As an alien to the US education system, I am always completely confused by these 'pre-' course designations. What on earth is 'pre-trig' or 'pre-calc'? I mean, I got all the way up to undergraduate level in mathematics and I never needed to learn 'pre-' anything.

They're not always required, but they try to bridge what you already know (or are supposed to know) with what is to come and move at a slower pace. It's also sometimes like an extra option for the less mathematically inclined who are still required to take such a number of math courses. On the other hand the only 'pre-' course I ever took (I tested out of pre-algebra somehow) was 'pre-calculus with honors'. I don't remember it much but I think it was mostly reviewing the harder topics from intermediate algebra aka 'algebra 2', which included trig (no separate trig course in my system), introduction to limits, and toward the end differentiation and maybe discrete summation. The 'honors' variant was also geared toward students who were planning on taking the more comprehensive 'AP Calculus BC' variant rather than the 'AB' variant.

There's a difference between AP calculus in Alberta and British Columbia? :)

Yes. In Alberta, all you care about is the rate of change of the the price of oil and computing the volume of manure, so only the basics about derivatives and integrals are needed. In British Columbia, you have to worry about how to fit your oddly-shaped modern furniture into your tiny Vancouver apartment and find the region of convergence for your mortgage, so more advanced techniques are necessary.

Hadn't thought of it like that before. :) A bit more usefully than the "one is harder one is easier" distinction, you can kind of think of the letters corresponding to semesters in a college course. A would be an introductory level (and possibly the only exposure a student might get if they're not interested in math but have to take a course), B would be a semester of Calculus 1, and C would be a semester of Calculus 2. Since high school the class goes year round you're still at a slightly slower pace than college, but if you do well on the AP BC test at the end many colleges will waive Calc 1 and Calc 2 from your requirements, whereas the AB test would only let you waive Calc 1. (A few other AP tests have different letter levels -- for physics only the C level seems to count and that's just basic Newtonian physics with very little calculus, though there is an optional E&M portion I never got to that may approach the Maxwell equations by the end... For computer science they used to have an A and an "AB", but they've dropped the "AB" since I took it. The "AB" basically got into actual algorithms and data structures, the A portion was basic programming and OOP heavy. All in Java.)

Just in case you didn't know calculus BC is considered the harder AP calculus while AB is considered the easier.

So I went to school in a country that is notorious for forcing kids to specialize early - the UK. In my age cohort, at age sixteen we had to pick just three subjects to study for the next two years. I chose 'pure and applied mathematics' as one of those three subjects. Some people chose 'pure mathematics' and 'applied mathematics' as Two of their subjects. I guess, vaguely, that doing the expanded applied maths would have included more calculus (not sure what that might have entailed - more second order differential equation stuff maybe?) - but there was definitely no point where I was faced with the choice of 'should I do a bit of calculus, or a lot of calculus?'. 16 year olds are not good at knowing how much calculus they need to learn. I was pretty happy just choosing 'do I want to learn some mathematics, no mathematics, or a lot of mathematics?' - and leaving it up to the school to figure out how much calculus to include. Based on my career since, the amount of calculus included was, it turns out, 'enough'.

Worth noting that the Scottish education system is different - people do 5 or 6 highers at 16/17 and those are used for university entrance rather than 3 A-levels at 17/18.

Scottish first degrees are 4 years rather than 3 in England - presumably to allow for this.

The idea of a "pre-" course is that you cover ideas needed for the later course. For example, a "pre-calc" course typically covers the sort of algebra that you would need in calculus but not actually integrating or differentiating anything. It's a matter of naming. You could call it "Algebra II" or "pre-calc".

I'm already baffled by the distinction between algebra, trig, and calculus.

Where I live, it was just called 'math'. The first time I encountered algebra was in university, and that started with groups (a set and an operation on pairs of items in the set)

As to the 'pre': I have a masters in math, and lots of what we did was in some sense pre.

For example, calculus on real variables showed you how to define differentiation and integration and how to rigorously prove lost of theorems (pro tip: if you can't make heads or tails of an exam question, at least write down "let epsilon > 0")

Next, we basically went through the same set of theorems but in multiple dimensions, but showed that those rigorous proofs had glaring holes, but hey, now you know better. Also: infinities are weird (pro tip: the area under a 2D curve can depend on the order in which you add up its parts).

Next, calculus on complex numbers extended that and showed that those rigorous proofs had glaring holes, but hey, now you know better (pro tip: every contour integral you compute at an exam has a value of plus of minus 2n pi, with n typically being plus or minus one)

For math majors, the next step was measure theory: that definition of integration we started with? Forget it. Lebesgue came up with something that's better. And by the way, those proofs we told you about have glaring holes (let's spend a few hours proving that cutting a rectangle across a diagonal gives you two parts that each have half the rectangle's area). A few of the functions that we proved cannot not be integrated can be, if you use this new definition of how integration works.

That seems a waste of time, but I don't think it is. Very few people can jump in at the deep end and survive; the first iterations are necessary to prepare one's mind for the next steps.

Given the above, I think you will have had various 'pre-' things, even though they weren't named so.

Same experience here. I went to international school, so I often ended up with American friends who'd talk about Algebra 1/2/3, pre-calc, trig, geometry, etc.

Makes no sense to me. All those things are related. There's a picture that shows you why Pythagoras' Theorem is true. And why the difference of two squares is never prime.

You'll have had a whole summer holiday between trig and algebra if they're separate things. Surely they are taught as a kind of whole?

Did you learn all of K-12 math in one year? Which year?

You certainly can't learn it as separate things. I had classes called "Mathematics" every year, all the way to the end of high school.

Got a bit more separate at university, but not really.

"pre-trig" doesn't exist most anywhere.

"pre-calculus" is whatever isn't covered in intro to algebra and geometry, but needed for differentiation and integration:

https://www.khanacademy.org/math/precalculus

* Trigonometric equations and identities

* Conic sections

* Vectors

* Matrices

* Imaginary and complex numbers

* Sequences, series and induction

* Probability and combinatorics <-- more of a side topic, usually.

I tried to post this yesterday but was getting rate-limited.

After Geometry we had Algebra 2 (quadratics, etc.), then Advanced Math (trig, pre-calc). To my detriment I made up "pre-trig" to illustrate being thrust back into a cold curriculum after (what I felt were) warmer concepts in Geometry.