Proof (new A level) - worksheet to teach & practise the whole topic

Proof (new A level) - worksheet to teach & practise the whole topic

This 10-page worksheet can be used to teach the whole topic of proof in the new A level specification for all exam boards. A great resource to help deliver this new topic - fully worked solutions included and a version with teaching notes added for some key points. It begins by reviewing all the required basic knowledge with some examples to work through, discusses particular errors in solutions/proofs, covers the use of ⇒, ⇐ and ⇔, interval and set notation, and then looks at the different methods of proving/disproving propositions. For each of the 4 methods (counter example, deduction, exhaustion and contradiction) there are a number of examples for you to work through as a class or get the students to attempt. I needed 4 hours of teaching time to get through this whole worksheet with my classes. There are also some suggested extension activities for students interested in doing some research that goes beyond the scope of the syllabus. Note that I designed this resource to work with a particular textbook accredited for the AQA course, so the references to exercises and page numbers may need to be amended for the exam board and textbook you are working from. A homework and test for this topic is also available - please see my other resources.
langy74
Quadratic functions (new A level) - worksheet and homework/test

Quadratic functions (new A level) - worksheet and homework/test

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. Note that the first resource makes reference to exercises in a textbook for additional practice - the references are for an AQA textbook but they can be amended to suit whatever book you are working from.
langy74
Graph transformations resources (new A level)

Graph transformations resources (new A level)

This set of resources includes everything you need to teach the graph transformations topic in the new A level. The printable resources will save you and your classes a lot of time which means there is more lesson time for them to practise and for you help develop their understanding. As the topic requires knowledge of the properties of some graphs (e.g. asymptotes) the first resource can be used to see which graphs they can already sketch and to discuss the asymptotes of particular graphs. The next resources are Geogebra files which can be used with the free Geogebra software. Each file can be used to discuss a particular type of graph transformation - there are sliders on each file that be changed or animated to see the initial graph transformed. This activity should help your class to visualise each type of transformation and start to get a feel for how the equation changes. The notes and examples start with revising each type of graph transformation - giving some different ways the transformations can be described and what the transformation looks like using y=f(x) and with a particular curve. Once completed this is a useful revision resource and helps them complete the exercise of questions on the reverse which includes questions asking for the new equation of a transformed graph, or for a description of the transformation applied. The final resource can be used to give your class practice of sketching transformations of y=f(x). The answers to all questions are included, including the sketches.
langy74
Vectors - perpendicular from a point to a line

Vectors - perpendicular from a point to a line

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.
langy74
Finding roots and real factors of z^n+k=0

Finding roots and real factors of z^n+k=0

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.
langy74
Using graphs resources (new A level)

Using graphs resources (new A level)

These resources cover the whole topic of using graphs in the new A level. Each resource can be used as a teaching aid or as extra practice for your students (all answers are provided). The resources cover the following: Intersections of graphs Inequalities on graphs Graph transformations Proportion Also included is a homework/test that can be used to assess this whole section of the A level - fully worked solutions are provided for this.
langy74
Homework or test on using graphs (new A level)

Homework or test on using graphs (new A level)

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.
langy74
Intersections of graphs (new A level)

Intersections of graphs (new A level)

This worksheet can be used to teach/practise the required knowledge and skills expected at A level for the intersections of graphs. The introduction discusses the different methods that can be used but then focuses on the method of substitution. There are then a few examples to illustrate the method, including questions about the geometrical interpretation of the answers. The final section shows how the discriminant can be used to determine/show the number of points of intersection, with examples to illustrate the method. Fully worked solutions to all examples are provided.
langy74
Proportion (new A level)

Proportion (new A level)

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.
langy74
Coordinate geometry (new A level) worksheet and homework/test

Coordinate geometry (new A level) worksheet and homework/test

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.
langy74
Finding gradients using dx/dy

Finding gradients using dx/dy

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.
langy74
Simplex algorithm worksheet and solver (Decision maths)

Simplex algorithm worksheet and solver (Decision maths)

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.
langy74
Volumes of revolution (integration)

