This 12 page resource covers the solution of 2nd order differential equations by finding the roots of its auxiliary equation, and its particular integral. The first section focuses on cases where the auxiliary equation has real roots (distinct or repeated). It begins by concentrating on finding only the complementary function - there are several examples to work through with your class and then an exercise with 14 questions for students to attempt. There are then a few examples that involve finding both the complementary function and the particular integral. The second section focuses on cases where the auxiliary equation has complex roots (a+/-bi or +/-bi). There are several examples to work through with your class and then an exercise with 18 questions for students to attempt. The exercise includes questions where students are required to consider the behaviour of the solution (bounded/unbounded oscillations) when x becomes large, as well as the function to which the solution approximates when x becomes large. Answers to both exercises are included.

This 26-page resource covers all the required knowledge and techniques for binomial expansions with positive integer powers, as required for the new AS level. In every section it contains notes, explanations and examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included). The types of questions included in the examples and exercises are: 1.Expand (ax+b)^n or (a+bx)^n 2.Find first 3 terms, in ascending powers of x, of the expansion of (a+bx)^n 3.Find the coefficient of x^k in the expansion of (a+bx)^n 4.Given the coefficient of x^k in the expansion of (a+bx)^n, find the value of a (or b). 5.Evaluating or simplifying nCr without a calculator 6.Given that (1+ax)^n = … find the value of n 7.Expand (ax+b)^n, hence expand (cx+d)(ax+b)^n 8.Use the first 3 terms of an expansion of (a+bx)^n to estimate k^n In all there are over 100 questions in the various exercises for your students to work through. This projectable and printable resource will save you having to create or write out any notes/examples when teaching the topic, and will make things easier for your students as they can just work directly on the given spaces provided for solutions. Answers to all exercises are included. Also included is a 16-question assessment that can be used as a homework or a test. 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

The introduction activity highlights the difference between bar charts and histograms and the fundamental area=frequency property. The main worksheet (drawing and using histograms) has an introductory section to summarise how histograms work, 3 examples to work through as a class and then 7 pages of questions for students to attempt. All answers are included, either at the end of the worksheet or on the separate solutions document. The final document has examples of finding the median and inter-quartile range from a histogram. This is designed to be done as a class and then the students can practise this using certain questions on the main worksheet.

These printable worksheets make it easier to teach this topic as the questions and solutions can just be projected onto a board or screen to work through or check as a class. This is suitable for the new GCSE spec (includes invariant points). I normally work use these resources in the following way: Do Q1 on the 1st resource as examples of questions using a positive scale factor > 1, then they do questions 1 to 8 on the 2nd resource on their own. Do Q2 on the 1st resource as examples of questions using a positive scale factor < 1, then they do questions 9 to 16 on the 2nd resource on their own. Do Q3 on the 1st resource as examples of questions using a negative scale factor, then they do questions 17 to 24 on the 2nd resource on their own. Do Q4 on the 1st resource as examples of describing an enlargement, then they do the questions on the 3rd resource on their own. Solutions to all questions are included.

Once your group has learned the rules for simplifying, manipulating and rationalising these resources are great for revising all the knowledge and skills they need. The revision sheet has 4 pages of questions covering all the expected skills at GCSE level for this topic - fully worked solutions are included. The worksheet/homework contain examination-style questions. I use the first worksheet as examples in class and then the second sheet can be used as a homework. The test is 3 pages long and covers the basic skills up to some demanding examination-style questions. A mark scheme with worked answers is included.

These resources will help your class understand how performing 2 transformations on a graph will affect its equation. The first worksheet has several examples designed to help the students realise when the order in the which the transformations are performed is important. The second worksheet is split into 2 sections. Section A has 10 questions where students must use the description of the pair of transformations to find the equation of the resulting curve. Section B has 18 questions where students must describe the pair of transformations that map the initial graph onto the transformed graph. Solutions to both worksheets are included. Note that these worksheets assume that students are familiar with the functions e^x, ln x and inverse trigonometric functions.

These resources can be used as a test or a homework to assess how well your class has understood the equation of straight line graphs. The first resource is a 4-page test where students must draw graphs, find gradients or points using y=mx+c, find the equation of graphs and answer questions about parallel and perpendicular lines. The second resource is another 4-page test, similar to the first, with some slightly altered questions. The third resource contains 24 multiple-choice questions. This is a quick way of assessing knowledge and understanding and is a common style of question in the new GCSE papers. All answers are included.

