AP Calculus AB 12023109 - Home - Hillsborough County ... Calculus AB 12023109 ... Numerically...

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SECONDARY MATHEMATICS CURRICULUM GUIDE

AP Calculus AB

12023109

Textbook: Calculus Concepts and Calculators, 2nd

edition

Best, Carter, Crabtree, Venture Publishing

HILLSBOROUGH COUNTY SCHOOL DISTRICT

2010 - 2011

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AP CALCULUS AB OUTLINE

2010-2011

Use of the TI-83, TI-84, TI-89 series or equivalent is allowed on one portion only of the SDHC semester exam. . of 9

GRAPHING CALCULATORS: Students are expected to use a graphing calculator throughout the course,

and to learn the paper-and-pencil techniques of calculus. County exams, as well as the AP exam, will have

both calculator and non-calculator parts. Students are expected to be able to do the following on their

graphing calculator:

Plot the graph of a function within an arbitrary viewing window;

Find the zeros of functions (solve equations numerically);

Numerically calculate the derivative of a function; and

Numerically calculate the value of a definite integral.

It is imperative that the teacher establish a level of rigor appropriate to the demands of this course.

Cumulative District exams are provided for Semester 1 and Semester 2. Use of the TI-83, TI-84, TI-89

series or equivalent is allowed on one portion only of the District semester exam.

This outline is based on material supplied by the textbook publisher. It is provided as a general guideline

to the teacher. The suggested problems are not meant to be exclusionary. The timeline is approximate.

The following points are offered:

The teacher may wish to reduce the amount of time suggested for Chapter 1 Functions and Graphs,

and instead review these topics within the study of the Calculus.

Please make note of the cut-off point for material on the SDHC Semester One exam.

Some topics are required for AP Calculus BC only, and not for AP Calculus AB.


2010-2011


BEGINNING OF SEMESTER ONE

Ch 1 Functions and Graphs

(21 days)

Day Section Topic Problems

1 1.1 What is a Function Page 5: 1 –4; 7,11,25

2 1.1 What is a Function Page 5: 5, 9, 12-17, 26

3 1.2 Basic Functions and Transformations Page 7: 18, 19, 21, 23; Page 12: 1-19 odd

4 1.2 Basic Functions and Transformations Page 8: 20; Page 13: 20, 21, 22ab, 24, 26 & Read 1.3

5 1.3 Linear Functions and Models Page 14: 25; Page 22: 1-17 odd

6 1.3 Linear Functions and Models Page 22: 2 – 10 even, 16; Page 76: 4,11,14,16,20,27,30a

7 Test 1.1 – 1.3

8 1.4 Exponential Functions Page 30: 1, 3a-e, 5-15 odd

9 1.4 Exponential Functions Page 30: 4 – 18 even, 19

10 1.5 Compound Interest and e Page 37: 1 – 17 odd; Page 33: 20

11 1.5 Compound Interest and e Page 37: 2 - 18 even; Page 33: 21

12 1.6 Inverse Functions Page 42: 1 – 27 odd

13 1.6 Inverse Functions Page 42: 2-28 even

14 1.7 Logarithms Page 49: 1 – 4; 5,7,9,11,13

15 1.7 Logarithms Page 49: 6, 10, 12, 14, 17, 19-25 odd

16 Supp Review Page 76: 8, 9, 15, 24, 30b

17 Test 1.4 – 1.7

18 1.8 Polynomial and Rational Functions Page 58: 1 - 8,10,15,19

19 1.9 Composition of Functions Page 58: 11,13,16,21; Page 66: 1, 2, 4, 7, 9, 10, 12, 13

20 1.10 Trigonometric Functions Page 66: 8, 14, 16; Page 73: 1-6, 7, 9, 11,12

21 Supp Review Page 73: 14, 17; Page 76: 1, 2, 3, 5, 12, 13, 17, 18, 23, 25,

31

22 Test Chapter 1


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Ch 2 Derivative Functions (19 days)


23 2.1 Average and Instantaneous Velocity Page 87: 1 – 13 odd

24 2.1 Average and Instantaneous Velocity Page 87: 2 – 12 even; Page 79: 19,28

25 2.2 Derivative of a Function at a point Page 97: 1 – 8, 10 a, b, c

26 2.2 Derivative of a Function at a point Page 98: 9, 10 d,e,f; 11 – 17, 19

27 2.3 The Derivative Function Page 105: 1 – 19 odd, 20

28 2.3 The Derivative Function Page 105: 2 – 12 even, 21,23,26,27

29 2.4 Calculating Derivative Numerically Page 105: 28,29; Page 112: 1 – 13 odd

30 2.4 Calculating Derivative Numerically Page 112: 2 – 12 even

31 Test 2.1 – 2.4

32 2.5 Critical Numbers; Relative Max/Min Page 116: 1 – 15 odd, 22

33 2.5 Critical Numbers; Relative Max/Min Page 116: 8 – 18 even, 23, 25

34 2.6 Inflection points and Second Derivative Page 125: 1, 2, 4, 5, 7, 9, 10, 11

