UKMT Maths Challenges

The UK Maths Challenges provide a wonderful library of multiple choice problems; note the past papers where you will find questions and full solutions. Check also the Individual Challenges pages where you will find details of the challenge and see sample materials. Check the Junior Challenge for example. Note the extended solutions.

As well as a full solution which does not use the multiple choice answers further ideas are given for investigation.

UKMT Extended Solutions

Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem solving skills at all levels. On the outstanding Diagnostic Questions site you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)

UKMT Diagnostic Questions

Another way to access Maths Challenge questions by topic for Junior, Intermediate and Senior is from Dr Frosts’s wonderful website full of outstanding resources.

Very conveniently it is possible to download zip files of questions by topic.

For an alternative way to search, search the UKMT database by curriculum topic, the database includes Junior Maths Olympiad.
UKMT by topic Dr Frost Maths

Another possibility, generate a random quiz, using Mathster’s UKMT Mathematics Challenge Online Quiz. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.

UKMT Mathster

UK Maths Challenge Online Quiz – Mathster

Team Challenge

Links for students, including advice for young mathematicians are provided on Mathematics for Students. Further outstanding resources from UKMT include the Team Challenge resources.

The UK Maths Challenges are included on the Problems & Activities page.

For more sources of multiple choice questions see this post.

Daisy C Multiple Choice

Daisy Christodoulou on Multiple Choice Questions

Mathematical Miscellany #9

Now on the outstanding Diagnostic Quesions site – United Kingdom Mathematics Trust Quizzes – choose a theme or a quiz with random topics. To use the resources will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.” (See this post for Diagnostic Examination Questions).

aqa-ao3From AQA, on their ‘All About Maths‘ site see their Further Guidance and Practice Questions for the AO2 and AO3 requirements of the new 8300 GCSE. The 120 questions in this resource have been selected from legacy specifications which, to quote AQA “exemplify each of the strands of these Assessment Objectives and would therefore be suitable questions for the new GCSE as well.” AQA have arranged the questions in approximate order of difficulty andhave also divided them into those suitable for Foundation tier only, common to both tiers, and those suitable for Higher tier only, as well as by Assessment Objective. To

Remember fAQA 90 Problemsrom AQA we also have the excellent, GCSE Mathsematics: 90 maths problem  solving questions. These problems have been designed for use in supporting the teaching and learning of mathematics. There is a helpful intruductory section for teachers and note also the helpful Classification Tables by Strategy and by Content Area. Em,  has a brilliant PowerPoint with all the questions and answers – see it here.


Staying with problem solving, on TES Resources cchristian’s Multi-Stage Problem Solving is an excellent resource. These problems could make great starter activities.

Also, remember the GCSE Problem Solving Questions of the Day – Compilation from The White Rose Maths Hub Team, @WRMathsHub available on TES Resources.

White Rose Maths Hub problems

The booklet contains over 50 problem solving questions suitable for KS3 and GCSE classes, answers are also provided. Also from the team, their mastery schemes of learning now includes Year 7 material (UK age 11-12); an assessment is also available.

scooby-mysteryFrom author Captain Loui a TES resource, BIDMAS – Solve a Scooby Doo Mystery! Note that answers are provided in the author’s description of the resource. The theme is engaging but doesn’t get in the way of doing plenty of Mathematics!  Captain Loui’s resources are all free to use and as you can see have very favourable reviews.

Splat - Steve Wyborney

Splat – Steve Wyborney

A resource that caught my eye recently is Steve Wyborney’s Splat! Definitely a resource I wnt to explore further; you can read Steve’s blog post and download the lessons here.

Thursday 2nd March is World Book Day; we could bring books and Mathematics together with some Statistics (at any time); have a look at this resource from TES, World Book Day Maths Data Investigation where students analyse word length and sentence length in some book extracts. UK readers who remember Statistics coursework, this brings back memories of AQA’s coursework task ‘Read All About It’ where students considered various newspapers and magazines for readability. Note too the launch of a new website, is an international research-based initiative which sets out to explore various aspects of integrating stories reading and writing in mathematics instruction.

AQA - Read All About It

AQA – Read All About It

The extension task for the TES resource above considers the reading age of a text, you may wish to consider further readability formulae; if you paste some text to this site, Readability Formulas you can easily check statistics for your chosen text and generate a reading age according to the various tests.

WolframAlpha can be used for Words and Linguistics, note the various examples given, including number names.and document length.

Analyze My Writing

Alternatively, try Analyze My Writing. Simply paste in some text for a comprehensive analysis including basic statistics, word and sentence length and readability. It is also possible to create Cloze tests.  You can read more about this resource on Richard Byrne’s always impressive “Free Technology for Teachers”.

It seems appropriate to check some world records on books!

On the subject of books see the free books information and note in particular Colin Foster’s Instant Maths Ideas – lots of ideas you can try in the classroom.

View more posts in the Mathematical Miscellany Category.


Diagnostic Questions – Quizzes


To use the links in this post you will need to be logged in to Diagnostic Questions. Create an account if you have not already done so as this site with thousands of high quality diagnostic questions and additional analytical features is free and note the reassurance on the site that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”

quiz-libraryI wrote earlier on the brilliant collections of Diagnostic examination questions available. As well as the various Collections, there is an extensive library of quizzes are available ready for you to use.

It is very simple to create a quiz of your own using the Instant Quiz Facility. The following slideshow shows how I created a quiz on logs and exponentials. To create a new quiz I make sure that the Instant Quiz has no questions currently in it so have got into the habit of clearing it out once I have created a new quiz. The instructions for doing so are included here.

To see the pdf version choose this file: Logs & Exponentials Diagnostic Questions and to view the quiz online then follow this link. I have created several quizzes, some simply to gather question types together; see for example the many questions on Probability and Venn Diagrams.included in this Venn Diagrams collection. I created a quiz of all these questions so I could download the pdf for reference. Included in the Further Resources section on Iterative Methods for Numerical Solution of Equations I have included the whole collection of Trial and Improvement and Iterative Methods diagnostic questions; the complete quiz is here.

Checking Insights for my Year 11 class I can see that students have completed many of the diagnostic examination questions. Two students in particular have been rather busy completing 253 and 484 questions, they both got 9s in their mock examinations! (We used AQA Practice Papers set 3).

There is also a mobile app which students can use to complete quizzes assigned to them by their teacher. Testing this recently it works on both my Android tablet and phone.

Extensive help on Diganostic Questions is available on the site. Clear step by step instructions are given.