# data[].attributes.attachment_link.title
Solution Banks for Maths A-level - Physics & Maths Tutor

# data[].attributes.attachment_link.description
Solution banks for the Edexcel Maths A-level textbooks

# data[].attributes.attachment_link.readable_text
Choose your exam board:

We're not here to give you "The Importance of A Level Exams" chat. We're here to help you feel cool, calm and confident on A Level day because you know you've got the knowledge you need to get the result you want. Just choose your A Level subjects and exam board for expertly-written revision notes, our custom-made diagrams (including the A Level periodic table, quadratic graphs and more), test yourself with our course-specific questions and model answers, and then have a go at an A Level past paper. We've even included top tips on what A Level examiners are looking for and what might catch you out so you can maximise your marks in your exams!

# data[].attributes.attachment_link.title
A Level Past Papers & Questions by Topic

# data[].attributes.attachment_link.description
Exam paper questions organised by topic and difficulty. Our worksheets cover all topics from GCSE, IGCSE and A Level courses. Give them a try and see how you do!

# data[].attributes.attachment_link.title
A Level Mathematics - multiple choice questions.

# data[].attributes.attachment_link.description
A Level Mathematics - multiple choice questions for revision.

# data[].attributes.attachment_link.title
A-Level Maths: 1:1 Tuition & Free Resources | John Armstrong

# data[].attributes.attachment_link.description
Online 1:1 A-Level Maths & Further Maths tutor with Easter revision courses, plus free notes, past papers and video lessons. Start improving your grade today.

# data[].attributes.headline
Excellent resource explanations videos questions by topics and past papers

# data[].attributes.subject
Excellent resource explanations videos questions by topics and past papers

# data[].attributes.attachment_link.readable_text
Ofqual
Approved

Qualifications

© 2023 MME

When you visit or interact with our sites, services or tools, we or our authorised service providers may use cookies for storing information to help provide you with a better, faster and safer experience and for marketing purposes.

# data[].attributes.attachment_link.description
Whether you are looking A Level Maths past papers or you are searching for A Level Maths revision materials MME is here to help.

# data[].attributes.attachment_link.description
Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

# data[].attributes.attachment_link.title
GeoGebra - the world's favorite, free math tools used by over 100 million students and teachers

# data[].attributes.attachment_link.description
Free digital tools for class activities, graphing, geometry, collaborative whiteboard and more

# data[].attributes.attachment_link.readable_text
I am a full time Mathematics teacher and the aim of this website is to give away mathematical resources, free of charge! It will give me absolute pleasure to know that I have contributed to the education of mathematics and to the development of mathematicians!

I will be mainly producing and collecting a huge number of resources to help students in their revision and passing their exams and assisting other teachers in teaching the subject. I will be writing exam style questions tailored to the new GCSE (9-1), new A level and new Further Maths specifications, which can be used by students for revision and teachers in the classroom. I aim to produce worked solutions for most of the questions on the website although that will take some time.

Some of the contents are not available yet but I will be adding contents and resources on an ongoing basis.

Latest Updates :
Dec 2020 - 4 Practice Papers, including both Pure & Applied, for Year 12 have been uploaded to 'Year 1 AS Pure' page under 'Extra Resources'. Those are perfect revision materials for the Year 12 students at the end of their Year 12 course and who are about to start the Year 13 curriculum. Those papers provide a smooth transition to Year 13 as they focus more on problem solving skills

July 2020 - 15 A level Pure Practice Papers & 17 Mechanics A level Papers have now been uploaded to 'A level Practice Papers' page. These papers are excellent revision resources for A level exam revision

If you can help support my running costs with a donation or wish to sponsor the site then please get in touch.

# data[].attributes.attachment_link.description
I am a full time Mathematics teacher and the aim of this website is to give away mathematical resources, free of charge! It will give me absolute pleasure to know that I have contributed to the education of mathematics and to the development of mathematicians!

