AP CALCULUS BC PACING GUIDE AND COURSE DESCRIPTION
Day 1 - (27 Jan) Admin, Overview, & Review Activity
Day 2 - (28 Jan) Lessons 1.8 & 4.7, Limits & L'Hopital's Rule
Day 3 - (29 Jan) Lessons 1.7 Continuity & AP Exam Problems
Day 4 - (30 Jan) Complete Review of Limits, Continuity, LHR, Growth
Day 5 - (2 Feb) Club Picture Day. Review Homework
Day 6 - (3 Feb) Derivatives Review
Day 7 - (4 Feb) Derivatives Review
Day 8 - (5 Feb) Limits/Continuity Exam
Day 9 - (6 Feb) Lesson 7.2, Integration by Parts
Day 10 - (9 Feb) Review of Exam and Homework Questions
Day 11 - (10 Feb) Lesson 7.2, Integration by Parts cont
Day 12 - (11 Feb) Lesson 7.4, Partial Fractions
Day 13 - (12 Feb) Lesson 7.4, Partial Fractions cont
Day 14 - (13 Feb) Derivatives Exam
Day 15 - (16 Feb) Lesson 7.7, Improper Integrals
Day 16 - (17 Feb) Improper Integrals continued
Day 17 - (18 Feb) Lesson 7.8, Comparison Test & Arc Length
Day 18 - (19 Feb) Operational Pause - Worksheets #8 and #9
Day 19 - (20 Feb) Math Club Competition - Operational Pause
Day 20 - (23 Feb) Lessons 11.1 & 11.2, Differential Equations & Slope Fields
Day 21 - (24 Feb) Lesson 11.3 Euler's Method
Day 22 - (25 Feb) Lessons 11.4, & 11.5, Sep of Var, & Growth and Decay
Day 23 - (26 Feb) Lesson 11.7, Logistics Model
Day 24 - (27 Feb) Integration Exam
Day 25 - (2 Mar) Lesson 4.8, Parametric Equations
Day 26 - (3 Mar) Operational Pause due to Caps Homeroom
Day 27 - (4 Mar) Parametric continued
Day 28 - (5 Mar) Supplemental Lessons - Vectors
Snow Day - (6 Mar) Operational Pause - HW #12, & #13
Day 29 - (9 Mar) Wrap up Vectors and Review for DE Exam
Day 30 - (10 Mar) DE Exam
Day 31 - (11 Mar) Review DE Exam, and Review HW
Day 32 - (12 Mar) Lesson 8.3, Polar
Day 33 - (13 Mar) Polar
Day 34 - (16 Mar) Review
Day 35 - (17 Mar) Lesson 9.1, Series & Sequences
Day 36 - (18 Mar) PVP Exam
Day 37 - (19 Mar) PVP Exam
Day 38 - (20 Mar) Lesson 9.2, Series & Sequences
Day 39 - (23 Mar) Lesson 9.3, Convergence of Series
Day 40 - (24 Mar) Lesson 9.4, Tests for Convergence
Day 41 - (25 Mar) Lesson 9.4 continued
Day 42 - (26 Mar) Homeworktime, Operational Pause
Day 43 - (27 Mar) Practice Exam
Day 44 - (30 Mar) Series Exam
Day 45 - (31 Mar) Review
Day 46 - (1 Apr) Midterms 1 & 3
Day 47 - (2 Apr) Midterms 2 & 4
Day 48 - (13 Apr) Lesson 9.5, Power Series and Interval of Convergence
Day 49 - (14 Apr) Lesson 10.1, Taylor Polynomials
Day 50 - (15 Apr) Lesson 10.2, Taylor Series
Day 51 - (16 Apr) Lesson 10.3, Finding and Using Taylor Series
Day 52 - (17 Apr) Lesson 10.4, The Error in Taylor Polynomial Approximations
Day 53 - (20 Apr) Review
Day 54 - (21 Apr) Review
Day 55 - (22 Apr) Review
Day 56 - (23 Apr) Taylor Series Exam
Day 57 - (24 Apr) AP Calc BC MC Exam Part I
Day 58 - (27 Apr) AP Calc BC MC Exam Part II
Day 59 - (28 Apr) AP Calc BC Free Response Part I
Day 60 - (29 Apr) AP Calc BC Free Response Part II
Day 61 - (30 Apr) Mock AP Exam Part I & II
Day 62 - (1 May) Mock AP Exam Part III & IV
Day 63 - (4 May) Review Mock AP Exam
Day 64 - (5 May) Free Response Review
Day 65 - (6 May) AP Calc BC Exam
Day 66 - (7 May) Assignment of final lessons and prep time
Day 67 - (8 May) Review Free Response Questions
Day 68 - (11 May) Operational Pause
Day 69 - (12 May) Operational Pause - AP Chem Exam (majority of class)
Day 70 - (13 May) Lesson 4.4, Applications to Marginality (Brian C)
Day 71 - (14 May) Lesson 8.4, Density and Center Mass (Mike L)
Day 72 - (15 May) Operational Pause
Day 73 - (18 May) Lesson 8.5, Applications to Physics (Marguerite L)
