The first resource guides your students through the whole process of using the Simplex algorithm to solve a linear programming problem. The first page explains how the initial tableau is formed, how the objective function must be written and how the inequalities that represent constraints must be written as equations with the introduction of slack variables. The first exercise (11 questions) gives them the opportunity to practise writing the initial tableau correctly for different problems. Grids are provided so students focus their time and energy on only the values in the tableau. The next section describes how an iteration of the algorithm is performed and links the iterations to the graphical solution, showing how each iteration moves to a different vertex of the feasible region. There is then another exercise with 10 questions for students to practise performing iterations and finding the optimal solution. Again, grids are provided so students focus their time and energy on only the steps of the algorithm and the values in the tableau. Fully worked solutions are provided to all the questions in the exercises. The second resource is a spreadsheet that automatically solves any simplex tableau in 2/3 variables with 2/3 constraints - a useful resource for doing/checking solutions to other questions from a textbook or examination paper.

This resource is designed to introduce the method of finding dx/dy and using this to work out the gradient of a curve. There are 3 examples to work through as a class - these will show that to differentiate a curve in some cases it is necessary to have the equation of the curve in the form x=f(y). There is then a short note to summarise the method and then 3 pages of examination-style questions for students to practise. Answers are included.

I designed this worksheet to try to teach a weak GCSE group how to change the subject of a formula. The introduction explains what is meant by the "subject", and has a few examples to make sure this is clear in the students' minds. In exercise A there are 17 multiple-choice questions where students simply circle what they think is the correct rearrangement of the formula. The idea is that, as they are multiple choice, all students will be prepared to have a go at these questions and as you go through the answers there will be discussion points about the step(s) required and different ways you might set out your working or final answer. In exercise B there are 15 questions where the students must change the subject of the formula themselves. Solutions to the worksheet are provided. Note that the sheet contains questions where the new subject appears once only.

This worksheet can be used to teach/practise the required knowledge and skills expected at A level for the topic of proportion. The first page focuses on writing down the correct equation in different cases of direct and indirect proportion. The second page focuses on the graph(s) that can represent different types of proportion. The final page has a number of problems to solve with variables that are directly or inversely proportional. Fully worked solutions to all questions are provided.

This resource is a great way to assess your class after teaching all the "using graphs" topic. There are 12 questions in total, covering the following: 1. Intersections of graphs 2. Using the discriminant to show/determine the number of points of intersection 3. Graph transformations 4. Proportion 5. Inequalities on graphs Fully worked solutions to all questions are provided.

This worksheet is designed so that students will hopefully gain an understanding of the process of converting mixed numbers and improper fractions, without having to write down a series of steps or instructions to follow. For both conversions the first set of questions are scaffolded, then for later questions the scaffolding is removed so they are doing the whole conversion themselves. There are 20 conversions in both directions, worked solutions are provided.

The first resource guides your class through the process of using the real and complex roots of z^n+k=0 to write down its real factors. The introduction includes the important result about the sum of conjugates and then uses equations of the form z^n=1 or z^n=-1 to establish that there is always an even number of complex roots, which can be put into conjugate pairs. It is then shown how each conjugate pair of roots produces a real quadratic factor, while each real root produces a real linear factor. To practise all this there is an exercise with 7 questions for students to complete. Solutions to all the examples and the exercise are included. The second resource contains an exercise with further examination-style questions on this topic. This could be used as additional practice in class or as a homework/test. Answers are provided.

These are two 2-sided worksheets that cover all calculations with fractions. The adding/subtracting worksheet goes step-by-step through the process of making the denominators equal prior to the calculation. The first exercise (12 questions) involves adding/subtracting fractions and mixed numbers where the denominators match, the second exercise (34 questions) involves adding/subtracting fractions and mixed numbers where the denominators do not match. The multiplying/dividing worksheet begins with a reminder of the method, together with a few examples to work through as a group. There are then two exercises, each with 20 questions, first to practise multiplying and then to practise dividing fractions and mixed numbers. Fully worked solutions to all questions are provided.

These 3 resources cover the following types of percentage question: 1. Writing one quantity as a % of another 2. Finding a % of a quantity 3. Increase/decrease by a % 4. Finding the % change Each resource is split into a non-calculator section and a calculator section. Each section has an introduction where the method(s) is/are explained with some examples to illustrate, followed by an exercise for students to complete. In total there are over 150 questions for students to work through - all solutions are provided.

