***Guide to math placement and skipping levels of math***

Pre-College Issues High School Life
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Hello! I see posts pretty frequently about people wanting to skip math classes to get into a higher one and I thought I’d write a big ol’ master post as a person who’s in the process of this right now. Hopefully the things I’ve learned can be useful to others! For clarity, when I say “skip” I mean teaching yourself the material and/or taking a course outside of school.

OVERVIEW OF COURSES

First of all, let’s look at how math placement works in most schools. Unfortunately I don’t know how the “math I, II, III” sort of system works so this will be focused on algebra 1/2, precalc, geometry, etc.

The more or less typical flow goes: algebra 1 -> geometry -> algebra 2 -> precalc -> calculus. Sometimes algebra 1 and algebra 2 and geometry might be switched around, but it usually looks something like this. So, here are some things to know about each one, as relevant to skipping classes. Note that just because it’s a “good” course to skip does NOT necessarily mean that it’s going to be easy.

ALGEBRA ONE: Usually the first of these courses and usually taken in grades 7-9. Algebra 1 is typically very different from middle school math, if you haven’t taken this course already then you’ve probably only taken middle school math before. I don’t think there’s really any reason to skip this class, so I wouldn’t really advise anybody to try to skip it.

GEOMETRY: Typically taken in grades 8-10. Geometry is an odd course because people have very different experiences with it. For some this is a “joke class”, an easy A. However, some people who’ve glided through all their other math classes get stumped with geometry. Some kids who’ve struggled with math forever have an easy time with geometry. Geometry is typically one of the easiest classes to skip. Whether you /should/ skip it is another debate, but it’s possibly the easiest one to skip. If you are interested in skipping it, maybe try to teach yourself some skills before committing so you can get an idea which type of student you may be. Some schools will allow you to take geometry simultaneously with another math class, so this may be a good option for you.

ALGEBRA TWO: Typically taken in grades 9-11. It’s important to distinguish if your school teaches trig with algebra 2 or with precalc. Whichever includes trig, you probably don’t want to skip. Although this is actually the class that I tried to skip, it’s usually a poor choice to skip. This course usually covers a lot of material and moves quickly. While not impossible to skip, it’s not advised for most people. If you are going to skip it, my main advice would be not to try to shove it into a summer course. Most likely you’ll have to take a summer course in order to get credit, but I wouldn’t rely solely on this. Start teaching yourself the material during the school year before the summer.

PRECALCULUS: Typically taken in grades 10-12. If your school teaches trig with algebra 2 and not with precalc, this is probably one of the best courses to skip. In a lot of schools, precalculus builds heavily off of algebra 2 but with more challenging problems and aims to solidify the concepts you’ve learned. If you feel like you know your algebra 2 inside and out, precalc is probably a breeze. If you’re doing this course over summer then you should try to find out what your summer course will cover beforehand. If it’s mostly review then you should be fine without doing any prep, but if there’s a lot of new concepts it would be wise to get a head start.

CALCULUS AB AND BC: Typically taken in grades 11+. It’s important to note that different schools handle AB and BC in different ways. At some schools, AB is equivalent to calc I and BC to calc II, while at other schools BC is equivalent to calc I and II. In some schools BC students are expected to know AB already, so going straight to BC without AB requires skipping AB. In other schools, BC assumes you only know precalc and covers AB and BC material. Figure out which type your school is. I wouldn’t really suggest trying to skip either of these.

CONSIDERATIONS BEFORE SKIPPING*

Before trying to skip a class, thoroughly consider why you want to. Most colleges couldn’t care less if you take calc AB or calc BC your senior year. If you only want to impress colleges, there are better ways to invest your time.

It’s also important to look at if skipping will make you run out of math class that your high school offers. If you exhaust the options your school offers, then you have a few options:

  1. Higher level classes through community college. Consider if this is going to be feasible for you.
  2. Taking a “softer” math class, like statistics.
  3. Not taking a math class

If you choose 2 or 3, the year off from more rigorous math might leave you rusty when you next have to take a math class, so that’s another thing to consider.

