x Turn on thread page Beta
 You are Here: Home >< Maths

# Further maths syllabus watch

1. First, I'm from Scotland and am hopefully going to study maths at Oxford next year: I got a list of stuff to learn, and I was wondering what level I had to learn it to: as understand the maths syllabus in England has just changed (edexcel's site says so, anyway) I'd like to check with this year's A2 students. I've got the A-Level Maths guide, so I know I've covered that.

What did you do, roughly, in the following?

Calculus: Properties of hyperbolic functions; differentiation and integration techniques (which ones do you do in FM?)

Geometry: Plane analytical geometry of conics; properties of hyperbolas and ellipses

Algebra: matrices

I'm sure I've covered other aspects, in particular proof, complex numbers, series, newton-rhapson (which I'm about to do) and any number theory, but I'm not sure about the above: if there's anything I've not mentioned, can you draw my attention to it too? Thank you for any help you can give me
2. (Original post by mussed)
First, I'm from Scotland and am hopefully going to study maths at Oxford next year: I got a list of stuff to learn, and I was wondering what level I had to learn it to: as understand the maths syllabus in England has just changed (edexcel's site says so, anyway) I'd like to check with this year's A2 students. I've got the A-Level Maths guide, so I know I've covered that.

What did you do, roughly, in the following?

Calculus: Properties of hyperbolic functions; differentiation and integration techniques (which ones do you do in FM?)

Geometry: Plane analytical geometry of conics; properties of hyperbolas and ellipses

Algebra: matrices

I'm sure I've covered other aspects, in particular proof, complex numbers, series, newton-rhapson (which I'm about to do) and any number theory, but I'm not sure about the above: if there's anything I've not mentioned, can you draw my attention to it too? Thank you for any help you can give me
I don't get it, you wanna know whats in the new syllabus?
Its exactly the same, cept P1-P3 are now split into C1-C4. P4-P6 remain the same but with changed names.

If you wanna do f maths i think you should do all the pure modules...
3. (Original post by toxi)
I don't get it, you wanna know whats in the new syllabus?
Its exactly the same, cept P1-P3 are now split into C1-C4. P4-P6 remain the same but with changed names.

If you wanna do f maths i think you should do all the pure modules...
Okay, either you missed the fact that she's from Scotland or didn't know we have a different exam system here.

Mussed, like myself (presumably) did SQA AH maths, which covers A-level pure maths and a considerable amount of A-level further maths aswell.

Since she's going to study maths in England she wants to know what extra material students who've done A-level further maths will have done so she can catch up, and has identified these areas from the syllabus.

I'd be interested to know aswell, as I also did AH maths and plan to study at Oxford, but in my case engineering, which does contain a considerable amount of maths.
4. I'll get the OCR syllabus for you, typical Alevel Further maths will be P4-6, get http://www.ocr.org.uk/OCR/WebSite/Da...upe3oMsQ9U.pdf and goto page 44.

Then most people will have done like mechanics3/4 or stats 3/4 so check them out too. Bear in mind edexcel P5/P6 seems to have lots of things which are not on any OCR modules, so all those rectangular hyperbolae, etc.
5. P4 - series, complex numbers, iterative procedure, inequalities, first order differentials, 2nd order diff, polar co-oridnates

p5 - hyperbolics, diff, intergrate (completing the square, sinh tan, sin substitutions, standard forms), co-ordinate geometry (parabolas, hyperbolas, rectangular hyperbolas, ecllipse, instrinsics, arc length and surface area of rev)

av i left anythin out?

dont do p6
6. English universities generally only assume knowledge of Pure Maths, so here's a rough list of what I've covered in Further Pure Maths this year (Edexcel syllabus). It's not a comprehensive list. The best thing to do would be to visit the exam boards' websites and download a couple of papers to see what they're really like.

P4
* Solving inequalities algebraically and by sketching graphs. For example, solve x^3 > 6x - 2
* Summation of series using the method of differences
* Introduction to complex numbers: in the form a + bi and the form r(cosx + isinx). Algebraic manipulation of complex numbers (addition, division, etc). Sketches on the Argand plane. Solving equations like z^4 + 5z^2 + 4 = 0
* Finding numerical solutions using interval bisection, Newton-Raphson and linear interpolation
* Solving first-order differential equations by separating variables or using integrating factors
* Obtaining particular integrals and complementary functions for second-order differential equations
* Sketching simple polar graphs such as r = 2sin3theta and finding stationary points on the curves (by using differentiation); integration of formulae to find areas enclosed by polar curves

P5

* Definition of hyperbolic functions using exponentials (sinh, cosh, tanh, cosech, sech, coth) and their graphs; various hyperbolic identities and their relation to trig identities via Osborne's rule; definition of inverse hyperbolic functions in terms of logarithms (e.g. arcsinhx = ln[x+sqrt(x^2 + 1)])
* Differentiation of inverse trig and hyperbolic functions, and hence the integration of functions such as 1/(1 + x^2)
* The use of integration to find arc lengths and surface areas of revolution; reduction formulae for integrating functions
* Various properties of parabolas, ellipses and hyperbolas (parametric and Cartesian equations, focus-directrix properties, eccentricity, how to find normals and tangents, etc); intrinsic coordinate systems (Whewell equations for describing curves), radius of curvature of curves

P6
* Definition of Maclaurin and Taylor series; how to derive power series for functions such as sinx, cosx, e^x, sinx.coshx, etc; expressing the solution to differential equations as a Taylor series
* More work on complex numbers: proof that cosx + isinx = e^ix; expression of trig functions in terms of exponentials (e.g. cosz = 0.5(e^iz + e^-iz)); relationship between trig and hyperbolic functions (e.g. cos(iz) = cosh(z)); proof and use of de Moivre's theorem; sketching loci in the Argand plane; nth roots of a complex number; transformations from the z-plane to the w-plane
* Simple manipulation of matrices (adding, multiplying, etc); finding the inverse of 2x2 and 3x3 matrices; use of matrices to represent linear transformations; finding eigenvalues and eigenvectors; diagonalising a symmetric matrix
* Vectors: cross product, finding the volumes of tetrahedrons and parallelepipeds and the area of triangles; scalar product equation of a plane; vector equation of a plane; cross product form of a straight line; finding points of intersection of lines/planes, angles between lines/planes; distance between two points
* Numerical solutions of differential equations (Euler's method)
* Proof by induction
7. First, Calmuc's right - different system. And I only need to know the pure syllabus; I'm doing Maths&Phil so no applied maths required!

Thanks, Squishy - that was just what I needed to know!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 22, 2004
Today on TSR

### How much will your degree earn you?

Find out where yours ranks...

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams