Project Maths Question

lostatsea

There has been a lot of debate on this forum about Project Maths. I've attached a question from the Project Maths Higher Level paper here.

I would like to hear the views of Mathematicians on this forum as to what they think of this type of question: Too easy/hard, is it suitable material for Leaving Cert students....
Thanks.

Turtwig

Not a mathemagican but for what it's worth I don't see that question as too easy. Seems fair.

Michael Collins

That's really weird. I'm not sure what area of the course it is trying to examine exactly but I'd say a lot of students would have real problems with that. Clearly understanding is required for this but...there's something not nice about it.

For one, it's kind of unclear. They say there are 147g of 9-carat gold but this is a bit confusing, however, because it's not gold - it's a material which contains an amount of gold equivalent to its carat rating. Maybe they should say that there are 147g of 9-carat material.

I think if you're going to ask questions like this you need to be very careful how you state it, often the way something is phrased can make all the difference, and different people pick up things differently - for some people I reckon that issue I mentioned above would be a huge issue. I could see them starring at the page not being able to make any sense of it because it seems paradoxical.

The major positive is clearly that the abilitiy to do calculations like this is extremely useful. And problems like this tend to arise a lot in a real situations in my experience. Also it gets the student thinking. I certaintly had to think more about how to tackle these problems than I would a standard Leaving Cert Maths paper of the past. In those, you knew almost immediately what section of the course you were being examined on and how to go about the solution - in fact you probably saw a very similar question in a past paper. I don't know how repeatable this type of question will be - if there will be a standard Question 5 on applications of (very basic) algebra.

All in all I'm not sure I like it. There's more of a brain teaser feel about it than actually a proper exam question. It's not testing maths, it's testing logic - and to a certain extent common sense. All good things to examine someone on in a course on 'Education for Life'...but is it fair in a maths exam?

I still haven't made up my mind though!

RoundTower

I'm not a big fan of Project Maths, but I like this question. It's a great example of a practical use of maths, a question that doesn't require more than basic arithmetic but yet might trouble students who just want to learn off every possible question that can get asked.

I agree the idea that what is referred to as "gold" is not pure gold could be confusing, but it's also realistic, and should be clear from a careful reading of the question.

And the Project Maths course is meant to be maths "for life" -- there should be a separate maths course for future mathematicians, physicists, engineers etc but that isn't going to happen.

FoxT

I like the question.
A person who can answer this will have shown a clear understanding of ratios & fractions, and will have a good grasp of the subtleties involved in handling them. I also like part (d)

The question also has a 'real-life' feel to it which adds to the attraction.

I have a problem, though
This is a Leaving Certificate Higher Level Paper? The pinnacle of academic achievement in math for an 18-year-old student? it takes 14 years of study to get to this level of competence? Surely, surely, we can do better for our young people than this....

Podge_irl

Honestly, it's a nice question and I like how they're trying to make the student think but it would suit a Junior Cert paper better.

MathsManiac

Michael Collins wrote: »

...For one, it's kind of unclear. They say there are 147g of 9-carat gold but this is a bit confusing, however, because it's not gold - it's a material which contains an amount of gold equivalent to its carat rating. Maybe they should say that there are 147g of 9-carat material.

Poppycock! The question states exactly what is meant by the term "9-carat gold", "18-carat gold", etc., and uses the term in precisely the way that it is used in reality.

I am inspired to write a little play regarding what might happen if you took this attitude in the real world:

