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Math Hints & Tips for AP Chemistry Students

March 05, 2017

EDIT 06/02/2022 – This blog post was written in March of 2017 when calculators were not permitted on the MCQ portion of the AP chemistry exam. For 2023 forward, calculators WILL be allowed on the MCQ section of the exam. However, I still think a lot of the advice that follows is extremely useful in a wider context.

Wot? No Calculator? When students find out that they will not have access to a calculator on the MCQ section of the AP chemistry exam, they are often horrified. This speaks of course, to the bigger question of the reliance upon calculators in general, a point that I do not intend to address here.

So, how can we alleviate the stress that might actually impair AP chemistry, MCQ exam performance? Even though some of these hints bleed over into general good advice about mathematical operations, and the AP chemistry exam as a whole, (and are not necessarily all about not using a calculator per se), they all should prove to be useful.

Use only MCQ’s that are non-calculator based. Easier said than done, and I am guilty of not taking my own advice here, but every new MCQ that I write is designed to be answered without a calculator. It takes time to build that bank, but ultimately it will make things better.

Ensure the kids are proficient at estimation. For example, if, in a given calculation, P V = n R T boils down to;

(2.881) (1.99) = (x) (0.08206) (298)

then that’s really close to (3)(2) = (x)(0.1)(300) which is 6/30 = 0.2. Although exactly 0.2 is not likely to be an answer, answer choices will be given in such a way where it should be obvious which one is the correct one.

Teach the basic mechanics of logs and ln. Look, I’m no math teacher, and if I tried to be one it would be a bloodbath. Also, as far as I am concerned, “log” (or ln) is no more than a button on the calculator, but if students know that -log (1.0 x 10-6) = 6, and that -log (1 x 10-5) = 5, then they should know that without the use of a calculator the pKa of an acid with a Ka of 2.5 x 10-6 is somewhere between 5 and 6. Such knowledge is very handy when selecting acids to be used in certain buffer situations, e.g., the (previously NON-calculator FRQ) 1992, 6.

Also, given the sheer obsession with Q that the CB/TDC are showing these days, it’s very important to know what the consequence of the relative sizes of the numerator and denominator of Q are when ln is applied, i.e., the ln of Q’s > 1 are positive and the ln of Q’s < 1 are negative.

Encourage the kids to ask, “Does that number make sense?” This is good advice for both calculator based stuff, and non-calculator based questions. For example, when calculating the pH of any acid, that pH better be below 7 (assuming 298 K), otherwise something has gone horribly wrong.

Make sure the students know the basics of exponents, i.e., multiplying, add; dividing, subtract; square rooting, half the exponent; 10-6 < 10-5 etc. See #45, 1999 and #65 and #66 from 1989 for a good examples of such.

Reiterate the difference between the mathematical consequences of merging equations in terms of ∆H and K. i.e., add ∆H’s but multiply K’s; change the sign of ∆H but use the reciprocal of K; double ∆H but square K; halve ∆H but square root K.

Watch out for different values of R. See this.

Dimensional analysis. Honestly, I’m not a fan of dimensional analysis, period, but it may help to make sense of those non-calculator MCQ’s that show “set-ups” e.g., #35 from 1999.

Armed with these tools, multiple-choice questions should be a little easier for mathematically challenged students, despite this fact.


  1. Eric Sully

    Another tip that I have found helpful when working with any value, but especially decimals is to encourage students to think of money. They have trouble working with 0.25 in a problem, but have no trouble when they think of it as 25 cents.

  2. Josh Branham

    “I’m not a fan of dimensional analysis”

    Maybe this is my engineering side coming through (I’m not a fan of the “STEM” concept in education either but I do have two engineering degrees and a prior career as an engineer so my mind works that way) but I love dimensional analysis and I use it on some concepts in class the most common of which is in electrochemistry. Given a current and time and going to mass of metal plated can be done completely by dimensional analysis using the equation sheet without having a clue about the concept behind the question. I tell my students that if they aren’t sure what to do in a quantitative problem, consider what is given and manipulate the units to get them to be the same as what is being asked for. Maybe that isn’t quite as useful since the course redesign took out a lot of math but it is still useful.

    We spent time in my college engineering classes discussing units and whether or not an answer makes sense which you mentioned here too and units have to be consistent. It’s an easy way to eliminate choices in multiple choice or troubleshoot in free response in AP.

    • Adrian

      Well, firstly there’s a WHOLE other conversation about people that are NOT career educators. I’ll leave that alone here. Secondly, well, that’s a whole other conversation too….

    • Adrian

      Hi Josh – Thanks for taking the time. Honestly, I’m not “against” DA per se, but having never been taught it (it’s not at all common in England in my experience), I never found much use for it.

    • Drew

      I agree…I made it through engineering in college in large part due to dimensional analysis. I;m not sure how you solve any scientific problem without analyzing the units.

  3. Nicolle Arteaga

    I have an old IB test bank on my computer. I used to teach those kids how to do a bunch of mental math tricks bc Paper 1 is all MC without a calculator. I suppose I could supplement my AP stuff with some of those old IB MC questions. They were great.

  4. Rhonda Beasley

    Now that a calculator CAN be used on the MC, how will MC change, other than having more than mental math?

    • Adrian

      It likely means the removal of “set-up” questions, where the answer is shown in its unsolved version, and of course the use of what they call “authentic” data will mean mental math and importantly estimation, will be removed. For example, if you have 22.4 multiplied by 1.938, ALL of the MCQ answers could be in the region of 44 whereas previously perhaps only one answer would have been in that ballpark, and therefore the answer was easy to find.


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