# Irby Maths Shop

Welcome! Some of my resources consist of notes, examples and questions; others just have questions for extra practice. They’ve worked well for me - I hope you find them useful! John Doyle from Irby, Wirral, UK.

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Welcome! Some of my resources consist of notes, examples and questions; others just have questions for extra practice. They’ve worked well for me - I hope you find them useful! John Doyle from Irby, Wirral, UK.

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Welcome! Some of my resources consist of notes, examples and questions; others just have questions for extra practice. They’ve worked well for me - I hope you find them useful!
John Doyle from Irby, Wirral, UK.

Graphs of Linear Equations contains a selection of questions on graphs produced by equations of the form y = mx + c.
Early questions involve plotting straight line graphs from given equations. These are followed by questions where the gradient and y-intercept need to be found from given graphs. Finally, two longer questions requiring the drawing of lines of best fit and subsequent interpretation of the graphs of experimental data.
This unit of work is suitable for self-study and ranges from beginner to GCSE standard. Answers included.
Pdf and ppt versions of this resource are included in the download which contains 11 pages/slides.

Worked examples and 133 questions in five exercises illustrating the substitution of positive and negative numbers into algebraic expressions. Answers included.
“Substitution of Numbers into Algebraic Expressions” is suitable for self-study and ranges from beginner up to GCSE level. Pdf and ppt versions of this resource are included in the download which contains 12 A4 pages/slides.
This resource is part of my Algebra Bundle resource package.

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A range of notes, worked examples and questions ranging in standard from the beginner up to GCSE level. A total of 506 questions in 24 exercises (answers included). Pdf and ppt versions of each resource are included in “Algebra Bundle”.
Topics covered:
meaning and simplification of expressions
use of brackets
substitution of numbers into expressions
solution of linear equations
solution of fractional equations
solution of simultaneous equations
If you need revision questions on a variety of topics at GCSE standard then please have a look at Nine GCSE Maths Revision Exercises. This resource contains 124 questions with separate answers

Worked examples and exercises on rounding numbers to a specified nearest number or to a number of decimal places or significant figures. Four exercises in total contain over 130 questions (with answers). Exercise 4 involves estimating answers by approximating the numbers involved to 1 significant figure.
“Rounding and Estimating - Notes, Examples and Exercises” is a suitable unit of work for KS3.
Pdf and ppt versions of this resource are included in the download which contains 11 pages/slides.

“An Experimental Investigation of Logic Gates Using IC 4001” gives step by step instructions for investigating the properties of the 4001 integrated circuit.
Although I designed this activity for use in electronics, it could be used in mathematics lessons to demonstrate the use of truth tables and as background information about computers and the binary number system.
The 4001 chip contains four, two-input NOR gates. The NOR gates can be connected in different ways to mimic the properties of NOT, OR, AND and NAND gates.
Example voltage readings (using a fresh PP3 battery) and completed truth tables are given in the Answers section.
Pdf and ppt versions of this resource are included in the download which contains 9 pages/slides.
Apparatus required for this activity: breadboard, link wires, 9 volt battery (or equivalent supply), 4001 integrated circuit, multimeter.

Young chemists often struggle with ionic formulae - too many symbols and charges to master at the same time. “Ionic Formulae Cards and Worksheet” will help to alleviate this difficulty.
The Anions and Cations pdfs in this resource could be printed onto coloured paper but card is more durable. Cations could be printed onto one colour of card and anions onto a different colour. The printed sheets of ions need to be carefully cut out to give cards measuring approx. 8 cm by 5 cm. These cards can be arranged easily into formulae and can also aid discussions about reactions in aqueous solution. Names have been given for some of the ions; the remaining cards could be labelled if desired.
Fourteen different anions and fourteen different cations are provided. A blank page of ions is given at the end of each pdf to make your own ion cards if other ions are needed.
A worksheet is included (with answers) to develop and reinforce understanding of this topic.
These pdfs contain a total of 11 A4 pages.

“Nine GCSE Maths Revision Exercises” contains a total of 124 questions, at GCSE standard, arranged in nine exercises (with separate answers).
Beneficial for developing fluency in a variety of topics. Useful for revision in class or as homework tasks.
Pdf and ppt versions of this resource are included in the download which contains 18 pages/slides.
If you need additional revision questions on algebra then please have a look at my Algebra Bundle which contains over 500 questions in 24 exercises on equations, simultaneous equations, substitutions and simplifications.

