A Level Further Maths – Core Pure Year 1

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