AP Calculus - AB Syllabus Course Overview Textbook(s ...

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"straightens out". They will then be asked to explain the significance of this.1. Local linearization2. Tangent line approximation3. DifferentialsF. Particle motion, Position, velocity, acceleration, and jerk. We will explore this concept using a CBL(Calculator Based Labratory) attached to a graphing calculator, and have the students be the particle.G. Economics1. Marginal cost2. Marginal revenue3. Marginal profitH. Related RatesMIDTERM EXAMUnit 4: The Definite Integral (3–4 weeks)A. Approximating areas – Students will a Riemann Sums program on the calculator to visualize exactlywhat a Riemann sum is. The will then be asked to explain the differences between the four types.1. Riemann sumsa. Left sumsb. Right sumsc. Midpoint sumsd. Trapezoidal sums2. Definite integralsB. Properties of Definite Integrals1. Power rule2. Mean value theorem for definite integralsC. The Fundamental Theorem of Calculus1. Part 12. Part 2Unit 5: Differential Equations and Mathematical Modeling (4 weeks)A. Slope FieldsB. Antiderivatives1. Indefinite integrals2. Power formulas3. Trigonometric formulas4. Exponential and Logarithmic formulasC. Separable Differential Equations1. Growth and decay2. Slope fields (Resources from the AP Calculus website will be liberally used.)3. General differential equations4. Newton’s law of coolingD. Logistic Growth
Unit 6: Applications of Definite Integrals (3 weeks)A. Integral as net change1. Calculating distance traveled (particle motion)2. Consumption over time3. Net change from dataB. Area between curves1. Area between a curve and an axisa. Integrating with respect to xb. Integrating with respect to y2. Area between intersecting curvesa. Integrating with respect to xb. Integrating with respect to yC. Calculating volume1. Cross sections2. Disc method3. Shell methodUnit 7: Review/Test Preparation (Approximately 2– 4weeks)A. Multiple-choice practice (Items from past exams—1997, 1998, and 2003are used as well as items from review books.)1. Test taking strategies are emphasized2. Individual and group practice are both usedB. Free-response practice (Released items from the AP Central website are used liberally.)1. Rubrics are reviewed so students see the need for complete answers, written in full sentences.2. Students collaborate to formulate team responses3. Individually written responses are crafted. Attention to full explanations is emphasized.Unit 8: After the exam…A. Review of the AP exam and try to identify points that students felt confident with or points thatstudents felt they needed more work with. This will help strengthen those points before studentsgo to college, as well as help me adjust the course for next year.B. Students will be required to do and present projects designed to incorporate this year’s learning inapplied ways. Projects can be of the students own choosing with teacher approval or chosen fromone of the following sources.MAA Notes. Resources for Calculus Collection. , D.C.: MAA, 1993.Volume 3: Applications of Calculus, edited by Philip Straffin. MAA Notes Number 29.Volume 4: Problems for Student Investigation, edited by Michael B. Jackson and John R.Ramsay. MAA Notes Number 30.Volume 5: Readings for Calculus, edited by Underwood Dudley. MAA Notes Number 31.
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AP Calculus - AB Syllabus Course Overview Textbook(s ...

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