Is this the hardest A Level maths exam question? Watch

Notnek
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This question was done very badly by a cohort mainly made up of further maths students and for (iii)(b), "almost no students gave a correct solution based on their answer to part (iii)(a)".

Of course those used to harder exams like further maths / STEP etc. may think this is easy. If you've seen a harder A Level maths (not further maths) exam question in a real/practice paper then please post it below


OCR A Level Maths 2018 : Pure mathematics and statistics Q13

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DFranklin
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Yeah that seems pretty nuts. The 2nd part is pretty standard if you've seen something like it before, but a pretty huge leap for a non-FM student to make.

There are a few similar STEP questions FWIW.
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dextrous63
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Yep. Seems a bit silly to shove a fairly robust "pure" question bang centre of a stats one.
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DFranklin
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(Original post by dextrous63)
Yep. Seems a bit silly to shove a fairly robust "pure" question bang centre of a stats one.
It's a fairly standard stats topic (maximum likelihood estimation) though.
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dextrous63
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(Original post by DFranklin)
It's a fairly standard stats topic (maximum likelihood estimation) though.
I was referring specifically to the term to term ratio of a binomial expansion, which is more of a pure skill than stats.

I could quite easily imagine part (ii) being in the pure section of any paper.
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Glaz
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:vroam:
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dextrous63
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Without trying to write out details, simplifying 50Cr 0.15r 0.85n-r / 50Cr+1 0.15r+1 0.85n-r+1 has bugger all to do with stats, if you pardon my French
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DFranklin
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(Original post by dextrous63)
I was referring specifically to the term to term ratio of a binomial expansion, which is more of a pure skill than stats.

I could quite easily imagine part (ii) being in the pure section of any paper.
Yes, but it's part of the manipulation you do to find the MLE. Just like finding \sum_{n=1}^\infty n qp^n is just summing a series.
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Notnek
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(Original post by dextrous63)
Without trying to write out details, simplifying 50Cr 0.15r 0.85n-r / 50Cr+1 0.15r+1 0.85n-r+1 has bugger all to do with stats, if you pardon my French
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It is part of a pure maths & stats paper though...
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DFranklin
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(Original post by Notnek)
It is part of a pure maths & stats paper though...
More to the point, at A-level, pure is really "maths methods"; it's giving you techniques that you can apply to problems (which maybe pure or applied). So doing "pure maths" in the middle of an applied question shouldn't be surprising.

In practical terms, most CofM / MofI problems end up being largely exercises in integration, for example. But I've never heard someone complaining "what's this integration problem doing in the middle of an applied question?"
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dextrous63
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(Original post by Notnek)
It is part of a pure maths & stats paper though...
True, but it obfuscates focus.
For example, I'm sure we could all create some function which has an area of 1 between a pair of limits, and then call this our probability function and ask questions all about it.

But it would seem somewhat ill-placed if we asked students to find the probability of something which could only be done by a double application of integration by parts.

There's a time and a place for everything, and IMHO, (ii) is in the wrong place.
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DFranklin
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(Original post by dextrous63)
True, but it obfuscates focus. ~snip~
There's a time and a place for everything, and IMHO, (ii) is in the wrong place.
Should be noted that (ii) isn't a random bit of pure in the middle of the question; it's actually a really big hint about how to do part (iii). (In other words the question gets *harder* if you remove part (ii).

As far as focus goes - parts (ii) and (iii) are actually pretty focussed towards getting someone to find the MLE. The sad truth is that a lot of statistical analysis requires a certain amount of algebra grinding.
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dextrous63
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(Original post by DFranklin)
Should be noted that (ii) isn't a random bit of pure in the middle of the question; it's actually a really big hint about how to do part (iii). (In other words the question gets *harder* if you remove part (ii).
I'm well aware of that. However, although we won't agree, IMHO it would have been wiser to have just stated the result of (ii) as a "Given that..." and then ask (iii) rather than divert focus away from stats. If they had done, then students wouldn't have wasted valuable time on some unnecessary algebra (again, IMHO), not been "freaked out" by this diversion, and may well have been able to answer the rest of the question to better effect.
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DFranklin
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As you say, we're not going to agree. But to be honest part (ii) is a pretty trivial manipulation that shouldn't be completely unfamiliar to someone doing stats (it is the most efficient way of incrementally P(X=k) for a binomial).
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dextrous63
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(Original post by DFranklin)
As you say, we're not going to agree. But to be honest part (ii) is a pretty trivial manipulation that shouldn't be completely unfamiliar to someone doing stats (it is the most efficient way of incrementally P(X=k) for a binomial).
Fair enough and one bows to your greater experience and knowledge. I'm not naturally a "stats" man and have only had to start coming to terms with it properly since retiring and taking up private tuition. So, I've only come across and solved a few hundred such problems which have emerged in AQA, OCR, OCR/MEI and Edexcel and haven't come across a single one like this before today; not in any textbook nor sample nor limited past papers. It's all part of the learning curve!

It may well have been a standard sort of question for the old system in which student chose S1 and S2 but it doesn't seem to be the norm under the new curriculum which is why IMHO it seems out of place.

Anyway, back to topic and it'll be interesting to read of any other "hard" questions.
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Surfer Rosa
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Well said
(Original post by dextrous63)
True, but it obfuscates focus.
For example, I'm sure we could all create some function which has an area of 1 between a pair of limits, and then call this our probability function and ask questions all about it.

But it would seem somewhat ill-placed if we asked students to find the probability of something which could only be done by a double application of integration by parts.

There's a time and a place for everything, and IMHO, (ii) is in the wrong place.
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Dequavius
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As an A-Level student I think this question is very well placed and I can certainly see more like this coming up, the new A-Level definitely focuses on less routine stuff. You may be interested in the OCR B (MEI) comprehension section (the one I sat last year is https://www.ocr.org.uk/Images/535678...prehension.pdf), as these questions really aren't ones that can be practiced for in class like say R-alpha manipulation or ladder problems. These new questions really aren't like the old spec where it was more or less the same questions every year just with different numbers.

It's not even the case anymore that all COW maths applicants find A-Level trivial: I know a now Trinity offer holder who was worried he wouldn't get an A*. In fact for MEI there were 36 people nationally who took the exam last year (these people were the more capable of the FM students), of which only 11 achieved A* (source https://www.ocr.org.uk/Images/500691...-june-2018.pdf).
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dextrous63
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What's a COW applicant?
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dextrous63
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(Original post by Dequavius)
As an A-Level student I think this question is very well placed and I can certainly see more like this coming up, the new A-Level definitely focuses on less routine stuff.
An interesting view. The first aspect of any assessment is to determine the level of competence of a student and award marks/grades accordingly. This will include the bread and butter of any learnt skills and therefore must not exclude the majority from the bulk of any questions set. In the case of the question under scrutiny, it's my opinion that it does indeed require too deep an insight for "run of the mill" students to work with and sets the high bar too soon to ill effect.

The second aspect is to try to delineate between the "can do's" and the "really understand and can do's". There is a fine balance between these and most students recognise the difference.

Above all, those who simply "can do" should be given an opportunity to do so as much as possible. Therefore, to prevent a student from being able to progress through a question and demonstrate his/her knowledge due to a pre-requisite innate insight is unhelpful and (to put it bluntly) downright rude.
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Saman_B9
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Why does chi-squared test use a 0.95 value? Could anyone explain it to me?
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