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I think this set of resources covers everything your classes need to learn and practice on straight line graphs (up to GCSE level). All the resources are suitable to be projected or printed for students to work on, saving a lot of time for drawing graphs and allowing them to annotate or work on diagrams. All resources come with solutions included. Here is a brief description of each resource: 1. Basic straight lines - lines of the form x=a, y=a and y=x or y=-x 2. Drawing straight lines - 10 questions using the equation of a line y=mx+c to complete a table of values and draw the graph. 3. Cover-up method - 12 questions to practise drawing lines of the form ax+by=c 4. Using the equation - test if a point lies on a line, determine y-coord given x-coord and vice versa (70 questions) 5. Finding the gradient - 18 questions to practise finding gradients, including where the scales on the axes are not the same 6. Matching y=mx+c to the graph - they find the gradient and y-intercept for each given graph and equation, learning the connection between the equation and properties of the graph 7. Equation to gradient and y-intercept - simple worksheet to practice writing down the gradient and coordinates of y-intercept from the equation, and vice versa (24 questions) 8. Finding the equation of a line - 24 questions to practise finding the equation of the line from its graph, including where the scales on the axes are not the same 9. Finding equation using point and gradient - 10 questions to practise doing this with a grid as an aid, then 26 questions without a grid 10. Pairs of lines - 4 graphs, each with a pair of parallel or perpendicular lines. By finding the equation of each line the students should start to see the rules for gradients of parallel and perpendicular lines 11. Parallel and perpendicular lines - almost 50 questions finding the equation of a line parallel / perp to a given line that passes through (0,b) or (a, b) 12. Using two points A and B - find midpoint M of AB, gradient of line through A and B, equation of line through A and B, equation of line perp. to AB through A, B or M. 10 questions to learn the methods with grids as an aid, then an exercise for each style of question (over 50 questions in total). 13. Multiple choice questions - quick assessment covering most of the topic 14. Straight lines revision - 60 questions to revise the whole topic 15. Homework - 19 questions on all aspects of the topic, fully works solutions included I have just worked through all these with my year 10 group and it took around 5 hours of lesson time to complete. A more able group may need less time but you have enough resources here to keep your classes busy for a number of lessons.

This worksheet can be used to introduce de Moivre's theorem to your class and show how it can be used to find multiple angle formulae (e.g. sin 4theta = ...) and how these formulae help us to relate trigonometric equations to polynomial equations. The introduction shows how we can arrive at 2 different results for (c + is)^n by using de Moivre's theorem and a binomial expansion. There are then 3 examples of using this technique to derive multiple angle formulae. The second section focuses on relating trigonometric equations to polynomial equations and how this allows us to find exact values of trigonometric functions or to express the roots of a polynomial in trigonometric form. There are 3 examples to illustrate this, the first one is deliberately straightforward to help students see the connection between the trigonometric work and the polynomial equation. The solutions version of the worksheet has fully-worked solutions to all the examples and the notes in the introduction section are also completed. Once you have worked through this worksheet with your students they should be able to attempt an exercise of questions on their own.

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: /teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This 30-page resource covers all the required knowledge and techniques for logarithms, 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: 1.Writing and evaluating logarithms 2.Using base 10 and base e 3.Evaluating logarithms on a calculator 4.Logarithms as the inverse of raising to a power 5.Solving equations that involve logarithms 6.Laws of logarithms 7.Solving equations with an unknown power 8.Disguised quadratic equations In all there are over 300 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: /teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This 10-page resource covers all the required knowledge and techniques for related rates of change, as required for the new A level. 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). It begins with an introductory example which shows related quantities can change at different rates and how the chain rule can be used to connect them. There is then a summary of the method and a page of example questions to complete with your class. The exercise that follows contains over 40 questions for your students to attempt. 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: /teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This 19-page resource covers all the required knowledge and techniques for using the Newton Raphson method to find roots of an equation, as required for the new A level. In each 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). Also included is multiple-choice assessment that can be used as a plenary or brief homework. The sections/topics are: 1.Introduction to the method (a) the iterative formula and a graphical interpretation of the process (b) using the method to find successive approximations or an estimate of a root © different ways in which the formula may be written © illustrating the method on a diagram 2.Conditions where the Newton Raphson method fails (a) what happens if an approximation occurs at a stationary point of f(x) (b) situations where successive approximations converge to a different root © situations where successive approximations do not converge to a root (d) what happens if an approximation is outside the domain of f(x) 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. The exercises contains 35 questions for your students to complete. Answers to all exercises are included. Here is an example of one of my A level resources that is freely available: /teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This 25-page resource covers all the required knowledge and techniques for using fixed point iteration to find roots of an equation, as required for the new A level. In each 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/topics are: 1.Introduction to the method (a) creating an iterative formula from an equation f(x)=0 (b) using fixed point iteration to find successive approximations or an estimate of a root © illustrating the covergence of the approximations on a cobweb or staircase diagram 2.Conditions where fixed point iteration fails (a) situations where successive approximations do / do not converge to a particular root (b) situations where successive approximations do not converge to any root © how to predict whether an iterative formula will produce approximations that converge towards a root (d) illustrating the covergence / divergence of the approximations on a cobweb or staircase diagram 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 and diagrams provided for solutions. The exercises contains over 35 questions for your students to complete. Answers to all exercises are included. Here is an example of one of my A level resources that is freely available: /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.

