An Investigation of Logic Gates

An Investigation of Logic Gates

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.
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An Investigation of the Wood Mouse Population at a Farm

An Investigation of the Wood Mouse Population at a Farm

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).
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Standard Form

Standard Form

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.
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Trigonometry

Trigonometry

This pdf (18 A4 pages) contains examples, questions and answers illustrating the use of trigonometry in solving problems. Problems described in words which require the construction of a sketch diagram are included. This unit of work is also suitable for self-study. Two exercises containing a total of over 50 questions are included.
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Solving Equations

Solving Equations

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. The questions (with answers) are contained in six exercises. This unit of work (a pdf on 24 A4 pages) is aimed at KS3 and KS4 but is very suitable for self-study.
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Solving Simultaneous Equations Using The Elimination Method

Solving Simultaneous Equations Using The Elimination Method

Worked examples and 45 questions. 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. The questions (with answers) are contained in three exercises. This unit of work (a pdf on 13 A4 pages) is aimed at KS3 and KS4 but is very suitable for self-study.
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Algebraic Expressions: Meaning and Simplification

Algebraic Expressions: Meaning and Simplification

These pdfs (19 A4 pages in total) can be used for introducing algebra. Examples of mathematical expressions in algebraic "shorthand" and their "longhand" meanings are given. Sometimes expressions can be simplified. The use of brackets in algebraic expressions is discussed. A total of over 60 questions with answers are available in four exercises. Two activities (with teaching notes) are included in this package: (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 for an informative wall display.
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Substitution of Numbers into Algebraic Expressions

Substitution of Numbers into Algebraic Expressions

This pdf (6 A4 pages) contains examples, questions and answers illustrating the substitution of positive and negative numbers into algebraic expressions. Two exercises containing over 40 questions are included. The first exercise involves only positive numbers. The second exercise involves both positive and negative numbers.
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Circus 1

Circus 1

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.
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Calculus: Differentiation

Calculus: Differentiation

106 questions for extra practice on differentiation at AS/A level. The questions (with 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).
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