GCSE AQA Higher Further Maths topics
Every topic in this course, with the subtopics inside each one.
Topics and what they cover
- Number: 4 lessons: Knowledge and use of numbers and the number system, The product rule for counting, Manipulation of surds, including rationalising the denominator
- Algebra: 24 lessons: The basic processes of algebra, Definition of a function, Domain and range of a function, Composite functions, Inverse functions, Expanding brackets and collecting like terms
- Coordinate Geometry (2 dimensions only): 11 lessons: Know and use the definition of a gradient, Know the relationship between the gradients of parallel and perpendicular lines, Use Pythagoras' theorem to calculate the distance between two points, Use ratio to find the coordinates of a point on a line, The equation of a straight line, Draw a straight line from given information
- Calculus: 11 lessons: Know what the gradient function gives, Know that the gradient of a function is the gradient of the tangent at that point, Differentiation of kx^n and the sum of such functions, The equation of a tangent and normal at any point on a curve, Increasing and decreasing functions, Understand and use the notation d^2y/dx^2
- Matrix Transformations: 5 lessons: Multiplication of matrices, The identity matrix I, Transformations of the unit square in the x-y plane, Combination of transformations
- Geometry: 16 lessons: Core geometry knowledge, Understand and construct geometrical proofs using formal arguments, Sine and cosine rules in scalene triangles, Use of Pythagoras' theorem in 2D and 3D, Apply trigonometry and Pythagoras' theorem to 2D and 3D problems, Sketch and use graphs of y = sin x, y = cos x and y = tan x