Mathematics Advanced Level Resources

I have already looked at many excellent A Level resources – see the collection of pages here. This is a project I will continue working on, updating pages where necessary and adding further resources. In the meantime, some excellent resources I would like to highlight that I will be included in the collection.

From crashMATHS, act swiftly, you have until July 10th if you would like to download their 2019 AS & A Level Question Countdown sheets. See AS Level Question Countdown and/or the A Level Countdown. Each set provides 10 worksheets of mixed questions with 7 questions on each sheet, 5 are pure questions and 2 are applied. Whilst written in the style of Edexcel, the subject content is the same for all examination boards.

CrashMaths Countdown

I do like the way the pure section of the worksheets includes a mix of basic, problem and modeling questions.

Mrs G Resources.JPG

MrsG has been very busy! Use the link in her tweet for loads of challenging questions!


Dr Tom Bennison – A Level Mathematics Warmup

Somebody else who has been very busy this exam season (as well as the rest of the time!) is Dr Tom Bennison. If you look at his recent blog posts you will find many wonderful A Level (and GCSE) Maths and Further Maths resources – some great warm-ups for exams and much more. Try his A level warm-up sheets for example, these would be great for revision sessions too. A good time to get organised for next year perhaps – bookmark these now.

Regular readers of this blog will be aware of a favourite resource author of mine, Andy Lutwyche; there are references to his resources all over this blog, for A Level I have mentioned his excellent Erica’s Errors series– highly recommended, so many outstanding free resources in the series.

sim eq

You can find Andy’s latest resources (all key stages) here.

Find the radius - transum

Transum Mathematics – Advanced Starters

I must also mention again Advanced Starters from Transum Mathematics which I think could be useful for students aiming at the highest GCSE grades as well as for Advanced Level students. The problem, Find the Radius, is very neat!

Angle Thinking Transum.JPG

Angle Thinking – Transum Mathematics

How well do your students know the graphs of the trigonometric functions? Another opportunity here for a little technology, sketch all the graphs.

Looking at the Main Transum Starters page I see at the foot of the page we have various categories of starters including the Advanced Starters.
Transum Starters
I recommend exploring! With linear courses, starters provide an ideal opportunity for review.

Looking at Coordinate Distance, I can never resist a Desmos page to illustrate a problem! This starter could be also be used to review some coordinate geometry – find the midpoint? Find the equation of the line?

Coordinate Distance - Transum Advanced Starter

Quad Midpoints - Advanced Starter

Taster Lessons

Around this time of year, many UK schools will have taster sessions as part of a Sixth Form Welcome Event. What to do for such lessons?

I can never resist starting by asking students to do a graph sketch.
Graph with hole 1
We’ll see who is immediately familiar with my 11th Commandment!
thou shalt not divide by zero
Graph plotters cannot usually cope with graphs with holes, ask WolframAlpha for a plot for example and we see
Graph with hole 1

However, we can force WolframAlpha to show the point discontinuity
Graph with hole 2

See this cK-12 resource – Holes in Rational Functions for many examples.

Another possible graph sketch, y= x2  which could lead to futher discussion on line pairs. Graph sketching is of course ideal for illustrating how technology can help, something we should be doing as a natural part of A Level courses.

A very useful source of ideas for such lessons is Underground Maths. In fact it was Straight Lines from Underground Maths which led to my investigation of line pairs with a group of Level 2 Further Mathematicians, perfect since they are required to be able to factorise expressions such as 12x2 + xy − y2 .

Underground Maths is very helpful for teachers of A Level, I particularly like the Resource suggestions (scroll down the page) for the A Level specification.

For each content statement, Underground Maths have suggested up to three rich resources and up to three Review questions. Each suggestion is hyperlinked to take you directly to the resource on the Underground Mathematics site. Resources that are particularly good at supporting the overarching theme of Mathematical modelling have been highlighted.

I find the Review Questions can be excellent for either introducing ideas or for review and have created a spreadsheet of my own for just Review Questions which lists the questions by title rather than by number. I keep the latest version of the spreadsheet on this page. Excel File: Underground Maths Mapping Review Questions August 19 or the same file in pdf format: Underground Maths Mapping Review Questions August 19

I have found the Review questions a valuable source of tasks for Year 11, 12 and 13. You can browse all the Review questions or narrow your search by question type; note the O/AO-level questions which are questions from old papers, definitely a useful source of resources for planning taster sessions for new Sixth Form Students. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station. Try When is 6 × 7 = 42 a counter-example?

Working on these problems is ideal for students aiming for the highest grades and they are indeed appropriate for the more demanding A Level questions. Note the many Underground Mathematics Resource Types.

Review Questions in the words of the Underground Maths Team:

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

Read about the use of Review questions in the classroom on this Teacher Support page.

If you create an account you can easily save and organise your favourite resources. This list of favourites can be easily downloaded as a csv file.

