The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Hard maths questions for higher maths GCSE

Scroll to see replies

Original post by Zacken
There's no infinity involved here. If I'm using kk then that's any arbitrary integer that does not imply infinity in anyway.

Everything cancels out, but remember that in the ⋯\cdots there's something that cancels the 2k−32k-3 as well, so you're only left with...?


1/(2k + 1)?
Reply 41
Avatar for Zacken
Zacken
22
Original post by TheOtherSide.
1/(2k + 1)?


That's the denominator, yes. So what's 1/that? :biggrin:
Original post by Zacken
That's the denominator, yes. So what's 1/that? :biggrin:


I have got no idea what to do with this :facepalm:
Reply 43
Avatar for Zacken
Zacken
22
Original post by TheOtherSide.
I have got no idea what to do with this :facepalm:


So you've simplified 1blah\frac{1}{\text{blah}} to 112k+1\displaystyle \frac{1}{\frac{1}{2k+1}} can you simplify this any further?
Original post by Zacken
So you've simplified 1blah\frac{1}{\text{blah}} to 112k+1\displaystyle \frac{1}{\frac{1}{2k+1}} can you simplify this any further?


Oh right, that's the same as just 2k + 1.
Reply 45
Avatar for Zacken
Zacken
22
Original post by TheOtherSide.
Oh right, that's the same as just 2k + 1.


And that's the answer. :yep:
Original post by Zacken
And that's the answer. :yep:


Thanks for the help! :woo:
Reply 47
Avatar for Zacken
Zacken
22
Original post by TheOtherSide.
Thanks for the help! :woo:


Good work!
Original post by notnek
I sitll find that reaction crazy. It's a standard A* question and similar to ones I've seen in old GCSE and IGCSE papers.

If any GCSE students want a challenging paper, take a look at the Edexcel June 2004 non-calc. The A* boundary was only 61%.


Saw your post so I tried to complete it. Managed to get 88% but damn... so much harder than usual
Reply 49
Avatar for Notnek
Notnek
21
Original post by surina16
Saw your post so I tried to complete it. Managed to get 88% but damn... so much harder than usual

Yes I find that top students who get close to 100% in most GCSE past papers often get below 90 in the June 04 paper.
A circle is inscribed in an equilateral triangle of side 2, so that the sides of the triangle are tangent to the circle. Find the ratio of the area of the circle to the area of the triangle.
Find the value of

11+11+11+⋯\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+ \cdots}}}

where ⋯\cdots indicates that the fraction continues the same pattern to infinity.
Reply 52
Avatar for TeeEm
TeeEm
19
Original post by atsruser
Find the value of

11+11+11+⋯\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+ \cdots}}}

where ⋯\cdots indicates that the fraction continues the same pattern to infinity.


b15.gif
Find the value of

11+21+11+21+⋯\displaystyle \frac{1}{1+\frac{2}{1+\frac{1}{1+ \frac{2}{1+\cdots}}}}

where ⋯\cdots indicates that the fraction continues the same pattern to infinity.
Reply 54
Avatar for Zacken
Zacken
22
Original post by atsruser
Find the value of

11+11+11+⋯\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+ \cdots}}}

where ⋯\cdots indicates that the fraction continues the same pattern to infinity.


Solution:

Spoiler



What's with the recursive mood over the past few days? :lol:
(edited 8 years ago)
Reply 55
Avatar for Zacken
Zacken
22
Original post by atsruser
Find the value of

11+21+11+21+⋯\displaystyle \frac{1}{1+\frac{2}{1+\frac{1}{1+ \frac{2}{1+\cdots}}}}

where ⋯\cdots indicates that the fraction continues the same pattern to infinity.


Spoiler



D'you have a better way to justify taking the positive root?
Original post by atsruser
Find the value of

11+11+11+⋯\displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+ \cdots}}}

where ⋯\cdots indicates that the fraction continues the same pattern to infinity.


And for a bonus mark(or rather, for a gold star :ahee:), what is the special name given to 1+11+11+11+⋯1 + \displaystyle \frac{1}{1+\frac{1}{1+\frac{1}{1+ \cdots}}}
Reply 57
Avatar for Zacken
Zacken
22
Original post by atsruser
You're cheating as you're not a GCSE student. You really ought to spoiler these.


Apologies. I've spoilered them, might want to edit your post so you can remove the quote.
Original post by Zacken
Apologies. I've spoilered them, might want to edit your post so you can remove the quote.


No need to apologise - I find it hard to stop myself solving problems if I can see how to do them.
Original post by Zacken
This 6 mark question came up in my GCSE exam and I quite enjoyed it.Integers aa and bb are such that (a+35)2+a−b5=51(a + 3\sqrt{5})^2 + a - b\sqrt{5} = 51. Find the possible values of aa and the corresponding values of bb.

how do you do this? I expanded the double brackets and got

a^2+6 sqrt(5) a+45
(edited 8 years ago)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you