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Irby Maths's Shop

Welcome to my shop. My name is John Doyle and I live in Irby, Wirral. I started teaching Maths, Physics and Chemistry in the 1980s. As I changed schools and timetables changed, I taught some Computer Studies and I.T. but in later years I concentrated on teaching Maths up to A-Level. Some of the resources I’ve uploaded consist of notes, examples and questions and can be used for self-study. Other resources consist of just questions for extra practice (with answers). I hope you find them useful!

Welcome to my shop. My name is John Doyle and I live in Irby, Wirral. I started teaching Maths, Physics and Chemistry in the 1980s. As I changed schools and timetables changed, I taught some Computer Studies and I.T. but in later years I concentrated on teaching Maths up to A-Level. Some of the resources I’ve uploaded consist of notes, examples and questions and can be used for self-study. Other resources consist of just questions for extra practice (with answers). I hope you find them useful!
Algebraic Expressions: Meaning and Simplification
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Algebraic Expressions: Meaning and Simplification

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Worked examples, questions and answers introducing the use of algebraic notation, simplification of expressions and the use and expansion of brackets. The main resource (a pdf on 24 A4 pages) 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. Two additional resources (on 6 A4 pages in total) are included in this package These activities (with teaching notes) aid understanding for the beginner: (a) the game of “Find the Rule” is very useful in creating the idea of a connection between two variables. (b) “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.
Indices and Standard Form Test
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Indices and Standard Form Test

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A non-calculator test of 20 questions up to GCSE level on indices and standard form. 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 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 Tests - Number” can be downloaded from Irby Maths’ Shop for £3.00. If you need some notes, examples and exercises on the use of standard form then please have a look at my resource entitled “Standard Form”. This can be downloaded for just £2.00.
Trigonometry
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Trigonometry

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Notes, examples, questions and answers illustrating 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. This unit of work is suitable for self-study and ranges from beginner to GCSE level. Three exercises containing a total of over 60 questions (with separate answers) are included in this resource of 20 A4 pages.
Simplifications
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Simplifications

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36 questions up to GCSE level on the simplification of algebraic expressions. Answers included. This resource (on 2 A4 pages) is FREE to download. If you like this resource and would like some additional practice, then please have a look at “Algebraic Expressions: Meaning and Simplification”. This extensive resource on 24 A4 pages contains notes, worked examples and 195 questions in nine exercises (with answers). This resource is suitable for the beginner and goes up to GCSE level. "Algebraic Expressions: Meaning and Simplification " can be downloaded from Irby Maths’ Shop for £3.00.
Substitution of Numbers into Algebraic Expressions
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Substitution of Numbers into Algebraic Expressions

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Worked examples and 133 questions in five exercises illustrating the substitution of positive and negative numbers into algebraic expressions. Answers included. This unit of work (a pdf on 12 A4 pages) is suitable for self-study and ranges from beginner up to GCSE level. If you would like to try a FREE resource, then please have a look at “Substitutions” in Irby Maths’ Shop. This resource (a pdf on 2 A4 pages) contains 30 questions up to GCSE level on the substitution of numbers into algebraic expressions. The questions in this free resource are similar to the questions in Exercise D of my premium resource.
Solving Equations
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Solving Equations

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Worked examples and 115 questions up to GCSE level. The method of solving equations is introduced with easy examples and extended to equations where the variable is on both sides and equations involving brackets. A section on solving worded problems requiring the formation of an equation and a section on solving fractional algebraic equations are included. This unit of work (a pdf on 24 A4 pages) is suitable for self-study and ranges from beginner to GCSE standard. The questions are arranged in six exercises (with answers).
Standard Form
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Standard Form

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This pdf (10 A4 pages) contains an introduction to the use of standard form (scientific notation) with examples. The use of a calculator in performing standard form calculations is also discussed. Three exercises containing a total of over 30 questions with answers are included.
Algebra Bundle
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Algebra Bundle

4 Resources
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). 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
An Investigation of the Wood Mouse Population at a Farm
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An Investigation of the Wood Mouse Population at a Farm

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This investigation can be used as a KS3 statistics activity for up to 8 groups. Each group takes a sample of the population of wood mice living in the vicinity of a farm. 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. The activity is useful in promoting discussion about sampling and the use and misuse of surveys in everyday life. The two pdfs contain the information sheet for pupils (with teaching notes) and the data for the wood mouse populations at 8 farms (with answers).
An Investigation of Logic Gates
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An Investigation of Logic Gates

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This investigation can be used as a practical introduction to the properties of some logic gates. Although I designed this work for use in electronics it could be used in mathematics lessons to demonstrate the use of truth tables and as a simple introduction to the binary number system. The properties of a 4001 integrated circuit are investigated. This integrated circuit 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. The pdf (6 A4 pages) contains detailed instructions for the investigation of the logic gates. Example voltage readings (using a fresh PP3 battery) and completed truth tables are given in the accompanying Answers pdf. Items required for the activity: breadboard, link wires, 9 volt battery supply (or equivalent), 4001 integrated circuit, multimeter.
Solving Simultaneous Equations Using The Elimination Method
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Solving Simultaneous Equations Using The Elimination Method

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Worked examples and 63 questions up to GCSE level. Worded problems included. The elimination method of solving simultaneous equations is introduced with worked examples. Problems requiring the formation of simultaneous equations from given information are discussed. This unit of work (a pdf on 15 A4 pages) is suitable for self-study and ranges from beginner to GCSE level. The questions are arranged in four exercises (answers included).
Circus 1
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Circus 1

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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.
Calculus: Differentiation
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Calculus: Differentiation

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106 questions for extra practice on differentiation at AS/A Level. The questions (with separate answers) are contained in six exercises. Exercise A is on the differentiation of simple algebraic functions and is suitable for AS Level. Later exercises are more advanced and the function to be differentiated may need the use of the chain rule, product rule, quotient rule or a combination of these methods. Exercise B is on the differentiation of more complex algebraic functions. Exercise C (logarithmic functions), Exercise D (exponential functions), Exercise E (trigonometric functions) and Exercise F (implicit functions) complete this package (a pdf on 12 A4 pages).
Six Tests: Number
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Six Tests: Number

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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. This resource consists of 20 A4 pages.