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 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: 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

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.

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: https://www.tes.com/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.

This resource is a great way to cover this whole topic using prepared notes and examples to explain it to your students. Projecting the notes/examples will save you a lot of work on the board and your students will save time by working on the provided spaces and axes when doing sketches. You could also email/print some or all of this for students who have missed lessons or need additional notes/practice/revision. The sections cover the following: 1. Sketching graphs of the form y=mod(f(x)) e.g. y=mod(x-2) 2. Sketching simple transformations of y=mod(f(x)) e.g. y=mod(x)+4 3. Solving equations involving the modulus function. This covers the different types of equations and explains when a sketch may/must be used. e.g. mod(x-4)=6 vs 2x+3=mod(x-1) 4. Solving inequalities involving the modulus function. This covers the different types of inequalities and explains when a sketch may/must be used. e.g. mod(x-4)=mod(2x+1) vs 3x-1=4-mod(x) There are almost 100 questions in total across the different exercises. Answers to all questions in the exercises are provided, including 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

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 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 15-page resource covers all the required knowledge and techniques for hypothesis testing in the A2 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: The distribution of the sampling mean Hypothesis tests using sample means Hypothesis tests using correlation coefficients 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 3-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

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

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.

This 32-page resource covers all the required knowledge and techniques for the more sophisticated methods of integration, 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/topics are: 1.Integration using "reverse chain rule" 2.Integration by substitution (x=f(u) or u=f(x)) 3.Integration by parts 4.Using trigonometric identities 5.Using a trigonometric substitution 6.Integrating rational functions In all there are over 130 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 12-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

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 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 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 can be used to introduce the technique required to use trigonometry to find sides/angles in isosceles triangles. There are 2 example problems to work through as a class then an exercise with 10 questions. The first 6 questions have diagrams provided as an aid, the last 4 questions are without diagrams. Answers are provided.