Link to A.P. Calculus 15-16 Summer Assignment:

• A.P. Calculus 15-16 Pre-Assessment & Entrance Ticket

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:

• Course Syllabus, Expectations & Policies and Student/Teacher/Parent Contract
• Assignment Schedule for Marking Term #1
• Assignment Schedule for Marking Term #2
• Assignment Schedule for Marking Term #3

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: