# Maths Muscateer

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#### Trigonometric Ratios - Unit Circle

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Trigonometric Ratios – Unit Circle One of the new topics of the reformed GCSE Mathematics (9-1) syllabus is trigonometric ratios: students need to memorise the trig ratios for 0˚, 30˚, 45˚, 60˚ and 90˚. At A-level, students tend to find it difficult to learn these ratios by heart and GCSE students are most likely to struggle even more with this. The 'Unit Circle' shows the trig ratios (sine, cosine and tangent) in context and it has been my experience that students find it much easier to learn these ratios by heart using the unit circle rather than the traditional table used by most teachers. It takes a little bit of time to get used to the ‘Unit Circle’’ as most of us are so used to the table in conjunction with the graphs. However, once you have made the transition, your will see that the students will memorise the trig ratios very quickly. It works best if the ‘Unit Circle’ is used from the very start when the trigonometric ratios are being introduced. This resource consists of 11 pages: a blank ‘Unit Circle’, a completed ‘Unit Circle’ in degrees (both in colour and black and white), a completed ‘Unit Circle’ in radians (both in colour and black and white), four examples on how to find the ratios, using the sine-line, cosine-line and tangent-line, and for GCSE students just the first quadrant blank, completed, in colour and in black and white. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Aiming for Grades 7-9 Part 1

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This booklet is part 1 of a three-part series of grades 7, 8 and 9 questions for GCSE Mathematics. It has 99 pages and contains a selection of questions covering the first eight modules of a Scheme of Work. The answer booklet has step-by-step worked solutions and is ideal for independent revision at home. Teachers can use the questions in the booklet either selectively showing examples of possible examination questions or as a practice booklet for students to work on in class. The key idea of this resource is that students mark their own work and that they resolve any difficulties they may come across themselves first before asking their teacher. This resource allows for easy but effective differentiation in class as students can do the questions in this booklet independently and at their own pace. There is no need to give each student their own copy; students can download the booklet from their school's VLE and they can do the questions in their exercise book working from an electronic device of their choice.

3 Resources
This bundle consists of three booklets with grades 7-9 questions for GCSE Mathematics. Altogether it has 481 pages containing lots of reasoning and problem solving questions for the reformed GCSE Mathematics course. The answer booklets have step-by-step worked solutions and are ideal for independent revision at home. Teachers can use the questions in the booklets either selectively showing examples of possible examination questions or as practice booklets for students to work on in class. The key idea of this resource is that students mark their own work and that they resolve any difficulties they may come across themselves first before asking their teacher. This resource allows for easy but effective differentiation in class as students can do the questions in this booklet independently and at their own pace. There is no need to give each student their own copy; students can download the booklet from their school's VLE and they can do the questions in their exercise book working from an electronic device of their choice.

#### Algebraic Manipulation

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Three worksheets with in total 137 algebraic expressions, which need to be manipulated: writing two or three algebraic fractions as a single fraction, using the indices rules to simplify expressions, writing expressions without negative indices and writing fractions on one line using negative indices. These worksheets are aimed to improve fluency in algebraic manipulation. The first few questions on each of these worksheets are simple and straightforward expressions but then they get gradually more difficult. The worksheets include answers. The worksheets are targeted at students in the higher ability sets in Year 9 and GCSE Higher Tier students (grades 6 – 9). These resources are also very useful as a revision tool at the start of the AS-level course, making sure that all students have a good starting level of fluency in algebraic fractions and indices. It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete all three worksheets. For your convenience, the Word files are included and can be edited to meet the needs of your students.

#### Fractions of Quantities

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This simple worksheet consists of two pages with 96 questions. A mixture of units is used, which provides good opportunities for class discussions. For this worksheet, students are expected to know their times tables and therefore it would be better not to use calculators. This worksheet is ideal for students in Year 6 and Year 7 and can be used both in class and for homework. Answers are included. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Fluency in Number Work - No Calculator

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The reformed GCSE Mathematics (9-1) curriculum demands from students a higher degree of fluency in number work. This worksheet is aimed at showing students a variety of skills to evaluate numerical expressions more effectively and to solve multi-step number work problems more fluently. This worksheet has a total of 100 questions (80 numerical expressions and 20 number problems), involving the four operations, fractions, decimal numbers, percentages, indices, surds, standard form, multiplication factors, proportion, ratio, percentage change, simple interest and compound interest. Most of these questions can be solved in a variety of ways and students should try to pick methods which they feel comfortable with. The worked answers accompanying this worksheet have been written with the emphasis on accuracy, trying to show students methods of how to evaluate expressions without making calculation errors. This worksheet is excellent revision for all students sitting the non-calculator paper of the reformed GCSE Mathematics examination. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Linear Relationships (1)

