How to do well on NON-multiple choice math tests?

MITer94
Sun, 01 Oct 2017 01:23:53 +0000

How would you do if the test had been multiple choice? Unless the questions were plugging-in SAT-style, you still have to solve the question first for most problems. Making the jump to expressing those thoughts in a clear, logical, mathematically sound matter takes practice.

It sometimes helps to see an example of a bad solution and a good solution (and ask why they’re bad or good). Here is an algebra II - level example:

Find all real values of x that satisfy x = sqrt(x + 20).

Bad solution 1:
If x = 5, then we have 5 = sqrt(5+20) so the answer is x = 5.

Bad solution 2:
Squaring both sides, we have x^2 = x + 20, which rearranges to x^2 - x - 20 = 0. This factors to (x-5)(x-4) = 0, so the solutions are x = 5 and x = -4.

I have a couple more examples (more advanced than this one) that I’ve used for courses on mathematical proofs.