Is this the hardest A Level maths exam question?

Original post by IrrationalRoot

I feel like if there's a handful of 'high end' questions this will just equate to worse performances all round and thus more scaling which will result in 100s (or close to) for even those students who couldn't do the trickier questions. So it seems more or less impossible to discriminate at the top end with A Level results.

One possible solution is to introduce grades "above A*" (but arguably you should just have an AEA exam at that point).

FM can get even more problematic if you want to be fair across different A-levels. An A grade in normal maths is almost a prerequisite for doing even decently in FM.

Reply 42

Original post by Gregorius

Yet there seems to be a need for, what in America would be called, a "liberal arts" qualification at school level for those not going on to the mathematical sciences at university; maybe a padded-out and modified additional maths (GCSE) course in the sixth form.

So I think I'm for splitting the subject, as it's taught and examined, more appropriately for the needs of those studying it.

What I think's tricky is that A-level grades have become almost weaponized; if this additional course "isn't a full A-level", I can see a lot of people avoiding it. Conversely, if it is an additional A-level, I can see a lot of people saying "why do the current A-level and risk getting a poor grade when I can do the liberal-arts-A-level instead?".

I do suspect things will settle down a bit as people (and examiners) get used to the new system, but it's going to be an interesting teething period.

Reply 43

Dequavius

11

As far as the manipulation of ii) goes I haven't seen any examples of anything similar in the textbook questions. I don't yet have any experience of university exams but I'd imagine that their papers remain at a constantish difficulty each year (feel free to correct me here), so although the manipulations are definitely more difficult, students have lots of past examples to familiarise themself with so they're not so taken aback in a real exam.

I think I worded it badly in the previous post but lots of people do just do A-Level Maths because its seen as a "smart subject" and they think it looks "good".

Physics is another subject that's definitely been made more difficult since 2016 and I think German has too a bit (although that's of little relevance here). IDK if A-Levels need to be made more difficult in order to prepare students better for uni as the majority of people say that A-Levels are already harder than 1st year uni (obviously not true for "elite" courses but they're in a small minority).

@Notnek sorry for derailing the thread a bit but I can't find or remember any such difficult exam questions. Would you be interested in textbook questions too?

Original post by DFranklin

The thing is, the main thing people have been objecting to (in this thread) is the manipulation in (ii). Anyone doing the topics you mention (possible exception of CS) is going to be dealing with far more difficult manipulations during their course. It's like the removal of calculus from A-level physics, when there's no way you're going to be doing physics/engineering at university without doing lots and lots of calculus!

I kind of hope A-Level Maths isn't done to show "you're confident with working with numbers", because IMHO it's actually pretty poorly suited to that. (If you're not going on to the courses you describe, I think it extremely unlikely you'll ever be using trig identities, any non-trivial calculus, etc.)

I do take your point about not scaring people of A-level maths (and I can certainly see exams like this doing so!). But at the same time, if it's going to prepare you for university, it has to be more challenging than many are comfortable with. I don't know if the difficulty of the other A-levels is changing at the same time?

(edited 4 years ago)

Reply 44

Notnek

OP

21

Original post by Dequavius

@Notnek sorry for derailing the thread a bit but I can't find or remember any such difficult exam questions. Would you be interested in textbook questions too?

I couldn't think of any harder A Level exam question which is why I created the thread :smile:

If you know of textbook questions that are harder then please post them.

Reply 45

Original post by DFranklin

What I think's tricky is that A-level grades have become almost weaponized; if this additional course "isn't a full A-level", I can see a lot of people avoiding it. Conversely, if it is an additional A-level, I can see a lot of people saying "why do the current A-level and risk getting a poor grade when I can do the liberal-arts-A-level instead?".

Agreed. It would have to be a full A-level, and it would have to be a qualification that demonstrated useful skills and abilities different from those of "straight" maths. Speculation mode on: the analogy that I'm thinking about here is with philosophy as an academic subject at degree level. It's well liked by quite a few employers, as it's thought to show an ability to reason in ways that are applicable in difficult circumstances. Is there a sort of quantitative equivalent, where you can demonstrate useful conceptual understanding, without too much of the technical side?

I do suspect things will settle down a bit as people (and examiners) get used to the new system, but it's going to be an interesting teething period.

Agreed.

Reply 46

Original post by Dequavius

As far as the manipulation of ii) goes I haven't seen any examples of anything similar in the textbook questions.

Definitely have seen things like this before (at equivalent of A/S level!), but my A-levels were a long time ago.

But just to be explicit here (but using variables instead of numbers to make the TeX easier): the term T_k containing p^k in

(p+q)^n

is

\binom{n}{k} p^k q^{n-k}

and then to derive

\dfrac{T_k}{T_{k+1}} = \dfrac {\binom{n}{k} p^k q^{n-k}}{\binom{n}{k+1} p^{k+1} q^{n-k-1}} = \dfrac{(n-k-1)!(k+1)!q}{(n-k)!k!p} = \dfrac{(k+1)q}{(n-k)p}

is not at all unreasonable to ask at this level IMHO (particularly when you're given the desired answer).

Reply 47

Dequavius

11

This is a good idea IMO, but I think there would still be a negative stigma against it - people may consider it as the maths A-Level for less able students - and therefore students would just stick to the traditional course anyway. Though once it is more established this probably won't be an issue.

