Thai y10 question

I found this question in a Year 10 Thai maths textbook (it's been translated so I hope it makes sense to everyone):

6pq+r=\sqrt{r^2-4ps}, \ \ p\neq 0 \ \ (1)

Without squaring (1) or any of it's rearrangements, express p in terms of only q, r and s.

Maths (especially algebra) is taught much faster in Thailand so I'm wondering if any British GCSE students are able to do it. I managed it but I doubt I would've been able to do it when I was in y10/11.

Everyone else is welcome to try but post your solution as a spoiler.

(edited 11 years ago)

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Reply 1

Frankster

Original post by notnek

I found this question in a Year 10 Thai maths textbook (it's been translated so I hope it makes sense to everyone):

Maths (especially algebra) is taught much faster in Thailand so I'm wondering if any British GCSE students are able to do it. I managed it but I'm not sure how far I would've got back in y10/11.

Everyone else is welcome to try but post your solution as a spoiler.

I know I'm wrong but...

Spoiler

Reply 2

Notnek

Original post by Frankster

I know I'm wrong but...

Spoiler

It says only q,r and s so you can't have a p on the right-hand-side.

Reply 3

james22

Spoiler

I have to say this is a very hard question for year 10. It's what I would expect in a STEP 2 paper.

EDIT: p=0 is a solution I fogot.

(edited 11 years ago)

Reply 4

Frankster

Original post by notnek

It says only q,r and s so you can't have a p on the right-hand-side.

Aaaah right.. soz didn't read it properly!

Reply 5

Intriguing Alias

Original post by notnek

I found this question in a Year 10 Thai maths textbook (it's been translated so I hope it makes sense to everyone):

Maths (especially algebra) is taught much faster in Thailand so I'm wondering if any British GCSE students are able to do it. I managed it but I doubt I would've been able to do it when I was in y10/11.

Everyone else is welcome to try but post your solution as a spoiler.

Spoiler

Too difficult for a year 10 unless

Spoiler

Reply 6

Intriguing Alias

Original post by james22

EDIT: p=0 is a solution I fogot.

It says

p \neq 0

Reply 7

ElMoro

Original post by notnek

I found this question in a Year 10 Thai maths textbook (it's been translated so I hope it makes sense to everyone):

6pq+r=\sqrt{r^2-4ps}, \ \ p\neq 0 \ \ (1)

Without squaring (1) or any of it's rearrangements, express p in terms of only q, r and s.

Spoiler

I don't think I would've spotted that when I took my GCSE

Reply 8

Notnek

Original post by hassi94

Too difficult for a year 10 unless...

It was part of a mixed exercise at the back of a textbook. The topic you mentioned is one of the chapters of the book which may make it slightly easier than just seeing it as I've posted it.

I have a feeling that you could probably count on your hand the number of British GCSE students who could do this question.

Reply 9

Intriguing Alias

Original post by notnek

Really you think it's that bad? I think most top students should be able to do it were they given some introduction (i.e. being part of that chapter).

Even if not, whilst I don't think I'd have solved it without someone saying

Spoiler

, I think there are a fair few people who could considering olympiad is far harder than this in terms of both the initial thinking and the actual computation - and there are plenty of students who do that at Year 10/11 (me not being one of them, mind - I did qualify for an intermediate olympiad in Year 10 but failed miserably :wink:

Reply 10

ElMoro

Original post by notnek

I have a feeling that you could probably count on your hand the number of British GCSE students who could do this question.

I don't think it's quite that bad. I think a lot of kids that like maths and try maths challenges and olympiads etc. could probably work out it given enough time imo

Reply 11

Notnek

Original post by hassi94

Spoiler

It wasn't actually part of the chapter but it definitely helps that the relevant topic is part of the book.

OK I was exaggerating before - maybe you could count the number on your hand if you had 200 fingers :smile:

Reply 12

TheMagicMan

Original post by hassi94

Spoiler

In our year (don't know about others) there were

\approx 15

students who qualified for BMO2 in Year 11 or earlier. They would all have 'easily' been able to solve this at that stage, along with some undetermined larger number of people also in our year who either weren't significantly involved in the olympiads or who are decent mathematicians...the number wouldn't be that small tbh

If this problem is set in the context of an exam that features the quadratic formula it's not that much harder than IGCSE

(edited 11 years ago)

Reply 13

Intriguing Alias

Original post by TheMagicMan

In our year (don't know about others) there were

\approx 15

Yeah - quite my point that they would find it easy. However, 15 qualified for BMO2 before Year 12!? That just seems alien to me. Noone in my school has ever qualified for BMO1 nevermind 2, I've got the furthest out of anyone with an intermediate olympiad qualification :tongue:

Reply 14

Intriguing Alias

Original post by krisshP

What does the sign in

p \neq 0

mean?

P does not = 0

Basically just p = 0 crossed out :tongue:

Reply 15

usycool1

Original post by krisshP

What does the sign in

p \neq 0

mean?

P is not equal to 0 :smile:

EDIT: Beaten to it :tongue:

Reply 16

Notnek

Original post by TheMagicMan

In our year (don't know about others) there were

\approx 15

students who qualified for BMO2 in Year 11 or earlier.

Wow what school is that? I thought only around 100 qualify for BMO2 each year and most of them are A-Level students (I never did it so I may be wrong).

Reply 17

Notnek

Original post by TheMagicMan

If this problem is set in the context of an exam that features the quadratic formula it's not that much harder than IGCSE

I don't agree with that. I've never seen an IGCSE algebra question anywhere near the level of this question, even if the context of the question is known.

Reply 18

krisshP

A pretty hard question.

Reply 19

TheMagicMan

Original post by notnek

Wow what school is that? I thought only around 100 qualify for BMO2 each year and most of them are A-Level students (I never did it so I may be wrong).

Not just at my school. Among current year 13s across the country, roughly 15 qulaified for BMO2 in year 11 or before (sorry if that was unclear :wink:

). That stat is just from my personal experience and what the IMO guys have said.