Further Pure

Improper Integrals Process Notes

Flowchart style notes on process for finding improper integrals. Pdf version.

Improper Integrals Examples

An example each of undefined at one of the limits, undefined between the limits and infinity at one of the limits.

Notes on First Principles Process

Bulletpoint style recipe on how to find the gradient of curves using the differentiation from first principles process. PDF here.

Linear Laws Notes

Notes on converting non-linear equations into linear form. Pdf version.

Notes on Roots of Quadratics

Notes on finding sums and products of roots of quadratics. Pdf version.

Sums of Series

Short set of key notes on sums of series.

Notes on Finding Stationary Points on Rational Functions

Notes on finding single and more than one stationary point(s) on rational functions.

Complex Number Intro Exercises

Powerpoint, with answers as you go, of questions to ease students into working with complex numbers. Covers adding, multiplying, dividing, Argand diagram, argument-modulus form, solving complex quadratics and complex equations

General Solutions of Trig Equation Questions

See page 3 for six (or so) harder trig questions to find the general solution of.

Notes on General Solutions of Trig Equations

Concise notes and recipe for finding general solutions of trig equations.

Conics Autographs

Some pre-made Autograph files for teaching conics. Use the constant controller to change the constants and vary the functions.

Rectangular Hyperbola


Notes on Conic Sections

Includes eccentricity, focus, directrix and transformations of the standard equations.

Matrix Transformations

List of standard matrix transformations; enlargement, rotation, reflection and shear. (Translations omitted as these are created by matrix addition rather than matrix multiplication.)

Notes on Matrices

Matrix multiplication, finding the determinant and inverse matrices.

Multiplying Matrices Questions

Set of three differentiated worksheets on matrix multiplication, answers included. Lesson starter questions on matrix addition and scalar multiplication.

Matrix Transformations Matchup Activity

Students matchup the images, words and matrices. Deep questions could include "Why did you match up that matrix with that transformation?" or "How do you know which matrices represent rotations and which represent reflections?"

Combining Matrices Exercise

Rich, problem solving type task on matrix transformations. Pdf version.

Matrix Transformations Exercise

What are the matrices representing each of these rotations and reflections? Pdf version.

Numerical Solutions of Equations Notes

Notes on Interval Bisection, Linear Interpolation, Newton Raphson and Numerical Solutions of Differential Equations.

Rational Functions Match-up

Designed to highlight finding orientation of rational graphs and necessityfor checking either side of the asymptotes. Six graphs and eight equations, all with linear numerator and linear denominator. Match them, and draw the remaining two graphs that are given. Starter questions. Use this Autograph file.

Rational Functions Notes

Notes on how to draw graphs of rational functions, particularly for combinations of linear/quadratic numerator and denominators.

Rational Function Autographs

Some pre-made Autograph files for teaching rational functions. Use the constant controller to change the constants and vary the functions.

Linear / Linear
Quad (factorised) / Quad (factorised)
Quad (expanded) / Quad (expanded)

Links to External Videos

Multiplying Matrices 1
Multiplying Matrices 2
Multiplying Matrices 3
Solving Equations using inverse method
Inverse of a 3x3 matrix
Inverse matrix (Khan Academy)
Solving Linear equations using inverses 1
Solving Linear equations using inverses 2
Solving Equations using reduction method
Intro to Eigenvalues and eigenvectors
Solving Linear equations using inverses 2
Solving Equations using reduction method