Good Questions

Links to posts about good questions; or at least some that I like. Some are from past AP Calculus exams other from elsewhere.

Difficult problems and Why We Like Them

A Problem with 4 Solutions and 2 Morals

My Favorite Function A pre-calculus question on finding roots and why calculators can’t do this one.

At Just the Right Time – an easy question preparing for finding the tangent line to a graph.

Good Question 2008 AB 6 Extreme values, limits. L’Hospital’s Rule

Good Question – 2 2002 BC 5 Slope fields and differential equations and Good Question 2 Continued.

Good Question – 3 1995 BC 5 Using a graphing calculator to investigate a family of functions.

Good Question – 4 2008 AB multiple-choice #10 Riemann sums

Good Question – 5 1998 AB2/BC2 The correct use of infinity and DNE; solving a calculus question without calculus.

Good Question – 6  2000 AB 4

Good Question – 7 2009 AB 3 The Mighty Cable Company

Good Question  – 8 or not  On units of an integral

Good Question – 9 Related Rates

Good Question – 10 – The Cone Problem

Good Question – 11 Riemann Reversed

Good Question – 12 Parts with a Constant?

Good Question – 13 Same integral, four ways to handle it.

Good Question -14  The Integral Test

Good Question – 15 2018 BC 2(a) Units

Dominance and Far Out A really fun limit to investigate after student know how to find extreme values and points of inflection.

A Challenge question comparing the disk and washer method for volume and its solution.

Lin McMullin’s Theorem A sighting of the Golden Ratio in the points of inflection of any quartic polynomial.

More Gold another sighting of the Gold Ratio in cubic polynomials by David Tschappat

Variations on a Theme by ETS. 2008 AB 9 adapting an extreme value question.

The Marble and the Vase Extreme Values


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