The first resource introduces the technique for writing a complex number z=a+bi in (trigonometric) polar form, r(cos (theta)+ i sin(theta)), there are few examples of converting from one form into the other (to do as a class), and then an exercise of 30 questions for students to do. The next section introduces the exponential polar form re^(i theta), a few examples of converting from one form into the other (to do as a class), and then an exercise of questions for students to do. The exercise includes questions that get students to consider what z* and -z look like in both polar forms, as well as investigating multiplying and dividing complex numbers in polar form. Answers to the exercises are included. The second resource begins with a reminder of how to multiply/divide complex numbers in polar form, followed by an exercise of questions to practise. The remaining 3 pages cover the geometrical effect of multiplying, with several examples for students to learn from. Fully worked solutions are included. The final resource focuses on examination-style questions that consider the geometric effect of multiplying by a complex number in polar form. Fully worked solutions are included.

This 26-page resource covers all the required knowledge for diagrams and calculations to summarise or represent data in 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. Bar charts and pie charts - revision of interpreting these simple diagrams 2. Averages of a list of data 3. Range and interquartile range of a list of data 4. Histograms - drawing them, interpreting them and using them for probability 5. Cumulative frequency - using the diagram to find median, IQR, percentiles etc 6. Box-and-whisker plots - interpretation and use to compare 2 sets of data 7. Standard deviation - calculation from a list of data or summary statistics 8. Frequency tables - finding averages/measures of spread from (grouped) frequency tables 9. Scatter diagrams and correlation - interpretation of diagram, PMCC, use of line of best fit 10. Outliers - investigating presence of outliers in a list/table of data or a diagram Also provided is an 8-page resource which contains lots of practice of problems that involve finding the variance or standard deviation of different sets of data (answers are included). 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 axes, as well as drawing on the provided diagrams to help interpret them. Also included is a homework/test that covers the whole topic - 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

I'm teaching 3 different year 12 classes this year so I created 3 slightly different tests for the work I've covered with each. The first test focuses on quadratics (1 question on disproof by counterexample), the second and third both focus on quadratics and using graphs (also with 1 question on disproof by counterexample). All tests come with fully-worked solutions and they can be amended to your requirements.

This resource can be used to teach your students all the required knowledge for the topic of polar coordinates (FP2) and contains examples to work through with your students. As the resource can be projected/printed it saves you time and allows your class to focus on understanding the techniques and attempting questions. The resource is split into six sections: 1. Defining points in polar coordinates and sketching curves 2. Tangents at the pole 3. Lines of symmetry 4. Maximum value of r 5. Converting between cartesian and polar form 6. Finding areas Note that this resource does not contain the answers to the examples - sorry! If I get time I will add them, or if you download and use this resource and send me your solutions I will add them in, crediting you of course.

This assessment has a non-calculator section and a calculator section. it covers the following skills: 1. Writing one quantity as a fraction/percentage of another 2. Converting mixed numbers and improper fractions 3. All four calculations with fractions 4. Finding a fraction/percentage of a quantity 5. Percentage increase/decrease 6. Finding the percentage change Fully worked solutions are included.

This worksheet gives your students practice of converting the vector equation of a line into the cartesian equation, and vice versa (there are 10 of each).

This worksheet focuses on the skill of being able to find the point of intersection of the perpendicular from a point to a line. It includes related questions such as the perpendicular distance from a point to a line and the coordinates of the reflection of a point in a line. Some of the lines are given in vector form and some are in cartesian form, so students need to be confident with both. There are 16 questions in total, all answers are provided.

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.

I used this resource as a homework with my Year 10 group after finishing work on statistical diagrams and the calculation of averages and the range. It has at least one question on each of the following: 1. Bar charts 2. Pie charts 3. Mode, median, mean and range from a list of data 4. Finding the missing value in a set of data given the mode/median/mean. 5. Finding the new mean after a data point is added/removed. 6. Finding averages from a frequency table and a grouped frequency table. Fully-worked solutions are provided.

This 18-page resource covers all the uses/applications 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. Tangents and normals - finding the equations of tangents/normals to curves 2. Stationary points - finding them and determining their nature using first or second derivative 3. Smallest and largest values of a function - finding min&max value of f(x) in a set of values for x 4. Practical problems - using differentiation to find optimal solution to a problem in context 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 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