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What do your A level mathematics lessons look like?

When studying for my A levels, especially in mathematics, lessons usually followed a set routine. New information and examples were written up on the board to be copied down, then using the methods presented at the beginning of the lesson, the class set about attempting to solve a series of similar problems from the textbook. Often, this monotonous way of...

Sequences and Series

AS LevelUnderstand and use the binomial expansion of (a+bx)n for positive integer n; the notations n! and nCr; link to binomial probabilitiesA LevelExtend to any rational n, including its use for approximation; be aware of when the expansion is validWork with sequences including those given by a formula for the nth...
Publication date:
07 March 2017

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Trigonometry 1: Definitions and properties

AS LevelUnderstand and use the definitions of sine, cosine and tangent for all arguments; the sine and cosine rules; the area of a triangle in the form 1/2absinCUnderstand and use the sine, cosine and tangent functions; their graphs, symmetries and periodicityA LevelWork with radian measure, including use for arc...
Publication date:
07 March 2017

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Trigonometry 2: expressions and identities

AS LevelUnderstand and use tanθ=sinθ/cosθUnderstand and use sin^2θ+cos^2θ = 1Solve simple trigonometric equations in a given interval, including quadratic equations in sin, cos and tan and equations involving multiples of the unknown angleA LevelSec2 θ = 1 + tan2θ  and cosec2θ = 1 + cot2θUnderstand and use double...
Publication date:
07 March 2017

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Proof

AS LevelUnderstand and use the structure of mathematical proof, proceeding from given assumptions through a series of logical steps to a conclusion; use methods of proof, including proof by deduction, proof by exhaustionDisproof by counter exampleA LevelProof by contradiction (including proof of the irrationality of...
Publication date:
07 March 2017

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Vectors

AS LevelUse vectors in two dimensionsCalculate the magnitude and direction of a vector and convert between component form and magnitude/direction formAdd vectors diagrammatically and perform the algebraic operations of vector addition and multiplication by scalars, and understand their geometrical...
Publication date:
07 March 2017

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Differentiation

AS LevelUnderstand and use the derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a general point (x, y);the gradient of the tangent as a limit; interpretation as a rate of change; sketching the gradient function for a given curve; second derivatives; differentiation from first principles...
Publication date:
07 March 2017

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Algebra: Indices, linear and quadratic functions

AS LevelUnderstand and use the laws of indices for all rational exponentsUse and manipulate surds, including rationalising the denominatorWork with quadratic functions and their graphs; the discriminant of a quadratic function, including the conditions for real and repeated roots; completing the square;...
Publication date:
07 March 2017

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Algebra: Polynomials, transformations and partial fractions

AS level contentUnderstand and use graphs of functions; sketch curves defined by simple equations including polynomials, y=a/x and y=a/x2 (including their vertical and horizontal asymptotes); interpret algebraic solution of equations graphically; use intersection points of graphs to solve equationsUnderstand...
Publication date:
07 March 2017

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Bursary Supported CPD at The National STEM Learning Centre

There are a number of  upcoming ENTHUSE funded courses of interest to teachers of mathematics post -16.

Contextualising post-16 GCSE Mathematics (20/21 June)

Run in conjunction with MEI, this two day residential CPD activity is designed for mathematics specialist practitioners who...


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