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    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
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    (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...
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    (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.
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    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.
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    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
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    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
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    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!
 
 
 
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