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#1 2007-06-02 05:52:29

Daniel123
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Registered: 2007-05-23
Posts: 663

Questions

Hi everyone.

My Maths GCSE is on Monday, and I have totally run out of past papers etc to do. Can anyone think of a challenging GCSE question for me?

Thanks. big_smile:D:D

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#2 2007-06-02 06:07:19

Devantè
Real Member
Registered: 2006-07-14
Posts: 6,400

Re: Questions

Which tier? If you mean challenging, do you mean the sort of ... last-question-type of question that would help you prepare?

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#3 2007-06-02 06:09:30

Daniel123
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Registered: 2007-05-23
Posts: 663

Re: Questions

Higher.. and yes I mean those trickier ones. smile

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#4 2007-06-02 06:30:11

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Questions

Daniel123 wrote:

Can anyone think of a challenging GCSE question for me?

You want challenging? Well, this is one I made up myself. It may or may not be challenging, depending on how much maths you know.

Well, if you know Fermat’s little theorem, the answer will follow from it almost immediately, so it won’t be challenging to you. However, I don’t think you have learnt Fermat’s little theorem, so it is my bet that you will find it challenging to try and prove it yourself. big_smile

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#5 2007-06-02 07:12:52

Daniel123
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Registered: 2007-05-23
Posts: 663

Re: Questions

I have absolutely no idea. sad I am rather interested why, though. Would you care to explain?:)

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#6 2007-06-02 07:29:19

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

After going over 14 past papers, the hardest question and the only one I would get no marks for at all, is:

The probability that Betty will be late for school tomorrow is 0.05
The probability that Colin will be late for school tomorrow is 0.06

The probability that both Betty and Colin will be late for school tomorrow is 0.011

Fred says that the events 'Betty will be late tomorrow' and 'Colin will be late tomorrow' are independent. Justify whether Fred is correct or not.
(for 2 marks)

Last edited by Daniel123 (2007-06-02 07:29:33)

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#7 2007-06-02 07:38:08

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Questions

The way of checking independence is to multiply the probabilities of the two events together.
If it's equal to the amount you're told, then they're independent. If not, they're not.

0.05x0.06 = 0.003 ≠ 0.011, so they are not independent.


Why did the vector cross the road?
It wanted to be normal.

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#8 2007-06-02 07:41:39

Daniel123
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Registered: 2007-05-23
Posts: 663

Re: Questions

Aah rightyy. Thanks mathsy. smile

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#9 2007-06-02 09:13:53

Stanley_Marsh
Member
Registered: 2006-12-13
Posts: 345

Re: Questions

To Jane question
    I haven't learn Fermat's little theorem thought , there is way to do it

Is group helpful on this one?

Last edited by Stanley_Marsh (2007-06-02 09:14:56)


Numbers are the essence of the Universe

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#10 2007-06-02 09:46:58

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Questions

This is my method for proving the statement without using Fermat’s little theorem.

Consider the following integers: n−2, n−1, n, n+1, n+2. These are 5 consecutive integers, so one of them is definitely divisible by 5 (even if n isn’t). Therefore their product is divisible by 5: for some integer k

So n(n[sup]4[/sup]+4) is divisible by 5. Thus, if n itself is not divisible by 5, n[sup]4[/sup]+4 must be.

(FYI, Fermat’s little theorem states that if p is a prime and a is an integer coprime with p, then

So if n is not divisible by 5, n[sup]4[/sup] ≡ 1 (mod 5) by Fermat’s little theorem.)
­

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#11 2007-06-03 02:45:58

Daniel123
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Registered: 2007-05-23
Posts: 663

Re: Questions

That was sort of how I attempted it - I looked at n-2, n-1 etc, but I didn't know where to go from there. Oh well! My non-calculator exam is tomorrow! Wish me luck everyone! big_smile

Last edited by Daniel123 (2007-06-03 02:46:21)

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#12 2007-06-03 02:58:14

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: Questions

aaw, i prefer calc paper to non-calc paper, thanks for notifying me though, saves me bringing my calculator in smile


The Beginning Of All Things To End.
The End Of All Things To Come.

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#13 2007-06-04 03:50:54

Daniel123
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Registered: 2007-05-23
Posts: 663

Re: Questions

URGH!!!! I'm soo annoyed! The paper was the easiest paper I have ever done, but I made the most careless mistake that will cost me 2 marks. I could have got 100%! swearswearswear! But at least I got a question that I completely guessed right - it asked for the reciprocal of 2. I have never heard of 'reciprocal' in a maths context, but I guessed 2-¹ = ½.

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#14 2007-06-04 03:57:58

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Questions

well too bad you missed that, but seems like you did very well big_smile overall! Sometimes I wonder if exams really test your true knowledge of maths, or your skills at sitting exams, because its easy for even the best mathematician to make mistakes in a panic.

Last edited by Identity (2007-06-04 03:58:53)

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#15 2007-06-04 03:59:01

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

I know! The second I walked out of the exam room I realised what I had done wrong, so it's not even like I didn't know it!!!!

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#16 2007-06-04 04:40:46

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

Quick question - there was a question that said (I can't remember the figures) "3⅓ x 2¼, write your answer in its simplest form". I put 15/2.... is that write, or should it be 7 1/2?

Last edited by Daniel123 (2007-06-04 04:42:59)

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#17 2007-06-04 04:58:46

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Questions

they shouldnt be picky about things like that, by simplest form it will have just meant simplyfying the fraction so it isnt like 60/8 or something.

what exam board are you on? I had my maths exam today aswell, but none of the question's you are on about were on it? Or do you have modular maths?


The Beginning Of All Things To End.
The End Of All Things To Come.

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#18 2007-06-04 05:00:58

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

Ok good. Im on edexcel.. you? Was yours hard?

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#19 2007-06-04 07:55:28

luca-deltodesco
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Registered: 2006-05-05
Posts: 1,470

Re: Questions

ah ok, im on AQA for GSCE, and no, not really, i finished 1hr20min early, not that i expected any less considering ive done my A-level tongue


The Beginning Of All Things To End.
The End Of All Things To Come.

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#20 2007-06-05 04:03:32

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

Lol I finished mine in 25 minutes! It really worried me though, especially as I saw others using tracing paper (for angle bisector would you believe), which made me think i had missed a few pages! Such an easy exam though, i want the next one to be harder.

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#21 2007-06-05 06:32:37

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Questions

Yes, I never used any tracing paper for any of those exams either. I don't really see how it could be useful. For example, bisecting an angle just involves drawing some arcs and lines with a compass and ruler. How can tracing paper help with that?

The only possible thing I can think of for it to be used for is transformation questions. Draw the shape that needs to be reflected, rotated and/or moved, do that to the tracing paper and then use the result to draw the answer. But then again, that seems like more hassle than just doing it in the first place.


Why did the vector cross the road?
It wanted to be normal.

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#22 2007-06-05 06:42:45

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

Exactly. Im quite annoyed, as the surds and indice questions were easy, and I doubt they will put others in the calculator paper:

Write: 7² x 7³ as a power of 7.

Evaluate (√3 - √2) (√3 + √2).

Not exactly challenging....

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#23 2007-06-11 03:37:19

Daniel123
Member
Registered: 2007-05-23
Posts: 663

Re: Questions

I have just finished my paper 6! It was even easier than paper 5! It really is ridiculous. The 'A*' question at the end was calculating the height of a cone if you know the radius of the net (sector). There was no questions that challenged me! Oh well, I can't really complain big_smile

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#24 2007-06-11 04:08:12

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Questions

I just finished my Facts, Skills and Applications exam too big_smile, it was incredibly easy, hope the next one won't be! None of the questions were 'difficult', they just required checking and double-checking, so trickiest question was a simplifying surds one.

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