These worksheets can be used to introduce and practise the new GCSE topic of equation of a circle (centred at origin) and the equation of a tangent to a circle. The first worksheet starts with an activity that helps the students to realise that x^2 + y^2 = k is the equation of a circle and is followed by some questions to practise using it. The second document is an 8-page worksheet which can be used to revise all the necessary skills/knowledge required before studying the equation of a tangent to a circle. Working through this first seemed to really help my GCSE group with this topic. Answers are included. The third document is a 9-page worksheet which focusses on finding the equation of a tangent to a given circle at a particular point or with a particular gradient. All answers are included.

This worksheet is designed to develop students' knowledge and confidence when expanding and simplifying expressions that involve two brackets. The worksheet includes questions ranging from 2(3x+4) - 5(x-3), then (x+4)(x+2), (x-3)^2, and up to (2x+1)(x-4). The solutions are fully worked solutions showing each step of the expansion and simplification.

These resources can be used to teach the topic of estimation - where the result of a calculation is estimated by rounding the value of all numbers in the calculation to 1 significant figure. The powerpoint presentation introduces the method and contains examples for the students to practise. Students can use the print-version to make notes and attempt the practice questions. The group activity is a differentiated activity that allows each group to choose the difficulty of question they attempt in each round. Instructions, answers and a scoring spreadsheet are included. The estimation worksheet contains 18 questions. The treasure hunt is a group activity which can be done at desks or can involve the class moving around the room to find the next question - usually a very popular activity! All answers are included.

The first resource is table of 34 questions where the students must find, for example, the equivalent decimal and percentage for the given fraction. This worksheet does not require knowledge of recurring decimals. The second resource is for more advanced conversion of decimals to fractions and vice-versa. It is a 4-page worksheet which focuses on converting recurring decimals, including proofs. Answers to both worksheets are included.

The presentation introduces the idea of drawing a graph to represent how quickly a container fills with liquid over time. The print-version can be given to pupils to make notes on and complete as the presentation is shown. The worksheet is designed to test their understanding after completing the presentation (answers are included).

Each worksheet has a number of examples of graphs for students to learn/practise finding information from the graph. The worksheets include estimating velocity or acceleration by drawing a tangent to the curve. All solutions are included.

After teaching my classes how to integrate using "reverse chain rule" and giving them enough practice to feel confident about the method, I have used this worksheet to try to encourage them to use less time and steps. My classes enjoyed the challenge of trying to complete the sheet within the time - you can always amend the time limit for weaker/stronger groups. Solutions are attached. Note that this sheet assumes that students know how to integrate the function e^x and 1/x.

This resource is designed to introduce the method for finding the volume of a shape created when an area is rotated around an axis. The first side explains the derivation of the formulae - I would recommend you also try to show your students an animation that helps them visualise a 3D shape being created by a region rotating about an axis (lots are freely available online). There are then 5 pages of questions for your students to complete. Most of the questions are in two parts - the first part involves finding an area, the second part involves finding a volume (a very common style of question in examination papers). Note that students are expected to be able to integrate using ln, e and reverse chain rule. Answers to all questions are provided.

The first resource guides your students through the whole process of using the Simplex algorithm to solve a linear programming problem. The first page explains how the initial tableau is formed, how the objective function must be written and how the inequalities that represent constraints must be written as equations with the introduction of slack variables. The first exercise (11 questions) gives them the opportunity to practise writing the initial tableau correctly for different problems. Grids are provided so students focus their time and energy on only the values in the tableau. The next section describes how an iteration of the algorithm is performed and links the iterations to the graphical solution, showing how each iteration moves to a different vertex of the feasible region. There is then another exercise with 10 questions for students to practise performing iterations and finding the optimal solution. Again, grids are provided so students focus their time and energy on only the steps of the algorithm and the values in the tableau. Fully worked solutions are provided to all the questions in the exercises. The second resource is a spreadsheet that automatically solves any simplex tableau in 2/3 variables with 2/3 constraints - a useful resource for doing/checking solutions to other questions from a textbook or examination paper.

This resource is designed to introduce the method of finding dx/dy and using this to work out the gradient of a curve. There are 3 examples to work through as a class - these will show that to differentiate a curve in some cases it is necessary to have the equation of the curve in the form x=f(y). There is then a short note to summarise the method and then 3 pages of examination-style questions for students to practise. Answers are included.

