A Level Pure Maths

Mainly AS Mainly A2

Mainly AS

Quadratics Practice 2016

Six questions, of progressive difficulty, each on 'complete the square then solve', 'factorise then solve', 'quadratic formula to solve'. PDF here.

Quadratic Problem Solving Questions

Five worded problems requiring knowledge of quadratic algebra to solve.

Graphs of Related Functions

Crib sheet for how functions and their graphs relate to each other. PDF here.

Coordinate Geometry Questions

Some rich coordinate geometry questions about perpendicular & parallel tangents to the x2 graph. PDF here.

Four Circles

Not much info on this diagram but can you find the equation of the small blue circle? Includes Answers. PDF here.

Rationalise The Denominator

Intelligent variation examples ('my turn') and questions ('your turn') on rationalising the denominator. Includes answers. PDF here.

Playing With Indices

A couple of nice indices questions; what's going on here? Can you make another question like this?! PDF here.

Intro to Set Notation

An example of how to answer in set notation and interval notation, then some questions for practise. PDF here.

Points Of Inflection

Notes on stationary and non-stationary points of inflection. PDF here.

Quadratic Formula Synthesis

Complete the steps in the table to get from ax2+bx+c=0 to the quadratic formula. Or, cut out the steps and ask students to arrange them in the correct order. Answers on page 1, empty table on page 2, the peices in a random order on page 3. PDF here

Max Box

What's the biggest area you can contain with x cm of string? Whats the biggest volume you can contain with an A4 sheet of paper? Not as easy as it seems! Our answers and Autograph file used.

Remainder Theorem

An explanation via example of Remainder Theorem. PDF here. A set of Notes on Division of Polynomials.

Indices Rule

How the rules of indices work. Follow them and you can't go wrong! PDF here.

A Level Formulae

A lovely spider diagram jpeg noting all the useful formulas required for A Level Mathematics. Print out, explore, learn.

Key Pairs

Interactive match up pairs starter activity for key elements of A level maths basics, great for revision.

Quadratic Discs

Six questions to find everything out about the quadratic expressions. PDF here.

Factorising Quadratic Types

Prompt for learning where to put + & - symbols when factorising quadratics.

GCSE A Grade - As Level Question Cards

A set of questions taken from the AQA Additional Maths specimen paper. A great GCSE A/A* extension or As introduction. PDF here. Ask pupils to order by difficulty using this template and then attempt all that they can. Lesson plan.

GCSE A Grade Algebra Question Match-up Cards

A set of 26 A-Grade algebra questions on simplifying, rearranging and solving. Pupils match up questions to answers and then use as support, or just for checking, to solve questions. PDF here. A set of 'rich questions' to go with this activity.

Quadratic Practice

Three quadratic equations, of varying difficulty, to solve via each of the three methods: Factorising, Completing the Square & Quadratic Formula.

Three versions of this: Easy, Medium or Hard.

Practice at completing the square.

Differentiation, Coordinate Geometry and Factor Theorem Rich Task

Resources to test deep understanding of differentiation to solve problems, factor theorem for drawing polynomials and coordinate geometry. This activity composed the key part of a Yr11OFSTED OUTSTANDING lesson.

Starter Questions plus Autogrpah files: Coordinates, Factor Theorem
Polynomials and Differentiation to test prior understanding plus Autograph file
Main task on white background or on coloured background
Main task with hints on white version or on coloured background
Main task Autograph files: Coordinates, Differentiation, Factor Theorem
Lesson Plan

Factor & Remainder Theorem Questions

Some, relatively simple, questions on using the factor & remainder theorem.

Factorise these Cubics

Ten cubic expressions to factorise as well as an extension activity. Includes answers. PDF here.

Factorising Polynomials

Use combinations of the factors given to make the polynomials. An easier and harder version with answers included for both. Pdf here.

Coordinate Geometry Notes

Very simple notes on coordinate geometry: gradient of a line, distance between two points, midpoints, negative reciprocal... PDF here.

Differentiation Puzzle

Matchup the equation, differential, specific coordinate, gradient at specific points, stationary points and tangent. Includes two versions; one easier, one harder. Geogebra file used (edit the equation to fit). Images of graphs.

