[Back] − [bottom] − [Course Information] − [syllabus (3 pages)] − [College Board description May 2009]
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Calculus AB Summer Assignment − Review of Prerequisites to Calculus − Chapter 1.1−1.6 |
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| Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF) | |||||
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HW# |
Period 6 |
Period 4 |
Book |
First |
CALCULUS |
| 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); ° TI−83/84 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, 9−13, 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 60−90 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 1.1−1.6. Review: Practice for Calculus #210 (very important), homework, quizzes, and worksheets. Calculator required on some questions. No notes. | |||
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Calculus AB Homework Schedule − Chapter 1.6, 1.7, 1.8. Asymptotes, Continuity, Limits |
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Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF) |
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HW# |
Period 6 |
Period 4 |
Book |
First Page |
CALCULUS |
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6 |
1.6 |
42 |
HW #6 questions are also part of this unit. |
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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)(x−2)(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 I−IV). 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): 7−10. 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. |
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19A |
Tue 9/30 |
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. |
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| 201 |
1.1- 1.6 |
Review Chapter 1.1−1.6: Practice for Calculus #201 [Questions]- [Answers]. Pay attention to questions that were not suitable for the first test with a TI−83. | |||
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19B |
Not Collected |
Not collected |
1.6- |
Review Chapter 1.6−1.8 (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. |
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| 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. | |||
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Calculus AB Homework Schedule - Chapter 2: Concept of the Derivative |
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Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF) |
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HW# |
Period 6 |
Period 4 |
Book |
First Page |
CALCULUS |
| 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. | |||||
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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. B74: 66. B75: 72. B77: 87−88. 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, 68−70; B75: 76; B77: 86. Reading graphs of f '. Differentiability; Error and concavity; Definition of f '. B Sets. |
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38B =261 |
Tue 10/21 | Wed 10/22 | (2.6) | B79 | B Set 3 Multiple Choice: p.B79: 95−99. 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. | |||
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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. | |||
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Calculus AB Homework Schedule - Chapter 2: Derivatives: Interpretations and Applications |
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Note: C6=Period 6 (MTuTh), C4=Period 4 (MWF) |
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HW# |
Period 6 |
Period 4 |
Book |
First Page |
CALCULUS |
| 237 | (2.3) | Sheet #237: Rates of Change and the Derivative - [Questions] - [Solutions]. (Exactly same as Textbook 2.3,p.88: 37−40. 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. |
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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. |
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| 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. |
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| 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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