Download Pre calculus Topics

AP Calculus Debriefing
Pre calculus Topics
Applying The Derivative
 Rational functions
 Finding Tangent/Normal Line Equations
 Exponential functions
 Corresponding characteristics of graphs of f and f'.
 Logarithmic functions,
 Relationship between the increasing and
 Trigonometric functions,
decreasing behavior of f and the sign of f'.
 Inverse trigonometric functions
 Critical Numbers
 Piecewise functions
 Absolute (global) and relative (local) extrema.
 The Conic Sections
 Rolle’s Theorem/Mean Value Theorem
 Know the values of the trigonometric functions for
 Concavity
 Points of Inflection
the common angles such as /6, /4, /3, /2, /3
 Relationship between the concavity of f and the
3/4,5/6, etc
sign of f". (Points of inflection as places where
 Continuity
concavity changes). .
 Optimization Word Problems
Limits
 Newton’s Method
 One-Sided Limits
 Related Rates
 Infinite Limits
 Limits as x approaches infinity
Finding Anti-Derivatives
 Finding Asymptotes Analytically,(vertical,
 Antiderivatives following directly from derivatives
horizontal and oblique)
of basic functions.
 Calculating limits using algebra/L’Hopital’s
 Differential Equations
 Estimating limits from graphs or tables of data.
 The Antiderivative of Inverse Trigonometric
Functions
Derivatives
 Inverse Trigonometric Functions
 The Limit Definition of the Derivative
 Integration by Parts
 Alternative Form of Derivative
 Integration by Partial Fraction
 The Power Rule
 Antiderivatives by substitution of variables
 Velocity & Acceleration
(including change of limits for definite integrals).
 The Derivatives of Sine and Cosine
 Finding specific antiderivatives using initial
 The Product Rule
conditions, including applications to motion along
 Second Derivatives
a line.
 The Quotient Rule
 Solving separable differential equations
 Chain RuleTrig
 Slope Fields
 Derivatives with the natural log (ln x)
 Derivatives with the natural exponential function
Applying the Definite Integral
(ex)
 Sigma Notation
 Implicit Differentiation
 The Trapezoidal Rule
 Logarithmic Differentiation
 Area and The Limit Process,
 Derivatives of logs or exponentals with other
 Average Value of a Function
bases
 Use of the Fundamental Theorem to evaluate
 Derivatives of Inverse Functions
definite integrals.
 Derivatives with Inverse Trig Function
 Second Fundamental Theorem of Calculus
 Differentiability and continuity.
Integration (Substituting /Changing Variable)
 Slope of a curve at a point.
 Riemann sums using left, right and mid-points
 Linear approximation.
 Interpretations and properties of definite integrals.
 Instantaneous rate of change
 Area between curves
 Average rate of change.
 Volume by Cross Sections (washers and/or discs)
 Approximate rate of change from graphs and
 Volume by Cross Sections (non circular)
tables of values.
 Volume by Shell
 Arc Length
AP Calculus Debriefing
Parametric & Vectors
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Finding Position Vector
Finding Velocity Vector
Finding Acceleration Vector
Finding slope
Finding tangent line
Finding second derivatiive
Finding Speed
Find arc length.
Other _______________________________
Sequences & Series
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Polar
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Finding whether a sequence converges
Finding whether a series converges
Finding the sum of a geometric series
Finding the sum of a telescoping series
Finding a radius of convergence
Finding the interval of convergence
Creating a Taylor Series
Find the derivative of a series
Find the antiderivative of a series
Finding the Error in approximation
Other:_____________________________
Finding Slope
Finding Tangent line
Finding area between two polar graphs
Finding are inside one polar graph
Find the limits of integration in order to find
Other:_____________________________
1. Which topics did you feel we over-prepared for? (That we spent too much class time on)
2. Which topics (besides series) did you feel unprepared for? (That we spent too little class time on)
AP Calculus Debriefing
3. Taking into account that we lost six class days due to snow, how could the course be better organized for
next year? What should I do if we run into so many snow days again next year/ what should I do if there
are fewer snow days? For example I was thinking of running Saturday Prep Session(s) of BC calculus
students during the first semester.
4. What would you tell incoming students to do to better prepare for the course? What do you wish you had
done differently? What worked really well for you?
5. Include any other comments you would like to make about the exam and/or the course. Your input will
help me make the course even better for the students taking it in the future.
I hope you all did very well and that each of you enjoyed this course as much as I have enjoyed teaching it.