“Indices and Standard Form Test” is a non-calculator test of 20 questions up to GCSE level. There is space below each question where the answer can be written. This resource (on 3 A4 pages) is FREE to download. Answers included.
This free test is similar to one of the tests in my resource entitled Six Non-Calculator Tests - Number which you may like. This suite of non-calculator tests (with answers) on 20 A4 pages contains two tests on general arithmetic involving questions on whole numbers, fractions and decimals. Other tests in the suite concentrate on fractions, or decimals, or percentages, or indices and standard form.
Six Non-Calculator Tests - Number can be downloaded from Irby Maths’ Shop for £1.50.
If you need an introduction with examples and questions on the use of standard form then please have a look at my resource entitled Standard Form - Notes, Examples and Exercises which can be downloaded for just £1.50.

Worked examples and 63 questions on simultaneous equations in four exercises. Answers included.
“Solving Simultaneous Equations Using The Elimination Method” introduces the technique with worked examples. Problems solved by the formation of simultaneous equations from given information are included.
Pdf and ppt versions of this resource are included in the download which contains 15 pages/slides. This unit of work is suitable for self-study and ranges from beginner to GCSE level.
“Solving Simultaneous Equations Using The Elimination Method” can be downloaded as part of my Algebra Bundle resource package.

“Geometrical Transformations Worksheets” - reflections, rotations, translations and enlargements. A total of 14 questions, in two worksheets, to develop and reinforce understanding of this important topic. The questions, up to GCSE standard, are designed to fit onto A4-sized graph paper. Answers included.
Pdf and ppt versions of “Geometrical Transformations Worksheets” are included in the download which contains 6 A4 pages/slides.
I’ve also added a pdf of graph paper to this resource which was made using Excel. I’ve used it for online tuition and called it “pseudo-2 mm graph paper” as, on my printer, the grid is about 1.5 % too long and about 1.1 % too narrow but it’s good enough for most purposes!

“A Statistical Investigation of the Wood Mouse Population at a Farm” can be used as an activity for up to 8 groups of KS3 pupils.
No real wood mice are used in this activity! It’s a modelling exercise using dice.
Each group is given data about the masses of wood mice at one of eight farms. A sample of this population is taken randomly by rolling a die. The range, median, mode and mean mass of the wood mice are calculated for the sample and then compared to the values for the whole population at that farm.
Masses of the wood mice at each of the eight farms are given in the Wood Mouse Investigation Data Cards pdf.
This activity is useful in promoting discussion about sampling and the use and misuse of surveys in everyday life.
The download contains three pdfs: the Pupil Sheet pdf, the Teaching Notes pdf and the Wood Mouse Investigation Data Cards pdf (a total of 11 pages).

124 questions for revision practice on methods of differentiation. The questions (with separate answers) are contained in seven exercises.
Exercises A, B and C of "Calculus - Revision Exercises on Methods of Differentiation" cover basic methods including the product rule, quotient rule and use of a substitution (chain rule).
Later exercises are more advanced and differentiation may require a combination of methods. Exercise D involves logarithmic functions and Exercise E is on exponential functions. Exercise F (trigonometric functions) and Exercise G (implicit functions) complete this package.
Pdf and ppt versions of this resource are included in the download which contains 15 pages/slides.

Worked examples and three exercises containing a total of over 60 questions (with separate answers) are included in this resource which illustrates the use of trigonometry in solving problems. Diagrams are given for many of the questions but some problems are included which require the construction of a sketch diagram.
“Trigonometry - Notes, Examples and Exercises” is suitable as a self-study unit of work and ranges from beginner to GCSE standard.
Pdf and ppt versions of this resource are included in the download which contains 20 pages/slides.

Worked examples and 115 equations to solve in six exercises. Answers included.
“Solving Linear Equations - Notes, Examples and Exercises” introduces the method of solving linear equations with easy examples. Later examples include equations where the variable is on both sides and equations which involve the manipulation of brackets. A section on solving worded problems by forming and solving an equation and a section on solving fractional equations are included.
Pdf and ppt versions of this resource are included in the download which contains 24 pages/slides. This unit of work is suitable for self-study and ranges from beginner to GCSE standard.
This resource can be downloaded as part of my Algebra Bundle resource package.