Act 1, Scene 1.
Jeweller's shop. George, the proprietor, is busy at work.
Enter Micheal Collins, stage left.
George: Can I help you, sir?
MC: I wish to purchase a torus.
George (after a pause): A Taurus, sir? As a charm for a bracelet, is it?
MC: No, no. A torus. You know, the solid object obtained by rotating a circle about an axis that does not intersect it. Although I'm not especially fussy about the cross-section - I'm prepared to consider the solid of revolution on any simple closed curve about such an axis. Anyway, I want one to put on my finger.
George: Ah, you mean a ring?
MC: No, of course I don't mean a ring. If I wanted a ring I would obviously just select a nice set with two associative binary operations, such that the set forms an abelian group under the first operation, is closed under the other, and with the second being distributive over the first. I want a torus, dammit. Now do you have any?
George: Of course, sir. My apologies. We have a nice selection of ri.. eh, toruses over here.
MC: Tori.
George: Tory, sir? No, more of a Lib-Dem, really. Anyway, here they are. Is it a gold one you're interested in?
MC: Don't be daft. What kind of a jeweller are you? Everyone knows that gold is too soft to make practical jewellery from. My torus wouldn't be a torus for very long now, would it, if it were made of gold? Although I will concede that it would probably remain topologically a torus. But that's not much use to me if it's battered and dented and scratched, is it?
George: Indeed. Sir is a most discerning customer. But perhaps 18-carat gold, or 15-carat gold?
MC (nigh apoplectic): 18-carat gold? 18-carat gold? There's no such f-ing thing as 18-carat gold, you eejit. There is only 24-carat gold. Any substance whose carat value with respect to gold content is anything other than 24 is, by definition, not entirely made of gold, so you, who should know about such things, shouldn't be calling it gold. You, sir, are a charlatan. I'll have you for false advertising, trade descriptions act, and all that.
George: Begging you pardon, sir, but surely that interpretation of the term would make it rather pointless to define "carat rating" in the first place?
MC: I'm a mathematician, so the pointlessness of it doesn't concern me; (in fact - it's just an added bonus). It is the precision of the definition that is important, and the following through of that definition to it's logical conclusion that matters.
George: Fair enough, sir. What would you like your torus to made from?
MC: An alloy whose carat value with respect to gold content is 18.
George: Right, sir. Perhaps one of these then.
MC: This one looks quite nice. I'll take it.
[Telephone rings in the background, followed by muffled voice. Assistant jeweller (James) enters, stage right.]
James: George, that's the supplier you've been trying to get hold of all week.
George: Thanks, James, can you finish up with this gentleman. Just wrap that and take for it. I'm sorry, sir, but I need to take this call. James here will look after you. [Exits, stage right.]
James: Right, so that's one 18-carat gold ring. That'll be...
MC: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAArgh!
[Throttles James and exits, stage left.]


[Edit: P.S. no offense intended.]

japester

Really enjoyed that

Michael Collins

MathsManiac wrote: »

Poppycock! The question states exactly what is meant by the term "9-carat gold", "18-carat gold", etc., and uses the term in precisely the way that it is used in reality.

I am inspired to write a little play regarding what might happen if you took this attitude in the real world:

Act 1, Scene 1.
Jeweller's shop. George, the proprietor, is busy at work.
Enter Micheal Collins, stage left.
George: Can I help you, sir?
MC: I wish to purchase a torus.
George (after a pause): A Taurus, sir? As a charm for a bracelet, is it?
MC: No, no. A torus. You know, the solid object obtained by rotating a circle about an axis that does not intersect it. Although I'm not especially fussy about the cross-section - I'm prepared to consider the solid of revolution on any simple closed curve about such an axis. Anyway, I want one to put on my finger.
George: Ah, you mean a ring?
MC: No, of course I don't mean a ring. If I wanted a ring I would obviously just select a nice set with two associative binary operations, such that the set forms an abelian group under the first operation, is closed under the other, and with the second being distributive over the first. I want a torus, dammit. Now do you have any?
George: Of course, sir. My apologies. We have a nice selection of ri.. eh, toruses over here.
MC: Tori.
George: Tory, sir? No, more of a Lib-Dem, really. Anyway, here they are. Is it a gold one you're interested in?
MC: Don't be daft. What kind of a jeweller are you? Everyone knows that gold is too soft to make practical jewellery from. My torus wouldn't be a torus for very long now, would it, if it were made of gold? Although I will concede that it would probably remain topologically a torus. But that's not much use to me if it's battered and dented and scratched, is it?
George: Indeed. Sir is a most discerning customer. But perhaps 18-carat gold, or 15-carat gold?
MC (nigh apoplectic): 18-carat gold? 18-carat gold? There's no such f-ing thing as 18-carat gold, you eejit. There is only 24-carat gold. Any substance whose carat value with respect to gold content is anything other than 24 is, by definition, not entirely made of gold, so you, who should know about such things, shouldn't be calling it gold. You, sir, are a charlatan. I'll have you for false advertising, trade descriptions act, and all that.
George: Begging you pardon, sir, but surely that interpretation of the term would make it rather pointless to define "carat rating" in the first place?
MC: I'm a mathematician, so the pointlessness of it doesn't concern me; (in fact - it's just an added bonus). It is the precision of the definition that is important, and the following through of that definition to it's logical conclusion that matters.
George: Fair enough, sir. What would you like your torus to made from?
MC: An alloy whose carat value with respect to gold content is 18.
George: Right, sir. Perhaps one of these then.
MC: This one looks quite nice. I'll take it.
[Telephone rings in the background, followed by muffled voice. Assistant jeweller (James) enters, stage right.]
James: George, that's the supplier you've been trying to get hold of all week.
George: Thanks, James, can you finish up with this gentleman. Just wrap that and take for it. I'm sorry, sir, but I need to take this call. James here will look after you. [Exits, stage right.]
James: Right, so that's one 18-carat gold ring. That'll be...
MC: AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAArgh!
[Throttles James and exits, stage left.]

