Finding a Locus: Algebra and Geometry

Last time we looked at the meaning of the concept of locus. This time, we’ll explore seven examples, from two students. We’ll look at both algebraic (equation) and geometric (description) perspectives.

Probability of Consecutive Numbers in a Lottery

A recent question about lottery numbers reveals that a seemingly special event is in fact surprisingly common: namely, the presence of consecutive numbers in a lottery drawing. The calculation is an interesting one, and we’ll also see a way to check our answer, then compare it to reality.

How to Think About the Product and Quotient Rules

Last time, we considered the Chain Rule for derivatives. This time, we’ll look at the product and quotient rules, focusing on how to keep the formulas straight, and make them easier to apply. We’ll look primarily at the quotient rule to start with, and then examine the product rule at the end.

How to Think About the Chain Rule

Having recently helped some students (in person) with the rules of differentiation, I’m reminded to do so here, starting with the chain rule. It is easy to make this topic look harder than it really is; the two main ways to state the rule are often confusing, and different approaches fit different problems. We’ll try …

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Slow and Fast Ways to Solve a Probability Problem

Last week’s discussion reminded me of another question, from July, about a probability problem that was solved in a hard (but educational) way and an easy way. This instance is more extreme, and, due to its length, requires extreme editing in order to fit here.

More On Mixing Trig Functions

I’ve had several occasions in face-to-face tutoring lately to refer to a past post on mixing (that is, composition) of trig and inverse trig functions. Several recent questions have touched directly or indirectly on this same general idea and extended it, so I thought I’d post them.