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§ 6.3 Volume: The Shell Method
Objectives: (1) Find the volume of a solid of revolution using the shell method; (2) Compare the uses of the disk method and the shell method.
Day 1: p. 432 # 1 - 12 ALL.
Day 2: p. 432 # 17 - 22 ALL.§ 6.4 Arc Length and Surfaces of Revolution
Objectives: (1) Find the arc length of a smooth curve; (2) Find the area of a surface of revolution.
Day 1: p. 442 # 3, 7, 9 - 17 odd.
Day 2: p. 443 # 31 & 33.[ Back to TOP ]
§ 7.1 Basic Integration Rules
Objective: Review procedures for fitting and integrand to the basic integration rules.
Day 1: p. 479 # 15 - 33 odd.
Day 2: p. 479 # 35 - 45 odd.
Day 3: p. 479 # 47, 48, 49 - 59 odd.§ 7.2 Integration by Parts
Objective: Find an antiderivative using integration by parts.
Day 1: p. 487 # 15 - 33 odd.
Day 2: p. 487 # 35 - 45 odd.
Day 3: p. 487 # 47, 48, 49 - 59 odd.QUIZ: § 7.1-7.2 [This is a no calculator quiz for the entire quiz. Students will be allowed one 3x5 inch note card of notes (one side only).]
§ 7.3 Trigonometric Integrals
Objectives: (1) Solve trigonometric integrals involving powers of sine and cosine; (2) Solve trigonometric integrals involving powers of secant and tangent.
Day 1: p. 496 # 3 - 12 ALL.
Day 2: p. 496 # 13 - 16 ALL, 17, 19, 22, 23 - 31 odd.§ 7.5 Partial Fractions
Objectives: (1) Understand the concept of partial fraction decomposition; (2) Use partial fraction decomposition with non-repeating linear factors to integrate rational functions.
Day 1: p. 515 # 1, 4, 7 - 14 ALL.
Day 2: p. 515 # 15, 16, 27, & 38.§ 7.7 Indeterminate Forms and L'Hôpital's Rule
Objectives: (1) Recognize limits that produce indeterminate forms; (2) Apply L'Hôpital's Rule to evaluate a limit.
Day 1: p. 530 # 1 - 29 odd. Also … Discuss Gabriel's Horn - Surface Area & Volume.
Day 2: p. 530 # 31 - 47 odd.
Day 3: p. 531 # 59 - 62 ALL.QUIZ: § 7.3-7.5 [This is a no calculator quiz for the entire quiz. Students are allowed one 3x5 inch note card of notes (one side only).]
§ 7.8 Improper Integrals
Objectives: (1) Evaluate an improper integral that has an infinite limit of integration; (2) Evaluate an improper integral that has an infinite discontinuity.
Day 1: p. 540 # 1 - 6 ALL. [Use symbolic integration utility to evaluate integrals. Find limits by analytic methods.]TEST: Chapter 7 - Integration Techniques [Calculators are permitted for the entire test. Students are allowed one 3x5 inch note card of notes (one side only).]
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§ 8.1 Sequences
Objectives: (1) List terms of a sequence, (2) Determine whether a sequence converges or diverges, (3) Write a formula for the nth term of a sequence, (4) Use properties of monotonic sequences and bounded sequences.
Day 1: p. 555 # 1 - 22 ALL.
Day 2: p. 555 # 23 - 50 ALL.
Day 3: p. 555 # 51 - 66 ALL.
Day 4: p. 556 # 67 - 80 ALL, & 95 (as discussion).§ 8.2 Series and Convergence
Objectives: (1) Understand the definition of a convergent infinite series, (2) Use properties of infinite geometric series, (3) Use the nth-Term Test for Divergence of an infinite series.
Day 1: p. 564 # 1 - 25 odd.
Day 2: p. 564 # 31 - 43 odd.
Day 3: p. 465 # 45 - 59 odd.QUIZ: § 8.1-8.2 [Calculator permitted throughout quiz. Students will be allowed one 3x5 inch note card of notes (one side only).]
§ 8.3 The Integral Test and p-Series
Objectives: (1) Use the Integral Test to determine whether an infinite series converges or diverges, (2) Use properties of p-series and harmonic series.
Day 1: p. 571 # 1 - 11 odd.
Day 2: p. 571 # 15 - 21 odd, 22 - 29 ALL (skip 27).§ 8.4 Comparisons of Series
Objectives: (1) Use the Direct Comparison Test to determine whether a series converges or diverges, (2) Use the Limit Comparison Test to determine whether a series converges or diverges.
Day 1: p. 578 # 3 - 14 ALL.
Day 2: p. 578 # 15 - 28 ALL.
