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.

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.

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.

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.

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.

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.

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.

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.

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.

This worksheet has 30 parabolas drawn on individual coordinate systems. For each graph, the corresponding quadratic function needs to be found in the form of y = p(x + q)2 + r and then to be written in the form of y = ax2 + bx + c. The idea of this worksheet is to apply one or more transformations to the standard parabola with function y = x2 to find the functions of a range of parabolas. Transformations to be used are: horizontal translations, vertical translations, vertical stretches and reflections in the x-axis. This worksheet is not only useful to introduce transformations of graphs and the effect they have on functions, it also provides practice for expanding brackets and shows the link between the two formats of quadratic functions as a first step towards completing the square. In ‘Graphs of Quadratic Functions (2)’ this link is further explored. 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.

These two worksheets are a follow-up of the three worksheets in Linear Relationships (1) and their aim is to show the graphical representation of the solution of a pair of simultaneous equations. Each worksheet has 9 questions in which a pair of linear relationships is defined by two equations or by a given context. The graphs of the linear relationships need to be drawn and the point of intersection needs to be calculated by solving an equation. The first six questions on each worksheet are in abstract form and the last three question are given in context. The equations on the worksheet ‘Linear Relationships 4’ are given in the format ‘y = mx + c’ and the equations are expected to be solved simultaneously by using the balancing method. The equations on the worksheet ‘Linear Relationships 5’ are given in the format 'ax + by = c' and should be solved simultaneously by using the elimination method. 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 how and why we solve equations simultaneously. It should take students, depending on their ability level, between two and three hours to complete both 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.

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.

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.

This worksheet has 30 algebraic expressions involving indices and/or surds. By applying the indices rules, the expressions are to be simplified and answers need to be written without negative indices and/or without fractional indices. This worksheet requires a high level of algebraic manipulation. 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 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.

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.

This download consists of two worksheets on sequences. The first worksheet, ‘Recognising Sequences’, shows 24 sequences and students should establish the type of sequence (linear, quadratic, cubic, exponential, prime numbers) and write down the next two terms of each of these sequences. The second worksheet, ‘The nth Term of a Sequence’, consist of 45 sequences and students need to write down the nth term of each of these sequences. The first page has only linear sequences, the second page has only quadratic sequences and on the third page there is a mixture of different types of sequences: linear, quadratic and cubic. The nth terms of the quadratic and cubic sequences are to be derived from the standard quadratic and cubic sequences. The worksheets include answers. The worksheets are targeted at students at the top-end of Key Stage 3 and GCSE students (grades 4 – 7). It should take students, depending on their ability level and understanding of the topic, between one and two hours to complete both worksheets. For your convenience, the Word file is included and can be edited to meet the needs of your students.

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.

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.

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.

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.