Adapting 2021 BC 6

Nine of nine. We continue our look at the 2021 free-response questions. We will look at ways to adapt, expand, and explore this question to help students better understand it and look at other questions that can be asked based on a similar stem. 2021 BC 6 This is a Sequence and Series (Type 10)…

What’s the “Best” Error Bound?

A know a lot of people like mathematics because there is only one answer, everything is exact. Alas, that’s not really the case. Numbers written as non-terminating decimals are not “exact;” they must be rounded or truncated somewhere. Even things like  and 5/17 may look “exact,” but if you ever had to measure something to…

π from Collisions

  One of my sons sent me the link to the videos below. They show a very unusual way to find the digits of π. The problems and its two solutions show the connections and the interplay between mathematics and physics. The quality of the illustrations and the verbal explanations are excellent. Here are the…

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)…