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 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 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. 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) 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) 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.

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.

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.

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 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 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.

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.

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.

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.

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.

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.

Content of the resource This resource contains 6 Mini-Mocks, consisting of 20 questions each, covering the first 13 modules of the Scheme of Work we use at our school. Included in this download are 6 question booklets, 6 modelled answer booklets, and an overview of the module headings of all 24 modules of our Scheme of Work. Use of the resource As part of a new strategy to raise standards for mathematics at our school, we introduced Mini-Mocks at the start of last school year. Set by the Head of Maths, all Year 11 students must complete one Mini-Mock every week. After a week, teachers collect the Mini-Mocks from their students and check whether they have been completed to a good standard and chase up any students who have not submitted their work. Two days after the deadline has passed, modelled answers are being shared electronically and students self-mark their Mini-Mock. Teachers are free to decide when and where their students mark their work, which may depend on the group they teach. From experience, our more independent learners can be left to do their marking at home, while students who find it more difficult to organise themselves, should perhaps self-mark their Mini-Mocks in class. The worked answers are very detailed and sometimes include reminders of theory needed to do a question. We have issued every student with a small notebook to make notes based on their own mistakes. Teachers can monitor the quality of their students’ marking by checking marked Mini-Mocks, and by taking in students’ notebooks at regular intervals. Initial feedback from students and parents is extremely positive and students’ performance in our December Mock Examination improved significantly compared to the years before when students did not have the Mini-Mocks to help them revise for the the Mock Examination. When our examination results were published the following August, we were over the moon as we had our best GCSE examination results ever with 60% of the grades at 7 or higher: 23% of our candidates achieved a grade 9, 20% got a grade 8, and 17% got a grade 7. Also our students who find mathematics challenging did extremely well with only 1 student not achieving a pass. As a non-selective school, we were very pleased with our results and there is no doubt about it that our new initiative of Mini-Mocks has played a considerable role in our success. I hope that your students will find these Mini-Mocks useful as well.

Content of the resource This resource contains 6 Mini-Mocks, consisting of 20 questions each, covering the first 16 modules of the Scheme of Work we use at our school. Included in this download are 6 question booklets, 6 modelled answer booklets, and an overview of the module headings of all 24 modules of our Scheme of Work. Use of the resource As part of a new strategy to raise standards for mathematics at our school, we introduced Mini-Mocks at the start of last school year. Set by the Head of Maths, all Year 11 students must complete one Mini-Mock every week. After a week, teachers collect the Mini-Mocks from their students and check whether they have been completed to a good standard and chase up any students who have not submitted their work. Two days after the deadline has passed, modelled answers are being shared electronically and students self-mark their Mini-Mock. Teachers are free to decide when and where their students mark their work, which may depend on the group they teach. From experience, our more independent learners can be left to do their marking at home, while students who find it more difficult to organise themselves, should perhaps self-mark their Mini-Mocks in class. The worked answers are very detailed and sometimes include reminders of theory needed to do a question. We have issued every student with a small notebook to make notes based on their own mistakes. Teachers can monitor the quality of their students’ marking by checking marked Mini-Mocks, and by taking in students’ notebooks at regular intervals. Initial feedback from students and parents is extremely positive and students’ performance in our December Mock Examination improved significantly compared to previous years when students did not have the Mini-Mocks to help them revise for the Mock Examination. When our examination results were published the following August, we were over the moon as we had our best GCSE examination results ever with 60% of the grades at 7 or higher: 23% of our candidates achieved a grade 9, 20% got a grade 8, and 17% got a grade 7. Also, our students who find mathematics challenging did extremely well with only one student not achieving a pass. As a non-selective school, we were very pleased with our results and there is no doubt about it that our new initiative of Mini-Mocks has played a considerable role in our success. I hope that your students will find these Mini-Mocks useful as well.

These three worksheets combined have 180 quadratic equations. On the first page of 'Solving Quadratic Equations 1' the equations are organised by type of factorising: Highest Common Factor, Difference of Two Squares and Product-Sum Method. On the second page, the same three types have been mixed up, and students need to identify which type of factorising to use. 'Solving Quadratic Equations 2' and 'Solving Quadratic Equations 3' are more difficult, and can be used as a differentiated task either done in class or set for homework. 'Solving Quadratic Equations 3' is targeting students who are aiming for a grade 9. All three worksheets have answers. For your convenience, the Word files are included.

These five worksheets cover all levels of linear equations for Key Stage 3 and Key Stage 4. The linear equations range from simple ones with only positive terms in them to the more complicated ones with brackets, decimal numbers and fractions. Apart from just solving linear equations, some of the worksheets also contain some questions where students need to form linear equations themselves, and then solve them and interpret the answers. All worksheets include answers. Also included are the Word-files, which will allow you to adjust questions to the needs of your students. I hope you will find these worksheets useful. Thank you.