AP Calculus BC Timeline

By tScarff
  • Basic Integration Review

    *Reviewed integrals
    *Reviewed mean value theorem for derivatives
    *Reviewed Mean Value Theorem
    *Reviewed the first and second fundamental theorems of calculus
    *Worked through multiple practice problems
    *Also worked with u-substitutions Practice problems were pretty easy. Glad to have review with u-substitutions.
  • Slope Fields, Euler's Method, Growth and Decay

    Slope Fields:
    - Determine if f(x) is a solution of a Differential Eq.
    - Construct part of a slope field
    - Determine correct slope field
    - Look for slope at axes Euler's (pron. Oiler's) Method:
    - Start with initial point (x0, y0)
    - Use appr. step size (delta x)
    - Find dy/dx
    - find dy (dy/dx * delta x)
    - new point is (x + dx, y + dy) NEED TO SEPARATE VARS. ALWAYS.
    Learned growth and decay formulas. Appreciated review of growth and decay functions.
  • Infinite Series

    *Reviewed different types of series
    * reviewed tests for convergence and divergence
    * reviewed difference between sequences and series Glad for review on the different tests, and on geometric series.
  • Taylor Series & Power Series

    Overview: Appreciated the review on LaGrange Error Bounds, but remembered most other stuff. Need to review power series for transcendental functions. *Taylor Polynomials are polynomial approximations of transcendental functions
    *Maclaurin Series = Taylor series centered at 0.
    *Actual Error: |Rn(x)| = |f(x) - Pn(x)|
    *LaGrange Error Bound: next derivative of z times (x -center) to the next power all over (n + 1)!
    - z = a convenient maximum error.
    - for example, use 1 for sin or cos
  • Period: to


    Tests to practice for the AP
  • Looked at practice exams

    Went over practice tests. Didn't do horribly, but could have done better.
  • Shell & Disk Methods

    Glad for review.
    Was pretty confident before, now I hope not to lose any points on questions involving these.
  • Advanced Integration Techniques

    Reviewed partial fractions and u-substitions. I had forgotten about some of the u-substitution tricks, and was glad for the review. remembered partial fractions pretty well.
    best of all... NO TRIG SUB ON TEST!

    Surprisingly easy. Had maybe 2 or 3 multiple choice questions on series and part of a free response involved the ratio test. Some integration and derivatives, but nothing too difficult. One problem was almost like exponential growth, but not quite. Will be very dissapointed if I recieve anything less than a 5.