How is Further Maths different to Maths at GCSE?

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peterdxherty
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#1
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I'm transitioning between Year 10 and 11 right now, and I've been lucky enough to make it onto Further Maths next year. Most people doing Further Maths started at the beginning of Year 10 so they all have a year advantage over me. How is the Further Maths course different from usual GCSE and what new topics are there? How can I best prepare for the course before Year 11 starts.
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Loci Pi
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I did AQA Further Maths this year. The main difference is that it is more applying what you've learnt rather than having to think logically for problem solving questions like in 9-1 normal maths GCSE.

The other topics in FM that are not in GCSE maths are:
Matrices / Unit square transformations
Differentiation (first and second derivatives)
Finding minimum / maximum / points of inflection
Finding tangents and normals from differentiating
Trig identities
Trig Values in a given interval
Sketching and factorising cubic equations
Factor theorem
Remainder theorem (not on the syllabus but it helps)
Circle graphs where in the form (x-a)^2 + (y-b)^2 = r^2 where the centre = (a, b) or (0, 0)
Graphs in the form y-y1 = m(x-x1) although you may have covered this in GCSE maths
Domain / range of a function

I recommend the CGP revision and study guides. I self taught it and these, along with past papers, were the only resources I used. To prepare, I would attempt some past papers, but it isn't that much to learn in a year as it is so similar to normal maths. I think doing FM has helped me with normal maths which is good.

If you have any more questions about FM feel free to ask.
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thekidwhogames
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(Original post by Loci Pi)
I did AQA Further Maths this year. The main difference is that it is more applying what you've learnt rather than having to think logically for problem solving questions like in 9-1 normal maths GCSE.

The other topics in FM that are not in GCSE maths are:
Matrices / Unit square transformations
Differentiation (first and second derivatives)
Finding minimum / maximum / points of inflection
Finding tangents and normals from differentiating
Trig identities
Trig Values in a given interval
Sketching and factorising cubic equations
Factor theorem
Remainder theorem (not on the syllabus but it helps)
Circle graphs where in the form (x-a)^2 + (y-b)^2 = r^2 where the centre = (a, b) or (0, 0)
Graphs in the form y-y1 = m(x-x1) although you may have covered this in GCSE maths
Domain / range of a function

I recommend the CGP revision and study guides. I self taught it and these, along with past papers, were the only resources I used. To prepare, I would attempt some past papers, but it isn't that much to learn in a year as it is so similar to normal maths. I think doing FM has helped me with normal maths which is good.

If you have any more questions about FM feel free to ask.
Yep, that's a really good detailed answer. However you have missed limiting values of a sequence (i.e. the limit to infinity). I'd recommend OP to also read on L'Hopitals Rule for finding the limit to infinity of a function; and then apply this rule to find the limiting value of a sequence, it's a lot easier and more efficient than dividing by the highest power of n and then simplifying.
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Loci Pi
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(Original post by thekidwhogames)
Yep, that's a really good detailed answer. However you have missed limiting values of a sequence (i.e. the limit to infinity). I'd recommend OP to also read on L'Hopitals Rule for finding the limit to infinity of a function; and then apply this rule to find the limiting value of a sequence, it's a lot easier and more efficient than dividing by the highest power of n and then simplifying.
I've just looked up L'Hopital's rule and it's very interesting. I wish I'd known it for FM but this year the only limits question was a 1 mark question which could be solved by inspection. The denominator had a negative in it so I think AQA were trying to trick some people lol. L'Hopital's rule is useful for when the nth term of the sequence is more complicated, like the examples on Wikipedia. Thanks for mentioning it.
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rainbowcthulu
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This isn't really of help preparation wise but the questions are to the point in FM, compared to GCSE. What I mean by this is that there's no "Jane is travelling home from work at 60km/h and she drives 10 miles to Tesco and stays there for X minutes... what time does she get home?" The questions are very much just "prove this thing is equal to this thing" or "factorise this thing". In some ways it makes the exam less fun as you don't get to laugh at the people who make 500 cakes or do something ridiculous, but the questions are generally a bit harder and you'll find that the 4-5 mark questions at GCSE are only worth 1-3 marks in FM. I suppose if you're one of those people who get a bit muddled in the context of a question (not that you would!) and you just wanna get to the actual maths, FM is great.
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Kedhar.p
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(Original post by theeetimdoherty)
I'm transitioning between Year 10 and 11 right now, and I've been lucky enough to make it onto Further Maths next year. Most people doing Further Maths started at the beginning of Year 10 so they all have a year advantage over me. How is the Further Maths course different from usual GCSE and what new topics are there? How can I best prepare for the course before Year 11 starts.
I'm self learning FSMQ which is not that different becuase of bad teachers at my school. I advise buying textbooks and catching up on what you have missed in the last year as well as learning year 11 content so that you do not fall behind. CGP is useful but look on amazon for atleast 3 textbooks.
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OwlOfFire
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#7
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At my school everyone in top set for maths automatically got put down for AQA further maths, we had no choice in it. Throughout year 11 we didn't really do any work on it, we occasionally covered some of the basics in the last 15 minutes of the lesson. We certainly had no further maths lessons as such, it was just taught a little bit here and a little bit there, alongside the normal maths GCSE. We focused on the GCSE maths throughout the year and didn't worry about further maths as that was one of the last exams. Once we had done the maths GCSE exam our teacher got us back into class and did a two hour lesson on everything we needed to know for further maths. It was a total mess, I basically didn't understand any of it. We then were left to our own devices, I did a couple past papers the day before the exam and walked out with a grade A, even though I am rubbish at maths.
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