This set of resources covers evaluating and simplifying expressions with powers. The first resource is 18 multiple choice questions on evaluating powers for students to attempt (I usually get my class to do this in pairs/small groups). The second resource is a worksheet with different sections that focus on evaluating with postive integer powers and 0, negative integer powers, then fractional powers. Each section contains examples to work through as a class and then an exercise for students to attempt. Answers are included. The third and fourth resource cover simplifying expressions, following the same format and the 1st and 2nd. The powerpoint contains slides that revise how to evaluate and simplify expressions with powers - useful as a plenary or as a refresher at the start of a lesson. The multiple choice questions cover both evaluating and simplifying - useful as a revision resource or a quick assessment. Solutions provided. The final resource is a set of questions to cover the whole powers topic, some of which are examination style questions. Answers are included.

These resources are designed to introduce the vectors topic for the Core 4 module. The first resource introduces all the required skills and knowledge using just 2 dimensions, which enables students to use/draw diagrams to help them understand the steps in the solutions. At appropriate points within this resource there are prompts to attempt one of the other worksheets to focus on a particular skill or type of question. All the other worksheets work in 3 dimensions, so students may need help with the first couple of examples on each sheet. There are lots of examples on each sheet to help students become confident with that particular part of the vectors topic. Answers are provided for all the worksheets, either on the sheet or as a separate resource.

This printable worksheet makes it easy to introduce the route inspection algorithm and will help your students understand how to apply the algorithm. The first page reminds students about Eulerian and semi-Eulerian graphs, how these are the types of graphs we require to solve the route inspection problem, and then has an example where you can introduce the idea of adding/repeating arcs to create the type of graph you need. The next page summarises the steps of the general algorithm and then the set of example questions begins. There are 14 questions in total, all with diagrams, with some requiring a closed route and some that do not. Fully worked solutions for all examples 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 resources are designed to help to introduce your students to the AQA Large Data Set for 2018-19, to get them familiar with some of its properties and typical questions that can be asked about data taken from it. The worksheet begins by introducing the data selected by AQA and the regions of England that are referred to. There are then several pages of examples, chosen to illustrate particular properties of the data or a certain style of question. The examples cover the following: How data is categorised - shows students categories and sub-categories How data values are presented - shows students how the exact values in the LDS are rounded for tables/extracts Outliers - shows how outliers can be identified and common outliers in the data Interpretation of diagrams - allows students to consider what can and cannot be deduced from a range of diagrams The intention is that these examples are worked through and discussed with your class. Possible answers to the examples are given in the teacher version of the worksheet. There is then a 6-page exercise for students to complete. This exercise contains questions that are based on the style of the exemplar questions released by AQA, so they should be ideal practice for your students. Answers to the exercise are included. The spreadsheet is designed to make it easier and quicker to analyse certain aspects of the large data set. By simply selecting the 2 food categories you wish to investigate, the spreadsheet will: Pull all the relevant data onto a single sheet Calculate PMCC between the 2 food categories (for each region, and for each year) Calculate quartiles and indicate the presence of any outliers Draw scatter diagrams for each region, and for each year The spreadsheet is a really useful tool to help you quickly select some data from the LDS that can be used to illustrate/discuss a particular aspect of the data or to practise a particular style of question. Alternatively, the spreadsheet could be given to your students so that they are able to do some investigation of the data themselves, without needing to know much about using Excel. The final resource is just a set of notes on how to use the spreadsheet and its functionality.

This 21-page resource covers all the required knowledge for conditional probability in the A2 part of 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: Venn diagrams and set notation (revision of AS level work) Conditional probability using Venn diagrams Conditional probability using two-way tables Conditional probability using tree diagrams 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 diagrams. The 2 page assessment covers all aspects of the topic and 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

