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

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:



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