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.

Diagnostic Questions

To use the links in this post you will need to be logged in to the brilliant Diagnostic Questions site. 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. If you scroll down the page you’ll see that Diagnostic Questions are giving “you, the teacher in the classroom, a promise that Diagnostic Questions will always remain free.”

Diagnostic Questions provide a way of assessing your students’ knowledge and understanding, they are excellent for identifying misconceptions. Try for example the collections of GCSE 2017 examination questions from AQA, OCR and Pearson Edexcel.(scroll down each of the pages linked to for numerous quizzes on different topics on the GCSE syllabus).

Diagnostic Questions GCSE 2017 Collections

Diagnostic Questions GCSE 2017 Collections

Diagnostic Questions - GCSE examples

Diagnostic Questions – GCSE examples

You will find excellent coverage of topics new to the GCSE specification. You can also search all questions for a topic of your choice, for example a search on iteration will lead you to the whole collection of Trial and Improvement and Iterative Methods questions.

For bitesize revision assign your class a stream – just two questions a day in the run up to the exam.

When you are logged in to Diagnostic Questions, you can easily return to the menu using the menu icon on the left.
Returning to the collections, there are many – scroll down the page and you will see collections such as GCSE Maths Takeaway – 111 mini topic-specific quizzes covering all the content on Higher and Foundation GCSE (keep scrolling down the page for all the quizzes). These quizzes are ideal to use as baseline assessment before revising a topic, or as a measure of progress following the teaching of a topic.

For schools teaching AQA’s Level 2 Further Maths specification, the AQA Level 2 in Further Maths collection has 12 sections of very useful questions for this specification.

You will see choices for each quiz including the very useful option to download the questions as a pdf.

For example I created a quiz on Circles and Tangents, downloading this as a pdf creates this file. See the guide mentioned below for instructions on creating quizzes.

Extensive help is available to help you learn how to use the site. The Getting Started with Diagnostic Questions Frequently asked questions guide is very helpful for new users.

This post has looked at some of the questions available but note all the other features – start exploring!




Review Questions – Underground Mathematics

Underground Mathematics - QuadraticsI wrote earlier on the wonderful resources on Underground Mathematics from the University of Cambridge. Thinking about the new A level specifications  I believe this site will provide us with rich resources for these new specifications.

Each section includes Review Questions, look at Thinking about Algebra for example; scroll down the different resource types for the Review questions for this station.

Alternatively you can browse all the Review questions.

Review Questions - types
An excellent feature of Underground Mathematics is the excellent search facility; we could look at the Review questions by type. One can also search by line ( Number, Geometry, Algebra, Functions or Calcuus) and by Station.
Review Questions - search

See the example question below, for each review question you will find the question, a suggestion, the solution and sometimes suggestions for taking it further with for example GeoGebra resources.

Note the star by the title – if you choose to log on to the site (you don’t have to but it’s a very good idea!) you can save any favourite resources to your collection.

Review Question - Gemetry

I can never resist a quick illustration on Desmos! I think I’ll start an Underground Maths Desmos collection! Note the use of the hyperlink on Desmos to link to the question.
Select the image for the Desmos page.
Desmos illustration

I think we have a wonderful supply of excellent questions here to challenge our students and help them see connections between the various areas of the subject. These are ideal to use with A Level students; some are also useful for higher level GCSE students aiming at those top grades or Level 2 Further Maths students. Any student who wants to study Mathematics at university should certainly be using this site.

Diagnostic Examination Questions

Diagnostic exam question

Just a short post to capture the links to Craig Barton’s and Simon Woodhead’s excellent question collections of examination questions on their Diagnostic questions site. Note that you will need to create a (free) account to follow these links. As well as GCSE questions, there are quizzes for AQA’s excellent Level 2 Further Mathematics specification and for Core 1 at Advanced Level. Questions from the Oxford University Mathematics Admissions Test are also available.

I found the AQA taster quizzes useful with my students.

And now we have their latest addition, a GCSE Mathematics collection for the new GCSE specification from Cambridge University Press which include worked answers at the end of the quiz. These are suitable for Foundation students and provide useful revision for higher students too.

..and hot of the press, Craig has added a quiz on his predictions for the higher calculator paper!

I created this Circles & tangentsDiagnostic Questions Quiz for use with my GCSE Year 10 class.

Mathematics A level 1986

June 86
A trip down memory lane! (Edexcel’s Emporium has some papers from this era.)

Writing my earlier post on Multiple Choice Questions reminded me how much I used to like the first paper of the Mathematics A level from the University of London School Examinations Board – thirty multiple choice questions to complete in one hour, 15 minutes.

Multiple Choice Example

For questions 1 to 20, candidates had to select one answer from 5 and for questions 21-30 the instructions were as follows.
June 86 Mathematics 1

I will gradually upload these to create a collection of Multiple Choice questions, these could make good starters.

