This resource covers the use of graphs and/or the sign-change rule to investigate roots of equations, 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). The notes cover: (a) Use of a sketch of y=f(x) and y=g(x) to investigate roots of f(x) = g(x) (b) Using a sketch of y=f(x)-g(x) to investigate roots of f(x)=g(x) © Using the sign-change rule (d) Conditions where the sign-change rule can be misleading 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 the exercise are included. Also included is a short activity to show how this method can be used to find smaller intervals where a root lies, which can be used as an introduction to iterative methods. 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 worksheet has 10 pages of non-calculator questions on finding the surface area and volume of shapes, including cones and spheres. All answers are provided.

These resources are for teaching how to answer the following type of question, common on new GCSE papers: Points A and B have coordinates (2,3) and (8,-6). Point N is on line AB so that AN:NB = 2:1. Find the coordinates of N. The powerpoint presentation starts with a refresher question about using ratio and then has a number of examples of the above question, with diagrams, to work through as a class. The printable version of the presentation can be given to students for them to complete as you go through the presentation. The worksheet has 14 questions for students to complete on their own, initially with the aid of a diagram and then without for later questions. Fully worked solutions are provided.

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 short worksheet can be used to deliver the topic of proof by contradiction in the new A level specification for all exam boards. A useful resource to help deliver this new topic - fully worked solutions are included for all examples and questions in the exercise. It begins with 5 examples to work through with your class (the full proofs are given in the teacher’s version). The examples are carefully chosen so that, for the final example, students have seen the results/techniques they need to prove that the square root of 5 is irrational. Students are expected to be familiar with a proof of the infinity of primes, so on the next page this proof is given in full, together with some numerical examples that should help students understand part of its argument. There is then an exercise with 9 questions for students to attempt themselves (full proofs provided). A homework/test is also included (7 questions), with fully-worked solutions 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 use this worksheet to introduce the idea of a frictional force opposing motion and how the size of the frictional force changes depending on the pulling/pushing forces and the maximum possible value of friction. The examples and diagrams make students think about the circumstances where maximum friction will be acting on an object, and to consider whether an object will be at rest, in limiting equilibrium, or will move. In total there are 40 questions for students to complete - all answers are included.

Each worksheet contains 30 questions. The first worksheet has examples of the form (a+b)^2 and (a-b)^2. The second worksheet has examples of the form (a+b)(a-b). All answers are included.

This powerpoint presentation contains 25 multiple-choice questions on the topic of area and perimeter of circles and sectors. It is a fun way to assess the whole class at the end of teaching this topic, or it can be used as a competitive activity with the class divided into teams. The questions are designed to be attempted without a calculator. Each questions has 4 possible answers from A to D. This activity works best if each person/team has (coloured) cards with the letters A to D on to hold up to show what they think is the correct answer.

The first worksheet studies the interior angles of polygons and is designed to help students realise the method for working out the sum of the interior angles of an n-sided polygon. There is also a short exercise of questions to practise using the rules they have found. The second worksheet studies the interior and exterior angles or regular polygons and is designed to help students realise the easiest way to find the interior/exterior angle of an n-sided polygon or to work out the number of sides of a regular n-sided polygon with a given interior or exterior angle. There is also a short exercise of questions to practise using the rules they have found. Answers to both exercises are included.

The first worksheet has an introduction and explanation about increasing/decreasing functions, a few examples to work through as a class and then an exercise with 11 questions for students to complete. Answers to the exercise are included. The second worksheet gives students some practice at using differentiation to help sketch graphs. There are a couple of examples to go through with your class and then an exercise with 7 questions. Solutions are provided. Note that this resource was designed specifically for the Level 2 Further Maths qualification, so only covers differentiating functions with positive integer powers such as y=5x^3-4x+2, but can still be used an introduction to the general method of increasing/decreasing functions and sketching.

The first worksheet introduces the method for finding the point(s) on a curve with a particular gradient. There are a few examples to work through as a class and then 16 questions for students to attempt. The second worksheet focuses on finding stationary points. Again, it explains the method, has a few examples to work through as a class and then 20 questions for students to complete. The worksheet then has a section that can be used to explain how to determine the nature of a stationary point by considering the gradient of the curve just before/after the point. There are some examples to do as a class and then 8 questions for students to complete. The final worksheet can be used to explain and practise using the second derivative for determining the nature of stationary points. Answers to all exercises are included. Note that this resource was designed specifically for the Level 2 Further Maths qualification, so only covers differentiating functions with positive integer powers such as y=5x^3-4x+2, but can still be used an introduction to the general method of finding stationary points on a curve.

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

The worksheet contains 16 questions with linear simultaneous equations which are to be solved using the substitution method. This is ONE worksheet in two different versions (with and without the answers).

This worksheet can be used to teach and practise the method for finding the area between a curve and the y-axis using integration. The questions are designed so that students practise rearranging the curve y=f(x) into x=g(y) and then integrate with respect to y. The first page introduces this method and then there are 2 examples to work through as a class. There are then 3 more pages of questions, all with diagrams, for your students to attempt. Answers are provided.

This worksheet contains over 20 questions on the forces and motion of connected vehicles - ideal practice for students preparing to sit their Mechanics 1 module exams. It has an introductory section which explains the important principles and terminology used, then there are 23 (multi-part) questions for students to work through. Answers to all questions are provided.

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've always thought that graph transformations is a difficult topic to teach well from a textbook, that's the reason I created these worksheets so my classes could practise sketching the transformations without having to draw axes or try to copy the original curve. This worksheet has examples and an exercise which focuses on reflections but some questions also involve translations. The examples are designed to work through as a class and then the rules for the different reflections can be completed. There are 7 pages of questions for students to complete, including sketching the transformed graph and stating the equation of a transformed graph. All answers are included - I usually project these so that the whole class can check their answers.

The presentation shows examples with graphs to help students realise that a quadratic equation can have 0,1 or 2 (real) solutions. The worksheet has an introductory section intended to be worked through as a class to establish the rules about the value of the discriminant and the number of (real) roots. This is followed by 10 questions for students to practise applying what they have learned. Answers are provided.

Three resources to practice finding the equation of quadratic graphs from different types of information. This is a tricky topic and is likely to stretch an able GCSE group. The first resource is intended to be used as examples to work through as a group, the other resources are for additional practice. All solutions are provided. Note that simultaneous equations and solving quadratics by factorising is required prior knowledge.