AP AB Calculus (8 hours per week)

The Main Books Source:

Finney, Ross L., Franklin Demana, Bert Waits, and Daniel Kennedy. Calculus: Graphical,

Numerical, Algebraic. AP Edition. Fourth Edition. Pearson.2012

Supplemental Books Source:

S.P. Thompson Calculus Made Easy. Second Edition Enlarged. The Macmillan

Company, New York, 1943 (online version)

P. Dawkins. Calculus I. Complete Assignments Problems (online version)

P. Dawkins. Calculus I. Complete Notes (online version)

P. Dawkins. Calculus I. Complete Solution to Practice Problems (online version)

P. Dawkins. Calculus I. Complete Practice Problems (online version)

Course Revision:

Shirley O. Hockett, M.A. and David Bock, M.S. Barron’s AP Calculus 2008 with

CD-ROM, 9th edition.

Week Chapter Contents Critical Thinking

Questions

1

L1-2 Chapter 1.

Sections 1.1-1.3.

Prerequisites for

Calculus pp.3-28

L3-4 Chapter 1,

Section 1.4

Prerequisites for

Calculus pp.29-35

L5-6 Chapter 1

Section 1.5-1.6

Prerequisites for

Calculus pp.36-54

Lines. Increments. Slope of a line.

Parallel and perpendicular lines.

Equations of lines. Applications.

Functions and graphs. Functions.

Domain and ranges. Viewing and

interpreting graphs. Even and odd

functions – symmetry. Functions defined

in pieces. Absolute value function.

Composite function.

Exponential functions. Exponential

grows and decay. Applications. The

number .

Parametric equations. Relations. Circles.

Ellipses. Lines and other curves.

Functions and logarithms. One-on-one

functions. Inverses. Finding Inverses.

Logarithmic functions Properties of

logarithms. Applications.

1.1—p. 9-11, #40,

42, 49, 52, 53

1.2—p. 18-21,

#31, 41-48, 54, 71

1.3—p. 26-28,

#13-28, 38-39,

#40–42

1.4—p. 33-35,

#1–4 35, 36, 44

1.5—p. 42-44,

#1–12 50, 51

2.

3.

L7-8 Chapter 2,

Section 2.1 Limits

and Continuity

pp.59-77

L1-2 Chapter 2,

Section 2.2 Limits

and Continuity

pp.59-77

L3-4 Chapter 2

Section 2.3 Limits

and Continuity

pp.78-97

L5-6 Chapter 2

Section 2.4 Limits

and Continuity

pp.78-97

L7-8 Chapter 3

Section 3.1

Derivatives

pp.99-108

L1-2 Chapter 3

Section 3.2

Derivatives

pp.109-115

L3-4 Chapter 3

Section 3.3

Derivatives

pp.116-126

L5-6 Chapter 3

Section 3.4

Derivatives

pp.127-140

Trigonometric functions. Radian

measure. Graphs of trigonometric

functions. Periodicity. Even and odd

trigonometric functions. Transformation

of trigonometric graphs. Inverse

trigonometric functions.

Rates of change and limits. Average and

instantaneous speed. Definition of limit.

Properties of limits. One-sized and

two-sized limits. Sandwich theorem.

Limits involving infinity. Finite limits as

. Sandwich theorem revisited.

Infinite limits as . End behavior

model. “Seeing” limits as

Continuity. Continuity at a point.

Continuous functions. Algebraic

combinations. Composites. Intermediate

value theorem for continuous functions.

Rate of change and tangent lines.

Average rates of change. Tangent to a

curve. Slope of a curve. Normal to a

curve. Speed revisited.

Derivative of a function. Definition of a

derivative. Notation. Relation between

graphs of and . Graphing the

derivative from data. One-sided

derivatives.

Differentiability. How might fail

to exist. Differentiability implies local

linearity. Differentiability implies

continuity Intermediate value theorem

for derivatives.

Rules for differentiation. Positive

integer powers, multiples, sums and

differences. Products and quotients.

Negative integer power of . Second

and higher other derivatives.

Velocity and other rate of change.

Instantaneous rates of change. Motion

along a line. Sensitivity to change.

Derivatives in economics.

1.6—pp. 51-54,

#11–14; 24, 41,

42

2.1—pp. 66–69,

#44; 45–50, 56

2.2—pp. 75–77,

#9-12; 27-34;

53, 54

2.3—p. 84-86,

#25-30; 50; 52

2.4—pp. 92–95,

#9–12; 15-18;

31; 38

3.1–pp.105-108

#5-8; 23, 30, 32

3.2–pp. 114-115

#5-10; 31-37;

3.3–pp. 123-126

#15-22; 38; 46;

48

3.4–pp. 135-140

#3; 9; 13; 19;

26; 33; 35

L7-8 Chapter 3

Section 3.5

Derivatives

pp.141-147

Derivatives of trigonometric functions.

Derivative of sine function. Derivative

of cosine function. Simple harmonic

motion. Jerk. Derivatives of other basic

trigonometric functions.

3.5–pp. 146-147

#1-10 odd;

17-20; 32; 37

4.

5.

L1-2 Chapter 4:

Section 4.1: More

Derivatives

pp.153-161

L3-4 Chapter 4:

Section 4.2 More

Derivatives

pp.162-169

L5-6 Chapter 4:

Section 4.3 More

Derivatives

pp.170-176

L 7-8 Chapter 4:

Section 4.4 More

Derivatives

pp.177-185

L1-2 Chapter 5:

Section 5.1

Application of

derivatives

pp. 191-199

L3-4 Chapter 5:

Section 5.2

Application of

derivatives

pp. 200-208

Chain rule. Derivative of composite

function. “Outside-inside” rule.