HOW TO ACTUALLY SKIP A CLASS

The first step is to TALK WITH YOUR SCHOOL. Don’t be me and study for six months before being told that you can’t skip the class you’ve been studying. Find out what your school’s policy is. The sooner you do this, the better. If you still want to skip a course, be sure to go through all the proper channels to make sure your school allows it and you’ll still get all the credits you need and everything is taken care of.

If you’ve taken care of all that and you’ve got a plan in place, great! Here are some tips for getting the most out of your summer course/online course/whatever alternative you’re using.

  1. Treat it like a real class, not “just an online class”. Take good notes, and put in the effort to understand things you struggle with. Do plenty of practice problems.
  2. Get ahold of the textbook your school uses for the course you’re skipping and be sure to learn all the material in it (unless, of course, you know for sure that the course doesn’t stick to the book much).
  3. Take full advantage of all resources you have-- teachers, books, websites, even other students.

Some resources:
-Khan Academy
-PurpleMath (http://www.purplemath.com/modules/index.htm)
-Paul’s Online Math Notes (http://tutorial.math.lamar.edu)
-The Math Page (http://www.themathpage.com/Index.html)
-Math is Fun (https://www.mathsisfun.com)
-Life of Fred books (http://lifeoffredmath.com)

Wow, that was long! Hopefully some of this is useful to others. Feel free to add on to this or ask questions!

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Oh my gosh you win College Confidential with that.

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Thank you so much for this.

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I also generally don’t suggest skipping Algebra I/II, unless you already have a solid understanding of the material. If you take calculus or higher-level subjects without a firm elementary algebra background, you will be screwed. Literally.

I considered “high school geometry” a joke when I took it (and maybe I still do now) simply because it doesn’t go very deep, and its handling of “proofs” (i.e. “two-column proofs,” which no one in academia uses) is generally quite poor. Seems like a pretty skippable class to me.

As for pre-calculus, it is also a useful course, but my general impression is that the student doesn’t really understand what certain things are used for, or what their purpose is, until they take calculus or a more advanced subject. For example, why define e to be this random transcendental number that we use as the base of a logarithm? But in most cases, I don’t advise skipping pre-calculus unless you have already covered the topics previously.

If you have already exhausted the regular HS curriculum, I strongly suggest reading Richard Rusczyk’s article on the [calculus trap](Don’t Fall into the Calculus Trap).

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Thanks @awesomepolyglot and @Kelvin82 ! Glad I was able to help!

@MITer94 : Thanks for the additions! I agree with you, particularly on geometry and proofs. I definitely think there’s a value in doing proofs, but my geometry class didn’t go into enough depth for it to really be any different from any other part of the class. The precalculus course that I’ll be doing over summer is a bit of a joke tbh, it seems like algebra 2+vectors (although I suppose I am making the assumption that my algebra 2 course this year covers our entire textbook, which it may not).

I’ve read that article before and it’s definitely interesting. Actually,“If ever you are by far the best, or the most interested, student in a classroom, then you should find another classroom” pretty much sums up why I decided to accelerate. I think there’s huge value in learning discrete math or trying competition math or basically anything AoPS-related. I ought to do it, although at the moment I much prefer algebra and calc to discrete math.

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Yeah I skipped Geometry over the summer because I didn’t want to do proofs during the year, and I feel I made a great decision because algebra 2 is pretty simple after taking geometry.

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I placed one level ahead in math by taking a test in in middle school, so I can’t speak from experience of actually taking a course and taking a test to advance. Personally, geometry was extremely difficult. Even today, it’s hard for me to grasp geometry. Therefore, I wouldn’t recommend skipping it. Algebra II is probably the best math class to skip, because it is basically a review of Algebra I plus some pre-calc. Pre-calc is too important to skip, as it lays the basic foundation for calculus. I know this isn’t quite in line with OP’s viewpoint, but I wanted to include my two cents.

