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Quadratics, equilibrium, and AP Chemistry

October 06, 2020

Here’s a common question that I was asked once again today;

Adrian, why do some of your materials point to equilibrium problems that contain the need for quadratic equations, when we know that type of math will not be tested on the AP chemistry exam?

In other words, how do quadratics, equilibrium, and AP chemistry intersect? It’s a fair question, and it has multiple answers.

The ‘common knowledge’ that has been in the AP chemistry zephyr for an eternity is that ‘quadratics cannot be examined’. Somewhat interestingly, and typically, the College Board remains largely silent, and (officially) non-committal on the matter, at least in a formal, definitive sense. Those of use that watch the College Board closely know that this is typical, as well as being unhelpful. For example, there is no formal ‘ruling out’ of quadratics in the current CED, nor can I find any official declaration of quadratics being ruled out by an official College Board source ever being in place – not in previous CED’s or in any other document. If you know where an official word on this is (I’m not much interested in hearsay or anecdotal evidence), please let me know, but also quote me the source of your knowledge.

You may be surprised to learn that there’s a document called Quantitative Skills in the AP Sciences (2018) that is frankly hardly known by any AP Chemistry teachers. Oddly, but again in classic CB website impenetrable style, that link omits the AP chemistry chapter, and one has to do some URL parsing to find it here. Despite being potentially ‘out of date’ (written prior to the current CED), it too has no mention of quadratics (either in the positive or the negative), so who knows what the actual policy is here?

Having said all of that, I am on board with the idea of quadratics being 100% out for exam purposes for reasons that include no examples of them in contemporary exams, and their exclusion being in keeping with the idea that the AP chemistry exam should be examining chemistry not math skills. So why have quadratic examples in my materials at all?

Firstly, when a quadratic comes up, I never ask the students to solve for it, but given my obsession with all things AP chemistry I don’t feel as though the SET-UP that includes a quadratic is out of bounds. The set-up only requires chemistry knowledge, and as such I suppose, *could* be asked (yes, I know it’s highly unlikely, but …).

Secondly, (and this is perhaps even more unlikely, but the kind of thoroughness that makes me tick), there could, in theory, be a quadratic that is a perfect square, that would NOT require the quadratic formula and a bunch of complicated math. This happened in 1995. Is an exam from 1995 relevant? Well, coupled with the lack of an official word form the CB on this, and since I like watertight situations that cover ALL bases, for now, those examples stay in my materials.



  1. Anonymous

    Quadratics are a part of traditional equilibrium (and even some harder stoichiometry) problems. Why is AP changing their course versus a traditional college course? Isn’t the whole point of AP to ape a college class? Not to pave their own way?

    -AP chem 1982 student

    • Adrian

      I don’t think it’s at all clear if AP Chemistry has ever really, successfully “mimicked a college course”. I mean, how could it with such diversity across colleges, and perhaps more importantly, what’s the point of it attempting to do that anyway? I’ve always been confused by the idea of, “doing college work in high school”. It seems pointless to me; that’s what college is for! AP should simply be the gold standard for high school work, then, when you get to college, you do “the college work”. On one hand I DO understand what’s going on here since the American system is painfully inefficient, because that’s what generates $$$ for the colleges and the CB.

      As for quadratics specifically, the argument (that I somewhat agree with) is that the AP Chemistry exam should be examining chemistry, not math. Fair enough, but as I’ve said before, it’s also true that the AP chemistry course has almost totally abandoned inorganic, and organic, and is essentially a physical chemistry course, anyway. The whole system needs a massive overhaul and re-think IMO.

  2. Grant Colijn

    The closest I’ve come to seeing this addressed in the AP course description is this:

    SAP 9.C.2 (pg 160) “The pH of a weak acid solution can be determined from the initial acid concentration and the pKa”.

    The choice to specify “initial” acid concentration as opposed to “equilibrium” may imply that the difference between the two is negligible and that the use of quadratics may be circumvented. Still, there is a degree of interpretation involved with this and the statement could benefit from further clarification!

    • Adrian

      Great observation, although the chances of it actually being that deeply thought-out by the College Board is profoundly unlikely! On the other hand, they are fond of writing in absolutely riddles rather than saying, “Quadratics will never be used on the AP chemistry exam” as they certainly could do! Either way, quadratics can safely be left out of discussions in terms of the exam.

  3. Chad Schultz

    Have you seen the new (relatively) method for solving quadratic equations developed by Dr Loh from Carnegie Mellon? It is quite simple and eliminates the need for the quadratic formula. I have been playing around with it and so far it has worked for every chemistry problem I have tried.


    I’m considering adding this method to my AP Chem class and eliminating the quadratic formula and the 5% rule entirely.

    • Adrian

      I haven’t seen that, and I will check it out, but as far as AP chemistry is concerned it’s an entirely moot point. There is no “5% rule” that *actually* needs to be applied, since unless stated, we always assume x is negligible anyway.

  4. Wes Gillman

    Task 7.1 #2…
    Kc = x-squared / (1-x)(2-x), where Kc = 4
    The answer says x = 0.845. It also says you don’t need to use a quadratic equation on the AP exam. Am I missing something on this question? I don’t see how it’s possible to solve this without a quadratic equation.

    • Adrian

      It isn’t possible to solve without a quadratic, but as it literally says above, nobody at the CB has ever officially ‘ruled out’ the use of such. Is it likely? No, but it has never officially been removed. If you re-read above you’ll understand my position!


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