Over the years, we have received several questions about problems that give an “assertion” and a “reason”, and ask you to decide whether each is true, and also whether the latter is “the correct explanation” (that is, a valid reason) that the former is true. These can involve subtle reasoning, and subtle errors. Since some …
Let’s look at three similar questions we’ve received about Least Common Multiples, Greatest Common Factors, and so on, starting with a recent question and going back in time. We’ll see a bad question, a good question, and an interesting challenge.
Having looked into our explanations of transformations and symmetry, over the last weeks, let’s turn to the recent questions that triggered this series. Here we have an adult studying the topic from a good book, but tripping over some issues in the book. We’ll be touching on some topics we haven’t yet looked at, such …
What do you do when you are given a problem that starts with a “lie” and ends with a wrong answer? We’ll go in several directions with this problem, a system of two exponential equations in two variables.
It’s been a while since we’ve looked at probability. Here, we’ll look at three questions that we received last year. In each case, we have to detect an error! They’re good examples of what can go wrong, and what to do when your answer appears to be wrong.
Here are a pair of problems related to the last of the three we looked at last time, involving inverse trigonometric function identities with subtle issues. They were probably intended to be rather simple problems (though going beyond what I typically see in American classes) by ignoring the subtleties, but if you approach them as …
Inverse Trig Problems With Unstated Restrictions Read More »
A couple recent questions involved errors made both by students and by the authors of their textbooks, involving trigonometric or inverse trigonometric functions. These offer some good lessons in pitfalls to be aware of.
A recent series of questions from an insightful high school student about word problems, provided a number of opportunities to discuss how to find and correct your mistakes – or the book’s! We’ll look at five.
(A new question of the week) Trigonometry identities can be hard to prove, and more so when they are specifically about a triangle.
(A new question of the week) Last week we looked at how the adjugate matrix can be used to find an inverse. (This was formerly called the [classical] adjoint, a term that is avoided because it conflicts with another use of the word, but is still used in many sources.) I posted that as background …