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#### Simplifying Algebraic Expressions with Indices

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.

#### Linear Relationships (1)

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.

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.

#### Algebraic Manipulation

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.

#### Deck of Playing Cards

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&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.

#### 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.

#### Standard Form (No Calculator)

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.

#### Evaluating Powers (2)

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.

#### Solving Quadratic Equations

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.

#### Solving Linear Equations

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.

#### Simplifying Surds

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.

#### Numeracy Skills

This resource consists of nine simple worksheets, which can be used from Year 5 to Year 9 depending on the students' ability. It has a total of 610 questions, equating to roughly 5 hours of useful numeracy practice.
The main aim of the 'Fluency in Numeracy' worksheets in this resource is to show students smart ways to evaluate products and quotients, like for example the halving-doubling method, or using equivalent fractions to make divisions simpler. With the new GCSE (9-1) curriculum, these skills are becoming more important again.
The place value topic 'Dividing by Powers of 10' can be tricky for some students and the worksheets in this resource have proven to be a useful way for students to practise many questions in a short space of time.
All worksheets come with answers, and the worksheets are also in Word files, which will allow users to come up with their own questions very quickly.
I hope you will find this resource useful.
Thank you.

#### Rationalising Denominators

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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### 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.

#### Inequalities

This booklet has 58 questions on inequalities and is a very useful resource for students to practise this topic for the GCSE examination. It starts with easy questions and they gradually increase in difficulty level. There are some unusual inequalities, which may prove to be useful for the new (9-1) GCSE examinations.
Also included are questions where students need to shade in regions given a few inequalities, and also the other way around where a region is given and students need to find the inequalities that define the shaded region.
The last three questions are applications touching on linear programming.
Students will need at least four hours to complete all the questions in this booklet. This resource comes with worked answers and is therefore great for independent revision either in class or at home.