Day 3: p. 580 # 58 The Koch Snowflake area and perimeter. [Suggested resource: click]§ 8.5 Alternating Series
Objectives: (1) Use the Alternating Series Test to determine whether an infinite series converges, (2) Use the Alternating Series Remainder to approximate the sum of an alternating series, (3) Classify a convergent series as absolutely or conditionally convergent, (4) Rearrange an infinite series to obtain a different sum.
Day 1: p. 586 # 1 - 4 ALL, 9 - 28 odd.
Day 2: p. 587 # 29 - 36 ALL.
Day 3: p. 587 # 37 - 51 odd.§ 8.6 The Ratio and Root Tests
Objectives: (1) Use the Ratio Test to determine whether an infinite series converges or diverges, (2) Use the Root Test to determine whether an infinite series converges or diverges, (3) Review the tests for convergence and divergence of an infinite series.
Day 1: p. 594 # 1 - 4 ALL, 11 - 31 odd.
Day 2: p. 594 # 33 - 39 odd.
Day 3: p. 595 # 41 - 55 odd.TEST: Chapter 8 - Infinite Series, § 8.1-8.6 [Calculators are permitted for the entire test. Students will be allowed one 3x5 inch note card of notes (one side only).]
§ 8.7 Taylor Polynomials and Approximations
Objectives: (1) Find polynomial approximations of elementary functions and compare them with the elementary function, (2) Find Taylor and Maclaurin polynomial approximations of elementary functions, (3) Use the remainder of a Taylor polynomial.
Day 1: p. 604 # 1 - 4 ALL, 7 - 15 odd.
Day 2: p. 604 # 23, 24, 33, 34, 37, & 38.§ 8.8 Power Series
Objectives: (1) Understand the definition of a power series, (2) Find the radius and interval of convergence of a power series, (3) Determine the endpoint convergence of a power series.
Day 1: p. 613 # 1 - 25 odd.§ 8.9 Representations of Functions by Power Series
Objectives: (1) Find a geometric power series that represents a function, (2) Construct a power series using series operations.
Day 1: p. 620 # 1 - 15 odd. [Use your calculator to observe the graph of the first few terms of the series along with the original functions.]§ 8.10 Taylor and Maclaurin Series
Objectives: (1) Find a Taylor and a Maclaurin series for a function, (2) Use a basic list of Taylor series to find other Taylor series.
Day 1: p. 630 # 1 - 7 odd, 17.
Day 2: p. 630 # 43, 45, 49, & 51.TEST: Chapter 8 - Infinite Series, § 8.7-8.10 [Calculators are permitted for the entire test. Students will be allowed one 3x5 inch note card of notes (one side only).]
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§ 9.2 Plane Curves and Parametric Equations
Objectives: (1) Sketch the graph of a curve given by a set of parametric equations, (2) Eliminate the parameter in a set of parametric equations.
Day 1: p. 659 # 1 - 27 odd.§ 9.3 Parametric Equations and Calculus
Objectives: (1) Find the slope of a tangent line to a curve given by a set of parametric equations, (2) Find arc length of a curve given by a set of parametric equations.
Day 1: WORKSHEET.
Day 2: Arc length: p. 668 # 31 - 35 odd.§ 9.4 Polar Coordinates and Polar Graphs
Objectives: (1) Understand the polar coordinate system, (2) Rewrite rectangular equations in polar form and vice versa, (3) Sketch the graph of an equation given its specific polar form, (4) Find the slope of a tangent line to a polar graph, (5) Identify several types of special polar graphs.
Day 1: p. 678 # 1, 2, 3, 29, 31, 33, & 43.
Day 2: p. 679 # 45, 49, 51, 57, 58, 59, & 61. [See worksheet.]§ 9.5 Area and Arc Length in Polar Coordinates
Objectives: (1) Find the area of a region bounded by a polar graph.
Day 1: p. 687 # 1 - 7 odd.
- TEST: Chapter 9 - Parametric Equations and Polar Coordinates, § 9.2-9.5
- [Test will be in two parts: Part I = Multiple choice & No Calculators (identify "special" polar graphs and find area of enclosed regions). Part II = Open response questions, calculators permitted. No notes permitted for either part of the test.]
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- Differential Equations & Euler's Method
- Exploration of Euler's Method [Packet]
1998 AP Exam (BC) Question # 4 [DiffEQ & Euler's Method]
1999 AP Exam (BC) Question # 6 [DiffEQ & Euler's Method]
2000 AP Exam (BC) Question # 6 [DiffEQ]
2001 AP Exam (BC) Question # 5 [DiffEQ & Euler's Method]
- Vector-Valued Functions
- NOTES: Introduction to Vector-Valued Functions
§11.2 Differentiation and Integration of Vector-Valued Functions, p. 783 # 1-4 ALL.
Exploration: Introduction to the Calculus of Vectors
Vector-Valued Functions WORKSHEET #1
Vector-Valued Function Questions from the 1998 AP Calculus (BC) Exam
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