I have so many favourites on Underground Maths, here’s one – Scary Sum!

To further organise your favourites you can create subcollections.

2406 Problems

2406 problems – that’s 1000 from 1000 Problems to Enjoy and 1406 problems from the Nrich site, the results of a search on the World Mathematics Championships.

The 1000 Problems site is an excellent collection of resources organised into collections on Number, Algebra, Shape and Space and Statistics. Within each category problems are organised by age and key words and a clear description are given for each problem. Extension questions are available for each category. For each problem a file can be downloaded which includes solutions.

1000 Problems Number Extension

1000 Problems – Number, Extension

The other 1406 Problems are the results of a search on The World Mathematics Championships on Nrich. A large collection of problems can be found on Nrich and many more sample problems from selected rounds provide a rich source of problems.

WMC Junior Questions
Looking at the Mathematician sample problems for example we see a collection of  mostly Junior (Junior level is aimed for those in Middle School/lower High School (in Grade 9 and below)) resources including mixed question sets and also some by topic.


Further Mathematics Mapping Documents

Unlike Mathematics where the subject content is the same for all the examination boards, for Further Mathematics only half of the subject content is compulsory. The core content can be found on pages 7-10. This prescribed subject content can also be seen in my file of Technology Resources for Mathematics and Further Mathematics (still an ongoing project which will be developed further):
maths & further maths technology by content  
Technology Resources

The content of the remaining 50% is not prescribed and has been defined in the specifications from the examination boards who could build from the applied content in A level Mathematics, introduce new applications, or extend further the core content further or any combination of these. With such choice, the specifictions are very varied; from AMSP, we can see a very useful summary of the structure and content of the various specifications.

For any change in specification, I have always found mapping documents helpful, for Further Mathematics where resources are perhaps less plentiful than for Mathematics, then a clear mapping to the legacy specifications can be useful for finding practice questions.

Mapping documents:
These are all very clear and include helpful notes.

  • OCR A scroll all the way down to Teacher Guides for a document mapping new content to the legacy specification
  • OCR B scroll down to Teacher Guides
  • Pearson – GCSE 2017 and GCSE 2008 content mapping. This spreadsheet maps the 2017 specification content for Maths (sheets 1 and 2) and Further Maths (sheets 3 and 4) to the old specification.

For AQA there is a useful summary of the subject content available and on Mohammed Ladak’s ‘MathedUp’ see his A Level Further Maths Takeaway, a wonderful source of exam questions by topic with mark schemes. AQA questions have been used here.

Looking for further questions on core topic such as Proof by Induction I know I can look at sample questions from all the Examination Boards; see Teaching Resources in the Further Maths series of pages.

To take a look at an optional example, earlier this year, teaching Dimensions (MEI) to the Further Mathematicians, having taught legacy M3 before, I did know where to find many questions, but for anyone new to the subject, quickly consulting the mapping document, we can see that the required legacy unit is indeed M3.
OCR B Dimensions
There are many questions available from the old M3 papers. Looking at the other examination boards, I can see that AQA has Dimensions on its first optional application.

AQA Dimensions

AQA Subject Content

So I know I can find Dimensions questions on AQA specimen and practice papers. I can also check MathedUp where we see questions and solutions on Dimensional Analysis.
MathedUp Dimensions Looking at Revise, a video on the subject is available which includes the AQA legacy reference. Challenge and Ans provide examination questions with very clear solutions.

MathedUp Dimensions example

MathedUp! Further Maths Takeaway


Advanced Starters – Transum

Transum Advanced Starters

Chancing upon this tweet from Transum proved fortunate. Hidden gems indeed, I had not noticed the Advanced Starters before, some of which I think could be useful for students aiming at the highest GCSE grades as well as for Advanced Level students.
The problem, Find the Radius, illustrated in the tweet is very neat!

Looking at the Main Transum Starters page I see at the foot of the page we have various categories of starters including the Advanced Starters.
Transum Starters
I recommend exploring!

I wrote the above in February of last year and I see from Transum’s latest newsletter that The Advanced Starters collection has grown. I see many starters here I like, thinking about next year it’s a good time to check these. With linear courses, starters provide an ideal opportunity for review.

Looking at Coordinate Distance, I can never resist a Desmos page to illustrate a problem! This starter could be also be used to review some coordinate geometry – find the midpoint? Find the equation of the line?

Coordinate Distance - Transum Advanced Starter

Transum – Advanced Starters

Quad Midpoints - Advanced Starter

Transum – Advanced Starters

For more on Transum see this post which includes some great Venn Diagrams resources and a reminder that there is a very clear index for teachers and another for students. The extensive library of activities on Transum are all free to use.  Activities such as this Algebra resource on Completeing the Square can be checked as part of the free offering.
Completing the Square

A subscription offers teachers answers to for example the Advanced Starters and Exam Questions.