A LevelMath

A Level Further Maths – Core Pure Year 1

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Complex Numbers

Lesson 1 – Introduction and Complex Arithmetic
Lesson 2 – Solving Quadratics
Lesson 3 – Polynomial Equations
Lesson 4 – Argand Diagrams
Lesson 5 – Modulus Argument Form
Lesson 6 – Loci in the Complex Plane

Series

Lesson 1 – Introduction and Series
Lesson 2 – Series

Roots of Polynomials

Notes – Roots of Polynomials
Lesson 1 – Roots of Quadratics
Lesson 2 – Transforming Roots of Quadratics
Lesson 3 – Roots of Cubics
Lesson 4 – Quartic Equations

Volumes of Revolution

Lesson 1 – Volumes of Revolution

Matrices – Arithmetic and Transformations

Lesson 1 – Arithmetic of Matrices
Lesson 2 – Multiplying Matrices
Lesson 3 – Matrix Transformations
Lesson 4 – Matrix Transformations
Lesson 5 – Matrix Transformations

Matrices – Inverses and Simultaneous Equations

Lesson 1 – Determinants
Lesson 2 – Inverse Matrices
Activity – Self Inverse Matrices
Activity – Self Inverse Activity – teacher guide

Proof by Induction

Lesson 1 – Proof by Induction – Summations
Lesson 2 – Proof by Induction – Matrices
Lesson 3 – Proof by Induction – Divisibility
Lesson 4 – Proof by Induction – Recursive Formulae

Vectors – Lines and Planes

Lesson 1 – Vector Lines
Lesson 2 – Vector Lines
Lesson 3 – Vector Lines
Lesson 4 – Vector Lines
Lesson 5 – Vector Lines
Lesson 6 – Vector Planes
Lesson 7 – Vector Planes
Notes – Vectors 1a
Notes – Vectors 1b
Notes – Vectors 2a
Notes – Vectors 2b

Vectors – angles, intersections and shortest distances

Lesson 1 – Angle between 2 planes
Lesson 2 – Angle between line and plane
Lesson 3 – Points of intersection
Lesson 4 – Shortest distances
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