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Notes
A-Level Further Maths
3 min read
Elasticity & Collisions
Hooke's law, modulus of elasticity, elastic potential energy, elastic collisions in one and two dimensions, direct impact, oblique impact.
A-Level Further Maths
2 min read
Momentum, Impulse, Work, Energy & Power
The impulse-momentum principle, the principle of conservation of momentum, the work-energy principle, potential & kinetic energy, power.
A-Level Further Maths
5 min read
Complex Numbers, Argand Diagrams & Loci
Adding, subtracting & multiplying complex numbers, complex equations, locust of points, modulus-argument & exponential form and de Moivre's.
A-Level Further Maths
1 min read
Proof by Induction
Proof by mathematical induction with sums, proving divisibility results and proof with matrices.
A-Level Further Maths
2 min read
Series
Sums of natural numbers, squares & cubes, the method of differences, the Maclaurin series expansion and standard results.
A-Level Further Maths
2 min read
Roots of Polynomials
Won't lie, this topic isn't particularly fun. It's just a whole lot of algebra and equations that you need to know and get right. At...
A-Level Further Maths
3 min read
Vectors
Vector & Cartesian equations for lines & planes, scalar product, angles between lines & planes, points of intersection and perpendiculars.
A-Level Further Maths
3 min read
Further Integration
Improper integrals, converging/diverging integrals, mean value of functions, inverse trigonometry, partial fractions & volumes of revolution
A-Level Further Maths
2 min read
Polar Coordinates
Converting between polar and Cartesian systems, sketching polar curves, finding area enclosed by polar curves and finding tangents.
A-Level Further Maths
1 min read
Hyperbolic Functions
Hyperbolic functions as exponential functions, hyperbolic graphs, inverse hyperbolic functions, integrating & differentiating hyperbolics.
A-Level Further Maths
3 min read
Matrices & Linear Transformations
Matrix addition & multiplication, determinants, inverse matrices, matrix systems & geometry, reflections, rotations, stretches & reverses.
A-Level Further Maths
4 min read
Differential Equations
Integrating factor, second-order homogeneous and non-homogeneous differential equations, simple harmonic motion and coupled simultaneous.
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