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.
I have found plenty of resources to help students find Euler’s formula, but couldn’t find any where students can practise using it - so I made one!
This worksheet starts by reminding them of the result and then there are a few examples to work through with your class, followed by an exercise with 16 questions of increasing difficulty.
Note - some of the questions involve use of (basic) algebra
These resources deal with problems where 2 or more items are chosen at random, we are given the probability of a particular outcome, and this is used to derive a quadratic equation that then needs to be solved.
The first resource can be used to teach the topic. It is in two sections - section A deals with selection with replacement, section B deals with selection without replacement. In each section there are 2 examples to work through with the class, followed by an exercise with more than 10 questions of increasing difficulty for the class to attempt themselves. Fully worked solutions to the examples and exercises are included.
The second resource is another set of questions that can be used as a homework or revision - 8 questions that are a mixture of with/without replacement.
Also included is a spreadsheet that calculates the probabilities for all outcomes in situations where there are between 5 and 40 items - just in case your class loves this topic and wants more questions!
This worksheet focuses on quadratic expressions where the question requires the candidate to show that the expression is always positive, never negative, etc.
There is an introductory activity where students practise thinking about expressions of the form ax^2 + b, or a(x-b)^2 + c - doing a quick sketch of the graph and then deciding whether they are always positive, never negative, always negative or never positive.
Next is a page of example proofs to work through with your class, followed by an exercise with 15 questions for your class to attempt themselves.
Fully worked solutions to the examples and the exercise are included.
A simple resource to give your class practice of finding the area of a shape by counting squares.
It has brief notes and examples at the start, then an exercise with 18 questions for students to attempt (answers included).
The shapes are squares, rectangles, triangles and compound shapes using these 3 shapes (so no circles or parts of circles).
Together, these resources cover all aspects of using numerical methods for trying to find roots of equations, as required for the new A level specification.
This 11-page resource covers the different techniques for using integration to find the size of areas, 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 types of questions included in the examples and exercises are:
1.Area between a curve and the x-axis where some/all of the curve is below the x-axis
2.Area enclosed between two graphs
3.Area between a curve and the y-axis
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 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 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
