All my resources have been created to use with classes I teach. Often I've created resources because, for a particular topic, I haven't been happy with the number/standard of the examples in a textbook. Sometimes I've created worksheets for certain topics (e.g. graph transformations) because I feel my classes will make greater progress on a printed worksheet than trying to work from a textbook. I always aim to produce high-quality resources that improve the students' learning and understanding.
All my resources have been created to use with classes I teach. Often I've created resources because, for a particular topic, I haven't been happy with the number/standard of the examples in a textbook. Sometimes I've created worksheets for certain topics (e.g. graph transformations) because I feel my classes will make greater progress on a printed worksheet than trying to work from a textbook. I always aim to produce high-quality resources that improve the students' learning and understanding.
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.
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 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.
These 2 resources cover all the required knowledge and techniques for trigonometry, as required for the AS part of 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 first resource is a 27-page booklet which covers the following:
1.The graphs of trigonometric functions, their period and amplitude/asymptotes
2.Exact values of trigonometric functions
3.Trigonometric identities
4.Finding the value of other trigonometric functions given, for example, sin x = 0.5 where x is obtuse
5.Solving trigonometric equations (3 different exercises on this, with increasing difficulty)
The second resource is a 13-question assessment that can be used as a homework or test. Fully worked solutions to this assessment are provided.
The third resource is a 15-page booklet which covers the following:
1.Using the sine rule to find angles/sides in a triangle
2.Ambiguous case of the sine rule
3.Using the cosine rule to find angles/sides in a triangle
4.Area of triangle = 0.5ab sin C - using this, together with the other rules, to determine the area of a triangle
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.
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 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
This 10-page resource covers all the required knowledge and techniques for related rates of change, 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).
It begins with an introductory example which shows related quantities can change at different rates and how the chain rule can be used to connect them.
There is then a summary of the method and a page of example questions to complete with your class. The exercise that follows contains over 40 questions for your students to attempt.
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.
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 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 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
Contains 3 sets of detailed notes, examples and exercises to help you teach the whole topic of exponential models and fitting models to experimental data.
Also includes a 20-question assessement with fully-worked solutions that is ideal as an extended homework or a test.
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 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.
This is a simple worksheet I created for my year 7 class to practise identifying different types of triangles and for them to work things out using their properties.
The first page is to work through with your class to complete the notes on each type of triangle and its properties. This includes how sides of equal length may be indicated on a diagram.
There is then a 2-page exercise for your class to attempt themselves. The questions include:
State the type of triangle from its diagram and given information
State the size of and unknown angle in a triangle (does NOT assume knowledge of angle sum being 180)
State the type of triangle from some information about some of its sides/angles (no diagram)
Considering what type(s) of triangle can contain, for example, an obtuse angle
Answers to the exercise are included.
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 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.
