Just how much can you abuse nSolve on an exam?

[Aleksejs Popovs]

Imagine an HL Paper 2 problem like this (real example):

Given a pdf f(x) = k ln(x) for 1 ≤ x ≤ 3, find the median of X.

Finding k is easy enough, and then you get a problem of the form

Integral[k ln(x) dx, 1 ≤ x ≤ m] = 1/2

I imagine that the expected solution is using partial integration to obtain Integral[k ln(x) dx] = k x (ln(x) - 1), then using that to obtain an equation which can be solved numerically. In this case, the problem tests both your knowledge of the definition of a median and your ability to partially integrate ln(x).

However, on an nSpire, you can define a function g(t) := Integral[k ln(x) dx, 1 ≤ x ≤ t] and then just do nSolve(g(t) = 1/2, t, 2) (the initial value 2 is required to keep it from converging on a solution below 1) to get exactly the same answer. Note that you really do need to define a function first, because otherwise the calc complains about multiple non-valued variables in a single expression. I believe that this might be impossible to do on calculators like the TI 84. In this case, the problem is a one-liner and only requires knowing the definition of a median, as well as having a recent calculator and being somewhat good at using it.

The latter solution feels somewhat like cheating, but it's what came to me naturally during a test today, and I don't see any actual rule that would prohibit me from using it. Do you think both solutions would be accepted as equally valid on an exam?

 

Edited April 20, 2016 by Aleksejs Popovs

[kw0573]

I used the TI-84 Plus last year and it has a similar Solve function, but I mostly just graphed y =fnInt(k * ln(x), x, 1, x) (different syntax on newer versions of the system) and read off value at y = 1/2 or intersection with y = 1/2. Most graphing calculators do not find antiderivatives instead they use some numerical analysis to approximate the answer, some are explained here.