# data[].attributes.attachment_link.description
Searching for an AS Maths and AS further Maths tutor? Our experienced tutor help you achieve high grades in both subjects. Boost your understanding & confidence and with our expert tutoring.

# data[].attributes.attachment_link.title
Revisely | GCSE & A-Level Revision and Past Papers

# data[].attributes.attachment_link.description
Revisely combines the most effective GCSE and A-Level revision resources from around the web into one place; offering questions, videos, papers and more.

# data[].attributes.attachment_link.readable_text
Overview

Our resources are organised into topics or stations on a map or tubemap showing the connections between them.

Watch this video or use the preceding menu to find out more.

The map

The mathematics has been organised along a system of tube lines, which reflect big themes that run through mathematics. The tubemap offers a way to navigate to resources for teaching a particular area of mathematics; resources can be accessed by clicking on a station name. Some stations are still in development and this is indicated by a construction symbol.

You can access the map at any time by clicking the Map button in the main menu.

Stations

Each station features an overarching question that could be used to stimulate curiosity. There are a number of key questions that summarise the ideas that arise in the resources. You can filter resources by selecting a key question. You can also filter resources by tube line, if you wish to choose a resource with a particular emphasis.

The resources that are available at each station may come under three headings. Resources that introduce new ideas relating to the station are in the "Introducing" section. "Developing" resources may build on these ideas or earlier work. "Review questions" are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking.

Resources

To help you find the resources you are looking for, we have classified them according to twelve resource types.

Resources are divided into sections. In some cases this may be a warm-up followed by a larger task, and others may have a problem followed by a suggestion of how to tackle it. Almost all resources contain a solution or a "Things you might have noticed" section. This may help you to think about questions you might ask students, to see areas where students could get stuck, or offer further insight into how you might use the resource in your classroom. Further support is offered in the teacher notes.

Pervasive ideas

By clicking on a pervasive idea you will find a description of how the idea arises within the resources. If pervasive ideas are highlighted in a resource they appear in the sidebar (or bottom-bar on a small screen) and in the list of resources at the station (on a wide screen).
What are pervasive ideas?
Search

Use the Search button in the top menu bar to open the search dialog.

You can search for resources by title, keywords or text within the resource. Review questions can be searched by question Ref. You can also search for pervasive ideas and mathematical processes such as visualising.

You can also browse all our material with filtering options by clicking the Browse button in the main menu.

Saving resources

You can save a resource for later by adding it to your resource collection. To do this click the star next to the resource title. Note you must log in or register to use this facility. To access your resource collection, click the User button in the top menu bar then Your resource collection.

Within your resource collection, you can organise your resources by creating ordered subcollections. To add a resource to a subcollection, click the add to subcollection icon in your resource collection table. To select a subcollection, use the drop-down list above the table. You can also generate a PDF of resources from a subcollection, which could be used to generate your own exam from our review questions, for example.

Bundles and more

The More menu in the top right contains links to the Underground hub, our About and contact page and the Your mathematical classroom section of the site.

Our About page contains a video explaining our philosophy.

The Your mathematical classroom area of the site is accessible from the More menu and has been coloured purple to distinguish it from the rest of the site, as well as having its own menu once inside this area. It contains support for using our resources in the classroom as well as professional development opportunities. This includes the Bundles page, which contains small collections of resources that have a particular focus or goal, our Resources in action page, which provides detailed teacher support for a handful of resources, our blog, upcoming and recorded webinars, a courses page, and information about our Champions programme.

# data[].attributes.attachment_link.title
A level maths teaching resources | Underground Mathematics

# data[].attributes.attachment_link.description
Rich resources for teaching A level maths, enabling all students to explore the connections that underpin mathematics. The resources are free for all users.

# data[].attributes.attachment_link.description
Integral is an award-winning online teaching and learning platform designed to develop deep independent mathematical understanding.

# data[].attributes.attachment_link.readable_text
MadAsMaths.com :: Home

It is with great sadness that we announce the passing of creator/owner of the MadAsMaths website, Trifon Madas. This website will remain freely available for all its users, in his memory. However, please note that it will have a static format, there will be no further updates and the Contact form has been deactivated.