Well, never have I been so struck by the arts. The protagonist sounds like a delightful, handsome fellow - if a bit uncharacteristically impolite methinks.

OK, on a second reading I'll admit it is not as confusing as I first thought. I'm not suggesting that the carat system is pointless by the way! I'm more trying to put myself in the position of a 16/17/18 year old who doesn't have the same experience we do. (Too often people love to say Maths is getting too easy - maybe they've just gotten better! Or more likely they're trying to show off somehow. I'm not suggesting this is happening here at all.)

I do think there needs to be prudence when setting a question like this; not everyone will read the question the same way. For example, in that question, it is quite possible that a student would assume that the 147g refers to the "actual" gold content, and sub it in for [latex] m_g [/latex]. It seems obvious, but is it to everyone? (They might cop it when they have to calculate the value of the gold content - this would be quite easy if the latter were true!). Also, in part (b) you're not told that the other metals cannot be removed from the mixture - OK you're not told they are removed either, but I reckon for some people this might be an issue. (Again they might realise this if they work down and find an underdetermined system).

Anyway, if the task is to force the student to understand basic maths and logic, this question is excellent I think. For part (b) in particular, you really need to think about the whole context or you'll miss the constraint that the other materials generate. Quite challenging on your average student's basic logic skills at this level I think. There's almost no "maths" in it in some ways.

I'd be interested to hear people's opinions on a few things:

1) What is/should be the ultimate goal of Project Maths: get more students interested in maths? Foster a deep understanding of basic maths? Or prepare students for further studies in maths? All of the above?

2) How do you think a) an average honours C1/C2/C3 student would fare with the above question? b) how about an A1/A2 student from previous years?

3) Should there be a further paper for the interested, perhaps amalgamating - or tying in maybe - with the current Applied Maths curriculum (this hasn't be changed in a while - maybe never?), for those interested in pure maths?

4) Should honours maths teach basic skills for life like this, or take a more rigourous pure maths approch. Try to think of what the average student would benefit from i.e. if you're a maths student don't just say "more group theory and fractal geometry"!

5) Is the teaching ability out there to handle this type of shift in emphasis?

Exits via trapdoor

Ciaran

Michael Collins wrote: »

2) How do you think a) an average honours C1/C2/C3 student would fare with the above question? b) how about an A1/A2 student from previous years?

I can only answer for a single student from previous years but my reaction is "That's a Leaving Cert question?" I'd expect a decent Junior Cert student to be able to do that.

MathsManiac

Michael Collins wrote: »

Well, never have I been so struck by the arts. The protagonist sounds like a delightful, handsome fellow - if a bit uncharacteristically impolite methinks.

Dramatic license and all that - I got caught up in the moment!

The drama was inspired only by the comment, and not by the impeccable character of the commentator! Any resemblance to any real persons, living or dead, is etc., etc...

I'll throw in some views on your questions...

Michael Collins wrote: »

I'd be interested to hear people's opinions on a few things:

1) What is/should be the ultimate goal of Project Maths: get more students interested in maths? Foster a deep understanding of basic maths? Or prepare students for further studies in maths? All of the above?

Well, according to this information note for parents (from NCCA)...http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Project_Maths/Information_on_Project_Maths/Info_note_for_parents_June_2011.pdf
"It’s an initiative to change how maths is taught and learned in secondary schools. It’s about showing how maths connects with real-life problems, and about how skills developed in maths can be used in other subjects, in the workplace and at home. It also aims to change attitudes to maths and to encourage more students to take the subject at Higher level in their exams, and to study maths and maths-related subjects in college."

Michael Collins wrote: »

2) How do you think a) an average honours C1/C2/C3 student would fare with the above question? b) how about an A1/A2 student from previous years?

