An annual update on preparation for UK University Entrance Examinations for Mathematics; note that these resources provide challenging questions for any students anywhere studying Mathematics beyond age 16.

From Nrich, Prepare for University.

To further challenge yourself, MAT, STEP and AEA questions provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.

For mark schemes see:

• MAT (Maths Admissions Test), scroll down the page for past papers, solutions and additionally video solutions. For superb resources for these questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.
• STEP mark schemes can also be found on the Cambridge Assessment Preparing for STEP page. Note that STEP 1 will no longer exist from Summer 2021.
• The AEA questions are legacy questions, extended solutions are currently available for the papers which have been used from the University of Warwick. Legacy papers and mark schemes are available on Colmanweb.

The Underground Mathematics Review Questions include Oxford Mathematics Admissions Test questions and full solutions. 

TMUA is a newer admissions test only one question is available on the Underground Maths site, however, there is much overlap between the specifications for the TMUA and other tests such as the Oxford MAT, so these questions should provide useful resources for students taking this examination. Interestingly, Durham University states that “Those students already registered for MAT may substitute those results in place of our own test, if they do not wish to take both.”
Warwick University advise taking one of MAT, TMUA or STEP.

TUMA papers and mark schemes are available from Cambridge Assessment and I would highly recommend the presentation introducing the test, from Julian Gilbey. As suggested – try the questions first (pdf file) before watching the presentation.

Talking to Julian Gilbey, he recommends for the TMUA, the importance of working through the Extended specification notes on the website, to learn about the logic side. (See Test Specifications for the specification and enhanced specification with its notes on logic and proof.) He also stresses that the more Maths you can do, the more you work on stretching problems and think hard about maths the better you will get at maths. Examples he mentions for resources are any questions on the Underground Maths website, (not just the review questions already mentioned here), UKMT and olympiad problems, STEP problems.

“And essentially your ability to ‘think mathematically’ and to solve mathematical problems is all that these tests are testing”

For further resources try UKMT Senior Maths Challenge Questions.

…and also see MadAsMaths with its many papers and solutions increasing in difficulty.

You can download a free copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core Mathematics. Whilst written to support students taking STEP examination papers, Advanced Problems in Mathematics is excellent preparation for any undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 75 problems.

STEP (Sixth Term Examination Paper) Mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics.

………..

You will find free STEP soluions on MEI’s site. The STEP question papers are all available on the Cambridge Assessment website; note the STEP resources include a searchable database.  The AEA qualification from Pearson is based on the A Level specification and designed for the top 10% of students to help differentiate between the most able candidates. The Sample Assessment Materials provides a valuable source of challenging questions (with mark schemes) for A Level mathematicians.

STEP papers here. Underground Mathematics has STEP questions within their Review Questions. Each question comes with a fully worked solution.

See also, from Cambridge University, their STEP Support Programme. From the home page, access the resources, you will see STEP Support Programme Foundation modules, STEP 2 modules and STEP 3 modules.

… a basic skill any student of Mathematics needs.

An updated version of a slideshow with a few examples if you need a little reminder:

Complete the square examples from Colleen Young

When factorising quadratic expressions do you check coefficients first? If the coefficient of x² and the constant are prime for example you should be able to just write down the factorisation without needing an elaborate method.

However, when that is not the case then try these handy techniques.

Full details of the ‘box’ method and Lyszlowski’s method are provided in this post:
Factorisation of Quadratic Expressions.

Are you studying Mathematics at home?

Several posts and pages here may be useful. See:

• Reference
• Notes
• Revision
• Study Tips
• Videos
• Calculators
• Transition Time
• University Admissions Tests

Back in 2014 I was using free samples from Bring on the Maths resources with my students. A whole series of activities where you must pick out the correct answers is provided. Activities are available for young children right through to Advanced Level.

I must recommend the free samples from Bring On the Maths, the Core 3 activity – Logarithmic equations worked really well with my Year 13 class and next week I’ll use the C4 Binomial Expansion resource when we are talking about the validity of a given expansion. I have used the Trigonometric Ratios resource before – and will again; there are several other great resources in that list of samples – explore!

Free access is available to the complete set of these resources on the old Kangaroo Maths site. Log in with the user and password as above to access all the resources. This will give access to all the activities for students from Key Stage 2 right through to A Level – note that this being the old site, the resources are aligned to earlier schemes of learning but still so useful.

Looking at the old level 5 and 6 Algebra resources for example, we could try Simplifying Expressions  or Constructing and solving equations.

Distance Learning will be demanding, it’s certainly a chance to read more or perhaps get away from screens and listen to a story. For as long as schools are closed, Audible are providing stories which are free to stream on a desktop, laptop, phone or tablet. An extensive collection of stories, including titles across different languages is available. No accounts or passwords are needed. See Audible’s ‘How to Use Stories‘ and start listening; note the menu where children can select by age.

