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# FP2 Summer 2009 Q1 where am I going wrong here. Watch

1. The picture shows Q1 2009 FP2 OCR.
The answer I have is that there are two potential sets of rectangles to measure and the size comes down to

for one set of rectangles and

for the other.
The answers come out as -1.33131 and -0.5185 respectively.

Since we are asked for an upper bound and lower bound, I am tempted to put -0.5185 as the Upper Bound and -1.3131 as the Lower bound.

The Mark scheme says that the areas should be given as positive and if you use negative answers you lose two marks, which I find surprising.

The report goes so far as to say "A substantial number of candidates lost early marks by giving negative answers".

Whilst I understand a mark scheme (especially for Qu 1) giving full marks for UB 1.3131 and LB 0.5185 should we lose marks for giving negative areas for this Question, especially if we give the correct UB and LB for those numbers.

What am I doing wrong here to get different answers to the Mark scheme?
2. (Original post by nerak99)

The picture shows Q1 2009 FP2 OCR.
The answer I have is that there are two potential sets of rectangles to measure and the size comes down to

for one set of rectangles and

for the other.
The answers come out as -1.33131 and -0.5185 respectively.

Since we are asked for an upper bound and lower bound, I am tempted to put -0.5185 as the Upper Bound and -1.3131 as the Lower bound.

The Mark scheme says that the areas should be given as positive and if you use negative answers you lose two marks, which I find surprising.

The report goes so far as to say "A substantial number of candidates lost early marks by giving negative answers".

Whilst I understand a mark scheme (especially for Qu 1) giving full marks for UB 1.3131 and LB 0.5185 should we lose marks for giving negative areas for this Question, especially if we give the correct UB and LB for those numbers.

What am I doing wrong here to get different answers to the Mark scheme?
I don't know the specifics of the OCR FP2 syllabus, but from a common sense point of view, if you are estimating an area, you MUST get a positive value - it's the function that takes negative values, not the dimensions of the rectangle!
3. (Original post by nerak99)
What am I doing wrong here to get different answers to the Mark scheme?
Well since it asks for the area, it should be positive. However, if you were integrating it, you'd get a negative value.

Seems a mean markscheme, IMHO. A trick, rather than testing genuine understanding.
4. (Original post by nerak99)
...
The area of those rectangles is not negative.

You would get some credit for failing to realise this but you would lose the accuracy marks.
5. (Original post by ghostwalker)
Well since it asks for the area, it should be positive. However, if you were integrating it, you'd get a negative value.

Seems a mean markscheme, IMHO. A trick, rather than testing genuine understanding.
I beg to disagree - surely if you're asked for an area then you realize that it has to be positive. There isn't actually any integration mentioned in the question, unless there are extra parts. The really mystifying thing is what this is doing in an FP2 exam - I'm sure we used to estimate curved areas with rectangles at junior school
6. (Original post by ghostwalker)
Well since it asks for the area, it should be positive. However, if you were integrating it, you'd get a negative value.

Seems a mean mark scheme, IMHO. A trick, rather than testing genuine understanding.
Well I agree with that.
However, I don't see why an area can't be negative. After all, numbers can be negative, even mass can be negative and as you say, the answer to the integral would be negative.
My main gripe is the removal of two marks from a 5 mark question and in Q1, why on earth do an area under the x axis when you are not making some point about negative areas. At FP2 testing whether negative areas are appreciated is a perfectly legitimate question. Implying that the question is somehow testing this and then rejecting a sensible answer, (that shows real understanding of LB and UB (IMO) ) is, as you say, mean.
7. (Original post by nerak99)

Since we are asked for an upper bound and lower bound, I am tempted to put -0.5185 as the Upper Bound and -1.3131 as the Lower bound.
You need to take the magnitude of those numbers. Think of it graphically. What is the upper bound for the area under that curve? The upper bound is surely going to be larger than the actual area. Which, in this case is when you worked out when the rectangles were larger than the curve, ie the 1.3131

And also, if you do take it in the negative form, you get the upper and lower bound the wrong way round
8. (Original post by ghostwalker)
Seems a mean markscheme, IMHO. A trick, rather than testing genuine understanding.
I can enlighten you on how this allocation of marks *might* have come about.

Examiners meeting

Team Leader: "So we have looked at 40 sample scripts now and they have nearly all got question 1 right."

Principal Examiner: "What should we do?"

Team Leader: "A lot of them found the signs confusing."

Principal Examiner: "Perfect. We'll take the accuracy marks off the numpties with the wrong signs. Now for question 2 ..."
9. (Original post by Mr M)
...
Lol, nicely put. I was thinking they're just looking at ways to spread the marks out a bit.

@davros I stand corrrected. Still think it's a bit mean though for FP2. But I don't know the details of the syllabus (or even it in general actually).
10. (Original post by 2710)

And also, if you do take it in the negative form, you get the upper and lower bound the wrong way round
So far as I can tell, in pure maths, an area is a number, however if the convention is to take areas using magnitude then I am happy to go along.

