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 exam performance? Even though some of these hints bleed over into general good advice about mathematical operations and the AP chemistry exam, 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 PV = nRT 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, but if students know that -log (1.0 x 10-6) = 6, and -log (1 x 10-5) = 5, then they should know that without the use of a calculator, 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.