Free Resources for Students and Teachers of Mathematics.

In the 33 years of my involvement with mathematics I have produced, collected and accumulated a huge number of resources in many different forms.

I have used these resources with my teaching and lecturing, guiding several students into their mathematical careers.

Most of the material I have created is contained in this website and an overview is shown below.

Mathematical booklets, classified by topic, with a large number of questions and full solutions.

Practice papers with full solutions.

For the latest news click HERE .

The aim of this website is to give away mathematical resources, absolutely free!

It will give me immense pleasure to know that I have contributed to the education of yet more mathematicians, even if I did not personally meet them.

Enjoy !

[... and the homepage would not be complete without answering one of the most frequently asked questions ...

No, I do not post/help in TSR anymore because in my opinion it has little educational value, and is mostly run by talentless immature individuals ....]

SUBSCRIBE ON OUR BRAND NEW YOUTUBE CHANNEL!!!

Unfortunately I cannot put on the website past papers and solutions for examining boards or Universities due to copyright restrictions. I possess past papers for all A level boards and all modules, with some boards going back as far as the seventies. I will investigate ways into sharing these resources in the future.

# data[].attributes.attachment_link.title
UKMT Problem Solving Questions on Colmanweb

# data[].attributes.attachment_link.description
Great maths enrichment material: individual UKMT Senior Challenge questions arranged by topic. Try single questions or sets arranged by topic.

# data[].attributes.attachment_link.title
StudyWell - A-Level Maths (first teaching 2017) - StudyWell

# data[].attributes.attachment_link.description
StudyWell is the home for A-Level Maths. There are many resources for AS Maths and A2 Maths for the areas of Pure Maths, Stats & Mechanics

# data[].attributes.attachment_link.description
By converting our sims to HTML5, we make them seamlessly available across platforms and devices. Whether you have laptops, iPads, chromebooks, or BYOD, your favorite PhET sims are always right at your fingertips.Become part of our mission today, and transform the learning experiences of students everywhere!

# data[].attributes.headline
Good source for questions to incorporate into lesson plans

# data[].attributes.subject
Good source for questions to incorporate into lesson plans

# data[].attributes.attachment_link.readable_text
So my journey into finally making a website and a blog begins!

I have recently been having a lot of questions as to how I give examples in my lessons. I am honoured to be asked about this on a regular basis and am now excited to share all the types of examples I use for each topic with you.

It all started back in my training year (not that long ago) when I picked up the book "How I wish I'd taught maths" by the wonderful Craig Barton. I was fascinated by the simple, but incredibly effective method of example-problem pairs. These problem pairs became a regular occurrence in all of my lessons, however, this quickly got a little obsessive and I just thought that this was the answer to everything. I did not pay much attention to the rest of that chapter as I thought that my prayers had been answered! Turns out that there are more ways to present examples and it really does depend on the situation. I use example-problem pairs, supercharged worked-examples, examples by fading and supercharged examples with fading (my favourite).

Example-problem pairs are relatively easy to explain. They involve splitting the board into two with a fully worked example on the left of the board and a question on the right side of the board that students do to test whether they have grasped it or not. I often get students to be completely silent and refrain from answering any questions when I am going through the example. If I allow questions, then this interrupts the flow of me giving the example and can create misconceptions. Students copy the worked example into their books once I have fully explained it. I then get them to do a question from the right side of the board on their mini whiteboards. This is fantastic for AFL and discussing misconceptions that students have. I use example-problem pairs for when I am doing processes which are not particularly long. I sometimes do the process of giving an example followed by them doing a question twice. I like to cover all the situations. An example of an example-problem pair is given below.
Example-problem pair template
Supercharged worked examples involve almost the same thing as an example-problem pair, but we allow students to reflect on what they have done. I use this presentation method quite a lot with A-level groups. I even use this method for problem solving questions with my GCSE group. We write in the middle column about why we are doing each necessary step. This has had very positive results as the class progresses together in wider thinking of mathematical concepts. Here is a couple of examples of this below.
Supercharged template 1

Supercharged template 2

Examples by fading involve presenting a fully complete example on the board and then another example, but this time with one step removed. The number of blanks is increased with each following example until there is just the problem left for the students to solve. Simple but impactful! In Craig's book he references the work and evidence of Renkl and Atkinson towards this method. It is amazing to think that this research was actually written up in 2003, but not many teachers are taking note of this! I tend to use these with questions that involve a few distinct steps.

