Grade 9 Maths Paper GCSE (and other difficult GCSE questions) - 2018 thread

I glanced at all the questions a few days ago and I felt the same about this one. I thought I might have missed an easier method.

I haven’t tried all of them but I agree that it looks like a brilliant paper and I bet most A Level students couldn’t come up with a GCSE paper this good.

Thank you for the compliment. I will admit I do feel the same and I was torn between 4 and 5 marks.

Was your method the same as @I hate maths method?

I have been working on my paper for a while now and I am proud to announce that it is finally ready to submit...

A certain student of mine will be doing some of these tomorrow.

Thank you.

Was your method the same as @I hate maths method?

I'm in year 13 and I've been doing puzzle-y problems like this to prepare for some exams, not to mention I've seen a similar problem to this before, but even then I still took more than 4 minutes to think it through, solve, and write up. Heck, I'd probably spend 4 minutes just trying to cube 28 without a calculator haha. I doubt the majority of grade 9 students could complete it let alone in four minutes (looks like "mark a minute" judging by marks and time given), but maybe I'm out of touch with GCSE these days.

Looks amazing, thanks!!!

A certain student of mine will be doing some of these tomorrow.

Thank you.

It looks like you have a “hard GCSE maths questions” rival

Are you participating in the upcoming UKMT IMOK?

Question 15 is very similar in style to problems of Olympiad Maths e.g. integer equations and stuff. Enjoyed that question!

It looks like you have a “hard GCSE maths questions” rival

I’ll also be stealing some of these questions for students to try. I’m not sure I’m mean enough to set them the whole paper though

Yeah I based it off a mark per minute but I think I should really give students 1h 30minutes since this is much more difficult

thank you so much, i will definately try it out!

(also i think you accidentally spelt anyways wrong on your website, you spelt it "anywayways" lol)

Well in fairness, if every grade 9 student could get full marks or nearly full marks on your paper, then the paper loses its meaning, so it might not be a bad thing to have harsh discriminator questions. But the only way I see a GCSE student successfully doing the problem in time is if they've had a bit of exposure to extra-curricular maths (or they possess extreme ingenuity), or if they finished the other questions easily and had more time to think on this one and do the tedious calculations.

To make it more balanced you could choose a number with fewer factors than 60, say a prime number so it only produces one value of n, and just forego the $x^3$ which hardly tests maths. For example, $n^2+59$ would only be square for $n=29$. And $n$ is large enough to discourage trial and error.