This worksheet makes it easy to introduce and teach the trapezium rule to your classes. The first page has diagrams to illustrate the method and the derivation of the formula is broken down into steps for you to work through with your class. Projecting all this is so much easier than drawing it out by hand. The trapezium rule formula is then stated at the top of page 2, followed by 3 pages of examples of examination-style questions that test the use of the formula and your students’ understanding (is the answer from the trapezium rule an underestimate or overestimate, can they use their answer to deduce an estimate for a related integral, etc). Answers to all the examples 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 set of resources includes everything you need to teach the graph transformations topic in the new A level. The printable resources will save you and your classes a lot of time which means there is more lesson time for them to practise and for you help develop their understanding. As the topic requires knowledge of the properties of some graphs (e.g. asymptotes) the first resource can be used to see which graphs they can already sketch and to discuss the asymptotes of particular graphs. The next resources are Geogebra files which can be used with the free Geogebra software. Each file can be used to discuss a particular type of graph transformation - there are sliders on each file that be changed or animated to see the initial graph transformed. This activity should help your class to visualise each type of transformation and start to get a feel for how the equation changes. The notes and examples start with revising each type of graph transformation - giving some different ways the transformations can be described and what the transformation looks like using y=f(x) and with a particular curve. Once completed this is a useful revision resource and helps them complete the exercise of questions on the reverse which includes questions asking for the new equation of a transformed graph, or for a description of the transformation applied. The final resource can be used to give your class practice of sketching transformations of y=f(x). The answers to all questions are included, including the sketches. 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 4-page worksheet will give your students plenty of practice at representing linear and quadratic inequalities on graphs, as well as writing down the inequalities illustrated by given regions. This printable resource will make it much easier for your classes to work through this topic rather than working from a textbook or drawing axes/diagrams themselves. There are over 30 questions on the worksheet - solutions are provided.

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 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 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 33-page resource introduces the methods used to differentiate more complex functions, as required for the new A 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 sections are: Chain rule - how to differentiate a function of a function (2 pages of examples then a 4-page exercise) Product rule (1 page of examples then a 2-page exercise) Quotient rule (1 page of examples then a 3-page exercise) Implicit differentiation introduction (1 page of examples then a 1-page exercise) Implicit differentiation involving product rule (2 examples then a 3-page exercise) Applied implicit differentiation to find stationary points, tangents etc (2 pages of examples then a 3-page exercise) Differentiation of exponential functions (1 page of examples then a 1-page exercise) Differentiating inverse functions (2 pages of examples then a 1-page exercise) 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. Also included is a 10-question 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

These 2 resources cover all the required knowledge and techniques for trigonometry, as required for the AS part of the new A 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 first resource is a 27-page booklet which covers the following: 1.The graphs of trigonometric functions, their period and amplitude/asymptotes 2.Exact values of trigonometric functions 3.Trigonometric identities 4.Finding the value of other trigonometric functions given, for example, sin x = 0.5 where x is obtuse 5.Solving trigonometric equations (3 different exercises on this, with increasing difficulty) The second resource is a 13-question assessment that can be used as a homework or test. Fully worked solutions to this assessment are provided. The third resource is a 15-page booklet which covers the following: 1.Using the sine rule to find angles/sides in a triangle 2.Ambiguous case of the sine rule 3.Using the cosine rule to find angles/sides in a triangle 4.Area of triangle = 0.5ab sin C - using this, together with the other rules, to determine the area of a triangle 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. 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

My year 7 class struggled to learn the rules for doing calculations that involved negative numbers so I created these resources to try to help them understand the rules and to give them lots of practice. The first resource focuses on addition and subtraction, with explanations of how the calculations can be understood with reference to a number line, and then exercises with lots of practice (over 150 questions). The second resource focuses on multiplication and division, with a page dedicated to them just practising determining whether the answer of a calculation should be positive or negative, and then an exercise with lots of practice calculations (over 80 questions). The third resource contains mixed questions with all 4 operations (over 60 questions). Answers to all the questions are included. The final resource is a spreadsheet where pupils can practise calculations and get instant feedback on their accuracy. Note that the spreadsheet contains macros so when opening the file users may need to click on “Enable editing” or “Enable macros” for it to function correctly.

This resource is designed to help students understand the key properties of exponential models and to give them lots of practice of examination-style questions on the topic. It begins by recalling the key properties of exponential graphs and introduces the form of the equation used in most exponential models. The first section contains examples designed to help students realise that the same proportional change happens over equal time periods. There are a few examples that establish this property and then an exercise of questions for students to attempt. The main section focuses on using exponential models and begins with 2 pages of example questions chosen to show students the typical style and demands of examination questions on this topic. There is then a 17-page exercise with almost 70 questions for students to attempt themselves. The exercise includes questions where students are required to explain the significance of parameters in models, the limitations of models, and to suggest possible improvements. Answers to the exercises 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