Day 74 - (19 May) Lesson 8.6, Applications to Economics (Robert K)
Day 75 - (20 May) Lesson 8.7, Distribution Func (Louie L)
Day 76 - (21 May) Lesson 8.8, Probability and Mean (Jared L)
Day 77 - (22 May) Lesson 11.8, Systems of Differential Equations (Dave S)
Day 78 - (26 May) Lesson 11.9, Analyzing the Phase Plane (Amber S)
Day 79 - (27 May) Lesson 11.10, 2nd-Order Differential Equations (Allison C)
Day 80 - (28 May) Lesson 11.11, Linear 2nd-Order DE (Ally S)
Day 81 - (29 May) Homework Time
Day 82 - (1 Jun) Enhanced Lesson Exam and Homework Due
Day 83 - (2 Jun) Review
Day 84 - (3 Jun) Final Exam Review, and Final Project Due
Day 85 - (4 Jun) Final Exam Period 2
Day 86 - (5 Jun) Final Exam Period 3
Day 87 - (8 Jun) Final Exam Period 4
Day 88 - (9 Jun) Final Exam Period 1
Day 89 - (10 Jun) Make-Up
Final Exam will consist of two parts - Part I, 28 Multiple Choice Questions,
No Calc, & Part II, 17 Multiple Choice Calculator Active.
Final exam is worth 25% of final overall grade.
Course Description (lesson(s) alignment)
(* AB Topic, & + BC topic)
1. Functions, Graphs, and Limits
a. Limits of functions (including one-sided limits)
* An intuitive understanding of the limiting process (1.8)
* Calculating limits using algebra (1.8)
* Estimating limits from graphs or tables of data (1.8)
b. Asymptotic and unbounded behavior
* Understanding asymptotes in terms of graphical behavior (1.5)
* Describing asymptotic behavior in terms of limits involving infinity (1.7)
* Comparing relative magnitudes of functions and their rates of change (for
example, contrasting exponential growth, polynomial growth, and logarithmic
growth) ( 1.2, 1.4, & 1.6)
c. Continuity as a property of functions
* An intuitive understanding of continuity (1.7)
* Understanding continuity in terms of limits (1.8)
* Geometric understanding of graphs of continuous functions (Intermediate
Value Theorem and Extreme Value Theorem) (1.7 & 4.3)
d. Parametric, polar and vector functions.
+ The analysis of planar curves includes those given in parametric form,
polar form, and vector form. (4.8 & 8.3)
2. Derivatives
a. Concept of the derivative
* Derivative presented graphically, numerically, and analytically. (2.2)
* Derivative interpreted as an instantaneous rate of change. (2.2)
* Derivative defined as the limit of the difference quotient. ( 2.3)
* Relationship between differentiability and continuity. (2.6)
b. Derivative at a point
* Slope of a curve at a point. Examples are emphasized, including points at
which there are vertical tangents and points at which there are no tangents.
(2.2 & 2.4)
* Tangent line to a curve at a point and local linear approximation. (2.2)
* Instantaneous rate of change as the limit of average rate of change. (2.1)
* Approximate rate of change from graphs and tables of values. (2.3)
c. Derivative as a function
* Corresponding characteristics of graphs of f and f'. (3.1-3.10)
* Relationship between the increasing and decreasing behavior of f and the
sign of f'. (3.1-3.10)
* The Mean Value Theorem and its geometric consequences. (3.10)
* Equations involving derivatives. Verbal discriptions are translated
into equations involving derivatives and vice versa. (3.1-3.10)
d. Second derivative
* Corresponding characteristics of the graphs of f, f', and f''. (2.5)
* Relationship between the concavity of f and the sign of f''. (2.5)
* Points of inflection as places where concavity changes. (2.5)
e. Applications of derivatives
* Analysis of curves, including the notions of monotonicity and concavity.