This resource covers all the required knowledge and skills for the A2 topic of combined graph transformations. It begins by reviewing the individual transformations and their effects on the graph or its equation. The first section focuses on finding the equation of the curve resulting from 2 transformations - there are some examples to complete with your class and then an exercise for them to do independently. The exercise does include some questions requiring a sketch of the original and the transformed curve. Within that exercise there are questions designed to help them realise when the order of the transformations is important. The second section focuses on examples where the transformations must be applied in the correct order. There are examples to complete and then an exercise for students to attempt themselves. The exercise includes questions where the resulting equation must be found, where the required transformations but be described, and some graph sketching. Answers to all the questions in the exercises are included. Here is an example of one of my A level resources that is freely available: /teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This worksheet is a good way to give your class plenty of practice calculating and using the vector product. The first 2 questions just involve finding the vector product of two given vectors, both in column vector and in I,j,k form. The remaining questions introduce how the vector product can be used to answer particular questions such as converting vector eqn of plane to normal eqn, or finding the area of triangle in 3 dimensions. Fully worked solutions are provided to the questions.

I have used this resource a few times with my classes to cover the whole topic of groups. This 24-page worksheet covers all the required knowledge and skills for FP3. Each section starts with introductory notes or examples, followed by an exercise for students to attempt. The sections are: 1. Sets, binary operations, closed/commutative/closed operations, identity elements and inverses. 2. Groups - definition of a group, order of a group, group tables 3. Multiplicative groups and cancellation laws 4. Groups using modular arithmetic 5.Symmetries of shapes 6. The order of an element 7. Cyclic groups and generators 8. Subgroups 9. Lagrange's theorem 10. Isomorphic groups The completed worksheet with all notes, examples and exercises completed (with fully-worked solutions) is also included.

This resource can be used to guide your students through the different techniques that may be used to solve some first order differential equations. It begins with a reminder about the solution of 'variable separable' equations, with a couple of examples to work through. By means of an example, the next section shows how the use of an integrating factor can help to solve 1st order linear diff.eqns. After the method is summarised there are a further 2 examples to work through with your class. The worksheet then mentions the use of a substitution to simplify a complex diff.eqn into either a linear or variable separable one. There are no examples of such equations, just a table for students to practise determining if the resulting simplified equation is linear or variable separable. The remainder of the resource introduces the important method of finding the general solution by adding the complementary function and the particular integral. It begins with the method for finding the complementary function from the auxiliary equation, and then goes on to explain the method for testing a suitable function f(x) for the particular integral (including the case where the function f(x) appears in the complementary function). There are several examples of this method to work through with your students, followed by an exercise with over 20 questions for students to complete themselves. Answers to the exercise are included.

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 27-page resource introduces all the knowledge and skills required for the topic of integration in the AS part of the new A level. In every section it contains notes then examples to work through with your class, followed by an exercise of questions for students to attempt themselves (answers included). The sections are: Finding an expression for a curve from its gradient function / derivative Simplifying into the required form for integration Determining the equation of a curve from its derivative and a point it passes through Definite integrals Finding the area between a curve and the x-axis Finding the area between a curve and a straight line 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 diagrams and spaces provided for solutions. Also included is a 4-page (20 questions) 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: /teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This simple worksheet focuses on using the following 3 rules for working out angles: 1. sum of angles on a straight line = 180 2. sum of angles at a point = 360 3. vertically opposite angles are equal It begins with brief revision of the names for different sizes of angles and then there is a section for each of the 3 rules. Each section contains some example questions to work through with your class and then there is a short exercise for them to complete. At the end there is an exercise of mixed questions to practise using all 3 rules. Answers to the exercises are included. I used this sheet with my (bottom set) year 10 group. The idea was that printing/projecting the sheet would save me (and them) having to write out any examples/diagrams as notes, so that time is saved and they can focus on answering questions. After completing the sheet the class were ready to attempt additional exercises from a textbook.

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 worksheet will give your class a bit of practice of finding the reciprocal of different types of numbers. Each section starts with an explanation and/or examples, followed by a short exercise of questions for students to complete. The sections are: Reciprocal of an integer Reciprocal of a fraction of the form 1/n Reciprocal of a fraction of the form a/b (includes conversion of mixed fractions to improper) Reciprocal of a decimal (requires conversion of decimal to fraction) The answers to the questions in the exercises are included.