# Calculus BC Syllabus (AP)

advertisement ```AP® Calculus BC
Students enrolled in Calculus BC have already successfully completed a year of Calculus
in our Calculus AB course.
Course Overview
We cover everything in the Calculus BC topic outline as it appears in the AP®
Calculus Course Descriptions. The primary textbook is Calculus, Larson, Hostetler, et
al., 8th ed.. We study four major ideas: limits, derivatives, indefinite integrals, and
definite integrals. As we develop the concepts, we explain how the mechanics go along
with the topics, and stress application. Since concepts are so vital to AP® Calculus, there
is an attempt to balance understanding, skills, and use of technology. The course
provides students with the opportunity to work with functions represented graphically,
numerically, analytically, and verbally—and emphasizes the connections among these
representations.
Chapter 7 - Applications of Integration
7.4 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. 483 # 3, 6, 15 - 23 odd
Day 2: p. 483 # 41 & 43
Chapter 8 - Integration Techniques, L'Hôpital's Rule,
and Improper Integrals
8.1 Basic Integration Rules
Objective: Review procedures for fitting and integrand to the basic integration rules.
Day 1: p. 522 # 15 - 33 odd
Day 2: p. 522 # 35 - 49 odd
Day 3: p. 522 # 57, 58, 61 - 67 odd
Test 8.1 (7.4, 8.1)
8.2 Integration by Parts
Objective: Find an antiderivative using integration by parts.
Day 1: p. 531 # 17 - 35 odd.
Day 2: p. 531 # finish day 1 assignment.
Day 3: p. 531 # 47 – 63 odd.
8.3 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. 540 # 1 - 18 ALL
Day 2: p. 540 # 25 – 41 Odd
8.5 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. 559 # 1 - 16 ALL
Test 8.235 (8.2, 8.3, 8.5)
8.7 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. 574 # 5 - 53 odd
Day 2: p. 574 # 75 - 78 all
8.8 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. 585 # 5 - 10 ALL. [Use symbolic integration utility to evaluate integrals. Find
limits by analytic methods.]
Chapter 8 Test
Chapter 9 - Infinite Series
9.1 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. 602 # 1 - 41 odd
Day 2: p. 603 # 57 - 67 odd
9.2 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. 612 # 1 - 21 odd
Day 2: p. 612 # 23 - 28 all
Day 3: p. 613 # 57 - 69 odd
9.3 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. 620 # 1 - 17 odd
Day 2: p. 573 # 29 - 36 all
9.4 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. 628 # 3 - 14 ALL
Day 2: p. 628 # 15 - 28 ALL, 29, 36
9.5 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. 636 # 11 - 27 odd
Day 2: p. 636 # 47 – 59 odd
9.6 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. 645 # 1 - 4 ALL, 13 - 29 odd
Day 2: p. 645 # 37 - 49 odd
Day 3: p. 645 # 51 - 65 odd
Day 4: p. BC Packet p. 176
9.7 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. 656 # 1 - 4 ALL, 13 - 23 odd
Day 2: p. 656 # 33, 34, 45, 47
9.8 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. 666 # 5 - 29 odd
9.9 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. 674 # 1 - 15 odd [Use your calculator to observe the graph of the first few terms
of the series along with the original functions.]
9.10 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. 685 # 1 – 7
Day 2: p. 685 # 21 – 29 odd
Chapter 10 - Parametric Equations and Polar
Coordinates
10.2 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. 716 # 1 - 31 odd
10.3 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: Arc length: p. 724 # 5 - 13 odd, 17 – 25 odd
Day 2: 27 – 41 odd
10.4 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. 736 # 1 – 41 odd
Day 2: p. 736 # 61 - 79 odd
10.5 Area and Arc Length in Polar Coordinates
Objectives: (1) Find the area of a region bounded by a polar graph.
Day 1: p. 745 # 7 - 16
More on Differential Equations
Objectives: (1) Find numerical solutions of differential equations using Euler’s Method;
(2) Solve logistic differential equations and use them in modeling.
Days 1-3: Packet on Euler’s Method and logistic differential equations
Vector-Valued Functions
Objectives: (1) Analyze curves in vector form, and find derivatives of vector functions.
AP Review
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