University of London June 1986 Mathematics 1

The pdf file here has the paper, followed by the exam board answers followed by notes from the 1986 version of me! These days I would illustrate with Desmos and/or WolframAlpha for example as well where appropriate.
Colleen Young answers

Note the comment from Graham Cummings below, there are further papers available in the Edexcel’s Emporium:

The Emporium has some 17 multiple-choice question papers from the period 1988-1992 – by no means a complete set, but they range across the Mathematics, Further Mathematics, Pure Mathematics and Applied Mathematics syllabuses. You can find them in the “Pre-C2000” cabinet within GCE AS/A Level.

Signing up to Mathematics Emporium is highly recommended, note that it is a free website intended for the use of teachers of mathematics in secondary schools, regardless of what board you use. Register for an account and ensure you supply a correct centre e-mail address in your name for verification, your centre name and centre number.



UKMT Mathematics Challenge – Skills Builders

UKMT Skills Builders Topics

UKMT Skills Builders Topics

From UKMT, try their free Skills Builders, on-line problem solving questions for both junior and intermediate level. Note the user guide, which applies to both Junior (age 11-13) and Intermediate (age 13-16); this offers clear step by step instructions with screenshots.


UKMT Maths Challenge (Junior)

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.

The UK Maths Challenges provide a wonderful library of multiple choice problems; note the these 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 addition for 2015 of 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

UKMT Extended Solutions

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

Links for students, including advice for young mathematicians are provided on Mathematics for Students.

Team ChallengeFurther 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 #3

Exam PowerPoint @westiesworkshop

Mr Westwater – TES Resources

With revision still in mind, for some excellent PowerPoint resources with A Level questions and mark schemes by topic try Mr Westwater’s resources on TES. (Twitter @westiesworkshop). Though Edexcel questions these are clearly useful for other examination boards also. There are six of these PowerPoint files available:
Core 1   Core 2
Statistics 1  Mechanics 1
Core 3
    Core 4

Diagnostic Questions

Diagnostic Questions

Craig Barton’s and Simon Woodhead’s Diagnostic questions site includes some excellent question collections for revision; as well as GCSE questions, there are quizzes for AQA’s excellent Level 2 Further Mathematics specification and for Core 1 at Advanced Level. Questions from the Oxford University Mathematics Admissions Test are also available.


From AQA this set of revision tests and mark schemes is very useful and from Oxford University Press a lovely set of free revision resources is available. Under Mathematics Revision Guides, choose the ZIP file Worksheets. Note that these are headed New GCSE – this is the old new specification, not the new new specification! These are clearly perfect for UK students taking exams this year but still excellent for future years.

AQA Revision Algebra

For many more revision resources note the Revision Activities series of pages.

GCSE Problem Solving: Steve Blades’ site has many excellent resources; on the GCSE page Steve has a section (near the end of the page) of eBooks, and one of those is on GCSE Higher wordy questions. See also Steve’s Think like a problem solver and mathematician book.

For more Problem Solving Resources, see Problem Solving and Problem Solving 16-19.

Alec McEachran’s Furbles – a large data set!

Alec McEachran’s Furbles – a large data set!

Statistics – thinking about large data sets which we will need to for the new A Level specification – for an amusing large data set, how about the Furbles?! The images generated here are from the original 2003 version which is still available on Alec McEachran’s Talk to students about summarising this data, perhaps ask for their impressions as to which colour is the most or least common. Data can be presented as a bar chart or a pie chart and you can choose to categorise in various ways. It is also possible to vary the number of Furbles, the maximum and minimum number of eyes and sides. The illustration here show the largest data set possible.

Alec McEachran’s Furbles

Alec McEachran’s Furbles

Visual Patterns

Visual Patterns – Fawn Nguyen

From Fawn Nguyen comes the brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who’ve used visual patterns in their classrooms.



Multiple Choice Questions

Daisy Christodoulou on Life After Levels - conclusion

Daisy Christodoulou on Life After Levels – conclusion

Daisy C Multiple Choice

Daisy Christodoulou on Multiple Choice Questions

From researchEd 2015 and highly recommended, Daisy Christodoulou discussed the removal of National Curriculum Levels. Read Daisy’s post and see her slides on her blog you can also watch the presentation.
Note – researchEd Maths and Science 2016 – I already have my ticket!)

In that presentation Daisy discussed the use of Multiple Choice Questions, something I have always liked using in my teaching. Daisy’s discussion  of making questions harder by changing the number of correct answers reminded me of the, in my opinion excellent, Multiple Choice A Level papers which the then London board included in their A Level Mathematics examinations (London Syllabus B). I can see see some old papers in the ‘Very Past Papers’ section of the Edexcel emporium but sadly not Paper 1, the Multiple Choice paper. Fortunately I have print copies which I can use and I think a worthwhile project would be to use some of the question types from those papers in lessons, something I will work on.

In the meantime, happily we do have access to some Multiple Choice questions online and I thought it would be useful to bring them together in one place.

Diagnostic Questions

Diagnostic Questions

I have written several posts on the excellent Diagnostic Questions site which hosts thousands of multiple choice questions written by teachers designed to address student misconceptions. I have found it worthwhile to discuss the wrong answers with students so we are all aware of the kinds of mistakes it is easy to make. It is a site I use regularly, teaching Year 10 about the equation of a tangent to a circle at a given point for example, I created a Desmos page and a Diagnostic Questions Quiz using questions on circles (centre the origin) from Diagnostic Questions.
(pdf: quation of a Circle & Gradient of Tangent).

