Following on from Stuart’s (@sxpmaths) excellent blog post looking at the changes coming to A-Level mathematics in 2017 I thought I would take a bit more of a detailed look at the prescribed content of Further Mathematics than I did in my old post here. Since I wrote my original post there have been a few changes (notably clarification of how the prescribed content for AS-Level is decided) between the draft content and the finalised content document that was published in December 2014..
This post is my interpretation of the content contained in the content document and I would encourage everyone to look at the original!
Unlike the 100% prescribed core of the standard A-Level only 50% of the content for Further Maths (FM) is prescribed with awarding bodies able to determine the other 50%. I’m not sure how I feel about this: part of me likes the freedom that this gives the exam boards to potentially include novel content and explore different areas of mathematics. The other part of me would prefer a 100% prescribed A-Level as this levels the playing field for students who (at the moment) are often at the mercy of their schools in terms of what they study to bolster results, not necessarily preparing them as well for future mathematical study. I can see this kind of “game playing” potentially occurring if there are vast differences between individual boards.
In this post I will look at the prescribed content of the AS-Level further mathematics qualification
There is some prescribed core content for AS FM however a smaller proportion is prescribed than that for the full A-Level as explained in the original document.
- “At least 30% (approximately) of the content of any AS further mathematics specification must be taken from the prescribed core content of A level further mathematics.”
This 30% is composed of two parts. 20% of the overall content must come from the following areas
- Complex Numbers including: the solution of quadratic, cubic and quartic equations (with real coefficients), arithmetic operations on complex numbers including the use of the complex conjugate. Students are to be able to represent complex numbers on an Argand diagram and know that complex roots of a polynomial (with real values coefficients) occur in complex conjugate pairs. Manipulation of numbers in modulus argument form. Construction and interpretation of simple loci in the Argand diagram.
- Matrices including: Knowledge of the zero and identity matrices. Multiplication of a matrix by a scalar and addition, subtraction and multiplication of conformable matrices. Use of matrices to represent single linear transformations in 3D (some restrictions apply) and successive linear transformations in 2D. Finding invariant lines and points of linear transformations. Determinants and inverses of \(2\times2\) matrices.
- Further Algebra and Functions including: The relationship between the roots and coefficients of polynomial equations, up to quartic equations. Forming a polynomial whose roots are a linear transformation of the roots of a given polynomial equation, where the polynomial is at least of cubic degree.
Another (approximately) 10% of the overall specification must be taken from the rest of the prescribed content of A-Level FM, but it is up to the boards to decide what they take.
A few comments on the above
- When manipulating numbers in modulus-argument form knowledge of radians and compound angle formulae are assumed. Depending on how schools teach the AS this could prove problematic as radians are not introduced until A2.
- I like the inclusion of loci, in some boards this isn’t currently tackled until FP# and consequently may not be encountered by students at all.
- There seems to be more of a focus on finding invariants under linear transformations than at present.
- It’s nice to see the transformation of polynomials in there as it has wide ranging applications.
Essentially, only 20% of an AS qualification in further mathematics is necessarily common to all boards.
Come back early next week for my take on the rest of the prescribed content for the full A-Level further mathematics qualification.