Volumes of revolution (integration)

This resource is designed to introduce the method for finding the volume of a shape created when an area is rotated around an axis. The first side explains the derivation of the formulae - I would recommend you also try to show your students an animation that helps them visualise a 3D shape being created by a region rotating about an axis (lots are freely available online). There are then 5 pages of questions for your students to complete. Most of the questions are in two parts - the first part involves finding an area, the second part involves finding a volume (a very common style of question in examination papers). Note that students are expected to be able to integrate using ln, e and reverse chain rule. Answers to all questions are provided.
langy74
Representing inequalities on a graph (new A level)

Representing inequalities on a graph (new A level)

This 4-page worksheet will give your students plenty of practice at representing linear and quadratic inequalities on graphs, as well as writing down the inequalities illustrated by given regions. This printable resource will make it much easier for your classes to work through this topic rather than working from a textbook or drawing axes/diagrams themselves. There are over 30 questions on the worksheet - solutions are provided.
langy74
Combined graph transformations

Combined graph transformations

These resources will help your class understand how performing 2 transformations on a graph will affect its equation. The first worksheet has several examples designed to help the students realise when the order in the which the transformations are performed is important. The second worksheet is split into 2 sections. Section A has 10 questions where students must use the description of the pair of transformations to find the equation of the resulting curve. Section B has 18 questions where students must describe the pair of transformations that map the initial graph onto the transformed graph. Solutions to both worksheets are included. Note that these worksheets assume that students are familiar with the functions e^x, ln x and inverse trigonometric functions.
langy74
Linear programming problems - graphical solution (Decision maths)

Linear programming problems - graphical solution (Decision maths)

These resources are designed to aid the teaching and learning of using a graphical method to solve linear programming problems. The first resource introduces the idea of representing inequalities on graphs and finding the point(s) that maximise a given objective function. There are also some examples that require integer solutions so the optimal point is not at a vertex of the feasible region. The second resource provides practice of solving problems with a provided graph - these are examination style questions and involve considering how changes to the objective function may change the optimal point(s). The third resource has 2 example questions in context where the students must use a description of a problem to formulate the objective function and the non-trivial constraints, and then go on to solve the problem graphically. Grids are provided for all graphs and solutions are included for all questions.
langy74
Factorising quadratics - introduction and practice

Factorising quadratics - introduction and practice

I created these resources to try to help my classes understand the process of factorising quadratic expressions of the form x^2+bx+c. The idea behind them is to first get the class to practise finding the 2 numbers that have a specified product and sum, then to start to apply this to factorisation with some scaffolded questions. The first resource gets them to focus on finding the 2 numbers that have a specified product and sum. The 4-page worksheet is broken into four sections - both numbers positive, both numbers negative, one positive and one negative, and then a mixed section. The second resource is a spreadsheet activity where your classes can further practise the skill of finding the 2 numbers that have a specified product and sum. The questions are randomly generated and they get instant feedback on their answers, either telling them it is correct or telling them which requirement (product/sum) has not been met, giving them a chance to try again. It keeps track of how many each student has answered correctly so you can make this into a competitive activity. The final 4-page resource starts to apply the skill of finding 2 numbers that have a specified product and sum to factorising quadratics. Each section starts with a set of questions asking for 2 numbers with a specified product and sum, then asks the student to complete/write down the related factorisation. Each section concludes with some factorising questions with no scaffolding. Section A is both numbers positive, section B is both numbers negative, section C is one number positive and one number negative. Sections D has almost 50 quadratic expressions to factorise - starting with a few of each type and then moving onto mixed questions. Answers to both the worksheets are provided.
langy74
Graph transformations resources (new A level)

Graph transformations resources (new A level)