35 2.6 Inflection points and Second Derivative Page 125: 6, 12-17,19

36 2.7 The Limit of a Function Page 137: 1- 29 odd

37 2.8 Continuity Page 145: 1 – 15 odd, 16,17, 21

38 Supp Review Page 149: 1, 3, 5, 9,10,13,16, 17,20,21,25,29,33

39 Test 2.4– 2.8


2010-2011


Ch 3 The Definite Integral (10 days)


40 3.1 Calculating Distance Traveled Page 163: 1 – 6, 8

41 3.2 Calculation Areas; Riemann Sums Page 163: 7, 9; Page 169: 1 – 9 odd

42 3.2 Riemann Sums Page 169: 2-10 even, 11

43 3.3 Definite Integrals Page 176: 1, 2, 3, 5-17 odd

44 3.3 Definite Integrals Page 177: 8-18 even; page 179 lab project

45 3.4 The Fundamental Theorem of Calculus Page 184: 1-13 odd

46 3.4 The Fundamental Theorem of Calculus Page 184: 2, 4, 8, 10, 12, 15, 16

47 Supplementary Problems Page 187: 1,3,4, 7, 10 ,13, 16, 18, 22

48 Test Chapter 3

Ch 4 Differentiation Rules (16 days)


49 4.1 Derivative Rules for Basic Functions Page 200: 1, 5, 9, 13, 17, 19, 21, 23, 25, 27, 29, 31

50 4.1 Derivative Rules for Basic Functions Page 200: 3, 7, 15, 18, 20, 22, 24, 26,28, 30, 32

51 4.2 Differentiating Exponential Functions Page 206: 1 – 21 odd

52 4.3 The Product and Quotient Rule Page 206: 4, 6, 10, 14, 16, 18, 20;

Page 215: 1, 3, 5, 7, 10, 25

53 4.3 The Product and Quotient Rule Page 215: 2, 4, 6, 12, 15-23,odd; 26, 28

54 Test 4.1 – 4.3

55 4.4 The Chain Rule Page 215: 31, 32, 35, 37; Page 223: 1 – 21 odd

56 4.4 The Chain Rule Page 217: 36, 39; Page 223: 2, 4, 10; 14 – 22 even;

25, 27, 29

57 4.4 The Chain Rule Page 224: 23; 24 – 32 even; 35, 39, 40, 43, 45

58 4.5 Functions Defined Implicitly Page 223: 37, 41, 44; Page 229: 3 – 19 odd


2010-2011


Ch 4 Differentiation Rules (continued)

59 4.5 Functions Defined Implicitly Page 229: 4, 8, 10 – 22 even

60 Supplementary Problems Page 230: 21, 24, 27;

Page 245: 2, 5, 8, 9, 10, 15, 16, 20, 25

61 Test 4.1–4.5

62 4.6 Related Rates of Change Page 235: 3, 5, 7, 9, 11, 12, 19

63 4.6 Related Rates of Change Page 235: 4, 8, 10, 15, 18, 21

64 4.7 Approximations Page 243: 1-9 odd

65 4.7 Approximations Page 243: 4, 6, 8, 11, 13, 14, 16, 18-20

* Derivative of Inverse Functions Supplement

Ch 5 More Applications of the

Derivative (14 days)


66 5.1 Increasing and Decreasing Functions Page 260: 1; 5 – 11 odd;15, 17, 19; 21 – 27 odd

67 5.1 Increasing and Decreasing Functions Page 260: 6, 8, 10, 18; 28 – 36; 38, 41, 43

68 Test 4.6-4.7 and 5.1

69 5.2 Applications of the Second Derivative Page 268: 2 – 4; 8 – 11; 17, 18, 20, 21, 22;

Page 260: 12, 23, 24, 44

70 5.2 Applications of the Second Derivative Page 269: 13, 15, 16, 19, 25, 28, 31, 32

71 5.3 Limits at Infinity Page 268: 24, 26, 29; Page 275: 1 – 19odd

72 5.4 Optimization Problems Page 275: 4, 8, 12, 16; Page 281: 1, 4, 7, 8

73 5.4 Optimization Problems Page 281: 2, 5, 10, 11, 12, 13, 18

74 Test 5.2–5.4

75 5.5 The Mean Value Theorem Page 282 : 15, 17; Page 285: 1– 11 odd

76 5.6 Antiderivatives Page 285: 4, 8, 12; Page 291: 1 – 19 odd

77 5.6 Antiderivatives Page 291: 4 , 8, 12, 16, 18, 20, 21, 23

END OF SEMESTER ONE CUT-OFF FOR MATERIAL, SEMESTER ONE EXAM


2010-2011


BEGINNING OF SEMESTER TWO

Ch 6 Integrals (9 days)


