### All resources

#### Converting Fractions to Decimals

This worksheet consists of four pages with 181 fractions/mixed numbers to be converted into a decimal number. The first page shows the fractions/mixed numbers students are expected to know for this worksheet and the following three pages are a mixture of questions to practise these conversions. This worksheet is ideal for students in Year 6, Year 7 and Year 8 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.

#### Expanding Brackets

This file has in total 347 algebraic expressions with brackets, which need to be expanded and simplified. The questions are organised by type and each of the seven pages have their own heading and as such can be used as an independent worksheet. All worksheets include answers.
Because of the range of difficulty levels of the questions in this file, they can be used, selectively, in Key Stage 3, Key Stage 4 and even at the start of the AS-level course, making sure that all students have a sound understanding of how to expand brackets in more difficult expressions. It would also be a very 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.

#### Trigonometry (2)

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) syllabus. For the majority of these questions, students are required to interpret the context and use their reasoning and problem solving skills. The 48 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. The worked answers also show students how to communicate their reasoning and calculations. Calculators are allowed for the questions in this booklet.
Topics covered in this booklet are: sine rule, cosine rule, area of a triangle, bearings, identifying and applying the different rules in 2D and 3D, sketching graphs of trigonometric functions, interpreting transformations applied to trigonometric functions, finding trigonometric functions of graphs given, solving simple trigonometric equations graphically, using and applying trigonometric functions and graphs in cyclic contexts.

#### Factorising (1)

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.

#### Factorising (3)

This worksheet has 36 algebraic expressions, which need to be factorised. The questions are not organised by type and therefore students are expected to identify how to factorise the expressions using an appropriate method: taking out the highest common factor, difference of two squares, product-sum method, by pairing or a combination of these methods. The worksheet includes worked answers.
The worksheet is targeted at GCSE students (grades 7 - 9) and it should take them, depending on their ability level and understanding of the topic, between two and three hours to complete. Fluency in factorising algebraic expression is essential at the start of the AS-level course and this worksheet is very useful for students who need to revise this skill after a long summer holiday.
The worked answers accompanying this worksheet allow the teaching and learning to continue beyond the classroom and it is therefore an ideal resource on a school’s VLE as a revision tool for independent study at home. Students aiming for the highest grades 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.

#### Factorising (2)

This worksheet has 48 algebraic expressions, which need to be factorised. The questions are not organised by type and therefore students are expected to identify how to factorise the expressions using an appropriate method: taking out the highest common factor, difference of two squares or the product-sum method. Answers are included.
The worksheet is targeted at GCSE students (grades 5 - 8). It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete the worksheet.
For your convenience, the Word file is included and can be edited to meet the needs of your students.

#### Factorising (4)

This worksheet has 36 algebraic expressions, which need to be factorised. The questions are not organised by type and therefore students are expected to identify how to factorise the expressions using an appropriate method: taking out the highest common factor, difference of two squares, product-sum method, by pairing or a combination of these methods, which trains students to double-check if they have fully factorised expressions. The worksheet includes worked answers.
The worksheet is targeted at the most able GCSE students who are aiming for grade 9. Fluency in factorising algebraic expression is essential at the start of the AS-level course and this worksheet is very useful for students who need to revise this skill after a long summer holiday.
The worked answers accompanying this worksheet allow the teaching and learning to continue beyond the classroom and it is therefore an ideal resource on a school’s VLE as a revision tool for independent study at home.
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

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.

#### Trigonometric Ratios - Unit Circle

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

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.

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

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.

BUNDLE

#### Aiming for Grades 7-9

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.

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

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.

#### Trigonometry (1)

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) syllabus. For the majority of these questions, students are required to interpret the context and use their reasoning and problem solving skills. The 54 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. The worked answers also show students how to communicate their reasoning and calculations. Calculators are allowed for the questions in this booklet.
Topics covered in this booklet are: Pythagoras’ Theorem, finding the distance between two points, trigonometry in right-angled triangles, angles of elevation, bearings and identifying and applying trigonometry and Pythagoras’ Theorem in 2D and 3D.

