## The long way round

Today one of my Y12s was looking through a C3 paper he found on my desk. *(For those unaware A level maths, studied in Y12 and Y13, ie from 16-18, is currently modular. There are 4 Core Pure modules known as C1, C2, C3 and C4. The first two are studied in Y12 and the second two in Y13.) *He came across this question:

While looking at it he said, “are you sure this is a C3 question?” I told him it was and he then said “But I can answer it.”

I looked at the question, all the main skills it tests are taught at C1 and C2, but the chain rule for differentiation isn’t taught til C3. I thought about it and realised that yes, with the application of the binomial expansion (a C2 skill), or indeed a long winded brackets expansion, it would give him a polynomial he could differentiate.

Then it occurred to me that it was in fact a brilliant question to set my Y12s as revision. It allows them to see links between the things they’ve learned, allows them to practice important skills from C1 and C2, namely the differentiation, the coordinate geometry involved finding te equation of a tangent and the binomial expansion, and to solve a problem using those skills.

It took them longer than it would have taken someone who knew about the chain rule, but it was time we’ll spent and I got some perfect answers from them. I didn’t tell any of them how to do it, they managed to talk each other through it, and I only had to pick up on one slight error when one of them had a slight hiccup with a power. I think I need to have a good look through some more higher level papers to see if I can find any other gens to test the earlier skills.

*This post has been cross-posted to Betterqs here.*

## Revenge of the real life questions

Last year I wrote this piece discussing some of the worst pseudo-contexts that I’d come across in maths exams. You know the ones, the ridiculous made up contexts that are supposed to give a real life twist to a question but Ard actually anything but. Well this year’s C2 Edexcel A Level paper has two of the worst I’ve ever seen!

**Exhibit A**

Aaaaaaaarrrrrrggggghhhhhh!!!!!!

*“Figure 1 shows a sketch of a design for a scraper blade. The blade OABCDA consists of an isosceles triangle COD joined along its equal sides to sectors OAB and OCD of a circle with centre 0 and radius 8cm. Angles AOD and BOC are equal. AOB is a straight line and is parallel to the line DC. DC has length 7cm.”*

There are a few issues I have with this question. Firstly we have a whole paragraph that is entirely unnecessary! The only purpose this paragraph would serve was to test the ability to sketch or visualise but this us completely negated by the diagram. One of my year 12s asked, “what’s the point in that writing on the sectors question? It just described the picture.” I had to agree.

That wasn’t the worst bit though, the worst bit is there at the beginning .

*“Figure 1 shows a sketch of a design for a scraper blade”*

I can imagine the examiner’s meeting now: “I’ve got a great sectors question, it uses area, arc length, cosine rule, sine rule for area…. it’s a classic.” “Great, but we said that was going to be a real life question this year.” “Oh b@#@##ks, what can I do?” “Just make it about a scraper blade!”

What even is a scraper blade, and why do we need this question be about one?! This was actually a great question, or would have been if it had only one of the picture or the paragraph and no stupid mention of a scraper blade.

**Exhibit B**

*“A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75pi cm^3.*

*The cost of polishing the surface area of this glass cylinder is £2 per cm^2 for the curved surface and £3 per cm^2 for the circular top and base areas. Given that the radius is r cm…”*

Show that the cost is, then find the minimum.

This question is pseudo-context at its worst. A part for an expensive laser amplifier will be the required size for said amplifier. It will need to fit abd as such it’s length and radius will be far more important that it’s volume, do there’s no way at all that they would design the laser around the minimum cost of polishing a cylinder with a certain volume! Why would you create such a convoluted, nonsensical, bogus context?! If you want to ask questions in context fine, but please make it a believable one!

## A few thoughts on this week’s exams

This week my A Level students sat their Core 1 and Core 2 exams. Both papers were, in my opinion, fairly nice. Although there were questions on each paper that were asked a tad differently that threw a few students.

The general consensus amount my students, and other teachers I’ve spoken to, differed majorly between the year 12 students and the year 13s who were re taking for whatever reason. Year 13, on the whole, found the papers much easier than year 12.

This got me thinking about the make up of the A Level course and the placement of exams. I’ve long thought that sitting all the exams at the end if year 13 would be beneficial. When I arrived at university I met friend Steve for the first time. In one if those early conversations we discussed the make up of our A-level courses and he explained how he had done a modular course, but sat them all at the end. I suggested that seemed silly and he disagreed, saying “but P1 is well easy once you’ve done P6” (those were the days before “pure” modules became core modules).

We’re both maths teachers now, and at somepoint recently we had a similar discussion and we both agreed that this was probably the case. And anecdotal evidence from this week’s exams seems to suggest that this is indeed true. So perhaps the move to terminal exams is better? (Although I do think 3 and a half hours is too long for an exam, and would rather see more papers!)

Another thing struck me about the discussions around these papers I had with year 12. One student, who is extremely gifted at maths, commented on the C2 exam “that’s the most enjoyable exam I’ve ever had, it was ace.” Another commented that she “proper loved it” when asked about the C1 exam. This made me look at the papers again, with the first student I mentioned. He said he didn’t understand why some people had found it difficult, and it occurred to me that the ones who had found it easier in year 12 were the ones who had spent more time on the underlying mathematical concepts, and the ones who had focused on “will this be in the exam” were the ones that struggled, relatively speaking. This is why I try to answer “yes” to every variant of this question. (The only exception being a few proofs that may be nice, but don’t enhance understanding and aren’t required to access the content.)

The other exam this week was M3, this was nice enough, for an M3 paper. It was hard, but M3 IS hard. I don’t understand why it was scheduled so early on in the session.

All in all quite a nice set of papers, I’m quite looking forward to the next ones!

## Revision Quizzes

Currently my further maths class are revising for tomorrows D1 exam. Due to the fact we changed the order of the modules we teach the year 12s are also revising for the same exam and I have my class last lesson on a friday at the same time my ATL has year 12, so over the ast few weeks we have been joining up for the last 20 minutes or so and facing of in a head to head “pub quiz” type revision event, these quizzes came from the ATL. They worked really well, helped consolidate some of the learning and gave the students chance to see where they needed to put more work in. In this vein I have made a C1 and a C2 quiz ( http://www.tes.co.uk/teaching-resource/Core-1-and-2-revision-Quizzes-6334839/ ). The C1 quiz went really well and I am going to run the C2 quiz for the first time tomorrow.

Given the success of these quizzes I am planning on doing some similar ones for GCSE classes next week!

Edit – 09/12/13 – I have added some new rounds to the C1 quiz and have also uploaded exported ppts for those of you unable to access notebook.