Guardian Newspaper - could do better

Oh dear, Guardian.  You posted a set of ten questions under the heading "A-levels: test your maths" leading people to assume that this is representative of A-level mathematics. Unfortunately you failed to give the background to this, failed to explain how you cherry-picked the questions you gave, failed to explain that mathematics A-level modules are not multiple-choice and included errors in the questions/answers too.  See me after school.

First of all, is this really a problem?  Surely people realise that a set of multiple-choice questions on a website is only a bit of fun and shouldn't be taken seriously.  Unfortunately this has been taken seriously as the comments beneath the article attest.

The lack of context is a genuine concern.  We are used to smiling cynically when a footballer or politician claims that something he said has been "taken out of context" but here the background to the exam is rather important, particularly to respond to those who contrast the 10/10 they achieved on this test with the D-grade they gained back in 1979.  Nowadays A-level mathematics is modular.  The first three modular exams are generally taken during Yr 12 (the Lower Sixth) and are AS-level standard.  At the end of that year a student can 'cash in' their three modules and gain an AS-level in mathematics.  This is not an A-level.  In Yr 13 (the Upper Sixth) three further modules are studied and they are more challenging than those taken in Yr 12.  The six exams together form the full A-level.

The paper the Guardian article used is from module C1.  This is the very first module from AS mathematics, includes more difficult applications of some GCSE topics and some of the core mathematics required for other topics and modules.  The full paper contributes one-sixth of the marks for the final A-level grade.  The material is covers is arguably the easiest part of AS-level, which is the easier year of the A-level course, so the mathematical demand here is less than one-sixth of that required for A-level mathematics.

Some of the comments recognise this:

The next problem is that multiple-choice answers have been given.  I appreciate that it is difficult to mark algebraic answers via computer, but it should have been made clear to readers that A-level mathematics is not a multiple-choice exam!  [Or perhaps the fact that some people clearly believe that A-level mathematics is multiple-choice shows the degree of scepticism amongst the general public about A-level standards.]

Even after other comments have pointed out that A-level maths is not multiple-choice other commentators persist in assuming it is.  The comments below are given in chronological order, so if some of the later commentators had read the earlier ones before posting then they could have saved themselves the trouble.  [I have excerpted these from the comments threads - other comments intervened between some of these.]

And this raises one of the issues about making it multiple choice.  You can not only just blindly guess (and on average you should get 5/10 by doing this) but can also in many cases dismiss an obviously wrong answer, or in some cases can work backwards from the two given answers and find out which is correct.

The comment above clears this one up and also points out that this paper is not representative of A-level mathematics.  More than an hour after this comment was posted someone else asked whether A-level mathematics is multiple-choice or not.

Another problem with deciding to have multiple-choice answers is that they cannot use any questions that need explanation, which means some of the more challenging questions cannot be used.

As other comments point out, the quiz has cherry-picked its questions and it often includes just the easiest part of a multi-part question.

Here are further comments about the individual questions:
Question 1:

Because this has two answers to choose from, it is really asking "do you know the difference between integration and differentiation", which is significantly easier than asking someone to carry out the integration for themselves.

Questions 2&3:

One problem here is that Q3 relies on the answer to Q2, so it would have made sense to have allowed people still to be able to see the answer to Q2.  Unfortunately neither answer is correct for Q2.  As has been noted in the comments, the first answer is closer but is missing a power of (1/3), which should appear next to the second x.

Question 4:

Oh dear.  Several problems here.  The misspelling in the question is by the Guardian and was rendered correctly in the original exam paper.  Commentators have pointed out that this is rather straight-forward.  They are correct, but haven't been made aware that this is the initial part of a 4-part question.
The big error here, though, is in the first answer, which is the one the Guardian considers to be correct, but which has errors in the units that are provided.  The answer is £0.80, which can also be written as 80p.  As given it is meaningless.

Questions 5 & 6:

These have been cherry-picked.  They are each worth one mark.  The rest of the question, which hasn't been included here, is worth 6 marks.

Question 7:

Cherry-picked.  This is the first part of a 5-part question.  It is worth one mark out of the 15 available for the complete question.  Again, the answers that are given are helpful.

Question 8:

The typo is the Guardian's.  The two answers are so far apart and the first clearly must be wrong because it is so large.  Had two closer answers been given then this would be more challenging.

Question 9:

I think it is worth seeing the original question from which this has been taken.

The typo in the Guardian question doesn't appear in the original.  It is also Question 2 from the original exam paper (which the Guardian quiz links to) and should therefore be expected to be easier than some of those that have preceded it.  Giving multiple-choice answers makes it easier, and part (b) of the original question, which is harder, has been omitted here.

Question 10:

The typo in this question isn't just a misspelling and makes the question meaningless.  Also, because only one of the two answers includes 'c' the way the Guardian has done it really boils down to whether you understand what "write an expression in terms of c" means.

Here is the original question from the exam paper:

Once again, the first part of the question has been cherry-picked, giving only one mark out of the 7 available for the full question.


How different this could have been.  Imagine an article that explained properly about AS-levels and the different modules that are available in A-level mathematics.  Imagine if it quoted some questions in full and then explained the answers and what students need to know to be able to answer the question.  Imagine if it also included questions from several different modules.

The result of this?  The Guardian could do better.