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 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 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 26-page resource covers all the required knowledge and techniques for binomial expansions with positive integer powers, as required for the new AS 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 types of questions included in the examples and exercises are:
1.Expand (ax+b)^n or (a+bx)^n
2.Find first 3 terms, in ascending powers of x, of the expansion of (a+bx)^n
3.Find the coefficient of x^k in the expansion of (a+bx)^n
4.Given the coefficient of x^k in the expansion of (a+bx)^n, find the value of a (or b).
5.Evaluating or simplifying nCr without a calculator
6.Given that (1+ax)^n = … find the value of n
7.Expand (ax+b)^n, hence expand (cx+d)(ax+b)^n
8.Use the first 3 terms of an expansion of (a+bx)^n to estimate k^n
In all there are over 100 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 16-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 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.
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 assessment covers all aspects of the exponential models topics for all examination boards.
It contains 20 questions, ranging from simple multiple-choice questions that would be worth 1 mark, to demanding multi-stage problems typical of specimen examination questions.
An answer sheet is provided for students to work on (with axes provided for questions that require graph work).
Fully-worked solutions are included.
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 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 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
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 30-page resource covers all the required knowledge and techniques for logarithms, 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 are:
1.Writing and evaluating logarithms
2.Using base 10 and base e
3.Evaluating logarithms on a calculator
4.Logarithms as the inverse of raising to a power
5.Solving equations that involve logarithms
6.Laws of logarithms
7.Solving equations with an unknown power
8.Disguised quadratic equations
In all there are over 300 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 16-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
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 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 33-page resource introduces the methods used to differentiate more complex functions, 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 are:
Chain rule - how to differentiate a function of a function (2 pages of examples then a 4-page exercise)
Product rule (1 page of examples then a 2-page exercise)
Quotient rule (1 page of examples then a 3-page exercise)
Implicit differentiation introduction (1 page of examples then a 1-page exercise)
Implicit differentiation involving product rule (2 examples then a 3-page exercise)
Applied implicit differentiation to find stationary points, tangents etc (2 pages of examples then a 3-page exercise)
Differentiation of exponential functions (1 page of examples then a 1-page exercise)
Differentiating inverse functions (2 pages of examples then a 1-page exercise)
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.
Also included is a 10-question 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
This activity is a nice way to check your whole class is secure on multiplying or dividing by 10, 100, 1000 etc.
The powerpoint has 20 multiple-choice questions of increasing difficulty, and there is an answer grid for your students to indicate their answers.
There is a second powerpoint that can be used to check the answers.
I used this with my year 7 group and they all got quite competitive trying to get all 20 questions correct.
This 13-page resource introduces basic differentiation and integration of exponential and trigonometric functions (in the A2 part of the new A level). The calculus work does NOT require chain rule, product rule, quotient rule, integration by parts… etc
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:
1.Differentiation of e^x and ln(x)
2.Differentiation of trigonometric functions (sin, cos and tan only)
3.Integration of e^x, 1/x, and trigonometric functions (sin and cos only)
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.
Note: some examples with trigonometric functions require knowledge of radians, double and compound angle identities, and small angle approximations.
This 17-page worksheet can be used to deliver the topic of proof in the new AS 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. It discusses particular errors in solutions/proofs, covers the use of ⇒, ⇐ and ⇔, and writing solutions to inequalities in interval and set notation. For each of these 3 topics there are notes, then examples to work through with your class, then an exercise for students to complete.
For each of the 3 methods of proof (counter example, deduction, and exhaustion) there are a number of examples for you to work through as a class, followed by an exercise for students to attempt themselves.
There are also some suggested extension activities for students interested in doing some research or additional work that goes beyond the scope of the syllabus.
The fully-worked solutions to the exercises are included in the students’ version, and fully-worked solutions to all the examples are also included in the teachers’ versions.
I needed about 3 hours’ of teaching time to get through this whole worksheet with my classes.
A homework/test is also included, 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 is a sample from a collection of short tests on trigonometry in right-angled triangles. All the tests are quite short (3/4 questions, so 5-10mins max). I created them so that I was able to test my classes more regularly on topics at different points through the year - each test is similar enough so that classes hopefully improve at the “standard” questions but there is also some variety in the later questions in each test and a progression in difficulty as you go through the tests.
There are 10 tests designed to be done with a calculator, 10 tests to be done without a calculator.
The questions include:
1.Finding an angle or a side of a right-angled triangle
2.Stating the correct value of e.g. sin A for a given triangle (requires Pythagoras)
3.Knowing and using exact values of trig functions
4.Using trigonometry in isosceles triangles
5.Using trigonometry in 3D shapes
6.Using trigonometry where side lengths are given as surds
7.Proving identities/results with trig functions
8.Questions with bearings, angle of elevation/depression
All tests come with fully-worked solutions which makes them easy to mark. This means that the tests could also be used as a revision resource for students.
The full set of tests are available here:
https://www.tes.com/teaching-resource/trigonometry-tests-x20-11931966
These resources are a collection of short tests on trigonometry in right-angled triangles. All the tests are quite short (3/4 questions, so 5-10mins max). I created them so that I was able to test my classes more regularly on topics at different points through the year - each test is similar enough so that classes hopefully improve at the “standard” questions but there is also some variety in the later questions in each test and a progression in difficulty as you go through the tests.
There are 10 tests designed to be done with a calculator, 10 tests to be done without a calculator.
The questions include:
1.Finding an angle or a side of a right-angled triangle
2.Stating the correct value of e.g. sin A for a given triangle (requires Pythagoras)
3.Knowing and using exact values of trig functions
4.Using trigonometry in isosceles triangles
5.Using trigonometry in 3D shapes
6.Using trigonometry where side lengths are given as surds
7.Proving identities/results with trig functions
8.Questions with bearings, angle of elevation/depression
All tests come with fully-worked solutions which makes them easy to mark. This means that the tests could also be used as a revision resource for students.