This KS3 Mathematics activity is useful as an end of term competition or for a change from routine revision sessions. Up to 10 teams compete against the clock to answer as many questions as possible in each round before moving on to the next round. Sufficient questions for 10 rounds plus two sets of bonus questions are supplied.
The five pdfs contain questions (for duplication), answers, templates for team scores and a suggested routine for running the competition.
Questions are on topics such as arithmetic with whole numbers, positive and negative numbers, expansion of brackets, solution of equations, percentages, simplification of indices, standard form, use of a calculator.

Worked examples, questions and answers introducing the use of algebraic notation, simplification of expressions (including fractional expressions) and the use and expansion of brackets.
“Algebraic Expressions - Meaning and Simplification” contains 195 questions in nine exercises (with separate answers). Early exercises are suitable for the beginner. Exercise H on the simplification of fractional algebraic expressions and Exercise I on proving identities are suitable for the more able candidates at GCSE. Pdf and ppt versions of this resource are included in the download which contains 24 pages/slides.
Two additional resources with teaching notes (on 6 pages/slides in total) are included in this package These activities aid understanding for the beginner:
the game of “Find the Rule” is very useful in creating the idea of a connection between two variables.
“Think of a Number” is a well-known number puzzle. Here, examples are worked through and algebra is used to show why the puzzles work. Pupils should create their own puzzles on posters which can produce an informative wall display.
These resources can be downloaded as part of my Algebra Bundle resource package.

“Standard Form - Notes, Examples and Exercises” introduces the use of standard form (or scientific notation) for very large or very small numbers. A section on using standard form on a calculator is included.
Display screens on calculators have improved over the years but entering numbers in standard form and interpretation of what is displayed on a screen can still cause many problems.
Four exercises containing a total of over 50 questions with answers are included in this unit of work which is suitable for self-study and ranges from beginner to GCSE standard.
Pdf and ppt versions of this resource are included in the download which contains 12 A4 pages/slides.

A set of six, non-calculator tests (with answers) suitable up to GCSE level. Ideal for quick revision tests. Working and answers can be written in the space below each question.
The first two tests contain a mixture of questions including addition, subtraction, multiplication and division of whole numbers, decimals and fractions - I’ve classed these tests as “general arithmetic”.
Remaining tests concentrate on fractions or decimals or percentages or indices and standard form.
“Six -Non-Calculator Tests - Number” contains 20 A4 pages.

36 questions up to GCSE level on the simplification of algebraic expressions. The worksheet starts with easy questions on collecting similar terms together and moves on to questions involving the expansion of brackets and fractional expressions. The last three questions involve surd form. Answers included. “Simplifications Worksheet” (pdf and ppt versions) is FREE to download.
My resource Algebraic Expressions: Meaning and Simplification explores this topic in more detail. It contains notes, worked examples and 195 questions on algebraic simplification in nine exercises (with answers). This resource (on 24 A4 pages) is suitable for the beginner and goes up to GCSE level. Algebraic Expressions: Meaning and Simplification can be downloaded from Irby Maths’ Shop for £1.80.

“Differentiation from First Principles” starts by illustrating the difficulty of finding a reliable answer for the gradient at a point on a curve by drawing a tangent to the curve. Pupils compare their answers for the gradient at two points on a cubic graph. The method of approximating the gradient of a chord to the gradient of the tangent at a point is then introduced.
Twelve examples are given for pupils to work through (in groups) to find the formula for the gradient at a point on a curve. Hopefully, the connection between the gradient formulae and the original equations will be spotted!
“Differentiation from First Principles” (pdf and ppt versions on 19 pages/slides) is FREE to download.
If you are interested in some revision exercises for A2 classes on different techniques of differentiation then please have a look at “Calculus: Revision Exercises on Methods of Differentiation”. This extensive resource (available in pdf and ppt versions) contains 124 questions in seven exercises (with answers). “Calculus: Revision Exercises on Methods of Differentiation” can be downloaded from Irby Maths’ Shop for £1.80.