This is a tricky little topic so this worksheet may be useful extra practice for your class. Six questions, some with diagrams as an aid. Answers 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.

The first resource is a 9 page printable worksheet that you can work through with your class to cover the whole topic of quadratic functions in the new A level. Each section has a brief introduction or summary of key knowledge, then there are some examples to work through as a class to practise the skills. The worksheet covers: 1.Solving quadratic equations 2. Sketching graphs or finding the equation from the graph 3. Completing the square and its application for sketching, solving, vertex etc 4. Solving quadratic inequalities 5. Using the discriminant 6. Disguised quadratics Answers to all the examples are given at the back. The second resource is a set of questions designed to test the whole of the topic with some examination-style questions. Worked solutions are provided for these questions. 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 15-page worksheet takes your students through the whole topic of functions which is in the new GCSE. The worksheet has 3 sections. Section A covers function machines, substitution of values and values where the function is not defined. Section B covers inverse functions. Section C covers composite functions. Each section has an introduction with some examples, followed by an exercise for the students to work through. Answers to all exercises are included.

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 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 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: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

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 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

This 33-page resource covers all the required knowledge and techniques for the topic of differential equations, 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 17-question assessment that can be used as a test or homework. The sections/topics are: 1.Finding the equation of a curve from its gradient function (a) from dy/dx = … find an expression for y (b) finding general and particular solutions 2.Variable separable equations (a) practice of separating the variables into the form f(y) dy = g(x) dx (b) solving variable separable equations 3.Forming differential equations from a description of how a quantity is changing 4.Modelling with differential equations (a) Constructing the appropriate differential equation to model a given situation (b) Solve differential equations and interpret/use the solutions © Consider the assumption(s) or limitation(s) of a model and suggest possible improvements 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 comprehensive set of exercises contains around 100 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: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This 28-page resource covers all the required knowledge and techniques for the topic of parametric equations, 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: Parametric graphs (a) sketching graphs with parametric equations (b) finding the value(s) of the parameter at a particular point on the graph Converting parametric to cartesian equations (a) converting parametric equations that are polynomials, rational functions, exponential functions… (b) converting parametric equations that involve trigonometric functions Finding the intersection of a parametric graph and a graph with cartesian equation (a) Converting the parametric equation to cartesian (b) Substituting the parametric equations into the cartesian Finding gradients of parametric curves (a) Finding an expression for dy/dx and the gradient of the curve at a point (b) Finding stationary points and points where tangent is parallel to x-axis or y-axis © Finding the equation of the tangent or normal to the curve Finding the area between a parametric curve and the x-axis 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 comprehensive set of exercises contains around 100 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: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

This 28-page resource covers all the required knowledge for the normal distribution in the A2 part of the new A level. In every section it contains notes 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. Discrete vs continuous random variables 2. Properties of the normal distribution curve 3. Using a calculator to find probabilities 4. z-scores 5. Standard normal distribution 6. Conditional probability 7. Questions that involve both the normal and binomial distribution 8. Inverse normal distribution 9. Finding unknown parameters 10. Using the normal distribution as a model 11. Approximating a binomial by a normal 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 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 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.

This worksheet contains over 20 questions for students to practise solving 3-term quadratic inequalities. For the first handful of questions a sketch of the quadratic graph is provided as an aid. The questions become increasingly difficult and this worksheet will be a good challenge for able GCSE pupils who know the methods for solving quadratic equations. All answers are included at the end of the worksheet.

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.

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 printable resources are ideal for getting students to practise working out coordinates for quadratic functions and drawing their graphs. Partially completed tables and graph paper are provided for each question. The first worksheet contains 10 questions all of the form y=x^2+ax+b. The second worksheet contains 8 questions, some of the form y=x^2+ax+b and some are y=ax^2+bx+c where a>1. Some of these questions are harder that the first worksheet because there isn’t any “symmetry” within the y-values in the table, which serves as a check. The homework contains 6 questions: 4 of the form y=x^2+ax+b, 2 of the form y=ax^2+bx+c where a>1. All solutions are included to print or project for your class to check their tables and graphs.

A set of resources to teach and practise solving quadratic equations by factorising. The first two resources (worksheet + powerpoint) can be used to show how the factorised version of a quadratic is linked to the graphical solution of the equation. The first worksheet has two sections. Section 1 has lots of examples similar to the presentation where they solve the equation using the graph and then by factorising. In section 2 the graph is no longer provided and they just solve the equation by factorising. The last two worksheets are for additional practice, split into the cases where the coefficient of x^2 is 1 and where it is larger than 1. All answers are provided.

Two worksheets to practise solving quadratic equations using completing the square. The first worksheet contains the answers, so is intended to be used as practice in the classroom, while the second worksheet does not include the answers, intended as a homework. Note that the solutions must be given in simplified surd form, so students need to be able to simplify surds. The coefficient of x^2 is always 1 throughout these worksheets.