White Rose Maths has so many free high quality resources, see for example Secondary Schemes of Learning and Assessments for End of Block or End of Term. Check their Home Learning, the White Rose Maths Team has prepared a series of five maths lessons for each year group from Year 1-8. More will be added each week for the next few weeks. Every lesson comes with a short video showing  clearly and simply how to help children to complete the activity successfully.

Try

• CorbettMaths,
• MathsBot
• Mathsgenie
• Exam Solutions

The summer term includes work on consolidation for the year, see this collection from Nicola Whiston who has started a collection of Knowledge Organisers which follow

the White Rose Schemes of Learning, she is sharing the collection here, via Dropbox. These are really attractive.

CK-12 Foundation has created a resource page with hand-picked lessons in math and science popular during the month of March.

From Bobby Seagull, “The Magic of Numbers: Why Everyone Should Love Maths”.

And of course you will need a break, maybe a puzzle? Try Futoshiki and other puzzles.
It’s certainly a chance to read more or perhaps get away from screens and listen to a story. For as long as schools are closed, Audible are providing stories which are free to stream on a desktop, laptop, phone or tablet. An extensive collection of stories, including titles across different languages is available. No accounts or passwords are needed. See Audible’s ‘How to Use Stories‘ and start listening; note the menu where you can select by age.

Stay safe everyone.

For students studying Decision Mathematics try Linear Programming from Transum. This provides you with a reminder of inequalities and gives you 5 problems to try.

If you need some notes and further activities on Linear Programming then try these from CIMT which provide an excellent introduction as well as exercises with answers.

This earier post post looks at the use of Technology to interpret solutions to such problems and includes online utilities and instructions on the use of the Excel Solver. Examination questions are used to illustrate the use of these tools.

An annual update on preparation for UK University Entrance Examinations for Mathematics; note that these resources provide challenging questions for any students anywhere studying Mathematics beyond age 16.

From Nrich, Prepare for University.

To further challenge yourself, MAT, STEP and AEA questions provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This document is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.

For mark schemes see:

• MAT (Maths Admissions Test), see the right-hand menu, question papers, followed by solutions as separate documents. For superb resources for these questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.
• STEP mark schemes can also be found on the Cambridge Assessment Preparing for STEP page. Note that STEP 1 will no longer exist from Summer 2021.

The Underground Mathematics Review Questions include Oxford Mathematics Admissions Test questions and full solutions. TMUA is a newer admissions test only one question is available on the Underground Maths site, however, there is much overlap between the specifications for the TMUA and other tests such as the Oxford MAT, so these questions should provide useful resources for students taking this examination. Interestingly, Durham University states that “Those students already registered for MAT may substitute those results in place of our own test, if they do not wish to take both.”
Warwick University advise taking one of MAT, TMUA or STEP.

TUMA papers and mark schemes are available from Cambridge Assessment and I would highly recommend the presentation introducing the test, from Julian Gilbey. As suggested – try the questions first (pdf file) before watching the presentation.

https://youtu.be/8VaEbRwJiYE
Talking to Julian Gilbey, he recommends for the TMUA, the importance of working through the Extended specification notes on the website, to learn about the logic side. (See Test Specifications for the specification and enhanced specification with the notes on logic and proof.) He also stresses that the more Maths you can do, the more you work on stretching problems and think hard about maths the better you will get at maths. Examples he mentions for resources are any questions on the Underground Maths website, (not just the review questions already mentioned here), UKMT and olympiad problems, STEP problems.

“And essentially your ability to ‘think mathematically’ and to solve mathematical problems is all that these tests are testing”

For further sources try UKMT Senior Maths Challenge Questions and see also MadAsMaths with its many papers and solutions increasing in difficulty.

You can download a free copy of  Stephen Siklos’ Advanced Problems in Mathematics and Core Mathematics. Whilst written to support students taking STEP examination papers, Advanced Problems in Mathematics is excellent preparation for any undergraduate Mathematics course.

Following each question, you will find a discussion and a full solution. The clear Contents page lists all 75 problems.

STEP (Sixth Term Examination Paper) Mathematics is a well-established mathematics examination designed to test candidates on questions that are similar in style to undergraduate mathematics.

You will find free STEP solutions on MEI’s site. The STEP question papers are all available on the Cambridge Assessment website; note the STEP resources include a searchable database.  

Underground Mathematics has STEP questions within their Review Questions. Each question comes with a fully worked solution.

See also, from Cambridge University, their STEP Support Programme. From the home page, access the resources, you will see STEP Support Programme Foundation modules, STEP 2 modules and STEP 3 modules.

For age 16+, a mixed set of worked examples….
C1 tricky compilation