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What level of math would you recommend as a prerequisite to Discrete Math with Statistics and Probability?

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@photogeek Thanks for contributing! (That seems so sarcastic but I don’t mean it sarcastically). I don’t doubt that you’re right when it comes to your school, I think the parts where we “disagree” are just due to differences in our schools. As far as geometry goes, that’s why I recommend getting a taste of geometry before skipping it, because everyone will have a different experience with it. For me personally, skipping geometry would have been no problem in a “pass the test” way, but it would’ve been much harder for me to learn the details since I don’t really care about geometry as much.

As far as Algebra II goes, it varies by school. At my school, Algebra II doesn’t have very much review of Algebra 1 (that is, review without building on it) and introduces a ton of new topics. Precalc is basically Algebra 2 with some more depth and harder problems at my school.

I actually wanted to skip Algebra II but my school said that the course is too important and I absolutely cannot skip it, so as a compromise I was offered to take the two simultaneously (Algebra II and precalc) or do precalc over the summer. I’ll be doing precalc this summer so I technically haven’t skipped the class yet. Since I went back and forth about it with the school for so long and I would say my self study has been pretty successful (I’m acing algebra 2 trig atm, woo) I figured that I know enough to make this thread, lol.

TL;DR We’re probably both right, different schools do different stuff

@awesomepolyglot I really don’t know, if I absolutely had to guess then I’d say Algebra 2 (assuming this is a high school class, not college) since I know that’s a commonly suggested prereq for AP Stats but don’t quote me on that. Your school or whatever program you’d be taking the class with probably has a suggested prequisite or a list of topics to know. Maybe somebody else can chime in on this?

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I will love you forever thank you so much.

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@awesomepolyglot depends. If it’s at a high school level (which usually covers some elementary number theory, counting/combinatorics/probability, proof-writing etc.), an algebra II background is usually sufficient.

Many intro-level discrete math courses at the university level (e.g. 6.042 at MIT) may require calculus.

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Do you think I can skip Algebra 2 and precalculas over the summer? I’m a sophomore in geometry honors right now and am self studying Algebra 2. I actually passed the kids taking Algebra 2 honors this year (I find Algebra 2 easier than geometry). I’ve already told my councler but she said I should just skip precalculas next year which I don’t want to do since I came so far with Algebra 2. My councler told me to talk to my math teacher who is the head of the math department, but I didn’t want to talk to her until after I finish Algebra 2 since I might actually finish the course by April or May and start on precalculas.

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@FutureMathLegend What would your math classes for the next two years look like if you followed your counselor’s recommendation or if you skipped both?

I had the same idea of waiting until I was further along before talking to my school about skipping, and the result of this was that I had already taught myself a huge portion of it by the time my school told me that I was absolutely not going to be permitted to skip algebra 2/trig. So I wouldn’t really suggest waiting. Although I’m glad for the experience of teaching myself math and I wouldn’t change the past if I could, I’m really bored in my current class, so that’s something to consider.

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My school offers both AB and BC Calculas but I was going to try to get into BC calculas depending on how I do in precalculas over the summer and take math at a local college for my senior year.
Why didn’t your school allow you to skip of it was obvious that you were too advanced for algebra 2?

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I see, I think you should discuss this with your teacher because whether or not you should skip is irrelevant if you’re not allowed to.

My school has a restriction that you can only get 10 credits over summer and doing algebra 2/trig through summer school would count as 20 (10 for algebra 2, 10 for trig), even though the normal algebra 2/trig course is 10 credits. And one of the math teachers who’s the head of the math board or something similar said that algebra 2 is too fundamental to skip. She wasn’t my teacher so I wish I had a chance to demonstrate what I know, though.

My school did compromise with me though and agree to let me take precalculus this summer and take calc next year, so I get to the same place in the end.