This set of resources includes everything you need to teach the graph transformations topic in the new A level. The printable resources will save you and your classes a lot of time which means there is more lesson time for them to practise and for you help develop their understanding. As the topic requires knowledge of the properties of some graphs (e.g. asymptotes) the first resource can be used to see which graphs they can already sketch and to discuss the asymptotes of particular graphs. The next resources are Geogebra files which can be used with the free Geogebra software. Each file can be used to discuss a particular type of graph transformation - there are sliders on each file that be changed or animated to see the initial graph transformed. This activity should help your class to visualise each type of transformation and start to get a feel for how the equation changes. The notes and examples start with revising each type of graph transformation - giving some different ways the transformations can be described and what the transformation looks like using y=f(x) and with a particular curve. Once completed this is a useful revision resource and helps them complete the exercise of questions on the reverse which includes questions asking for the new equation of a transformed graph, or for a description of the transformation applied. The final resource can be used to give your class practice of sketching transformations of y=f(x). The answers to all questions are included, including the sketches.
langy74
Quadratic functions (new A level) - worksheet and homework/test

Quadratic functions (new A level) - worksheet and homework/test

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. Note that the first resource makes reference to exercises in a textbook for additional practice - the references are for an AQA textbook but they can be amended to suit whatever book you are working from.
langy74
A "treasure hunt" activity on substitution

A "treasure hunt" activity on substitution

A treasure hunt activity for a class to attempt individually or in groups. There are 24 questions, numbered from 1 to 24. Each group chooses a number from 1 to 24 at random (or you can assign them a start number), and this is the number of the first question they should attempt - this should be written in the top-left circle on their answer grid. Their answer to their first question should be a whole number from 1 to 24 - this should be written in the next circle on their grid and this is the number of the next question they should attempt. e.g. if a group starts on Q6 and they think the answer to Q6 is 13 then after Q6 they should attempt Q13 (and they should have 6 -> 13 on their answer grid). If they answer the questions correctly they end up with the same chain of answers as on the solution, if they make a mistake they will repeat an earlier question and at that point you can decide how much help to give them sorting out their error(s). This activity works best if you can stick the 24 questions around a large classroom or sports hall so the groups have to run around to find their next question. All the classes I've done these activities with have loved them.
langy74
A "treasure hunt" activity on powers (includes negative and fractional powers)

A "treasure hunt" activity on powers (includes negative and fractional powers)

A treasure hunt activity for a class to attempt individually or in groups. There are 24 questions, numbered from 1 to 24. Each group chooses a number from 1 to 24 at random (or you can assign them a start number), and this is the number of the first question they should attempt - this should be written in the top-left circle on their answer grid. Their answer to their first question should be a whole number from 1 to 24 - this should be written in the next circle on their grid and this is the number of the next question they should attempt. e.g. if a group starts on Q6 and they think the answer to Q6 is 13 then after Q6 they should attempt Q13 (and they should have 6 -> 13 on their answer grid). If they answer the questions correctly they end up with the same chain of answers as on the solution, if they make a mistake they will repeat an earlier question and at that point you can decide how much help to give them sorting out their error(s). This activity works best if you can stick the 24 questions around a large classroom or sports hall so the groups have to run around to find their next question. All the classes I've done these activities with have loved them.
langy74
Area between curve and y-axis worksheet (integration)

Area between curve and y-axis worksheet (integration)

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.
langy74
Area between graphs worksheet (Integration)

Area between graphs worksheet (Integration)

This worksheet has 4 pages of questions, each with a diagram, for your students to practise finding the area between two graphs. The first 4 questions are on areas between a curve and a line, the remaining questions are on areas between 2 curves. Answers to all questions are provided.
langy74
Trapezium rule worksheet to introduce and practise using it (new A level)

Trapezium rule worksheet to introduce and practise using it (new A level)

This worksheet makes it easy to introduce and teach the trapezium rule to your classes. The first page has diagrams to illustrate the method and the derivation of the formula is broken down into steps for you to work through with your class. Projecting all this is so much easier than drawing it out by hand. The trapezium rule formula is then stated at the top of page 2, followed by 3 pages of examples of examination-style questions that test the use of the formula and your students' understanding (is the answer from the trapezium rule an underestimate or overestimate, can they use their answer to deduce an estimate for a related integral, etc). Answers to all the examples are provided.
langy74