Repeated use of the chain rule. Slopes of

parametrized curves. Power chain rule.

Implicit differentiation. Implicitly

defined functions. Lenses, tangents and

normal lines. Derivatives of higher order.

Rational order of differentiable

functions.

Derivatives of inverse trigonometric

functions. Derivative of inverse

functions Derivative of the arcsine.

Derivative of the arctangent. Derivative

of the arcsecant. Derivative of other

three trigonometry functions.

Derivatives of exponential and

logarithmic functions. Derivative of

Derivative of Derivative of

Derivative of . Power rule for

arbitrary real power.

Extreme values of functions. Absolute

(global) extreme values. Local (relative)

extreme values. Finding extreme values.

Mean value theorem. Mean value

theorem. Physical interpretation.

Increasing and decreasing functions.

Other consequences

4.1—p. 158-161,

#9-12; 33-38;

50; 64

4.2—p. 167-169,

#27-30, 45; 58

4.3—p. 175-176,

#20-22; 23-25,

30

4.4—p. 183-185,

#29–32, 51-53

5.1—p. 197-199,

#5-10, 35-42

5.2—p. 206-208,

#7-8, 11; 43-45

6.

7.

L5-6 Chapter 5:

Section 5.3

Application of

derivatives

pp. 209-222

L7-8 Chapter 5:

Section 5.4

Application of

derivatives

pp. 223-236

L1-2 Chapter 5:

Section 5.5

Application of

derivatives

pp. 237-249

L3-4 Chapter 5:

Section 5.6

Application of

derivatives

pp. 250-259

L5-6 Chapter 6:

Section 6.1 The

definite integral

pp. 267-277

L7-8 Chapter 6:

Section 6.2 The

definite integral

pp. 278-288

L1-2 Chapter 6:

Section 6.3 The

definite integral

pp. 289-297

L3-4 Chapter 6:

Section 6.4 The

definite integral

pp. 298-309

Connecting and with the

graph of First derivative test for

local extrema. Concavity. Points of

inflection. Second derivative test for

local extrema. Learning about functions

from derivatives.

Modeling and optimization. Examples

from mathematics. Examples from

business and industry. Examples from

economics. Modeling discrete

phenomena with differentiable

functions.

Linearization and Differentials. Linear

approximation. Differentials. Estimating

change with differentials. Absolute,

relative and percentage change.

Sensitivity to change. Newton’s

method.

Related rates. Related rate equations.

Solution strategy. Simulating related

motion.

Estimating with finite sums. Distance

traveled. Rectangular approximation

method (RAM). Volume of a sphere.

Cardiac output.

Definite Integral. Reimann sums.

Terminology and notation of

integration. Definite integral and area.

Construct functions. Discontinuous

integrable functions

Definite integrals and antiderivatives.

Properties of definite integrals. Average

value of functions. Mean value

theorem for definite integrals.

Connecting differential and integral

calculus.

Fundamental theorem of calculus.

Fundamental theorem, part 1.

Graphing the function

Fundamental theorem, part 2. Area

connection. Analyzing antiderivatives

5.3—p. 218-222,

#11–12, 21, 23;

31; 41-42; 47

5.4—p.230-236

#7-9; 19; 28; 31;

45; 48-49

5.5—p. 246-249,

#27-30; 41;

51-52

5.6—p. 255–259,

#7; 13; 19; 22;

31-32; 34-35

6.1—p. 274–277

#15-16; 22; 26;

29

6.2—p. 286–288,

#33, 34, 57, 58

6.3—p. 294-297,

#3; 6; 15; 37-38;

40-41

6.4—p. 306-309,

#25-26; 45-48;

58-59

8.

L5-6 Chapter 6:

Section 6.5 The

definite integral

pp. 310-318

L7-8 Chapter 7:

Section 7.1

Differential

equations and

mathematical

modeling

pp. 325-335

L1-2 Chapter 7:

Section 7.2

Differential

equations and

mathematical

modeling

pp. 336-344

L3-4 Chapter 7:

Section 7.3

Differential

equations and

mathematical

modeling

pp. 345-353

L5-6 Chapter 7:

Section 7.4

Differential

equations and

mathematical

modeling

pp. 354-365

L7-8 Chapter 7:

Section 7.5

Differential

equations and

mathematical

modeling

pp. 366-375

graphically.

Trapezoidal rule. Trapezoidal

approximations. Other algorithms.

Error analysis.

Slope fields and Euler’s Method.

Differential equations. Slope fields.

Euler’s method.

Antidifferentiation by substitution.

Indefinite integrals. Leibniz notation

and antiderivatives. Substitution in

indefinite integrals. Substitution in

definite integrals.

Antidifferentiation by parts. Product

rule in integral form. Solving for the

unknown integral. Tabular integration.

Inverse trigonometric and logarithmic

functions.

Exponential grows and decay.

Separable differential equations. Law of

exponential change. Continuously

compounded interest. Radioactivity.

Modeling grows and other bases.

Newton’s law of cooling.

Logistic grows. How populations grow.

Partial fractions. The logistic differential

equation. Logistic grows model.

6.5—p. 316-319

#9-10; 19; 29-30

7.1—p. 331–335

#21, 23, 25, 28;

41-46; 64-65

7.2—p. 342–344

#35-40; 60-66;

69-70

7.3—p. 350–353

#17-20; 21-24;

35

7.4—p. 361–365

#22-23; 27-28;

40-43

7.5—p. 373–375

#15-18; 19-22;

34-38