AQA Level 2 Certificate in Further Maths

2.1 The basic processes of algebra Knowledge and use of basic skills in manipulative algebra including use of the associative, commutative and distributive laws, are expected

2.10 Use and manipulation of formulae and expressions Rearrange

2.11 Use of the factor theorem for rational values of the variable for polynomials

2.12 Completing the square Work out the values of a, b and c such that

2.13 Drawing and sketching of functions

2.14 Solution of linear and quadratic equations

2.15 Algebraic and graphical solution of simultaneous equations in two unknowns, where the equations could both be linear or one linear and one second order

2.16 Algebraic solution of linear equations in three unknowns

2.17 Solution of linear and quadratic inequalities

2.18 Index laws, including fractional and negative indices and the solution of equations

2.19 Algebraic proof Prove (n + 5)

2.2 Definition of a function Notation f (x) will be used, e.g. f (x) = x

2.20 Using nth terms of sequences

2.21 nth terms of linear sequences A linear sequence starts 180 176 172 …

2.22 nth terms of quadratic sequences Work out the nth term of the quadratic sequence

2.3 Domain and range of a function Domain may be expressed as, for example,

2.4 Composite functions The result of two or more functions, say f and g, acting in succession. fg (x) is g followed by f

2.5 Inverse functions The inverse function of f is written f-1

2.6 Expanding brackets and collecting like terms

2.8 Factorising Factorise fully (2x + 3)

2.9 Manipulation of rational expressions:

3.1 Know and use the definition of a gradient

3.2 Know the relationship between the gradients of parallel and perpendicular lines

3.3 Use Pythagoras’ theorem to calculate the distance between two points

3.4 Use ratio to find the coordinates of a point on a line given the coordinates of two other points.

3.6 Draw a straight line from given information

3.9 The equation of a tangent at a point on a circle

4.2 Know that the gradient of a function is the gradient of the tangent at that point.

4.4 The equation of a tangent and normal at any point on a curve

4.5 Increasing and decreasing functions When the gradient is positive/negative a function is described as an increasing/decreasing function

4.7 Use of differentiation to find maxima and minima points on a curve

4.8 Using calculus to find maxima and minima in simple problems

4.9 Sketch/interpret a curve with known maximum and minimum points

5.1 Multiplication of matrices Multiplying a 2 × 2 matrix by a 2 × 2 matrix or by a 2 × 1 matrix

5.2 The identity matrix I 2 × 2 only

5.3 Transformations of the unit square in the x – y plane

5.4 Combination of transformations Using matrix multiplications

6.1 Knowledge of perimeter and area of rectangles and circles; and of the area of triangles, parallelograms and trapezia; and of the surface area and volume of prisms, cylinders, spheres, cones and pyramids

6.10 Solution of simple trigonometric equations in given intervals

6.2 Understand and construct geometrical proofs using formal arguments

6.4 Use of Pythagoras’ theorem in 2D and 3D Recognise Pythagorean triples; 3, 4, 5; 5,12,13; 8,15,17; 7, 24, 25 and simple multiples of these

6.5 Be able to apply trigonometry and Pythagoras’ theorem to 2 and 3 dimensional problems

6.6 Sketch and use graphs of y = sin x, y = cos x and y = tan x for angles of any size

6.7 Be able to use the definitions sin θ, cos θ and tan θ, for any positive angle up to 360°(measured in degrees only)

6.8 Knowledge and use of 30°, 60°, 90° triangles and 45°, 45°, 90° triangles

1.2 The product rule for counting

1.3 Manipulation of surds, including rationalising the denominator