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Hard maths questions for higher maths GCSE

I Want people on this thread to share their ideas on tricky maths questions they have experienced in the past
:biggrin:

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Reply 1
Avatar for TeeEm
TeeEm
19
Original post by DANIELREED
I Want people on this thread to share their ideas on tricky maths questions they have experienced in the past
:biggrin:


I posted hard GCSE questions in a thread around Xmas of 2014 in maths Exams
Reply 2
Avatar for Zacken
Zacken
22
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.
Here's one I've just made up, TeeEm style:

A sphere of radius 1 is placed on top of a sphere of radius 2 so that the line joining their centres is vertical. Find the radius of the base of the smallest right circular cone in which they will fit, with both spheres in contact with the cone.
Reply 4
Avatar for TeeEm
TeeEm
19
Original post by atsruser
Here's one I've just made up, TeeEm style:

A sphere of radius 1 is placed on top of a sphere of radius 2 so that the line joining their centres is vertical. Find the radius of the base of the smallest right circular cone in which they will fit, with both spheres in contact with the cone.


I have also made one but I need to type it
Reply 5
Avatar for TeeEm
TeeEm
19
Here is one I just made
(I got the idea a few days back when I was helping somebody)

In fact I think this is hard enough to go into one of my IYGB Special Papers (calculator versions)

Attachment not found


Any brave students there?
(edited 8 years ago)
Angles.jpg26.7KB
Original post by TeeEm
Here is one I just made
(I got the idea a few days back when I was helping somebody)

In fact I think this is hard enough to go into one of my IYGB Special Papers (calculator versions)

Attachment not found


Any brave students there?


Haven't got the time yet as I have cadets... however when I come back I am going to steam roll this question until I get the answer!! Spent 10 minutes on it and it makes my brain shrivel.
Reply 7
Avatar for TeeEm
TeeEm
19
Original post by BTAnonymous
Haven't got the time yet as I have cadets... however when I come back I am going to steam roll this question until I get the answer!! Spent 10 minutes on it and it makes my brain shrivel.


if you are a GCSE student this will hurt ...
I dare say most A level students will be brought to their knees by it.

Enjoy the cadets.
All the best!
Original post by TeeEm
Here is one I just made
(I got the idea a few days back when I was helping somebody)

In fact I think this is hard enough to go into one of my IYGB Special Papers (calculator versions)

Attachment not found


Any brave students there?


does north east mean a bearing of 045 or does north east mean a bearing in the range 000 to 090?
Reply 9
Avatar for TeeEm
TeeEm
19
Original post by DylanJ42
does north east mean a bearing of 045 or does north east mean a bearing in the range 000 to 090?


..
Original post by TeeEm
..


the term NE is used loosely these days, so i was just clarifying :hide:
Reply 11
Avatar for TeeEm
TeeEm
19
Original post by DylanJ42
the term NE is used loosely these days, so i was just clarifying :hide:


these terms are very specific
Reply 12
Avatar for Notnek
Notnek
21
I may have posted this before but this is one of the hardest I've seen, mainly because of the amount of work you had to do for one question. It's from an IGCSE exam a few years ago:

FInd the percentage of each shape that is shaded. The radii in diagram 6 are 2 and 5.



If I remember, the percentage of students who got full marks on this question was extremely low.
Reply 13
Avatar for Zacken
Zacken
22
Original post by notnek
...


Oh dear, I remember doing this a few days before my exam, definitely scared me. :afraid:
Reply 14
Avatar for Notnek
Notnek
21
Original post by Zacken
Oh dear, I remember doing this a few days before my exam, definitely scared me. :afraid:

I couldn't imagine them ever putting a question like that in a GCSE exam. Twitter would blow up.
Original post by notnek
I couldn't imagine them ever putting a question like that in a GCSE exam. Twitter would blow up.


throwback to this :laugh: oh god i remember the madness on social media haha

Reply 16
Avatar for Notnek
Notnek
21
Original post by DylanJ42
throwback to this :laugh: oh god i remember the madness on social media haha

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%.
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%.


its probably something to do with the difficulty some pupils had with picking out the relevant maths from the wordy scenario :dontknow: or maybe removal without replacement stumped people?

but i agree, it was definitely over-hyped in terms of difficulty
Original post by TeeEm
if you are a GCSE student this will hurt ...
I dare say most A level students will be brought to their knees by it.

Enjoy the cadets.
All the best!


Well it hurts... but hey, I had fun at cadets :colondollar:.

I guess I'll wait till next year when I start my AS levels!
Reply 19
Avatar for TeeEm
TeeEm
19
Original post by BTAnonymous
Well it hurts... but hey, I had fun at cadets :colondollar:.

I guess I'll wait till next year when I start my AS levels!


then it is officially becomes available to any A level student !!
Definitely it is hard to model ...

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