Topic module: Further-Core-Maths-AS OCR

Solving three linear simultaneous equations

Angle between a line and a plane

Exam Questions – Matrix transformations

Exam Questions – Finding roots

Shortest distance of a point to a line

Shortest distance from a point to a plane

Geometrical effects of conjugating a complex number

Modulus-argument form of a complex number

Transposed and symmetric matrices

Finding the inverse of a 3×3 matrix where it exists

Finding the determinant of a 3×3 matrix

Relationships between the roots and coefficients of a quartic equation

Relationships between the roots and coefficients of a cubic equation

Relationships between the roots and coefficients of a quadratic equation

Exam Questions – Volume of Revolution about the y-axis

Volume of revolution about the x-axis generated between curves

Volume of Revolution about the y-axis generated between curves

Volume of Revolution about the y-axis

Exam Questions – Matrix proofs

Exam Questions – Vectors

Exam Questions – Parallel intersecting and skew lines

Exam Questions – Scalar product

Exam Questions – Volume of revolution about the x-axis

Solving quartic equations

Solving cubic equations

Solving quadratic equations with complex roots

Square roots of a complex number

Exam Questions – Loci in the complex plane

Exam Questions – Further complex numbers

Exam Questions – Divisibility and multiple tests

Exam Questions – Sum of series

Exam Questions – Series

Exam Questions – Identity and inverse of a 2×2 matrix

Exam Questions – Complex numbers

The angle between two planes

Finding the point of intersection between a line and a plane

Scalar product forms of a plane

Cartesian form of a plane

Parametric vector form of a plane

Cartesian form of a line

Using complex numbers to represent regions on an Argand diagram

The locus of a point moving along a half-line

The locus of a point moving along a perpendicular bisector

The locus of a point moving in a circle

Multiplication and division rules for mod and argument of two complex numbers

Matrix proofs

Divisibility and multiple test proofs

Proof for other series

Proof of the sum of the series ∑r³

Proof of the sum of the series ∑r²

Proof of the sum of the series ∑r

Using known formulae to sum more complex series

Sum of the cubes of the first n natural numbers ∑r³

Sum of the squares of the first n natural numbers ∑r²

Determinant as the area scale factor of a transformation

Inverse matrices to reverse linear transformations

Combinations of transformations

How well do you know your transformations?

Linear transformations – enlargement

Linear transformations – reflections

Linear transformations – rotations

Solving simultaneous linear equations in 2 unknowns

Sum of the first n natural numbers ∑r and the results for ∑a and ∑(ar+b)

Identity and Inverse of a 2×2 matrix

Matrix multiplication

Addition and subtraction and multiplying a matrix by a scalar

Introduction and dimension of a matrix

Solving problems with complex numbers

Modulus and argument of a complex number

Argand diagrams

Division of a complex number by a complex number

Complex conjugates

Addition, subtraction and multiplying complex numbers and simplifying powers of i

Real and imaginary numbers

Closest point to a line and shortest distance from the origin

Intersecting and skew lines

Parallel lines

Angle between two lines

Vector equation of a line

Perpendicular vectors

Scalar product

Volume of revolution about the x-axis