This resource was designed to help students learn how graphs with logarithmic scales are connected to models of the form y=ab^x and y=ax^n. The first section focuses on models of the form y=ab^x. There are examples to work through as a class, with axes provided, to establish that if y=ab^x then there is a linear relationship between log(y) and x. There is then a page of examples to practice changing from y=ab^x into the linear equation, and vice versa. The examples conclude with 2 questions where students are given experimental data and required to use a graph to estimate the values of a and b in the model y=ab^x - which is typical of an examination-style question. There is then an exercise with 11 questions for students to complete on their own (again, all axes are provided). The second section focuses on models of the form y=ax^n. There are examples to work through as a class, with axes provided, to establish that if y=ax^n then there is a linear relationship between log(y) and log(x). There is then a page of examples to practice changing from y=ax^n into the linear equation, and vice versa. The examples conclude with 2 questions where students are given experimental data and required to use a graph to estimate the values of a and n in the model y=ax^n - which is typical of an examination-style question. There is then an exercise with 11 questions for students to complete on their own (again, all axes are provided). Answers to all questions in the exercises 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

This resource is designed to introduce the key properties of exponential and logarithmic graphs that students need to understand for the topic of exponential models. Explaining the key properties of exponential graphs to students who haven’t learned chain rule is tricky so this printable/projectable resource may be a good way to help improve your students’ understanding and save you time as it has examples and exercises already prepared. It begins with learning the shape of exponential graphs by plotting points, drawing the curves and then summarising the properties of each graph (first y=a^x and then y=a x b^x). There is then a short exercise (23 questions) where they practice sketching exponential graphs and determining the equation of a given graph. The next section involves sketching the gradient function for different types of graph (linear, quadratic, cubic and reciprocal) and this work leads towards the idea that the gradient function of an exponential graph is itself exponential. To build on this the students are then given the result for the gradient of y=a^x. The exercise that follows allows them to establish by themselves that for dy/dx=y we require that a = e. Students can then prove (without use of chain rule) that the gradient of y=e^(kx) is y=ke^(kx), a key property of exponential models. There are then some examples and an exercise for students to practise using this result. The final section gets students to plot the graph of y=ln(x) and summarise its properties. Some examples and an exercise of questions connected the graph of y=ln(x) then follow. Answers to all the exercises 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

These resources will give your class plenty of practice of using the factor theorem and the common questions that follow finding a factor of a cubic polynomial. The first resource focuses on showing that (ax+b) is a factor of f(x) and then using it to write f(x) as a product of a linear and quadratic factor. There is an example to work through as a group and then an exercise with 14 questions - answers are provided. The second resource has 2 sections. The first section focuses on factorising cubics fully, either as a product of a linear and quadratic factor, or as a product of 3 linear factors. The second section focuses on solving f(x)=0 and, in later questions, relates the solutions to the graph of f(x). In total there are 26 questions - answers are provided.

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

These resources are a good way to quickly cover/revise the whole topic of linear equations. The first resource begins with a few notes on what forms linear equations can take and some of the steps or methods that may be required to solve them. There are some parts of the notes that need to be completed with your students, to practise the algebraic steps involved in solving linear equations. There are then several sections, each section focussing on a particular form of linear equation. There are a few examples to complete with your students as practice, then an exercise for students to complete on their own. There is also an exercise of mixed questions at the end. Answers to all the exercises are included. Section A - Solving x+a=b, x-a=b, a-x=b Section B - Solving ax=b Section C - Solving x/a=b and a/x=b Section D - Solving ax+b=c, ax-b=c, a-bx=c Section E - Solving x/a+b=c, x/a-b=c, a-x/b=c, a-b/x=c Section F - Solving (ax+b)/c=d, (ax-b)/c=d, (a-bx)/c=d Section G - Solving a(bx+c)=d, a(bx-c)=d, a(b-cx)=d Section H - Solving ax+b=cx+d, ax+b=c-dx Section I - Solving a(bx+c)=dx+e, a(bx+c)=d-ex Section J - Solving (ax+b)/c=dx+e, (ax-b)/c=dx+e, (a-bx)/c=d-ex Section K - Mixed exercise The second resource gives your students practice of solving linear equations using a graph. Worked solutions to this sheet are included. The final resource is a homework/test with 35 questions that cover the whole of the topic, including solving linear equations using a graph. Worked solutions are included.

A simple resource to give your class practice of finding the area of a shape by counting squares. It has brief notes and examples at the start, then an exercise with 18 questions for students to attempt (answers included). The shapes are squares, rectangles, triangles and compound shapes using these 3 shapes (so no circles or parts of circles).

This worksheet focuses on using the sum of angles in a quadrilateral to find missing angles. It assumes that students are already familiar with angles in triangles, on a straight line, vertically opposite angles, and angles in parallel lines. The first section covers different types of quadrilaterals and their properties. There is a short exercise where students practise choosing the correct type(s) of quadrilateral based on the information given. The second section begins with the result for the sum of angles in a quadrilateral. There are then some examples of finding angles - these are to be completed with your class. The exercise that follows is for students to attempt themselves. Answers to both exercises are included.

This simple 2-sided worksheet can be used with your class as practice or revision of trigonometry in non right-angled triangles. The answers are included but can be removed if you want to use the sheet as a homework or test. Note that one of the questions involves bearings.