To what extent can you use advanced techniques

I've heard that as long as you use any mathematically valid method to solve a question in either A-Level or GCSE, you should get your marks and I was wondering whether this was actually true.

For example, the popular Hannah's sweets question that's been all over the board. Would I have been able to answer that with a hypergeometric distribution approach and get the marks?

Or using countour integration to solve problems

\displaystyle \int_0^{\infty} \frac{1}{1+x^4} \, \mathrm{d}x

that might pop up in an A-Level paper.

Would using things like this just make me seem like a smartass and cost me marks or would the examiner actually understand it and mark it seriously?

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Reply 1

Smaug123

Original post by Zacken

\displaystyle \int_0^{\infty} \frac{1}{1+x^4} \, \mathrm{d}x

that might pop up in an A-Level paper.

Would using things like this just make me seem like a smartass and cost me marks or would the examiner actually understand it and mark it seriously?

Risky, I'd say - you might end up with a non-mathematician marking it.

Reply 2

Jai Sandhu

Original post by Zacken

\displaystyle \int_0^{\infty} \frac{1}{1+x^4} \, \mathrm{d}x

that might pop up in an A-Level paper.

Would using things like this just make me seem like a smartass and cost me marks or would the examiner actually understand it and mark it seriously?

Wouldn't risk it for a chocolate biscuit.

Reply 3

Zacken

Original post by Smaug123

Risky, I'd say - you might end up with a non-mathematician marking it.

Original post by Jai Sandhu

Wouldn't risk it for a chocolate biscuit.

I see where you're coming from and I'd be unlikely to use it in any actual examination. But I do think I'll be using it for my in-class tests just to irritate my teacher a little. Thanks! :smile:

Reply 4

lizard54142

Original post by Zacken

\displaystyle \int_0^{\infty} \frac{1}{1+x^4} \, \mathrm{d}x

that might pop up in an A-Level paper.

Would using things like this just make me seem like a smartass and cost me marks or would the examiner actually understand it and mark it seriously?

It depends how "advanced" the techniques are. I used a logarithmic method in my GCSE maths, rather than "guessing" as we were taught, and I got the marks.

I wouldn't use contour integration in an A Level paper, and definitely not a hypergeometric distribution approach to "Hannah's sweets".

Reply 5

Zacken

Original post by lizard54142

At what point does a technique become 'too advanced' though?

Reply 6

poorform

I wouldn't recommend it. I lost marks for bringing out calculus in Yr 9 sats paper. :frown:

They wanted me to count squares when I can easily integrate over the region to find the area and use the derivative to find the gradient.

(edited 8 years ago)

Reply 7

Zacken

Original post by poorform

I wouldn't recommend it. I lost marks for bringing out calculus in Yr 9 sats paper. :frown:

They wanted me to count squares when I can easily integrate over the region to find the area and use the derivative to find the gradient.

Boss. xD

Reminds me too much of Physics though... why would I spend all that time counting squares when it was a simple quadratic that I could integrate over to find the area. ._.

Reply 8

rayquaza17

Original post by Zacken

Reminds me too much of Physics though... why would I spend all that time counting squares when it was a simple quadratic that I could integrate over to find the area. ._.

Lol too true.

I remember my physics teacher complaining about the lack of maths in physics, and I never truly understood what he meant until today (actually) when I looked at the 'real equations' that correspond to the electric and magnetic fields topic in A2 physics. :eek:

Reply 9

Zacken

Original post by rayquaza17

I expected a lot more out of my Physics course. Didn't learn much maths in there, so I picked up a few lecture notes at home and went through those. Did some heavy second order differential equations involving variable force, mass, power and work. Made me a lot happier. Also, I really liked the differential equations with air resistance. Made Physics fun! :biggrin:

Reply 10

lizard54142

Original post by Zacken

At what point does a technique become 'too advanced' though?

If you're considering not using a technique because you're worried it might be to advanced, then it most probably is.

At A Level I would stick to the course, but you could probably delve into some Further Maths techniques (but I wouldn't start using de Moivre's for C4 trig!). In STEP by all means use all of the techniques you know, but quote what you're using if it is a bit "unusual"; e.g. "by the AM-GM inequality we have..."

Reply 11

Zacken

Original post by lizard54142

Fair enough, this thread was more me wondering how much smartassery I could get away with anyway. :wink:

Thanks.

Reply 12

lizard54142

Original post by Zacken

Fair enough, this thread was more me wondering how much smartassery I could get away with anyway. :wink:

Thanks.

I know what you mean, for my example of using logs in the GCSE paper, I did it twice, the way they wanted us to and using a logarithmic method, because I was so worried they wouldn't give me the marks. I was just being a show off to be honest :wink:

Reply 13

Zacken

Original post by lizard54142

I remember this one anecdote where a class test had asked me to show that

f(x) = \sqrt{x}

was a one-to-one function. The graph was given and you were meant to draw horizontal lines.

I decided to prove that the function was strictly increasing over the domain. xD

Teacher was tearing her hair out. xD

Reply 14

Renzhi10122

Original post by lizard54142

I would love to be able to use some nice theorems in STEP, but they always say 'hence' or 'similarly' or 'deduce' which annoys me so much, especially when the method they're looking for is rather dumb.

Reply 15

rayquaza17

Original post by Zacken

I really enjoyed a level physics mind (enjoyed it more than a level maths lol). It's funny how they can reduce like really hard looking equations into simple equations that are GCSE maths standard.

I love applied maths now though, it's like the best parts of maths and physics put together. :heart:

TBH to answer the question, I would never risk it for GCSE/a level.

Reply 16

lizard54142

Original post by Zacken

I remember this one anecdote where a class test had asked me to show that

f(x) = \sqrt{x}

See I would say that's acceptable! That's just differentiation, which is in the A Level syllabus. I did a proof by induction on a C3 mock because I had spare time, and the teacher gave me the marks :wink:

Reply 17

Zacken