Original post by Gregorius

Agreed. It would have to be a full A-level, and it would have to be a qualification that demonstrated useful skills and abilities different from those of "straight" maths. Speculation mode on: the analogy that I'm thinking about here is with philosophy as an academic subject at degree level. It's well liked by quite a few employers, as it's thought to show an ability to reason in ways that are applicable in difficult circumstances. Is there a sort of quantitative equivalent, where you can demonstrate useful conceptual understanding, without too much of the technical side?

Agreed.

With regards to scaling, UMS doesn't exist in the new exams anymore so the top end of students achieving 95+ would still be distinguishable from the merely "good" students scoring in the 80s. @IrrationalRoot

Reply 48

Original post by Gregorius

Agreed. It would have to be a full A-level, and it would have to be a qualification that demonstrated useful skills and abilities different from those of "straight" maths. Speculation mode on: the analogy that I'm thinking about here is with philosophy as an academic subject at degree level. It's well liked by quite a few employers, as it's thought to show an ability to reason in ways that are applicable in difficult circumstances. Is there a sort of quantitative equivalent, where you can demonstrate useful conceptual understanding, without too much of the technical side?

I think what's tricky about this is that I feel what you'd need to be able to test is "practical application", and without a suitable background in the "practical course" that's very difficult.

To unpack that a little: there's obviously a lot of cross-over between computing and maths, and I think a lot of people would benefit from learning how to solve mathematical problems on a computer (or conversely, use maths to solve problems that arise in computing). But at the same time, how side-tracked do you want to get with teaching people computing during a maths A-level, and why prioritize computing over physics, or economics, or engineering, all of which would have similar claims.

Arguably, you could specifically aim at the same people who do things like "business studies" A-level as they're the one's most likely to struggle with the current A-level anyhow.

(edited 4 years ago)

Reply 49

IrrationalRoot

20

Original post by Dequavius

With regards to scaling, UMS doesn't exist in the new exams anymore so the top end of students achieving 95+ would still be distinguishable from the merely "good" students scoring in the 80s. @IrrationalRoot

Oh. That's a very good thing imo, as long as they keep the difficulty levels of the papers consistent. So no more 75% raw = 100 UMS in C4 lol.

Reply 50

Notnek

OP

21

Original post by IrrationalRoot

Oh. That's a very good thing imo, as long as they keep the difficulty levels of the papers consistent. So no more 75% raw = 100 UMS in C4 lol.

Unfortunately keeping the difficulty levels consistent will probably lead to better grades as students/teachers get more used to the new spec and have lots of past papers to practice with. I hope that the exam writers try hard to make questions that require good understanding and not just familiarity with the exam, which was the problem with the old spec.

Reply 51

IrrationalRoot

20

Original post by Notnek

Unfortunately keeping the difficulty levels consistent will probably lead to better grades as students/teachers get more used to the new spec and have lots of past papers to practice with. I hope that the exam writers try hard to make questions that require good understanding and not just familiarity with the exam, which was the problem with the old spec.

I mean consistent from some point onwards. If there's no scaling then it's simply unfair to allow to difficulty of the papers to vary greatly from year to year. Well unless the grade boundaries vary too, but I'm not up to date enough with this stuff to know whether they do or not.

Reply 52

Surfer Rosa

10

Original post by Gregorius

Yes, it is a relatively recent subject; but no, all the basic terms are well defined!

What I'm getting at is, for instance:

1) Where is Q2 for a population of size n = ...
a) 5
b) 10
c) 100
d) 1000
2) What is an outlier? (And what is a fence?)
3) What is the co-efficient of skewness?
4) When should the median be preferred to the mean ?
5) When should the variance be preferred to the IQR?

All of these are from a Year 1 Stats books or a 2018 A-Level Paper. I'm not sure any of them have definitive, or even clear, answers.

Reply 53

Original post by Surfer Rosa

What I'm getting at is, for instance:

1) Where is Q2 for a population of size n = ...
a) 5
b) 10
c) 100
d) 1000
2) What is an outlier? (And what is a fence?)
3) What is the co-efficient of skewness?
4) When should the median be preferred to the mean ?
5) When should the variance be preferred to the IQR?

All of these are from a Year 1 Stats books or a 2018 A-Level Paper. I'm not sure any of them have definitive, or even clear, answers.

...and all standard stuff...

is this as or a2?

Apart from 1a) and b) maybe, (as I said) I don't think there are definitive, or even clear, answers to these questions. Do you? If so, what are they?

Original post by Gregorius

...and all standard stuff...

Reply 56

Cat?

I think I might have found a question that may be more difficult!!

Reply 57

Notnek

OP

21

Original post by Gent2324

is this as or a2?

It was in an A Level paper but parts (ii) and (iii) only require Year 1 knowledge (and also (i) if you use trial and error on your calculator).

Reply 58

Original post by Surfer Rosa

Apart from 1a) and b) maybe, (as I said) I don't think there are definitive, or even clear, answers to these questions. Do you? If so, what are they?

I hope I don’t seem obstructive here, but I’m genuinely puzzled about your puzzlement. May I turn the question around and ask why you think these are not well defined? Have you seen different sources with contradictory answers? (Remember my remark that I’m appalled at the way stays is taught at school level; things do get put right later on!)

Reply 59