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# Mr M’s Edexcel GCSE Linear 1380 Higher Tier Calculator Paper 4 Answers Nov 2011

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1. (Original post by metaltron)
Wow that's gone completely over my head. To show 8 x 4 whole CDs and then give an answer of 36 is outstanding. Thinking like this is going to solve the dark matter/energy problem of the universe! Did you get both marks for 32,33,34,35 and 36?

Thanks again.
Yes full marks were awarded for the wrong answers of 34, 35 and 36. One mark was awarded for 44 (the answer you get if you melt down the rectangle and reform it into CDs).
2. (Original post by Mr M)
Yes, I know the *real* answer is higher than 32. In the unofficial mark scheme I gave an answer that was accessible for Foundation students.

You suggested the answer might be 38. The official Edexcel mark scheme says 36 but they are wrong.

I have actually written an article about this that has been accepted for publication in a forthcoming issue of Mathematics in School. The true optimal answer is 33.

I didn't do the paper but this question has my interest.

I thought that it was Area of Sheet/Area of Circle = 44.

The mark scheme says award 1 mark for this answer, and that the correct answer is 36. Clearly you've said that the mark scheme itself is wrong, but how is what I posted above incorrect?
3. (Original post by Mr M)
If you know the configuration you are looking for (this is the difficult bit) you don't need anything more complicated than Pythagoras. It is possible to produce a picture than appears to show 34 circles inside the rectangle but Pythagoras reveals a tiny overlap.

I used Autograph to plot the diagram.
Does your article discuss the proof for an answer of 33? If so could you provide it here on the forums or is there copyright issues with that? The book costs £80 which is a bit expensive for a book in my opinion.
4. (Original post by ThatPerson)
I didn't do the paper but this question has my interest.

I thought that it was Area of Sheet/Area of Circle = 44.

The mark scheme says award 1 mark for this answer, and that the correct answer is 36. Clearly you've said that the mark scheme itself is wrong, but how is what I posted above incorrect?
because when you cut circles out of a rectangular sheet there's always some waste. Circles don't tesselate.
5. (Original post by Micky76)
Does your article discuss the proof for an answer of 33? If so could you provide it here on the forums or is there copyright issues with that? The book costs £80 which is a bit expensive for a book in my opinion.
Sorry, the article belongs to The Mathematical Association now.

All I can offer is evidence that 36 doesn't work.

Attached Thumbnails

6. (Original post by gdunne42)
because when you cut circles out of a rectangular sheet there's always some waste. Circles don't tesselate.
Ah I understand; I think I've got a better idea.

The diameter is 12, so I made a square of 12x12, which has an area of 144cm. The total area is 5000cm of the sheet so,

5000/144= 34.72, which would mean 34 circles can fit onto the sheet?

Is their a problem with that?

EDIT 2:

Another idea is add on anywhere from 0.1-0.5cm onto that diameter to give it some space, so I end up with a general value of 32-34, with an average of 33; that was Mr.M's optimal answer.

That is my best shot with my primitive math.
7. (Original post by ThatPerson)
Ah I understand; I think I've got a better idea.

The diameter is 12, so I made a square of 12x12, which has an area of 144cm. The total area is 5000cm of the sheet so,

5000/144= 34.72, which would mean 34 circles can fit onto the sheet?

Is their a problem with that?

EDIT 2:

Another idea is add on anywhere from 0.1-0.5cm onto that diameter to give it some space, so I end up with a general value of 32-34, with an average of 33; that was Mr.M's optimal answer.

That is my best shot with my primitive math.
The question was supposed to be handled by candidates with basic maths skills so I imagine the sophisticated solution discovered by Mr M and his students was not the one the examiners anticipated.

The approach you have taken is still flawed. Imagine a sheet that measures 17 cm x 36 cm.
Area = 612 cm^2
612/144 = 4.25
But you could only cut 3 12x12 squares from it and then be left with a strip of scrap measuring 5 x 36

For the most basic approach to a solution, you need to work out how many whole discs fit across the sheet and how many would fit down the sheet. (or how many whole 12/12 squares fit in across and down).
100/12 = 8 across 50/12 = 4 down then 8x4 = 32
8. This paper was easier than the one we had

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