Further Pure

Autograph file: Volumes of Revolutions (setup page)

Axes etc setup & ready for doing Volumes of Revolutions. My best example and another example.

Volume of Revolution Formula

Formula for Volume of Revolution. PDF here.

Standard Integrals

Notes and proofs of standard integrals for AQA Core 3. Suggested use in classroom; pupils to read and understand proof of integral of 1/(a2+x2) and then construct a similar proof for integral of 1/[(a2+x2)1/2]. Pdf version.

Intersection Of Three Planes

Summary notes on intersection of three planes; all parallel, two parallel, tri-prism, sheaf and single point. Includes summary table plus extra notes and links to a couple of good youtube videos. Pdf here.

3D Planes

Questions to get you thinking about the crtieria for planes to intersect, be parallel etc. A few great tasks here with answers included. Works great together with dynamic graphing software such as Autograph, Geogebra etc. Pdf here.

Useful Vector Formulae

Lots of useful formulae to do with vectors including dot and cross products, volume of parallelopiped, vector equations of lines and planes. Pdf here.

Ei pi

Derivation of the eipi formula from Maclaurin Expansions. Pdf here.

Vectors Probing Questions

A set of questions to really check understanding of several vector concepts such as magnitudes of vectors, vector equations of lines, scalar product and closest distance between a point and a line. Answers included. PDF here.

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.

Notes on Maclaurin Series Expansions

Notes on the general format of the expansion, some standard expansions and a couple of initial teaching ideas. 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. PDF here.

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). PDF here.

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