ap ab math

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Teaching Strategies

Applications

Chinese students, who are the main audience at the location of my school, have built a strong

foundation in algebra, geometry, trigonometry, and pre-calculus at this stage of their education.They experience little to almost no difficulty in understanding mathematical concepts. A second

textbook is added to provide students with more real-life applications which are commonly

ignored in local curriculum.

Calculator

y students use Casio fx-!"#$%&&.

'eferences

a(or textbook

'on, )arson. *ruce, +. dwards. Calculus of a Single ariable arly Transcendental /unctions,

#ed. *rooks0Cole, Cengage )earning, 1$22.

3ther textbook

*ill, Armstrong. 4on, 4avis. *rief Calculus, Solving 5roblems in *usiness, conomics, and the

Social and *ehavioral Sciences, 1ed. 5earson ducation Asia )imited, 1$$6.

A5 Calculus A* Course 3utline

Chapter 2 5reparation for Calculus

7September 8eek 29196:

5resenting a function verbally, numerically, analytically, and graphically

&ntercepts and symmetry of a graph

&ntroduction to mathematical models

Average rates of change

ssential functions linear functions, polynomials, power functions, rational functions,

algebraic functions, trigonometric functions, exponential functions, logarithmicfunctions, and inverse trigonometric functions

Concepts related to a function symmetry, odd and even functions, combinations of

functions, composite functions and inverse functions The use of a graphing calculator 2 graphing functions

Chapter 1 )imits and Their 5roperties



7September 8eek ; 3ctober 8eek 291:

Comparison of problem solving between without calculus and with calculus

&ntroducing the tangent line problem

&ntroducing the area problem

<nderstanding limits from a numerical table

<nderstanding limits from a graph

valuating limits analytically

2. *asic limits

1. )imit of a polynomial6. )imit of a rational function

;. )imit of a composite function

#. )imit of transcendental function Strategies for evaluating limits dividing out techni=ue, rationali>ing techni=ue, the

s=uee>e theorem, and limits involving trigonometric functions 3ne-sided limits

<nderstanding continuity from a graph 4ifferent types of discontinuity from a graph

/ormal definition of continuity

5roperties of continuity

The intermediate value theorem

<nderstanding infinite limits from a graph

ertical asymptotes

5roperties of infinite limits

Term Test 2

Chapter 6 4ifferentiation73ctober 8eek 69; ?ovember 8eek 291:

Approaching the slope from a graph

Approaching the slope as a limit

Calculating the derivative from the definition as a limit

<nderstanding of differentiability intuitively from a graph

<nderstanding differentiability formally as a limit

4ifferentiation rules

2. 4erivative of a constant function

1. The power rule6. The constant multiple rule

;. The sum rule

#. The difference rule@. The product rule

". The =uotient rule

. 4erivative of exponential functions!. 4erivative of logarithmic functions



2$. 4erivative of trigonometric functions

22. 4erivative of inverse trigonometric functions

21. The chain rule &mplicit and explicit relations

&mplicit differentiation

4erivatives of inverse functions 'elated rates

?ewtonBs method

The use of a graphing calculator 1 finding derivatives

Chapter ; Applications of 4ifferentiation

7?ovember 8eek 69; 4ecember 8eek 2:

Absolute maximum and absolute minimum

'elative maximum and relative minimum

Critical numbers 'olleBs theorem

The mean value theorem

&ncreasing and decreasing functions

The first derivative test

Concavity and points of inflection

The second derivative test

nding behavior of a function

2. )imits at infinity1. &nfinite limits at infinity

6. +ori>ontal asymptotes

Curve sketching and graph analy>ing Solving problems involving optimi>ation

4ifferentials

2. Tangent line approximations1. rror propagation

6. Calculating differentials

Term Test 1

Chapter # &ntegration

74ecember 8eek 1969; anuary 8eek 2:

Antiderivatives

*asic integration rules

&nitial conditions and particular solutions

Approximating the area of a plane region

<pper and lower sums

'iemann sums

4efinite integrals



5roperties of definite integrals

The fundamental theorem of calculus

The mean value theorem for integrals

Average value of a function

The second fundamental theorem of calculus

?et change theorem &ntegration by substitution

The trape>oidal rule

SimpsonBs rule

&ntegration involving logarithmic functions

&ntegration of trigonometric functions

&ntegration involving inverse trigonometric functions

The use of a graphing calculator 6 calculating integrals

Chapter @ 4ifferential =uations

7anuary 8eek 196:

%eneral and particular solutions

Slope fields

ulerBs method

&ntroducing differential e=uations

5opulation growth and decay

Separation of variables

+omogeneous differential e=uations

Applications wildlife population, finding orthogonal tra(ectories, modeling advertising

awareness, modeling a chemical reaction, modeling population growth, and modelinghybrid selection

)ogistic differential e=uation

/irst-order linear differential e=uations

*ernoulli e=uation

Term Test 6

Chapter " Applications of &ntegration

7anuary 8eek ; /ebruary 291:

Calculating the area between two curves

&ntegration as an accumulation process

/inding volumes

2. The disk method

1. The washer method6. Solids with known cross sections

;. The shell method

Arc length



Area of a surface of revolution

8ork done by a constant force

8ork done by a variable force

ass

Center of mass

Chinese ?ew Dear +oliday

7/ebruary 8eek 69;:

Chapter &ntegration Techni=ues, )B+opitalBs 'ule, and &mproper &ntegrals

7arch:

'eview of basic integration rules

&ntegration by parts

Tabular method

Trigonometric integrals

2. 5owers of sine and cosine

1. 5owers of secant and tangent

6. Sine-cosine products with different angles Trigonometric substitution

5artial fractions

&ntegration by tables

'eduction formulas

'ational functions of sine and cosine

&ndeterminate forms

2. $0$

1.∞∞ 0

6. $E∞

;.

∞

2

#. $$

@.∞−∞

)B+opitalBs 'ule

&mproper integrals

Term Test ;

Study onth for the A5 xam 7April:

5ro(ects

7ay 8eek 69; une 8eek 291: 7After the A5 xam:

Selected pro(ects from F*rief Calculus, Solving 5roblems in *usiness, conomics, and

Social and *ehavioral SciencesG



Course xamination

ap ab math

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