Could I better at Maths (even get a Grade 9) if I teach myself Pure Maths? Watch

Hiro2468
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For GCSE I really want a Grade 8 but so far my current grade is a Grade 6. On TSR I read that someone did pure maths became good at maths and really loved it that they would do it everyday even when they had to revise for another test. I would really love that to happen to me as well.

Do you think that learning pure maths would help boost my grades? Since I think Pure Maths is about the “why” in Maths.

If you think it’ll help boost my grades then how can I start teaching myself Pure maths please? Or is it an A-Level or Uni sort of thing? Online I seen some complicated stuff which counted as the basics of Pure Maths which kinda scared me a bit.

Any advice? I already know about past papers if anyone mentions it. Thank you in advance!
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GreenSpoon125
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If you're currently predicted a six, then focus on the grade seven topics to boost your grade (use a CGP revision guide or go on maths genie). After that, you can move onto level eight/nine topics.

You don't want to get confused with unnecessary information!
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jmaw
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(Original post by Hiro2468)
For GCSE I really want a Grade 8 but so far my current grade is a Grade 6. On TSR I read that someone did pure maths became good at maths and really loved it that they would do it everyday even when they had to revise for another test. I would really love that to happen to me as well.

Do you think that learning pure maths would help boost my grades? Since I think Pure Maths is about the “why” in Maths.

If you think it’ll help boost my grades then how can I start teaching myself Pure maths please? Or is it an A-Level or Uni sort of thing? Online I seen some complicated stuff which counted as the basics of Pure Maths which kinda scared me a bit.

Any advice? I already know about past papers if anyone mentions it. Thank you in advance!
What's known as "pure" maths is a very different type of mathematics to that taught at GCSE, A-Level, and even for the most part most university engineering and physics courses. Pure mathematics has a focus on constructing what are known as mathematical "proofs", statements in mathematics that are consistent with basic underlying mathematical rules or "axioms" as they are sometimes called.

For example, consider the Wikipedia article on the mathematical proof of the "real" number set (https://en.m.wikipedia.org/wiki/Cons...e_real_numbers). This is a summary of the proof that the real numbers, those that lie on the usual number line from minus infinity to infinity, exist. In proving their existence in this fashion, mathematicians may then use the mathematical properties of the real plane identified as part of the initial proof to construct further proofs involving the real numbers.

For pretty much all practical purposes though, you can safely assume that the real numbers exist, and you can put them to good use even with only the basic rules of addition, subtraction etc. Most mathematics teaching outside of pure mathematics is done for the purposes of this practical usage, and so while a pure mathematician is likely to be very good at practical maths, then

a) They were certainly likely to be already good at the practical maths before they went to university to train as a pure mathematician and
b) it takes a very long time to develop those skills to the point where you could reasonably provide a pure mathematical proof of things that basic GCSE maths takes for granted. Just proving that the real numbers exist and that two numbers can be added together would be what I would consider to be a first year university pure mathematics exam question.

So to answer your question (and I appreciate that I've taken a while in doing so), while pure maths is indeed a beautiful thing, it's unlikely to help you with GCSE maths any time soon. However, don't be discouraged from looking at pure mathematics even if you don't decide to pursue it at university. There are some excellent books out there (I would recommend Roger Penrose's "The Road to Reality", which is a heavy read but well worth it) which deal with pure mathematics in an accessible way.

Good luck with your GCSEs, and I hope you found this useful.
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DerivativeName
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Nah just focus on GCSE. A lot of GCSE maths is ‘core’ maths that is used in all fields, especially pure. Things like quadratics, simultaneous equations, forming equations, inequalities, vectors, sequences proofs etc. are all vital to understand.

Not to sound harsh but if you’re getting 6’s you’re obviously not good enough at the core stuff at the moment to specialise.

There’s plenty of fun stuff in GCSE to keep you excited about maths. Start with practice papers, but just do the first 18 questions or so (not the big 5 markers at the back). Keep doing them until you’re getting everything mostly right. This should get you a solid grade. Then start doing the big, hard 5 markers. Keep doing them. Eventually you’ll be able to do any of them easy, and get an 8/9.
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Hiro2468
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(Original post by GreenSpoon125)
If you're currently predicted a six, then focus on the grade seven topics to boost your grade (use a CGP revision guide or go on maths genie). After that, you can move onto level eight/nine topics.

You don't want to get confused with unnecessary information!
Thank you for your response! I agree with you too, I’ve gotten the Edexcel CGP Exam style questions for 9-1 book so I’ve started practicing with it. I also use Maths Genie and their videos. I just really want to improve before I go to Year 11.
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Hiro2468
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(Original post by TurquoiseTurtle)
I completely agree, I was predicted a 6 and practiced loads of past papers and used CGP revision guides and came out with an 8. I have just finished my Further Maths AS Level too!

