   Note, the sign of the second derivative is the same as the concavity (up is positive and down is negative).  [Answers]
36 Mon 11/3 Mon 11/3 2.5 97 Textbook: 14, 16, 20, 21, 22. Concavity and  f '': Applications; Graphs. [Answers]
37 Mon 11/3 Mon 11/3 2.6 101 Textbook: 1, 2, 4, 6, 10[f " is "concavity"], 11[Sketch in units of R or set R=1]. Differentiability. [Answers].
50 Thu 10/23 Wed 10/22 3.1 115 Textbook Chapter 3.1: 9, 15, 23, 51, 53, 56*, 63, 67, 69.  Power rule (xn) and tangent lines. *=challenging and required.
38A Tue 10/21 Wed 10/22 (2.6) B73 etc. B Set 3 Multiple Choice. p.B73: 63, 64 [63, 64: graphs are of derivatives. Can you reconstruct the original function?].  B74: 65, 67, 6870; B75: 76; B77: 86.  Reading graphs of f '.  Differentiability; Error and concavity; Definition of f '. B Sets.
38B
=261
Tue 10/21 Wed 10/22 (2.6) B79 B Set 3 Multiple Choice: p.B79: 9599. Two extra questions: graph f ' and also find f " (pay attention!).  Corrections: 96 is numbered 97, interval in 98 is 6<x<3.    Questions are also available as Sheet #261: Derivative and Continuity [Questions] - [Answers].
38C B70 B Set 3 Multiple Choice: p.B70: 35, 36. Recognizing limits as derivatives.
39A
39B
39C
Tue 10/28 Wed 10/29 Chapter 2 Test Review.  Hand in HW#39A at Test.  Turning in HW#39B will be noted positively.  Note: answer correction to Question 25 (See Review page).
Thu 10/30 Fri 10/31 Test 3. Covers Chapter 2. 60 minutes. No notes.  Calculator allowed but not required.

 

Calculus AB Homework Schedule - Chapter 2: Derivatives: Interpretations and Applications

Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF)

HW#

Period 6
Date due   

Period 4
Date due   

Book

First Page

CALCULUS
Description

237 (2.3) Sheet #237: Rates of Change and the Derivative - [Questions] - [Solutions](Exactly same as Textbook 2.3,p.88: 3740. Barron's, p.B74: 66, 67.)
34 Tue 11/4 Wed 11/5 2.4 91 Textbook: 2[f '(20)=5, not 2 as given, is more consistent with common sense and with Question 3 in 11.5,p.547], 3, 6, 12, 18, 19. Interpreting f '[Answers]
241 Tue 11/4 Wed 11/5 (2.4) Sheet #241: Advertising Expenditures vs. Revenue Increase [Questions] - [Solutions]. (Based on 2.4,p.92: 19.)
252 (2.5,
2.6)
Sheet #252: Second Derivative and Differentiability including graphs and concavity.
254 in class in class F3.4 Sheet #254: F3.4 Motion Explorations with TI-83 (expanded from FBook F3.4 p.F127).|
Period 6 did Explorations 2 and 3.  Period 4 only did Exploration 3.
handed
out
handed
out
F3.4 Sheet #253: FBook F3.4. Velocity and Other Rates of Change. (handout). [Answers online]
253A Thu 11/6 Fri 11/7 F3.4 F129 FBook F3.4 (see above), Exercises (not Quick Review): 3, 5; 21; 23, 29.  Motion: algebraic; numerical; graphical ... and verbal. [Answers]
253B Mon 11/10 Mon 11/10 F3.4 F129 FBook F3.4 (see above), Exercises: 1; 9; 13, 20, 27; 37.  Applications: geometry; flow; motion; odd/even. [Answers]
253C Tue 11/11 Wed 11/12 F3.4 F130 FBook F3.4 (see above), Exercises: 11[Use TI−83; skip b]; 14[Use TI−83 for b]; 15[Use TI−83]; 25[Note: 25a says "speed up" so sketch speed]; 31; 33. Numerical derivative (NDER): Y2=nDeriv(Y1,X,X). Applications: marginal revenue; family of curves; profit; v(t) graph; balloon; volcano. [Answers]
New: complete solutions to all questions 1−30 in FBook F3.4.
253D Thu 11/13 Fri 11/14 • Get some sleep!  So many of you look tired.
• Redo Question 25 in HW#253C.  [Note: 25a says "speed up" so sketch speed.] Add "part e" to Question 25: Mark vertical axis with v ranging from −2 to 2 m/sec.  Find the change in position from t=0 to t=1, from t=0 to t=2, etc. for every second, finishing with t=0 to t=9 seconds.  For help, read p. 243 and the top of p. 244 in the CSV textbook.
• Start reviewing early and often.
Mon 11/17 Mon 11/17 Final Exam Review:  Sheet #265: Review Chapter 1 and 2 - [Questions, version 1] - [Answers, version 2].
Notes:
Update on Question 22c: V'(3)=24(correct answer), V'(4)=28(not asked for).  Skip Question 25 or replace every "1" with "15." Work will be collected at the time of the final examination.
at Final at Final Turn in Final Exam Review work.
Wed 11/19 Wed 11/19 Final Examination (Test 4).  Comprehensive.  Limits, continuity, derivatives, motion and other applications using rates of change.  Study the review Sheet, all material including Chapters 1 and 2, FBook 3.4 and all other handouts, quizzes, and homework.  Test 1 topics are not emphasized except in connection with the calculus material.  Timed test, 120 minutes.  Use your time wisely.  No graphing calculator allowed.  No notes.

 

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