This 17-page resource covers all the required knowledge and techniques for hypothesis testing in the AS part of the new A level. It contains detailed notes, examples to work through with your class, and exercises of questions for students to attempt themselves (answers included). The topics covered are: 1. Sampling - different methods of sampling, biased and representative samples 2. Unbiased estimators - estimating the population mean and variance from a sample 3. Setting up a hypothesis test - null and alternative hypotheses 4. Making a conclusion - p-values, significance levels, 1-tail and 2-tail tests 5. Critical regions - finding the critical region for a hypothesis test 6. Significance levels and errors - probability of incorrectly rejecting null hypothesis, nominal vs actual significance level This projectable and printable resource will save you having to write out or create any notes/examples when teaching this topic. It also increases how much you can get through in lessons as students don't have to copy notes/questions and can work directly onto spaces provided for solutions. You could also email/print some or all of this for students who have missed lessons or need additional notes/practice/revision. The second resource is a set of multiple-choice questions that can be used a quick assessment or as part of a revision/refresher lesson. There is also a 6-page resource which contains lots of practice of problems that involve estimating population parameters from sample data (answers are included). Also included is a 2-page assessment that covers the whole topic. Fully worked solutions are included. 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

The first 3 resources help students to learn to label the sides of the triangle correctly (adjacent, opposite and hypotenuse). There are then 2 worksheets, each with 18 questions to practise finding angles or sides using trigonometry. Answers are included. The short worksheet on angle of elevation/depression explains what the angles represent and has 4 examples for students to complete - answers are included. The multiple choice questions (including some non-calculator) can be used as an assessment after covering this topic. Answers are also included.

These worksheets together contain over 30 pages of questions on objects on slopes - ideal practice for students preparing to sit their Mechanics 1 module exams. Many of the questions have accompanying diagrams as an aid. Answers to all questions are provided.

The worksheet is a 20-page resource that covers everything your students need to know about straight lines and circles for the new A level. Each section has an introduction with the required knowledge or formulae, then there is an exercise full of questions for you to work through with your class or for them to do on their own (answers are provided). The questions in the exercises start with the basics and progress up to more demanding examination-style questions. In total there are over 100 questions for your students to work through and there is enough material here to fill several lessons. The different sections cover: distance between 2 points, midpoints, gradient of a line, equation of a line, parallel and perpendicular lines, equation of a circle, tangents/normals to a circle, intersections of lines and circles, and determining whether 2 circles intersect, are disjoint or tangent to each other. The assessment contains 12 questions covering all aspects of straight lines and circles, which could be used as either a homework or a test. 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

This 29-page resource covers all the required knowledge for probability in the AS part of 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. Sample space diagrams 2. Two-way tables 3. Tree diagrams 4. Venn diagrams and set notation 5. Independent, mutually exclusive and complementary events 6. Probability distributions 7. Arranging items (preliminary work for Binomial distribution) 8. Binomial distribution 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 diagrams. Also included is a worksheet designed to specifically practise writing cumulative probability calculations in the required form for using a calculator. The 2 page assessment covers all aspects of the topic and fully worked solutions are provided. Lastly, I have included a spreadsheet that calculates and illustrates probabilities for any Binomial distribution with n up to 100. You may find this resource useful to show the shape of the distribution and, in later work, how the distribution approximates a Normal distribution in certain conditions. 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

This 21-page resource introduces the method of differentiation as required for 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. Gradient function - sketching the graph of the derivative of a function 2. Estimating the gradient of a curve at a point, leading to differentiation from first principles 3. Differentiation of ax^n 4. Simplifying functions into the required form before differentiating 5. Using and interpreting derivatives 6. Increasing and decreasing functions 7. Second derivatives This projectable and printable resource will save you having to write out any notes/examples or draw any graphs when teaching the topic, and will make things easier for your students as they can just work directly on the given axes and spaces provided for solutions. Also included is a 2-page assessment that can be used as a homework or test. Fully worked solutions to this assessment 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

This 18-page resource covers all the uses/applications of differentiation as required for 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. Tangents and normals - finding the equations of tangents/normals to curves 2. Stationary points - finding them and determining their nature using first or second derivative 3. Smallest and largest values of a function - finding min&max value of f(x) in a set of values for x 4. Practical problems - using differentiation to find optimal solution to a problem in context This projectable and printable resource will save you having to write out or create any notes/examples when teaching this topic. It also increases how much you can get through in lessons as students don’t have to copy notes/questions and can work directly onto spaces provided for solutions. You could also email/print some or all of this for students who have missed lessons or need additional notes/practice/revision. Also included is a 2-page assessment that can be used as a homework or test. Fully worked solutions to this assessment 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