(New questions of the week) Two recent questions (five days apart, from high school students in different countries) were about nearly the same thing, and fit nicely together: What do you get when you square a square root, or take the square root of a square, but don’t know the sign of the number ahead …
Last time, we looked at some ideas about appropriate graph types, and the references I found put this in the context of identifying types of data. Here we’ll look at questions about two such classifications: nominal/ordinal/cardinal (with variants), and continuous/discrete. We’ll see that classifications can become distorted as they filter down from higher levels to …
Types of Data: Discrete, Continuous, Nominal, Ordinal, … Read More »
Graphs are used to display data. But sometimes we aren’t quite sure what sort of graph will best represent the data (or what kind of graph our teacher is expecting). We’ll look at a couple questions asking when a graph consisting of lines should or should not be used.
(A new question of the week) Trigonometry identities can be hard to prove, and more so when they are specifically about a triangle.
It’s been a while since we’ve done a puzzle, just for fun. Here we’ll look at two versions of a riddle, about finding children’s ages from a known product, a partially known sum, and a bizarre fact about the oldest. Then we’ll close with an interesting variation.
Looking for a cluster of questions on similar topics, I found several from this year in which monotonic functions (functions that either always increase, or always decrease) provide shortcuts for various types of problems (optimization with or without calculus, and also algebraic inequalities). We’ll look at a few of these.
Students sometimes wonder why the trigonometric functions (sine, cosine, tangent, secant, and so on) have the names they do, and how they relate to the corresponding terms in geometry. How are the tangent and secant functions related to tangent and secant lines in trigonometry? And what in the world is a sine? Here we’ll look …
Since we’ve been looking at an example of ambiguity in notation, let’s look at a very different one. There is a lot to be confused by in inverse trigonometry! We’ll try to untangle the notations of \(\sin^{-1}\) and \(\arcsin\).
This is the last of a series on our discussions, since I closed comments at the end of 2021, of Implied Multiplication First (IMF), the idea that multiplications written by juxtaposition, rather than with a symbol, are to be done before other multiplications or divisions. Last time, we saw that there is no “official” answer. …
This is part 2 of a series of extracts from discussions we have had on whether multiplication implied by juxtaposition is to be done before division (which I call IMF, for Implied Multiplication First). Some people write to us claiming that there is one official correct answer. Are they right?