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These three worksheets have in total 26 questions linking the four representations of linear relationships with each other: descriptions, tables, formulae and graphs. The aim of these questions is to develop an understanding of the constants of the equation of a line and what these constants represent in graphs. All questions are contextual and there is no mention of y-intercepts and gradients. Instead, starting points (height of a candle before it is being lit) and rates of change (how quickly a candle gets shorter) are used to give meaning to the equation of a line. Students who have completed these three worksheets will find it much easier to understand the abstract equation of a line (y = mx + c) and are better equipped to interpret the gradient of a line. All worksheets include answers. The worksheets are targeted at Year 8 and Year 9 but also GCSE students would still benefit from this resource as it further enhances their understanding of lines and their equations. It should take students, depending on their ability level, between two and three hours to complete all three worksheets. The worked answers accompanying these worksheets allow the teaching and learning to continue beyond the classroom and it is therefore an ideal resource for a school’s VLE. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Factorising (1)

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This worksheet has in total 192 algebraic expressions. The questions are organised by type with 96 expressions to be factorised by taking out the highest common factor, 48 expressions to be factorised by the difference of two squares and 48 expressions to be factorised by applying the product-sum method. The questions range from basic expressions to difficult expressions involving larger numbers, decimal numbers, fractions and mixed numbers. This worksheet is not only useful for practising factorisation but it also will enhance students’ fluency in number work. The worksheet includes answers. Because of the range of difficulty levels of the questions on this worksheet, it can be used, selectively, in Key Stage 3, Key Stage 4 and even at the start of the AS-level course as a revision tool, making sure that all students have a sound understanding of factorising more difficult algebraic expressions. This would also be a useful resource on a school’s VLE where students can use it for independent study. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Aiming for Grades 7-9 Part 2

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This booklet is part 2 of a three-part series of grades 7, 8 and 9 questions for GCSE Mathematics. It has 161 pages and contains a selection of questions covering the second eight modules of a Scheme of Work. The answer booklet has step-by-step worked solutions and is ideal for independent revision at home. Teachers can use the questions in the booklet either selectively showing examples of possible examination questions or as a practice booklet for students to work on in class. The key idea of this resource is that students mark their own work and that they resolve any difficulties they may come across themselves first before asking their teacher. This resource allows for easy but effective differentiation in class as students can do the questions in this booklet independently and at their own pace. There is no need to give each student their own copy; students can download the booklets from their school's VLE and they can do the questions in their exercise book working from an electronic device of their choice.

#### Aiming for Grades 7-9 Part 3

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This booklet is part 3 of a three-part series of grades 7, 8 and 9 questions for GCSE Mathematics. It has 221 pages and contains a selection of questions covering the last eight modules of a Scheme of Work. The answer booklet has step-by-step worked solutions and is ideal for independent revision at home. Teachers can use the questions in the booklet either selectively showing examples of possible examination questions or as a practice booklet for students to work on in class. The key idea of this resource is that students mark their own work and that they resolve any difficulties they may come across themselves first before asking their teacher. This resource allows for easy but effective differentiation in class as students can do the questions in this booklet independently and at their own pace. There is no need to give each student their own copy; students can download the booklet from their school's VLE and they can do the questions in their exercise book working from an electronic device of their choice.

#### Simplifying Surds

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This worksheet has 36 questions covering the rules for simplifying surds: adding, subtracting, multiplying, expanding brackets and evaluating indices. It includes worked answers for self-marking. As a tool for Assessment for Learning, teachers can use this worksheet in class or set it for homework once the teaching of this topic has been completed. It can also be made available to students on a school's VLE as a revision tool for independent study. The worksheet is targeted at GCSE students (grades 6 - 9) and AS-level students. It should take students, depending on their ability level and understanding of the topic, between two and three hours to complete this worksheet. The worked answers accompanying this worksheet allow the teaching and learning to continue beyond the classroom and GCSE students aiming for a grade 9 will find this a very useful resource. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Standard Form (No Calculator)

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This worksheet has 9 questions covering the rules for numbers in standard form for the GCSE Mathematics (9-1) non-calculator paper: converting between ordinary numbers and numbers written in standard form, converting between numbers in words and numbers written in standard form, sorting numbers in standard form and using the four operations to evaluate expressions involving numbers written in standard form. The worksheet includes answers. As a tool for Assessment for Learning, teachers can use this worksheet in class or set it for homework once the teaching of this topic has been completed. It can also be made available to students on a school's VLE as a revision tool for independent study. The worksheet is targeted at the full range of students (grades 4 - 9) doing GCSE Mathematics Higher Tier. It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete this worksheet. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Rationalising Denominators