I designed this worksheet to try to teach a weak GCSE group how to change the subject of a formula. The introduction explains what is meant by the "subject", and has a few examples to make sure this is clear in the students' minds. In exercise A there are 17 multiple-choice questions where students simply circle what they think is the correct rearrangement of the formula. The idea is that, as they are multiple choice, all students will be prepared to have a go at these questions and as you go through the answers there will be discussion points about the step(s) required and different ways you might set out your working or final answer. In exercise B there are 15 questions where the students must change the subject of the formula themselves. Solutions to the worksheet are provided. Note that the sheet contains questions where the new subject appears once only.

This worksheet can be used to teach/practise the required knowledge and skills expected at A level for the intersections of graphs. The introduction discusses the different methods that can be used but then focuses on the method of substitution. There are then a few examples to illustrate the method, including questions about the geometrical interpretation of the answers. The final section shows how the discriminant can be used to determine/show the number of points of intersection, with examples to illustrate the method. Fully worked solutions to all examples are provided.

This worksheet can be used to teach/practise the required knowledge and skills expected at A level for the topic of proportion. The first page focuses on writing down the correct equation in different cases of direct and indirect proportion. The second page focuses on the graph(s) that can represent different types of proportion. The final page has a number of problems to solve with variables that are directly or inversely proportional. Fully worked solutions to all questions are provided.

This worksheet is designed so that students will hopefully gain an understanding of the process of converting mixed numbers and improper fractions, without having to write down a series of steps or instructions to follow. For both conversions the first set of questions are scaffolded, then for later questions the scaffolding is removed so they are doing the whole conversion themselves. There are 20 conversions in both directions, worked solutions are provided.

The first resource guides your class through the process of using the real and complex roots of z^n+k=0 to write down its real factors. The introduction includes the important result about the sum of conjugates and then uses equations of the form z^n=1 or z^n=-1 to establish that there is always an even number of complex roots, which can be put into conjugate pairs. It is then shown how each conjugate pair of roots produces a real quadratic factor, while each real root produces a real linear factor. To practise all this there is an exercise with 7 questions for students to complete. Solutions to all the examples and the exercise are included. The second resource contains an exercise with further examination-style questions on this topic. This could be used as additional practice in class or as a homework/test. Answers are provided.

These are two 2-sided worksheets that cover all calculations with fractions. The adding/subtracting worksheet goes step-by-step through the process of making the denominators equal prior to the calculation. The first exercise (12 questions) involves adding/subtracting fractions and mixed numbers where the denominators match, the second exercise (34 questions) involves adding/subtracting fractions and mixed numbers where the denominators do not match. The multiplying/dividing worksheet begins with a reminder of the method, together with a few examples to work through as a group. There are then two exercises, each with 20 questions, first to practise multiplying and then to practise dividing fractions and mixed numbers. Fully worked solutions to all questions are provided.

These 3 resources cover the following types of percentage question: 1. Writing one quantity as a % of another 2. Finding a % of a quantity 3. Increase/decrease by a % 4. Finding the % change Each resource is split into a non-calculator section and a calculator section. Each section has an introduction where the method(s) is/are explained with some examples to illustrate, followed by an exercise for students to complete. In total there are over 150 questions for students to work through - all solutions are provided.

This 26-page resource covers all the required knowledge for diagrams and calculations to summarise or represent data in the new A level. In every section it contains examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included). The sections are: 1. Bar charts and pie charts - revision of interpreting these simple diagrams 2. Averages of a list of data 3. Range and interquartile range of a list of data 4. Histograms - drawing them, interpreting them and using them for probability 5. Cumulative frequency - using the diagram to find median, IQR, percentiles etc 6. Box-and-whisker plots - interpretation and use to compare 2 sets of data 7. Standard deviation - calculation from a list of data or summary statistics 8. Frequency tables - finding averages/measures of spread from (grouped) frequency tables 9. Scatter diagrams and correlation - interpretation of diagram, PMCC, use of line of best fit 10. Outliers - investigating presence of outliers in a list/table of data or a diagram Also provided is an 8-page resource which contains lots of practice of problems that involve finding the variance or standard deviation of different sets of data (answers are included). This projectable and printable resource will save you having to draw any tables/diagrams when teaching the topic and will make things easier for your students as they can just work directly on the provided tables and axes, as well as drawing on the provided diagrams to help interpret them. Also included is a homework/test that covers the whole topic - fully worked solutions are provided. Here is an example of one of my A level resources that is freely available: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

I'm teaching 3 different year 12 classes this year so I created 3 slightly different tests for the work I've covered with each. The first test focuses on quadratics (1 question on disproof by counterexample), the second and third both focus on quadratics and using graphs (also with 1 question on disproof by counterexample). All tests come with fully-worked solutions and they can be amended to your requirements.