I have been presenting examples using these three ways for my training year and most of my NQT year, but I have always had the thought "Can they be better?". Turns out that I think they can. The combination of supercharged examples and examples by fading has proved to be a big hit with students. You are probably thinking "I want an example of how this can be achieved" so here is one below.
Supercharged with fading template
This method allows all students to understand how to solve linear equations with unknowns on both sides of the equals sign, whilst allowing deeper thinking. I start from the top left and work across. Rather than me just telling students how to do a question like this, I give them chance to reflect and think about why we have done something in the first place to develop their connections with maths. Once they have thought about it a little and we have discussed it as a class, I move on to an example by fading so that I can pick up any students who just need that extra boost of confidence. I then get them to do the question under the title of "Your turn" for an understanding check. I then do exactly the same with the bottom example. I use this presentation method with topics that have a lot of steps within questions. As you can imagine, this is used a lot in my algebra lessons.

My hope is that you will find this website useful. I will be building this website with more and more examples for each topic, as well as exercises that involve the use of variation theory. Please tell me what you think on twitter by tagging me @BerwickMaths. If you would like to contribute to this website, then please use the templates below the pictures and send it through twitter!

# data[].attributes.attachment_link.description
So my journey into finally making a website and a blog begins! I have recently been having a lot of questions as to how I give examples in my lessons. I am honoured to be asked about this on a regular basis and am now excited to share all the types of examples I use...

# data[].attributes.attachment_link.description
Solve definite and indefinite integrals (antiderivatives) using this free online calculator. Step-by-step solution and graphs included!

# data[].attributes.attachment_link.readable_text
Above, enter the function to derive. Differentiation variable and more can be changed in " Options". Click " Go!" to start the derivative calculation. The result will be shown further below.

How the Derivative Calculator Works

For those with a technical background, the following section explains how the Derivative Calculator works.

First, a parser analyzes the mathematical function. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). In doing this, the Derivative Calculator has to respect the order of operations. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". The Derivative Calculator has to detect these cases and insert the multiplication sign.

The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. MathJax takes care of displaying it in the browser.

When the "Go!" button is clicked, the Derivative Calculator sends the mathematical function and the settings (differentiation variable and order) to the server, where it is analyzed again. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima.

Maxima takes care of actually computing the derivative of the mathematical function. Like any computer algebra system, it applies a number of rules to simplify the function and calculate the derivatives according to the commonly known differentiation rules. Maxima's output is transformed to LaTeX again and is then presented to the user.

Displaying the steps of calculation is a bit more involved, because the Derivative Calculator can't completely depend on Maxima for this task. Instead, the derivatives have to be calculated manually step by step. The rules of differentiation (product rule, quotient rule, chain rule, ...) have been implemented in JavaScript code. There is also a table of derivative functions for the trigonometric functions and the square root, logarithm and exponential function. In each calculation step, one differentiation operation is carried out or rewritten. For example, constant factors are pulled out of differentiation operations and sums are split up (sum rule). This, and general simplifications, is done by Maxima. For each calculated derivative, the LaTeX representations of the resulting mathematical expressions are tagged in the HTML code so that highlighting is possible.

The "Check answer" feature has to solve the difficult task of determining whether two mathematical expressions are equivalent. Their difference is computed and simplified as far as possible using Maxima. For example, this involves writing trigonometric/hyperbolic functions in their exponential forms. If it can be shown that the difference simplifies to zero, the task is solved. Otherwise, a probabilistic algorithm is applied that evaluates and compares both functions at randomly chosen places.

The interactive function graphs are computed in the browser and displayed within a canvas element (HTML5). For each function to be graphed, the calculator creates a JavaScript function, which is then evaluated in small steps in order to draw the graph. While graphing, singularities (e. g. poles) are detected and treated specially. The gesture control is implemented using Hammer.js.

If you have any questions or ideas for improvements to the Derivative Calculator, don't hesitate to write me an e-mail.

# data[].attributes.attachment_link.description
Solve derivatives using this free online calculator. Step-by-step solution and graphs included!

# data[].attributes.headline
Mr Harrison invites you to experience very tough problem solving

# data[].attributes.subject
Mr Harrison invites you to experience very tough problem solving

# data[].attributes.attachment_link.title
Can you solve the secret werewolf riddle?

# data[].attributes.attachment_link.description
You’re on the trail of a werewolf that’s been terrorizing your town. After months of detective work, you’ve narrowed your suspects to one of five people. You’ve invited them to dinner with a simple plan: to slip a square of a rare antidote into each of their dinners. Unfortunately, you only have one square left. Can you divide it into perfect fifths and cure the werewolf? Dan Finkel shows how. [Directed by Artrake Studio, narrated by Addison Anderson, music by Nemanja Petrovic].

# data[].attributes.headline
Good Help for extra resources for your A Levels.

# data[].attributes.subject
Good Help for extra resources for your A Levels.

# data[].attributes.attachment_link.description
GCSE to A Level Transition Core Maths A Level (16+) Resources A Level Further Mathematics Subject Content Mapping Documents Specifications, Sample & Practice Papers Teaching Resources Further Calculus Differential Equations Linear Programming Notes & Examples Legacy Papers Into the archives ...

# data[].attributes.attachment_link.readable_text
Motion of changing speed

When a force of a certain size and direction acts on an object, the object moves at a constant rate of speed. These movements are easy to find around us.
For example, the speed of a skier descending a slope by gravity increases. However, when a running car stops by applying the brakes, the speed gradually slows down due to friction.
When an object is dropped straight or thrown up, the object's speed is constantly changed by force.

Time-speed graph when dropping objects

If you drop a hardball off a cliff, assuming there is no friction, you can see that the ball's speed constantly increases over time. This is because gravity acts in the same direction as the object's motion.
In this way, if a certain amount of force continues to act in the same direction as the object's motion direction, the object's speed increases.
If a force of a certain amount continues to act opposite to the direction of motion, the speed decreases. In other words, if the force acts in parallel with the direction of motion of the object, the speed of the object changes constantly.

Acceleration

Acceleration is the degree to which the speed changes over a period of time. Acceleration is obtained by dividing the amount of change in velocity by time.
If the initial velocity was V ₁, and the velocity changed to V ₂ after time t, then the acceleration a is calculated as follows.

If the speed increases, the acceleration has a positive (+) value, and if the speed gradually decreases, the acceleration has a negative (-) value.

Newton's second law of motion

When a force is applied to an object, a change in velocity (acceleration) occurs. The greater the applied force, the greater the acceleration. And the acceleration that occurs is inversely proportional to the mass. In other words, the heavier the object, the more difficult it is to change the motion.

# data[].attributes.attachment_link.description
Motion of changing speed When a force of a certain size and direction acts on an object, the object moves at a constant rate of speed. These movements are easy to find around us. For example, the speed of a...

# data[].attributes.attachment_link.readable_text
The worksheets have been grouped by chapter order from the Pearson Edexcel Textbook
Mark schemes at the end of each file.

We all make mistakes!
​If you find one, please let me know at devinaj90@gmail.com or hit the contact button on the header bar

# data[].attributes.attachment_link.description
A-level practice papers, questions, starters and more

# data[].attributes.attachment_link.title
Edexcel A-level Further Maths Exam Questions by Topic