The kinds of skills needed to solve this kind of problem are not a focus of the existing (old) syllabus in maths and/or its exams, and, in my experience, they are extremely challenging skills for students at this level to master. If you are talking about students who have followed the old syllabus, then I think they would almost all have difficulty with this, especially under exam condidtions. C-students might have some hope of attempting part (a) and part (c)(i), but would be clueless on the remaining parts. Some A-students could have a reasonable shot at the remaining parts, but certainly not all. Mind you, it's difficult to be definitive, because the students who have high levels of the skills mainly being tested by this question may not be the same students as have high levels of the more traditional maths skills.

However, if a person has followed a programme of study that involves a lot of this kind of problem - extracting maths from text-based problems and dealing with unfamiliar scenarios - then that changes the game, and they should then be more capable of engaging with this.

Michael Collins wrote: »

3) Should there be a further paper for the interested, perhaps amalgamating - or tying in maybe - with the current Applied Maths curriculum (this hasn't be changed in a while - maybe never?), for those interested in pure maths?

The more maths courses there are available to people the better! But, realistically, given the timetabling constraints in schools, what kind of traction are you likely to get for another subject on top of those available? Some friends tell me that the Applied Maths course is under review at the moment, but I don't know whether it's taking a different direction or just being updated.

Michael Collins wrote: »

4) Should honours maths teach basic skills for life like this, or take a more rigourous pure maths approach. Try to think of what the average student would benefit from i.e. if you're a maths student don't just say "more group theory and fractal geometry"!

I think it's a bit optimistic to be referring to these as "basic skills". I suggest that the ability to handle this kind of question is not at all basic, and is possessed by a fairly small proportion of the population.

I'm a pure mathematician at heart, so I love the more abstract stuff. But I do recognise that not everyone feels the same way. The ability to extract mathematical meaning from a situation, use maths skills to solve the mathematical problem, and then interpret the solution intelligently in the original context, subject to all its constraints and assumptions, is a skillset that has a huge importance too. It has probably been ignored for too long, so I find it hard to argue against this shift in emphasis.

Also, of course, this is only one question on the exam. I think if you look at all the questions across the two papers together, there's an interesting blend of "pure" maths and maths in context.

On a related point, I think there is no harm in asking people to explain their reasoning, and articulate their understanding of concepts, as in some of these questions (at all three levels actually - higher, ordinary and foundation). People often assume that if the students can "do the sums" then they understand what's going on. It's only when you ask them to explain it that you realise they actually haven't a clue! Also, the capacity to explain and communicate in technical contexts is a valuable skill to develop in its own right. Maths is just one element of the whole programme of secondary education, and should be considered in that context. This link seems to capture the NCCA's view of the overall plan, and is worth thinking about how maths education fits into this: http://www.ncca.ie/en/Curriculum_and_Assessment/Post-Primary_Education/Senior_Cycle/Key_Skills/

Michael Collins wrote: »

5) Is the teaching ability out there to handle this type of shift in emphasis?

Not without a heck of a lot of inservice training and other support.

later12

Am I right in saying that that 50 mark question would give a full marks student 8⅓% in the examination?

If that's the case, the question is far too easy for those marks.

There is no such thing as a question being too easy or too difficult, it depends on how many marks are being awarded. 50 marks, for that, on a higher level paper, is much too generous imo.

red_fox

I think many students are coming to university unable to answer questions like this (but probably a lot of this is from ordinary level, I can't even guess). It's not something that a student can just recognise the topic and fit a solution to problem that they remember, it takes reasoning to solve. So it's a good skill that students should have. I'm not convinced that this is the level of mathematics that should need to be examined at leaving certificate higher level, perhaps if it involved some calculus also, it might be getting close to physics or engineering but I would be ok with that.

Edit: a torus? Cheapskate, that would have zero weight! You should get a nice [latex]S^1 \times D^2 [/latex]

henbane

I have to say that I think that the people who are calling this too easy are either too advanced in their mathematical studies or too far removed from doing the leaving cert. Certain parts are simple re-arrangements and plug in the numbers which was definitely part of the old syllabus so I don't see the problem. The rest require applied reasoning which can only be a good thing. The ability to deduce a (set of) valid equation(s) from a statement is relevant to problem solving at 3rd level and in real life so this question ticks every box a higher mathematics question should.