(4.1 & 4.2)
+ Analysis of planar curves given in parametric form, polar form, and vector
form, including velocity and acceleration. (4.8 & 8.3)
* Optimization, both absolute (global) and relative (local) extrema. (4.3)
* Modeling rates of change, including related rates problems. (4.4 & 4.5)
* Use of implicit differentiation to find the derivative of an inverse
function. (3.7)
* Interpretation of the derivative as a rate of change in varied applied
contexts, including velocity, speed, and acceleration. (4.6)
* Geometric interpretation of differential equations via slope fields and
the relationship between slope fields and solution curves for differential
equations. (11.2)
+ Numerical solution of differential equations using Euler's method. (11.3)
+ L'Hospital's Rule, including its use in determining limits and convergence
of improper integrals and series. (4.7)
f. Computation of derivatives
* Knowledge of derivatives of basic functions, including power, exponential,
logarithmic, trigonometric, and inverse trigonometric functions. (3.1-3.7)
* Basic rules for the derivative of sums, products, and quotients of
functions. (3.1 & 3.3)
* Chain rule of implicit differentiation. (3.6 & 3.7)
+ Derivatives of parametric, polar, and vector functions. (4.8 & 8.3)
3. Integrals
a. Interpretations and properties od definite integrals
* Definite integral as a limit of Riemann sums (5.1 & 5.2)
* Definite integral of the rate of change of a quantity over an interval
interpreted as the change of the quantity over the interval. (5.3)
* Basic properties of definite integrals (examples include additivity and
linearity). (5.4)
b. Applications of integrals
* Appropriate integrals are used in a varity of applications to model
physical, biological, or economic situations. (8.1-8.8)
c. Fundamental Theorem of Calculus
* Use of the fundamental Theorem ot evaluate definite integrals. (5.3)
* Use of the Fundamental Theorem to represent a particular antiderivative,
and the analytical and graphical analysis of functions so defined. (5.3)
d. Techniques of antidifferentiation
* Antiderivatives following directly from derivatives of basic functions.
(6.1-6.5)
* Antiderivatives by substitution of variables (including change of limits
for definite integrals). (7.1)
e. Applications of antidifferentiation
* finding specific antiderivatives using initial conditions, including
applications to motion along a line ( 7.1-7.8)
* Solving separable differential equations and using them in modeling (in
particular, studying the equation y'=ky and exponential growth). (11.1-11.11)
+ Solving logistic differential equations and using them in modeling. (11.7)
f. Numerical approximations to a definite integrals
* Use of Riemann sums (using left, right, and midpoint evaluation points)
and trapezoidal sums to approximate definite integrals of functions
represented algebraically, graphically, and by tables of values. (7.5)
4. Polynomial Approximations and Series
a. Concept of series. A series is defined as a sequence of partial sums,
and convergence is defined in terms of the limit of the sequence of partial
sums. Technology can be used to exlore convergence or divergence. (9.1,
9.2 & 9.3)
b. Serieis of constants
+ Motivating examples, including decimal expansion. (9.2)
+ Geometric series with applications. (9.2)
+ The harmonic series. (9.3)
+ Alternating series with error bound. (9.4)
+ Terms of series as areas of rectangles and their relationship to improper
integrals, including the integral test and its use in testing the
convergence
of p-series. (9.4)
+ The ratio test for convergence and divergence. (9.5)
+ Comparing series to test for convergence or divergence. (9.5)
c. Taylor series
+ Taylor polynomial approximation with graphical demonstration of
convergence.
(10.1, 10.2 & 10.3)
+ Maclaurin series and the general Taylor series centered at x=a. (10.2)
+ Maclaurin series for the functions e^x, sin x, cos x, and 1/(1-x). (10.2)
+ Formal manipulation of Taylor series and shortcuts to computing Taylor
series, including substitution, differentiation, antidifferentiation, and
the formation of new series from known series. (10.3)
+ Functions defined by power series. (10.2)
+ Radius and interval of convergence of power series. (10.2)
+ Lagrange error bound for Taylor polynomials. (10.4)