If I am working on bounds with two negative numbers from a function, -1.3 and -0.5 (say) then the UB is -0.5 and the LB is -1.3. Those answers, given that I was being so radical as to consider a negative area, are not the wrong way round are they?
11. (Original post by nerak99)
So far as I can tell, in pure maths, an area is a number, however if the convention is to take areas using magnitude then I am happy to go along.

If I am working on bounds with two negative numbers from a function, -1.3 and -0.5 (say) then the UB is -0.5 and the LB is -1.3. Those answers, given that I was being so radical as to consider a negative area, are not the wrong way round are they?
They would be the wrong way round according to the mark scheme (and the right answer), because the upper bound should have the 1.313 figure. If they saw you put -0.5 as the upper bound, what would happen?

But I think you are over complicating. Its like I have a square on top of the x axis with area 4. If I move it under the x axis, it still has area 4. I mean, how can you have a square with -4 area? What would it look like in real life :P It might be possible, but thats outside my range of knowledge :P
12. (Original post by 2710)
They would be the wrong way round according to the mark scheme (and the right answer), because the upper bound should have the 1.313 figure. If they saw you put -0.5 as the upper bound, what would happen?

But I think you are over complicating. Its like I have a square on top of the x axis with area 4. If I move it under the x axis, it still has area 4. I mean, how can you have a square with -4 area? What would it look like in real life :P It might be possible, but thats outside my range of knowledge :P
Well, firstly this is pure maths and not mechanics, even if it were not pure maths, if we can have negative mass then negative area is not a problem.
Secondly, my last contribution concerned a general answer to a function that outputs two numbers at its bounds and in that case it would be perfectly legitimate to have -0.5 as an UB and -1.3 as a LB. I do realise that that is not the case in this question, I should have made my writing more simple to read. Obviously, the mark scheme is right but that does not mean it is not mean. :-)
13. (Original post by nerak99)
Well, firstly this is pure maths and not mechanics, even if it were not pure maths, if we can have negative mass then negative area is not a problem.
Who told you you can have negative mass? Mass is a scalar (ok this does not prohibit negative numbers but it has a positive magnitude in every situation you will encounter).

If you are talking about exotic matter, it is purely theoretical.
14. (Original post by nerak99)
Well, firstly this is pure maths and not mechanics, even if it were not pure maths, if we can have negative mass then negative area is not a problem.
Secondly, my last contribution concerned a general answer to a function that outputs two numbers at its bounds and in that case it would be perfectly legitimate to have -0.5 as an UB and -1.3 as a LB. I do realise that that is not the case in this question, I should have made my writing more simple to read. Obviously, the mark scheme is right but that does not mean it is not mean. :-)
Well using your own words, this is not mechanics. Negative mass occurs in theoretical physics, so you cannot really conclude that negative area is Ok for pure math. IN fact this link might be helpful:

http://www.intmath.com/applications-...nder-curve.php
15. (Original post by nerak99)
Well I agree with that.
However, I don't see why an area can't be negative. After all, numbers can be negative, even mass can be negative and as you say, the answer to the integral would be negative.
My main gripe is the removal of two marks from a 5 mark question and in Q1, why on earth do an area under the x axis when you are not making some point about negative areas. At FP2 testing whether negative areas are appreciated is a perfectly legitimate question. Implying that the question is somehow testing this and then rejecting a sensible answer, (that shows real understanding of LB and UB (IMO) ) is, as you say, mean.
Integration is irrelevant to this question - I can't see the word "integral" mentioned anywhere in the screenshot.

Areas are always positive; integrals can be negative.

If you were asked to paint the area, would you go out and buy "minus 10 litres of paint"? I don't think so
16. In semiconductors, you have to use the concept of holes in order to explain the hall effect. The mass of holes can come out to be negative. As I said, if I can have to deal with negative mass in order to get some answers in Physics, then it does not seem to revolutionary to think about negative area in the purely theoretical area of pure maths.
17. (Original post by nerak99)
In semiconductors, you have to use the concept of holes in order to explain the hall effect. The mass of holes can come out to be negative. As I said, if I can have to deal with negative mass in order to get some answers in Physics, then it does not seem to revolutionary to think about negative area in the purely theoretical area of pure maths.
FP2 wouldn't want you to think so abstractly as to use negative area.
18. (Original post by Music99)
FP2 wouldn't want you to think so abstractly as to use negative area.
So in question 1 we have to make sure we are not so abstract as to think about a negative area but in Q2 we have to distinguish real numbers and by question nine deal with imaginary ones.

My line of "too abstract" is clearly moving in the wrong space.

Just to be clear, as I said before I accept the mark scheme interpretation.
19. (Original post by nerak99)
So in question 1 we have to make sure we are not so abstract as to think about a negative area but in Q2 we have to distinguish real numbers and by question nine deal with imaginary ones.
Consider yourself fortunate they stop at imaginary (complex) numbers.
20. (Original post by ghostwalker)
Consider yourself fortunate they stop at imaginary (complex) numbers.
It's all about the hyper reals .

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