Link to A.P. Calculus 15-16 Summer Assignment:
![](http://www.wlps.org/ckfinder/core/connector/cfm/connector.cfm?command=Thumbnail&type=Clipart¤tFolder=%2FSubjects%2Fmath%2F&langCode=en&hash=5A77D17426219003&FileName=math1.png)
A. P. Calculus AB
Course Objectives (Based on A.P. College Board Requirements):
Student will be able to:
- Understand and apply the concepts of limit, continuity, tangents, velocities & other rates of change
- Understand and apply the concept of a derivative in terms of limits and functions
- Recognize and apply differentiation rules including the product, quotient and chain rules
- Use implicit differentiation and find the derivatives of logs, exponentials and inverse trig functions
- Model, apply & interpret derivatives in real-world contexts such as related rates & optimization
- Represent first and second derivatives graphically and use them to analyze a function
- Understand and apply both parts of the Fundamental Theorem of Calculus
- Use limits, sequences and numerical methods to estimate the area under a curve
- Apply the Net Change Theorem to find quantities of change based on rates of change
- Recognize and apply integration techniques such as substitution method
- Use the substitution method to integrate exponential, logarithmic & natural log functions
- Use slope fields and integration methods to solve and interpret differential equations
- Apply/interpret integrals to find area between curves, volume of solid, & average value of functions
Scope and Sequence: (Based on A.P. College Board Approved Course Audit for 2014 - 15)
- Unit 1 – Limits, Tangents & Rates of Change – September (4 weeks)
- Unit 2 – Derivatives, Differentiation Rules & Related Rates – October/November (5 weeks)
- Unit 3 – Applications of Derivatives – Curve Sketching, MVT & Optimization – November/December (5 weeks)
- Unit 4 – Derivatives & Applications: Exponential, Log, Natural Log & Inverse Trig – January (2 weeks)
- MID TERM EXAM on Units 1 – 4: mid-January
- Unit 5 – Integrals & The Fundamental Theorem of Calculus – January/February (4 weeks)
- Unit 6 – Applications of Integrals: Areas, Volumes & Average Value – February (2 weeks)
- Unit 7 – Integrals & Applications: Exponential, Log, Natural Log & Inverse Trig – March (2 weeks)
- Unit 8 – Differential Equations, Slope Fields & Growth and Decay – March (2 weeks)
- REVIEW OF RELEASED AP EXAM ITEMS – April/May (4 weeks)
- Unit 9 – Integration by Parts, L’Hopital’s Rule, Cylindrical Shells, Partial Fractions – May/June (2 weeks)
Important Document Links:
Khan Academy Videos on Antiderivatives and Indefinite Integrals
Antiderivatives and indefinite integrals:
Khan Academy Videos on Indefinite Integrals of x raised to a power
Indefinite integrals of x raised to a power: