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 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.
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
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
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
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 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 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
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 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
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.
These resources will give your class plenty of practice of using the factor theorem and the common questions that follow finding a factor of a cubic polynomial.
The first resource focuses on showing that (ax+b) is a factor of f(x) and then using it to write f(x) as a product of a linear and quadratic factor. There is an example to work through as a group and then an exercise with 14 questions - answers are provided.
The second resource has 2 sections. The first section focuses on factorising cubics fully, either as a product of a linear and quadratic factor, or as a product of 3 linear factors. The second section focuses on solving f(x)=0 and, in later questions, relates the solutions to the graph of f(x). In total there are 26 questions - answers are provided.
This 2-page resource is a great way to assess your students after teaching them combined graph transformations and the modulus function for the new A level specification.
The resource is designed for students to write on the sheet in the spaces or on the axes provided for questions that require sketches.
Fully worked solutions are included.
This 17-page resource covers all the required knowledge and techniques for hypothesis testing in the AS 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:
1. Sampling - different methods of sampling, biased and representative samples
2. Unbiased estimators - estimating the population mean and variance from a sample
3. Setting up a hypothesis test - null and alternative hypotheses
4. Making a conclusion - p-values, significance levels, 1-tail and 2-tail tests
5. Critical regions - finding the critical region for a hypothesis test
6. Significance levels and errors - probability of incorrectly rejecting null hypothesis, nominal vs actual significance level
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.
The second resource is a set of multiple-choice questions that can be used a quick assessment or as part of a revision/refresher lesson.
There is also a 6-page resource which contains lots of practice of problems that involve estimating population parameters from sample data (answers are included).
Also included is a 2-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
These resources are a good way to quickly cover/revise the whole topic of linear equations.
The first resource begins with a few notes on what forms linear equations can take and some of the steps or methods that may be required to solve them. There are some parts of the notes that need to be completed with your students, to practise the algebraic steps involved in solving linear equations.
There are then several sections, each section focussing on a particular form of linear equation. There are a few examples to complete with your students as practice, then an exercise for students to complete on their own. There is also an exercise of mixed questions at the end. Answers to all the exercises are included.
Section A - Solving x+a=b, x-a=b, a-x=b
Section B - Solving ax=b
Section C - Solving x/a=b and a/x=b
Section D - Solving ax+b=c, ax-b=c, a-bx=c
Section E - Solving x/a+b=c, x/a-b=c, a-x/b=c, a-b/x=c
Section F - Solving (ax+b)/c=d, (ax-b)/c=d, (a-bx)/c=d
Section G - Solving a(bx+c)=d, a(bx-c)=d, a(b-cx)=d
Section H - Solving ax+b=cx+d, ax+b=c-dx
Section I - Solving a(bx+c)=dx+e, a(bx+c)=d-ex
Section J - Solving (ax+b)/c=dx+e, (ax-b)/c=dx+e, (a-bx)/c=d-ex
Section K - Mixed exercise
The second resource gives your students practice of solving linear equations using a graph. Worked solutions to this sheet are included.
The final resource is a homework/test with 35 questions that cover the whole of the topic, including solving linear equations using a graph. Worked solutions are included.
This worksheet is a good way to give your class plenty of practice calculating and using the vector product.
The first 2 questions just involve finding the vector product of two given vectors, both in column vector and in I,j,k form. The remaining questions introduce how the vector product can be used to answer particular questions such as converting vector eqn of plane to normal eqn, or finding the area of triangle in 3 dimensions.
Fully worked solutions are provided to the questions.
This resource is a great way to cover this whole topic using prepared notes and examples to explain it to your students. Projecting the notes/examples will save you a lot of work on the board and your students will save time by working on the provided spaces and axes when doing sketches. You could also email/print some or all of this for students who have missed lessons or need additional notes/practice/revision.
The sections cover the following:
1. Sketching graphs of the form y=mod(f(x)) e.g. y=mod(x-2)
2. Sketching simple transformations of y=mod(f(x)) e.g. y=mod(x)+4
3. Solving equations involving the modulus function. This covers the different types of equations and explains when a sketch may/must be used. e.g. mod(x-4)=6 vs 2x+3=mod(x-1)
4. Solving inequalities involving the modulus function. This covers the different types of inequalities and explains when a sketch may/must be used. e.g. mod(x-4)=mod(2x+1) vs 3x-1=4-mod(x)
There are almost 100 questions in total across the different exercises. Answers to all questions in the exercises are provided, including sketches.
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