Key A Level Maths Terminology

List of commonly confused exam terminology and thier meanings. PDF here. A3 poster version. Cut them out and match them up version.

Graph Transformations

Kinesthetic activity for students. PDF here. Print out the graphs onto A4 paper, then print the final 6 slides onto accetate and cut up. Pupils use the accetates to show the required graph transformations. Smaller print version, this one prints all the original graphs onto 2 A4 sides, another page on tracing paper for the graphs. PDF of this file here.

Compound Transformations

Students use the equations given, together with some of thier own creation, to match to the written transformations. Extension questions too on order of transformations.

Trigonometry Recap

Four questions based on each of; Pythagoras, standard right-angled trig, sine rule, cosine rule and sine rule for area. Answers included. PDF here.

Solving Trig Equations Tarsia

18 questions to thoroughly test students understanding of solving trig equations giving all answers in the correct region and using both degrees and radians. The Tarsia program for Windows is license free. Trig Identity warmup questions. PDF here.

APs & GPs

Notes on A Level APs & GPs (Arithmetic Progressions & Geometric Progressions). PDF here

Arithmetic Progression and Geometric Progression Intro Questions

Several quick - miniwhiteboard - questions to get students up to scratch on AP's. Includes sequence and series questions in both AP and GP.PDF APs here, PDF GPs here.

Series Questions

Questions and extensions based on an A level exam question involving sums of both arithmetic and geometric series. Includes answers. PDF here.

Logarithms Rule

Very simple notes on the rules of logarithms. PDF here. Some accompanying images...

Solar system log graph Old calculator
Old calculator Slide rule

Introducing Exponentials

A few quick starter questions on solving exponential and log equations as well as differentiating and integrating them. Includes Answers. PDF here.

Binomial Activity

Four different introductions to the binomial expansion. Spread around class, complete, and then present to other students. An activity to really reinforce the imprortance of the binomial expansion across several areas of Mathematics. PDF here.

Binomial smartboard file
Binomial lesson plan

Binomial Expansions

A progression of binomial expansions to take students from the very straightforward (x+1)3 to (3-2x)5 in easy steps.

Binomial Expansion Concept Questions

A couple of questions to highlight finding all terms vs using binomial formula to find just one term. Contains an easier and harder question, with answers.

Making Progress Revision Notes

All of the required formulae for the old AQA Core 2 module on a single side of A4. Arranged into those formula that must be remembered and those that are, or were, given in the formula book. Tested and much appreciated by my sixth form class!

Mainly A2

Making the Connection - Approximating Values using Binomial Expansions

A task to practice and re-inforce substitutions arising from binomial theorem expansions. Includes answers. PDF here.

Integration by Substitution Writing Frame

A writing frame for students to get used to method of integration by substitution. Includes blank template and a completed example, covers change of limits and re-sub methods. PDF here.

Integration by Substitution Clever Example

An example of how to deal with integrations with x-2 type terms in the denominator. PDF here.

Finding the Range of ex Transformations

Notes on how to break down / build up answers to these types of questions. PDF here.

Confusing Transformations

Describe the geometrical transformations of the graphs, building up from easier to more complicated compound transformations. Includes answers. PDF here.

Differentiating ax and akx

Notes and questions on differentiating ax and akx type functions. PDF here.

How to get Exam Marks...

Notes on how exam marks are typically awarded for Integration by Substitution, Integration by Parts and Differential Equation questions. Includes a writing frame, practice of several questions and answers (questions taken from the AQA syllabus).

...for Integration by Substitution and Pdf version.

...for Integration by Parts and Pdf version.

...for Differential Equations and Pdf version.

Chain, Product, Quotient Tough Recap

A set each of chain rule, product rule and quotient rule questions. Each set including easy, medium and hard questions (the rows) and polynomial, trigonometrical and exponential questions (the columns). My Yr13 students (single and further maths) really enjoyed recapping their knowledge with this task!

Answers included. As PDF version.

Methods for Integration

Info sheet on identifying aspects to look for when deciding which method for integration, followed by six (mostly exam) questions to practise each method. Includes answers. As pdf here.

Which Method to Integrate?