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This worksheet has 24 questions covering the rules for rationalising denominators of fractions. As a tool for Assessment for Learning, teachers can use this worksheet in class or set it for homework once the teaching of this topic has been completed. It can also be made available to students on a school's VLE as a revision tool for independent study. The worksheet is targeted at GCSE students (grades 6 - 9) and AS-level students. It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete this worksheet. The worked answers accompanying this worksheet allow the teaching and learning to continue beyond the classroom and GCSE students aiming for grades 8 and 9 will find this a very useful resource. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Evaluating Powers (1)

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This worksheet has 80 questions covering the rules for evaluating powers involving integer indices only. The bases of the powers on this worksheet are positive and negative integers, decimals, fractions and mixed numbers. This worksheet is not as simple as it seems and will require students to have a sound understanding of how to evaluate powers with a negative base and the effect the presence or absence of brackets have. The worksheet includes answers. As a tool for Assessment for Learning, teachers can use this worksheet in class or set it for homework once the teaching of this topic has been completed. It can also be made available to students on a school's VLE as a revision tool for independent study. The worksheet is targeted at the full range of students (grades 4 - 9) doing GCSE Mathematics Higher Tier. It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete this worksheet. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Evaluating Powers (2)

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This worksheet has 24 questions covering the rules for evaluating powers involving positive and negative fractional indices. The bases of the powers on this worksheet are integers, fractions, mixed numbers and surds. This worksheet is not for the fainthearted! It includes worked answers for self-marking. As a tool for Assessment for Learning, teachers can use this worksheet in class or set it for homework once the teaching of this topic has been completed. It can also be made available to students on a school's VLE as a revision tool for independent study. The worksheet is targeted at GCSE students (grades 7 - 9) and AS-level students. It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete this worksheet. The worked answers accompanying this worksheet allow the teaching and learning to continue beyond the classroom and GCSE students aiming for a grades 8 and 9 will find this a very useful resource. For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Patterns and Formulae

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This worksheet has 9 questions, which introduce the relationship between patterns and formulae. Each question explores a different pattern and through a series of small steps students will start to understand gradually what the variables in a formula represent. In this worksheet, students are not expected to come up with a formula themselves yet but towards the end they should have developed a sound understanding of what a formula is and they also should be able to select, from a group of formulae, the formula which describes a given pattern correctly. The worksheet includes worked answers for self-marking, which will allow students to progress through the worksheet at their own pace. The worksheet is targeted at students in Key Stage 3 and GCSE students doing Foundation Tier. This worksheet is best used in class where students can ask for support if needed. It should take students two lessons to complete this worksheet. For your convenience, the Word file is included and can be edited to meet the needs of your students.

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#### Sequences described by a written rule

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This worksheet has 35 questions, each showing a written rule defining a sequence of which three terms have already been given. Students need to find the next two terms of the sequences and also the two previous terms. This worksheet require students to know terminology like product, sum and mean and they also need to be able to apply inverse operations when trying to find previous terms. The worksheet includes answers. The worksheet is targeted at students in Key Stage 3 and GCSE students (grades 3 – 5). This worksheet is best used in class where students can ask for support if needed. It should take students between one and two hours to complete all the questions on this worksheet. Bonus worksheet: Special Sequences For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Deck of Playing Cards

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A handout for students doing questions on selecting cards from a pack of playing cards. When doing probability, some students have never played card games before, and they do not know what a pack of playing cards looks like. This simple sheet is a sample space, which gives students a comprehensive overview of all the types of cards in a deck of playing cards. This overview can be made smaller on a photocopier such that four of them fit on one A4 sheet of paper, which then can be photocopied. This saves photocopying and paper, and students can stick the small overviews in their exercise books. Before I issue each student with their own copy, I usually organise students in small groups, and give them a pack of playing cards, which they have to lay out on their table in the same way as on the overview. Students who have never used playing cards find this useful. When the playing cards have been laid out, we have a Q&amp;A session on probability questions related to selecting one card from a pack of playing cards. For your convenience, the Word file is included as well, which will allow you to adapt the overview. This is a simple resource, which I hope you will find useful. Please, feel free to leave comments. Thank you.

#### Mini-Mocks GCSE Mathematics Higher (Modules 1-11)

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This resource contains a set of six Mini-Mocks (Modules 1-11) and their modelled answers. Included is an overview of the 24 module headings of our scheme of work, giving you a rough idea of what the topics are in these six Mini-Mocks. Questions in these Mini-Mocks reflect the reformed Mathematics (9-1) syllabus. The questions have been selected from a range of sources while some questions have been adapted for the use in this resource. Students at our school have found the modelled answers extremely useful as it helps them to revise the GCSE Mathematics sylabus independently at home. It also has helped our students to identify types of questions which they need to further improve on. In summer 2019, our GCSE examination results increased considerably as a result of these Mini-Mocks and consequently I am developing more sets of Mini-Mocks, not only for Year 11 but also for Year 10. It would be great if you could rate this free resource. Thank you very much.