Good Luck!!

TurquoiseTurtle :turtle:
Thank you for your response too!! I kinda feel reassured now, as all I gotta do is practice. I was being naive thinking it’s possible to get a good grade without past papers. Thank you yet again!
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Hiro2468
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(Original post by jmaw)
What's known as "pure" maths is a very different type of mathematics to that taught at GCSE, A-Level, and even for the most part most university engineering and physics courses. Pure mathematics has a focus on constructing what are known as mathematical "proofs", statements in mathematics that are consistent with basic underlying mathematical rules or "axioms" as they are sometimes called.

For example, consider the Wikipedia article on the mathematical proof of the "real" number set (https://en.m.wikipedia.org/wiki/Cons...e_real_numbers). This is a summary of the proof that the real numbers, those that lie on the usual number line from minus infinity to infinity, exist. In proving their existence in this fashion, mathematicians may then use the mathematical properties of the real plane identified as part of the initial proof to construct further proofs involving the real numbers.

For pretty much all practical purposes though, you can safely assume that the real numbers exist, and you can put them to good use even with only the basic rules of addition, subtraction etc. Most mathematics teaching outside of pure mathematics is done for the purposes of this practical usage, and so while a pure mathematician is likely to be very good at practical maths, then

a) They were certainly likely to be already good at the practical maths before they went to university to train as a pure mathematician and
b) it takes a very long time to develop those skills to the point where you could reasonably provide a pure mathematical proof of things that basic GCSE maths takes for granted. Just proving that the real numbers exist and that two numbers can be added together would be what I would consider to be a first year university pure mathematics exam question.

So to answer your question (and I appreciate that I've taken a while in doing so), while pure maths is indeed a beautiful thing, it's unlikely to help you with GCSE maths any time soon. However, don't be discouraged from looking at pure mathematics even if you don't decide to pursue it at university. There are some excellent books out there (I would recommend Roger Penrose's "The Road to Reality", which is a heavy read but well worth it) which deal with pure mathematics in an accessible way.

Good luck with your GCSEs, and I hope you found this useful.
Thank you so much for your response as well!! The way you speak about pure mathematics strangely encourages me to work harder! I found your response greatly useful (^~^!) If I still want to persue Maths for A-Levels I’ll get the book you recommended me (I’m going to recommend it to my friend as well as she loves proofs and anything to do with Maths!) .

Thank you yet again!
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Hiro2468
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(Original post by DerivativeName)
Nah just focus on GCSE. A lot of GCSE maths is ‘core’ maths that is used in all fields, especially pure. Things like quadratics, simultaneous equations, forming equations, inequalities, vectors, sequences proofs etc. are all vital to understand.

Not to sound harsh but if you’re getting 6’s you’re obviously not good enough at the core stuff at the moment to specialise.

There’s plenty of fun stuff in GCSE to keep you excited about maths. Start with practice papers, but just do the first 18 questions or so (not the big 5 markers at the back). Keep doing them until you’re getting everything mostly right. This should get you a solid grade. Then start doing the big, hard 5 markers. Keep doing them. Eventually you’ll be able to do any of them easy, and get an 8/9.
That’s actually sounds like a really good strategy! And yea I agree I should probably aim to get better at core stuff before I think about aiming high. You were not harsh just honest (I totally agree!).

Is it possible for me to improve in maths if I continue to do your strategy? I would like to become better at maths before I get to Year 11.

Thank you for your response btw!!
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DerivativeName
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(Original post by Hiro2468)
That’s actually sounds like a really good strategy! And yea I agree I should probably aim to get better at core stuff before I think about aiming high. You were not harsh just honest (I totally agree!).

Is it possible for me to improve in maths if I continue to do your strategy? I would like to become better at maths before I get to Year 11.

Thank you for your response btw!!
Definitely. I’m in Year 11 now and getting 8’s and this is what I’m doing trying to push for a 9- and my first maths exam is on Wednesday.

Every single question you do will help you, whenever you do that. It’s not like other subjects when sometimes you’ll have done enough, or sometimes you can never improve in time. In maths you can never do too much, and you can improve in whatever time scale. Good luck!
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GreenSpoon125
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(Original post by Hiro2468)
That’s actually sounds like a really good strategy! And yea I agree I should probably aim to get better at core stuff before I think about aiming high. You were not harsh just honest (I totally agree!).

Is it possible for me to improve in maths if I continue to do your strategy? I would like to become better at maths before I get to Year 11.

Thank you for your response btw!!
It's very possible. I've seen people go from sixes to eights in the space of one year, you just have to put in the effort.
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