The idea that the study of higher maths at leaving cert should automatically lead to a student studying a maths related discipline at 3rd level is part of the problem. Plenty study higher level in other subjects they have no intention pursuing further so why is maths different. An effort to ground the higher maths syllabus in practical situations has to be applauded from the point of view of increasing maths literacy amongst the general population.

later12

henbane wrote: »

The idea that the study of higher maths at leaving cert should automatically lead to a student studying a maths related discipline at 3rd level is part of the problem. Plenty study higher level in other subjects they have no intention pursuing further so why is maths different. An effort to ground the higher maths syllabus in practical situations has to be applauded from the point of view of increasing maths literacy amongst the general population.

The curriculum, whose rigour is maintained through state examinations, has to prepare its students for being ready to pick up where they left off (or almost so) at third level. It is the same for students who study Irish, or English at university. They should be equipped with the appropriate training at higher level in school, so that they are ready for semester 1 in university.

It is perfectly reasonable that the same is expected from students studying higher level mathematics.

henbane

A leaving cert standard language essay wouldn't merit a pass at 3rd level. They're ready for the ideas but not ready to produce 3rd level thinking and their fellow leaving cert students who aren't pursuing further study in that discipline have a working knowledge of the fundamentals. Also, you conveniently ignored the first paragraph which provides context to the thoughts in the second para.

Turtwig

Michael Collins wrote: »

1) What is/should be the ultimate goal of Project Maths: get more students interested in maths? Foster a deep understanding of basic maths? Or prepare students for further studies in maths? All of the above?

MM answered that one way better than I could.:o

How do you think a) an average honours C1/C2/C3 student would fare with the above question? b) how about an A1/A2 student from previous years?

The A1/A2 should find it easy. Should being the operative word. The fact is that the problem with the present set up is that students frequently learn one way to do everything and understand very little of any of the concepts. Ask them a question that they've seen before and they can usually do it. However, if it's something they've seen before but presented somewhat differently they fumble over each other like a pack cards.
I honestly believe today's C1/C2/C3 LC student would struggle a lot with that question.

3) Should there be a further paper for the interested, perhaps amalgamating - or tying in maybe - with the current Applied Maths curriculum (this hasn't be changed in a while - maybe never?), for those interested in pure maths?

Any new subject is welcome. Unfortunately I don't see a great uptake for any of those papers. The option would be nice though but again MM answered this one better.:)

4) Should honours maths teach basic skills for life like this, or take a more rigourous pure maths approch. Try to think of what the average student would benefit from i.e. if you're a maths student don't just say "more group theory and fractal geometry"!

Pure maths, heck pure learning, begins with understanding. If they don't understand the utter basics what hope have they really for the abstract stuff? Never mind developing an interest in the subject and its deeper beauties. Also, I'm one of those people who believe that the entire world would benefit from greater proportions of the population understanding maths especially statistics. Newscientist did a sort of exposé on the how poor understanding of statistics can be detrimental to the health, welfare and even the judicial status! of a human being. I'll see if I can dig it up.

5) Is the teaching ability out there to handle this type of shift in emphasis?

Ok, I have no statistics or reports to support to me here but
I think its woefully inadequate. Don't get me wrong there are some quality teachers but the vast majority, in my experience, have themselves a poor enough standard of maths. By 'poor' I mean barely scraping through introductory level undergrad courses. I'm stressing though that's just my experience, its based on personal and anecdotal accounts and I very sincerely hope I'm wrong.

later12

henbane wrote: »

A leaving cert standard language essay wouldn't merit a pass at 3rd level. They're ready for the ideas but not ready to produce 3rd level thinking

Nobody suggested otherwise, the point is that mathematics is no different. The aim of leaving cert mathematics is to prepare the 'A grade' student for university mathematics, not to provide a university education itself. A B grade in honours maths is not a major achievement in itself.

and their fellow leaving cert students who aren't pursuing further study in that discipline have a working knowledge of the fundamentals.

Not sure what this means, many students need specific grade profiles, and therefore know that they need to get an A1 in a specific subject, say Irish or English, even though they know they have no desire to study it at third level. I would have loved to have been able to dismiss leaving certificate German to just learning 'the fundamentals', because I had no desire to study it later. However, I didn't and I couldn't, and even as someone with zero interest in the language, I was fairly well prepared for a university education in German.

