I imagine, if one put one’s mind to it, one could acquire copies of this year’s paper online - however, many schools plan to use it as a mock for next year’s candidates. In view of that, and at the request of my top-secret source, I’m not sharing the actual questions used. However, I’m treating the topics and techniques as fair game.
I once claimed not to be very competitive. My friends looked at me askance and told me I was one of the most competitive people they knew, and I said “What do you mean, one of the most?”
So, when @christianp tweeted about having a sub-20 minute record for a speed-run on the old-style papers, and wondering how he’d do on the new ones, it made me wonder. A top-secret source supplied me with the EdExcel non-calc paper and I rattled through it in about 23 minutes; on my way, I starred two questions where my answers felt a bit smelly, and went back to them after hitting the ‘lap’ button; I put my pencil down after 25:01.
Here are my, fairly unstructured, thoughts about the paper and my experience of doing it.
“Easy” vs “hard”
I understand the new GCSE is set up so that around half of the marks are awarded for material at grades 4-6 (an old-fashioned B-C grade), and half at grades 7-9 (A-, A*- and A**-grades). Questions 1 to 13 cover 41 marks and 14 to 22 the remainder. I felt the first three questions were very routine; questions 4, 5, 6 and 7 were not tough in terms of calculation skills, but required a spark of problem-solving. Questions 8 to 13 required a bit more mathematical knowledge, but no particular creativity - and that seems like a fair way to structure the first half of the paper. A few routine questions to check you have some skills, a few that stretch your problem-solving but not so much your syllabus knowledge, and a few that work vice-versa.
The second half gets quite involved, quite quickly. Questions 14 and 15 reward candidates who can organise their thoughts and think carefully while solving problems (the sums are not difficult). Question 16 is simple enough algebraically ((To my shame, I notice that I’ve messed up a minus sign in this question.)) but requires a bit of understanding and clarity of writing, while question 17 is a straightforward probability exercise.
The top-end questions, I really like. Question 18 combines coordinate geometry with knowledge about properties of shapes, question 19 is an unusual vector problem in which you need to read the question carefully, and draw extensions to the diagram; 20 is a tricky quadratic simultaneous equation; 21 is a proof that’s straightforward once you spot the nugget (again, it rewards clarity of communication), while question 22 is a stinker - although, as the last question on the paper, its role is to help distinguish between level 9 and level 8 students, the best mathematicians ((At least, if you accept that the best mathematicians are the ones getting the highest grades)) taking the exam.
From an assessment point of view, I like this paper. If you look at GCSE questions on two difficulty axes - let’s call them calculation competence on one axis and problem-solving on the other - the four quadrants are all well represented, with an emphasis in the second half on the top-right (the maths is tricky, and you’re not told precisely what to do). There is a good mixture of arithmetic, algebra and geometry.
I have my doubts about whether high-pressure, restricted-time exams are the best way to determine whether someone is a good mathematician, and further doubts about whether the mathematics syllabus is appropriate for a compulsory subject, especially one used as a benchmark by colleges and employers. And don’t get me started on the debacle of rolling out the new exams.
However, given the goals of mathematics education as I understand them - broadly, to have students who are competent at calculation and at solving problems - this strikes me as a good paper to test those skills.
In question 17, a balls-from-the-bag question that’s long been a staple of GCSEs, I don’t feel it’s clear whether the scenario is with or without replacement. I’ve re-read it several times, and I think it means without, but I don’t feel it’s clear enough for an exam question.
I suppose it’s possible that you’re meant to give both answers. If that’s the case, I think it’s bordering on the unfair.
Ones I found tricky
As I mentioned, there were two questions I asterisked to go back to.
The first of these was the multiple ratio problem in question 14. Whenever there’s a series of ratios, you know you’re going to have to tread carefully. My answer came out nicely, which I took as a good sign; however, I wanted to go back and check that the numbers I came up with satisfied the question. They did.
The second was the simultaneous equation in question 20, which I have to confess was a bit of a catalogue of errors. Fortunately, it was the kind of catalogue with a quick and simple returns policy and I managed to put everything right without too much hassle. In case you’re interested, the errors I made:
- I initially bodged the expansion of a pair of brackets. I caught it, but not until several lines later, when my quadratic didn’t factorise.
- It took me longer than it should have to factorise the quadratic even once I had it correctly. In fairness, it’s not a very nice quadratic, and there were an unusually high number of possible factor pairs, but all the same, it took time.
- I dropped a minus sign when substituting my x-answers back in, and got a y-value that looked fishy. When I returned to it, it quickly moved from ‘fishy’ to ‘obviously wrong’ - it was far too large to be a plausible solution to the first equation. Spotting that meant I could easily spot where I’d made the error, and put it right; this led to a solution that was much more plausible (and, with a moment’s thought, clearly satisfied the first equation.)
Things I could have done better
In question 3, which was a decimal multiplication exercise, I got the correct answer - but I didn’t estimate to make sure it was of the right order of magnitude. I was a little lucky there, I suppose. (Incidentally, this is one of the reasons I quite like the grid method for multiplication: the top-right corner of the grid is generally a passable first estimate, and the remainder of the grid adds the details.)
In question 15, an estimation question, I found myself second-guessing whether my estimate was bigger or smaller. I was right, as was my reasoning, but I could have been much clearer: had I rearranged before estimating, it would have been more obvious to me (and, presumably, to the imaginary examiner).
Where I’d expect students to struggle
I’d expect my typical student to clean up on the first half of the paper - perhaps stumbling a little on the decimal arithmetic or not making the link between the geometry and algebra in question 4. The means question (7) would likely trip up those with a gung-ho attitude ((“Answer first, read later”)), but I’d hope for a solid performance up to at least question 12 or 13.
I’d expect a lot of questions left blank in the second half, however much I’ve drilled “write something relevant down, just to make a start” into them. There are plenty of marks they could pick up in the later questions, but whether they have the confidence to apply good exam technique under pressure is the big question.
It was an interesting experience to do a paper against the clock, and not one I’ve tried in quite that way before. I certainly dropped a mark for a lost minus sign (I don’t even know the rules of this game! Is there a time penalty?) and I’m glad I went back to check on the questions I did.
As for the paper, I thought it was tough, but by and large a fair test within the parameters it’s meant to test. (The parameters? As I’ve said, I have doubts about those; personally, I’d like to see the return of the Intermediate tier.) I imagine the grade boundaries will be much lower than with the old-style papers, simply because of the shift towards examining more high-end material.
Key take-away for students: in an exam like this, exam technique is critical. Picking up a couple of marks here and there on top-end questions can lift your score dramatically. Check your work carefully. Keep an eye on the time you have available. I hope you knock it out of the park!
* Edited 2017-06-12 to fix a footnote.
A selection of other posts
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