78 6.1 The Definite Integral Again Page 304: 1-17 odd

79 6.2 Functions Defined by Integrals Page 304: 4, 8, 12, 16; Page 312: 1-11 odd

80 6.3 The Fundamental Theorem Again Page 318: 1 – 13 odd; Page 325: 6, 9, 16

81 6.3 The Fundamental Theorem Again Page 318: 2-10 even; Page 325: 18, 19, 21, 23

82 Test 5.5, 5.6 and 6.1-6.3

83 6.4 Areas of Plane Regions Page 324: 1, 5, 9, 13, 15, 17, 19,

84 6.4 Areas of Plane Regions Page 324: 4, 8, 12, 14, 16, 18, 20, 21

Ch 7 Finding Antiderivatives (14 days)


85 7.1 Antiderivatives Page 332: 1-29 odd

86 7.1 Antiderivatives Page 332: 2-30 even

87 7.2 The Chain Rule Page 333: 31, 33; Page 336: 3-33 by 3's

88 7.2 The Chain Rule Page 336: 2, 5, 8, 11, 14, 17, 20, 23, 28, 31, 35

89 7.3 Integration by Parts (BC required) Page 336: 32, 34, 36, 37; Page 340: 1, 3, 5, 9-17 odd

90 7.3 Integration by Parts (BC required) Page 340: 2-18 even, 21

91 Review Page 325: 7, 8, 10

Page 361: 3, 5, 6, 9, 11, 12, 15, 18, 20, 29, 41

92 Test 6.4 and 7.1-7.3

93 7.4 Trig Functions and Inverses Page 348: 1, 3-13

94 7.4 Trig Functions and Inverses Page 348: 4, 8, 12, 20, 21, 23-26, 31

95 7.5 Numerical Integration Page 349: 29, 30; Page 357: 1-9 odd; 13, 17, 19

96 Supp Review Page 348: 14-16; 22, 27; Page 357: 2, 6, 10, 14, 16, 18, 20

Page 361: 28, 43, 47

97 Test Chapter 7


2010-2011


Ch 8 Using the Definite Integral

(10 days)


98 8.1 Net and Total Distance Traveled Page 370: 1-15 odd

99 8.2 Volume by Slicing Page 370: 12, 14; Page 377: 1-4

1000 8.2 Volume by Slicing Page 377: 5-19 odd

101 8.3 Volume by Shell Method Page 378: 12, 16, 18; Page 382: 1-13 odd

102 8.4 Average Value of a Function Page382: 6, 8, 10, 14; Page 385: 1-13 odd

103 8.5 More Applications of the Definite

Integral

Page 385: 8, 10, 12; Page 388: 1, 3, 5, 7

104 Supp Review Page Page 389: 6, 9; page 390: 1, 3, 5, 8, 9, 11, 15

105 Test Chapter 8

Ch 9 Differential Equations (9 days)


106 9.1 Introduction Page 397:1-11 odd

107 9.2 Slope Fields Page 397: 6, 10; Page 402: 1-3

108 9.3 Euler's Method (BC required) Page 403: 4, 5, 7: Page 408: 1, 2

109 9.3 Euler's Method (BC required) Page 408: 3-8

110 9.4 Separation of Variables Page 411: 1-9 odd

111 9.4 Separation of Variables Page 411: 2-10 even; Page 415: 1, 2

112 Supp Review Page 413: 1-14; Page 415: 4, 5

113 Test Chapter 9

END OF NEW MATERIAL


2010-2011


Following the end of new material, approximately at the end of Quarter 3, the remaining time before the AP Exam

should be spent preparing for the exam through use of practice exams from various publishers, and through use of

released exams.

RESOURCES

Check the College Board’s Acorn Book, which is updated annually, for the AP Course Description.

The following books are good sources of activities and problems:

Barnes, Mary, Investigating Change. Curriculum Corporation, 1991. Reprinted 1993.

Best, George and Richard Lux, Preparing for the Calculus (AB) Exam 2004 Edition, Venture Publishing.

Finney, Calculus: Graphical, Numeric, Algebraic, Pearson/Prentice Hall

Hughes-Hallet, Deborah. Calculus. John Wiley & Sons, 1994.

Hyun, Thomas, Acing AP Calculus AB and BC, Greenhall Publishing, 2007

The Ithaca College Group, Calculus An Active Approach with Projects. John Wiley & Sons, 1994.

Note: The Instructor’s Guide for Calculus An Active Approach with Projects has several quizzes and

examinations in the back which contain some of the new types of questions.

Thomas-Finney, Calculus 9th Edition. Addison Wesley, 1996.

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