NCEA Level 2, 2016 Calculus Exam mistake

overview | two (b) mistake | conclusions

Overview

After the fiasco of the NCEA Level 1 MCAT exam (on two days) in September 2016 it's inconceivable that the NCEA Level 2 Calculus exam on 24 November 2016 could possibly have had anything wrong with it...

And yet...

It did.

One of my students reported that a tangent to a parabola did not touch the parabola at the point claimed. I found a copy of the paper and gave it a go. I got exactly the same result as he had: the supposed point of contact of the tangent did not lie on the parabola.

Once again I ask: Was the exam really "thoroughly checked"? Clearly, obviously, blatently NO.

The NZ Herald quotes a teacher regarding the question:

A "disappointed" student had raised the error with him, he said.

Students were unable to "do anything with it and it puts them off for the next questions", he said.

"[As a student], you're not going to be going, 'I wonder if the examiner for the whole of New Zealand's made a mistake here'."

He questioned how NZQA could have made such a bungle.

"If you go to systems like IGCSEs and IBs, the exams are spotless," he said.

"I don't know how it's possible for that to get in there. It's not a mistake that's hidden, it's glaringly obvious."

Quite a lot of students now have a very dim view of NCEA maths exams, so thinking another mistake has been made would very likely cross the students' minds. NCEA maths exams are known to be confusingly worded, ambiguous, and very vague in stating what is required.

QUESTION TWO (b) mistake

The line `y = ax + b` is a tangent to the graph of the function `y = 2x^2 - 3x + 1` at the point (3,2).

Find the values of `a` and `b`.

The point (3,2) does not lie on the parabola. What should the student do? What could the student do? Make something up and answer what would be a different question? That's not so far fetched – some NCEA maths questions are so vague and ambiguous (looking at you, NCEA Statistics!) that assumptions (ie, guesses) have to be made in order to answer them.

The actual point should have been (2,3), and that's what the downloadable paper now says, along with the note in bright red "This question has been corrected from that used in the examination."

Conclusions

As I said after the MCAT exam, serious questions need to be asked about the exam preparation process, including checking.

The teacher quoted above is correct about Cambridge Exams being spotless; they are well checked. The explanation for why NCEA exams are not is very obvious. I have heard that only two people check each exam. Whoever has the job simply isn't checking very well at all. Not every maths teacher – even if they are very good at maths – is good at checking exams for errors.

The process may also be at fault; we don't know if the final version is checked at all, or if it is only assumed that previous corrections have been made correctly.