#### Functions

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) Higher Tier syllabus. The 36 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. Calculators are not allowed for the questions in this booklet.
Topics covered in this booklet are: evaluating f(x) for given values of x, finding x for given values of f(x), composite functions, inverse functions and applying transformations to graphs and functions.
This booklet has excellent examples of questions of the new topics in the reformed GCSE Mathematics (9-1) curriculum.

#### Solving Equations (1)

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) syllabus. The 113 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. Calculators are not allowed for the questions in this booklet.
Topics covered in this booklet are: solving linear equations ranging from very easy to difficult, solving a range of different types of quadratic equations, solving exponential equations, solving simultaneous equations graphically, solving simultaneous equations algebraically and applying simultaneous equations for solving contextual problems.
This booklet has excellent examples of questions of the new topics in the reformed GCSE Mathematics (9-1) curriculum.

#### Fractions of Quantities

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.

#### Equations of Graphs

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) Higher Tier syllabus. The 58 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. Calculators are not allowed for the questions in this booklet.
Topics covered in this booklet are: coordinates in 3D, finding midpoints, finding gradients, finding equations of lines from a range of contexts (a given graph, parallel to, perpendicular to, passing through), finding coordinates of points on a line, identifying properties of lines from equations given, sketching graphs of quadratic functions, finding the turning point of a graph given its function, drawing different types of graphs using tables, exponential functions and their graphs, solving equations graphically, including drawing suitable lines, using rates of change to interprete graphs and linking different types of graphs to their functions.
This booklet has excellent examples of questions of the new topics in the reformed GCSE Mathematics (9-1) curriculum.

#### Units, Rounding and Graphs

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) Higher Tier syllabus. For the majority of these questions, students are required to interpret the context and use their reasoning and problem solving skills. The 183 questions in this booklet cover all grades of the new GCSE curriculum and can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. The worked answers also show students how to communicate their reasoning and calculations. Calculators are allowed for the questions in this booklet.
Topics covered in this booklet are: units of time, compound units, metric conversion, imperial conversions (conversion factors are given in most cases), converting compound units, scale involving length, area and volume, evaluating numerical expressions, rounding, estimating answers, upper and lower bounds, including bounds of compound units, distance-time graphs, speed-time graphs, calculation/estimation and interpretation of gradients of graphs, calculation/estimation and interpretation of areas underneath graphs, including the Trapezium Rule.
This booklet has excellent examples of questions of the new topics in the reformed GCSE Mathematics (9-1) curriculum.

#### Solving Equations (2)

This booklet contains a selection of questions covering a range of topics for the reformed GCSE Mathematics (9-1) syllabus. For the majority of these questions, students are required to interpret the context and use their reasoning and problem solving skills. The 96 questions in this booklet can be used by both teachers, to show examples of examination style questions in class, and students, for independent revision at home. The answers are particularly useful if students are not secure in certain topics as they show full step-by-step workings. Calculators are allowed for the questions in this booklet.
Topics covered in this booklet are: solving quadratic equations using the quadratic formula, solving equations using trial and improvement, solving equations involving algebraic fractions, solving simultaneous equations with one linear equation and one quadratic equation, using graphs to estimate solutions of equations, writing down equations from a given context and forming equations to solve problems related to the cost of products, angles, perimeters, areas, volumes, surface areas, 3D shapes, similar shapes, probability and compound measures.
This booklet has excellent examples of questions of the new topics in the reformed GCSE Mathematics (9-1) curriculum.

#### Graphs of Quadratic Functions (2)

This worksheet is a follow-up of ‘Graphs of Quadratic Functions (1). It has 30 quadratic functions of which the graphs need to be drawn on blank coordinate systems, one for each function. The first 18 functions given are in the form y = p(x + q)2 + r ; by applying appropriate transformations their graphs need to be derived from the standard parabola of the function y = x2. The last 12 functions are given in the form y = ax2 + bx + c and in order to draw the graphs of these functions, they need to be written in the form of y = p(x + q)2 + r by completing their square.
This worksheet is aimed to give the skill ‘Completing the Square’ a clear purpose and it also can be used as an introduction to transformations of graphs. The worksheet includes answers.
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.