An Easy But Impossible Probability Problem
I like looking a little deeper into problems; here we’ll find that although the problem is simple if you take it on its own terms, those terms are actually impossible. Does it matter?
Textbook errors
Assertions, Reasons, and Logic
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 …
Three HCF/LCM Problems
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.
Trouble with Transformations
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 …
A System of Exponential Equations
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.
How to Think Through Probability Problems
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.
Inverse Trig Problems With Unstated Restrictions
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 »
Pitfalls of Inverse Trig Functions
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.
Algebra Word Problems: Learning from Mistakes
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 Challenging Triangle Trigonometry Problem
(A new question of the week) Trigonometry identities can be hard to prove, and more so when they are specifically about a triangle.