So it isn't really clear what the point is that you are making in relation to mathematics specifically.

lostatsea

Thanks for all those comments regarding the type of question asked in Project Maths. I found the contributions very informative. Let me ask for further opinions on the other question from the Contexts and Applications section on the Higher LC Project Maths paper this year. Again I ask the same question as before: suitability for LC students, too easy or too difficult.....

Also have a look at this letter that appeared in the Irish Times today about the last HL paper from the old course which appeared in June which caused some controversy in the media about its perceived difficulty. I have attached the exam paper so you can see the questions (Question 8 (c) & 7(c)(ii)) to which the letter writer is referring.

Irish Times Letter (6 July 2011)
Sir, – You will be aware of the controversy concerning the 2011 Leaving Certificate Higher Maths Paper I, which was much more difficult than in previous years.
This may be disastrous for the 5 per cent of students who opted to take the Higher paper, many of whom are aiming for third-level courses with high entry requirements. This unusual paper – which they could not have anticipated – will cause many of them to under-achieve and miss their goals.
Question 8 (c) on integration depended on getting the initial substitution right (or no marks would be given), whereas in 1999 the same question gave this initial substitution as a hint. The degree of difficulty was far greater for 2011 students than it was for the students in 1999.
Question 6 involved the interpretation of graphs in an entirely new way. The students had to ignore much of the information provided by the graph, and focus simply on whether the second differential was positive, zero or negative. This would be a reasonable approach in the revised Project Maths curriculum, which commences next year, but it is not reasonable in the last paper of the current syllabus, which emphasises algebraic manipulation over graphic interpretation.
It is not possible to fix this by simply adjusting the marking scheme. Even Grade A students were so thrown by the unexpected difficulty of sections of the paper that they made uncharacteristic errors in the more standard parts of the paper. While Irish universities may compensate for this, foreign universities will not.
A political response is needed to ensure that an independent inquiry is made into the problems of the maths examination system, particularly in a wider context where the State has the goal of increasing take up of Higher Level Maths. This cannot be left to the State Examinations Commission.
There has recently been controversy regarding the administration of exams in the UK, and when questioned on this in parliament, Prime Minister David Cameron said, “You are right, this is not an acceptable situation. I’ve discussed it with the education secretary this morning, who in turn has discussed it with Ofqual, who are taking the toughest possible action to root out this failure and make sure it doesn’t happen again.”
There is a long history in this country of official bodies denying and covering up their mistakes. In this instance, the SEC has made serious errors. If the UK prime minister and minister can deal effectively with a body which has similar status to the State Examinations Commission (which operates under the aegis of the Minister for Education), then surely the Irish Minister for Education can do likewise on behalf of Irish students?
Additionally, a fair and effective solution must be found so that the students of 2011 are not disadvantaged. – Yours, etc,
ELIZABETH HOOD

Thanks for your time and interest. I am a teacher who is trying to make up my mind about the pros and cons of the new system.

Turtwig

Why have you only attached one question from Project Maths (two if you count the OP) yet an entire paper from the old syllabus? Bit of an unfair comparison in my book.

Regarding that letter I disagree thoroughly with Elizabeth. The 2011 paper was grand. I don't agree the SEC has made any such error especially when in my opinion the provision of hints is entirely optional anyways.

lostatsea

My first post in this thread contains the other question I referred to. The main difference in the Project Maths approach were the 2 questions contained in the Contexts and Applications sections. Some of this year's Project Maths Paper 1 contained part of the old course as it is being introduced in stages. Don't ask.

The way the whole course is being introduced is what is doing teacher's heads in. I don't know if any other country in the world has introduced a course in this fashion.

Anyway, here is the full Project Maths Paper 1 from June.

Michael Collins

lostatsea wrote: »

...Also have a look at this letter that appeared in the Irish Times today about the last HL paper from the old course which appeared in June which caused some controversy in the media about its perceived difficulty. I have attached the exam paper so you can see the questions (Question 8 (c) & 6(c)(ii)) to which the letter writer is referring...

I suspect she's referring to Question 7(c)(ii) there, and not sure why she's mentioning the second "differential" - the first derivative is all you need. Can't argue with her about Question 8(c) though, clearly an unequal level of difficulty when compared with 1999 (although you could argue that since it has appeared on a previous paper maybe the students should be more aware of the possibility of it arising and thus the hint is not necessary. Although 1999 was a long time ago!)