Flowchart for helping to decide when method of integration to use. Suggestions and comments welcome please! PDF here.

Integration - Choose Your Method

Here's a whole bunch of integration questions for you to decide how to integrate. These cover all methods including by substitution, by parts, by partial fractions etc. Some interesting limits for you to work your way through too. There is some structure to the layout of the questions on this document but we'll leave you to work out what that structure is! Includes answers. As pdf here.

Integrate These

Another selection of good integration questions to test your skills. Includes answers. As pdf here.

Further Trig Graphs

Trig graphs of cot, sec and cosec. The Autograph files used are cot, sec and cosec or alt versions with corresponding graphs cot, sec and cosec. PDF here.

Trig Identities for A Level

Lots of trig identities. Learn, explore, enjoy! PDF here.

Trig Compound Angles Recap

Here's a good set of questions to test your understanding of trigonometrical compound angles such as sin(a+b) etc. PDF here.

Important Trig Values

MS Word table of important trig values between 0 - 360. Learn them! PDF here.

Modulus Exercise

Very short activity to get students thinking about the modulus function. They could use the MS Excel file to help them.

Embedded Within

A template for students to create their own chain, product, quotient questions where chain, product or quotient rule is used within the whole question also of the format, chain, product, quotient. PDF here.

The Chain Rule

Nine questions of progressive difficulty for students to develop 'a rule' for differentiating y other methods than brute force expanding out.

Chain Rule Practice

Set of questions of progressive difficulty for students to familiarise themselves with the chain rule, answers included. PDF here

Lots Of Proof Questions

A whole bunch of OCR-A proof questions, arranged by types of proof required; contradiction, algebraic, exhaustion etc. PDF here.

Chain Rule, Product Rule, Quotient Rule Matchup Exercises

Three sets, each of three matchup puzzles, for pupils to practice chain rule, product rule and quotient rule. Answers included together with blank templates for pupils to create their own puzzles. PDFs here, here and here.

Integration By Parts

The formula and it's derivation from the product rule.

Integration by Parts Concept Questions

A set of questions of progressive difficulty to test students conceptual understanding of integration by parts. PDF Here

Functions Activity

A matchup cards activity to check & consolidate understanding of domain vs range and mapping.

Functions Notes

Notes on A level functions and Mappings. PDF here.

Functions Questions

Some harder functions questions to really test students understanding and ability in sketching diagrams. PDF here.

Numerical Methods

Notes on Numerical Methods.

Last Minute Revision Quiz

A lovely quiz to check pupils understanding of some key concepts of topics ahead of exams. PDF here.

Proving Trig Identities

Prove the trigonometric identities by matching up the peices (steps) in the correct order. Supports students with this topic by providing the steps , and avoiding alebraic mistakes that confuse the key learning outcomes, whilst challenging them to understand the order and making connections between each step. PDF here

Notes of Differential Equations

Notes on process for solving first order differential equations together with example question. Pdf version. Another, harder, example here (and as pdf).

Harmonic Form

The formula, or format, followed by a teaching activity and proof on the next page. PDF here.

Partial Fractions

The partial fractions formulae in big, to save writing it out. Plus a explanation of the various formats of partial fractions, such as when they include whole terms Ax + B etc. PDF here.

Binomial Theorem

The formula plus 8 questions to practice (answers on the second page), and teaching ideas on the third page. Pdf version.

Parametric Equations

Key notes on differentiating parametric equations and re-writing as Cartesian. PDF here.

Parametric Equation Integrating

An example of how to integrate underneath curves with parametric equations plus some questions to check your understanding. PDF here.

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.

GCSE-A Level Vector Notes

Notes on the key aspects of vectors that students ought to know and bring with them from GCSE. Three pages, all you need, one lesson. Its all here. PDF here. The Autograph file 1 and Autograph files 2 that were used to make it 'dynamic'.

Vectors to Resolve Forces

Dynamic Autograph file for demonstrating how vectors can be added and how to find the magnitude of a vector.

Vector Triangles in 3D Space

Sort these triangles into scalene, isosceles and equilateral. Which are right angled too? PDF here.

Vector Scalar Product Notes

Notes on Scalar Products of vectors. PDF here.