(A new question of the week) We have had a number of challenging questions about inequalities recently. I want to show one of those here, because it involved a useful discussion about how to prove them. A proof problem Here is the question: Q) Show that a^4 + b^4 >= (a^3)b + (b^3)a for all …
(A new question of the week) A recent question about probability has ties to Venn diagrams, tables, and Bayes’ Theorem. Questions about answering multiple-choice questions are common; this one offers a twist that provided opportunity to discuss several important concepts. Here is the initial question, from August: On a multiple choice question, only one answer is …
(A new question of the week) Since we’ve been doing a little trigonometry this week, let’s look at a recent set of questions from a student in the Philippines, all about compositions of trig and inverse trig functions. This is a topic with some interesting little surprises, and several of us answered, to give a …
(A new question of the week) I mentioned that we have had a number of questions related to Venn diagrams recently. Here I would like to show a couple of these, from a Philippine student. Even fluent English speakers can get confused in these problems; observing how a student new to the language misinterprets details …
(A new question of the week) Sometimes we give only minimal help on a question, to let a student puzzle over the problem and learn to figure it out herself. That may be enough, or we may go back and forth for some time, guiding her thinking until she finds the answer. In the latter …
(A new question of the week) In many areas of math, an answer can come in several forms, which can make it hard to know if you are right when you compare your answer to the answer in the back of the book. Even worse is when the problem is multiple-choice, and your answer has …
(A new question of the week) A recent question about an old puzzle leads to multiple references to our archive.
(A new question of the week) In Monday’s post about fallacies in calculus, one of them used the definition of the derivative (or rather, misused it). Today we’ll look at a short question about applying that same definition, that came in last month.
(A new problem of the week) We usually look here at problems or concepts that are relatively basic and generally applicable; that could give a wrong impression of the kinds of questions we get. Here I want to show a recent example of a discussion about a problem, related to a geometric figure called the …
Sometime soon I will do a series of posts on word problems, which are a common point of difficulty with students. But here is one recent example from a high school student, where language was the main difficulty, but the algebra is worth discussing as well. We’ll look a little more deeply into the problem …