Type 1 Questions: Rate and Accumulation

The Free-response Questions There are ten general categories of AP Calculus free-response questions. As I’ve done in part years, I will consider each individually over the next few weeks posting on Tuesdays and Fridays. These will be updates of last year’s posts. Here is the list of the types and the schedule: Tuesday March 5, 2019…

Power Series 2

This is a BC topic Good Question 16 (11-30-2018) What you get when you substitute. Geometric Series – Far Out (2-14-2017) A very interesting and instructive mistake Synthetic Summer Fun (7-10-2017) Finding the Taylor series coefficients without differentiating Error Bounds (2-22-2013) The alternating series error bound, and the Lagrange error bound The Lagrange Highway (5-20-15)…

Power Series 1

This is a BC topic POWER SERIES (Maclaurin series and Taylor series) Introducing Power Series 1 (2-8-2013) Making better approximations Introducing Power Series 2 (2-11-2013) Graphing and seeing the interval of convergence Introducing Power Series 3 (2-13-2013) Questions pointing the way to power series Graphing Taylor Polynomials (2-7-2017) Using a graphing calculator to graphs Taylor…

Sequences

This is a BC topic. SEQUENCES Everyday series (1-17-2017) The most familiar series: Numbers Amortization (2-9-2015) An important use of a (finite) series – Find you mortgage payment without calculus. Convergence Test List A summary of the tests. Download and copy for your students (and yourself) Which Convergence Test Should I Use? Part 1 (2-9-2018)…

Parametric Equations and Vectors

In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail and an outline of the topics. (only 3 items here) Motion Problems: Same Thing Different Context (11-16-2012) Implicit Differentiation of Parametric Equations (5-17-2014) A…

Differential Equations 1

Past posts on differential equations Differential Equations (1-5-2015) The basics and definitions. Domain of a Differential Equation (4-7-2017) notes and examples on finding the domain of the solution of a differential equation. (Updated thru the 2018 exam.) Slope Fields (1-9-2015) Graphical solutions: The solution is lurking in the slope field. Euler’s Method (1-12-2015) Numerical solutions (BC…

Applications of Integration – Accumulation 2

Happy New Year ! A few more links to posts on accumulation. Painting a Point (2-4-2013) Paint often and the paint accumulates. Good Question 6: 2000 AB 4 (8-25-2015) Accumulation Good Question 8 – or not? (1-5-2016) Accumulation Density (1-10-2017) Accumulation and Differential Equations  (2-1-2013) Solving differential equations without the “+C“  Review Notes: Type 1 Questions:…