Note the various collections on the site including those from AQA and OCR to support the teaching of GCSE Mathematics.

A Level topics are also covered on Diagnostic Questions; see for example this quiz I created on  Logarithms and Exponentials.

Ben Cooper Resources

Mega Maths Quiz from Ben Cooper

For a superb collection of Multiple Choice questions, great for starters, plenaries or any time, head for Ben Cooper’s resources; see for example Mega Revision from Ben Cooper and 30 Number StartersBen’s website is coops-online where he shares very high quality resources. Resources (all free) by Ben can also be found on TES.

Don Steward Multiple Choice

Don Steward – Rearrangements Multiple Choice Quiz

Don Steward has so many outstanding resources on his Median blog, including multiple choice quizzes, see this on rearrangement for example. Note that he also has a separate blog for GCSE practice resources. many of these quizzes are multiple choice.

UKMT Extended Solutions

From UKMT, the UK Maths Challenges provide a wonderful library of multiple choice problems; note the these 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 addition for 2015 of extended solutions.

mathisfunMathisfun has an extensive library of very clear diagrams and explanations and also multiple choice questions for most topics. Use the Index to find the topic you want and note that for most topics you will see some questions at the end.

mathisfun multiple choice

mathisfun – Simplifying Square Roots – select image

As you can see from the Index all ages are catered for including older students; I have used the clear explanations and questions on finding the inverse of a 3×3 matrix with Further Mathematicians for example. Once you have selected an answer a complete solution is provided. Note the Question Database – some exploring to do I think!

PowerPoint Millionaire

The Who Wants To Be A Millionaire format can provide a fun way to present Multiple Choice quizzes. A Google search returns various resources and of course provides you with PowerPoint Millionnaire templates you can adapt for your own use. Some highlights from that search, the Primary Resources files use a simple and clear format and William Enemy has described a resource on Great Maths Teaching Ideas which also uses that template; such a good idea to have all students answer all questions and add up their winnings! Another example – Algebra on TES.

For a alternative and slightly more sophisticated template see PowerPoint Games which includes templates for several games including Who Wants To Be A Millionaire?

June 86 Mathematics 1For older students the old London A Level Multiple Choice papers could be very useful, I have scanned one of my old collection and will add more.

Oxford Maths Admissions Test

Oxford Maths Admissions Test

FDesmosor an extensive collection of Challenging questions for Advanced Level students we can turn to the Oxford Maths Admissions Test, note the menu on the right hand side of the page, many papers and also solutions are available. I can never resist a quick graph on Desmos but note the very comprehensive solutions provided. For more Oxford MAT questions see this extensive collection on Underground MathematicsThese Underground Mathematics resources will provide so much more than the question in each case. Note the suggestions and solutions.


That QuizThere are various options for creating your own multiple choice questions.That Quiz is simple but effective – all free and no adverts. There are many quizzes already available on a variety of topics, it is also possible to create your own quizzes. Teachers can register and add classes if they wish. You can search the many quizzes available, searching for Fractions for example led me to this quiz.

Testmoz Directed Numbers


For an alternative way to set up a simple quiz try Testmoz. No registration is required. This has been written by Matt Johnson, an undergraduate student – the instructions are all very clear and you can check out the FAQ!  (I love those FAQ! For example: I lost my quiz URL can you retrieve it for me? Answer: No). Try this test on Directed Numbers – log in as a student, the passcode is cy090610

More to Explore!
British Columbia exam question
In Daisy’s talk mentioned at the beginning of this post she mentioned British Columbia questions in her discussion of multiple choice questions, a quick search led me to this Pre-Calculus paper for example; I also found a site I’ll return to have another look at: Mathematics 30-1.

From Australia, New South Wales Government, we have Multiple Choice Questions for the School Certificate and Higher School Certificate.
And, thank you,  Mark Greenawaymore resources! 
MG Twitter
If you want to write your own questions, you may find the references in Learning Scientists‘ post on Multiple Choice Questions useful (Smith, 2016).
Bibliography:Smith, M. (2016) Weekly digest #4: How to write good multiple-choice questions. Available at: (Accessed: 4 April 2016).

Diagnostic Questions – new features (select image for site)

I have written several posts on this excellent site and it now has a host of wonderful new features.

One can now register your school and students, set them quizzes for which they get feedback and so do you! You can read Craig Barton’s own description of the new features here and note the series of videos with clear instructions on many aspects of the site.

Testing this, all seems to be working well. I uploaded students easily using a spreadsheet as described in Craig’s video “How to add Schools, Teachers and Students”

It is very easy to assign one of the many available quizzes for your students or set them one of your own quizzes. Again, Craig has described the process in a video (it takes seconds to do!)
Standard Form

I thought I would try this with a quiz I created earlier on Standard Form and all worked well. I logged on as a student to test this and did very well! At the end of a quiz the student can review the questions, read explanations by other students and could also download the quiz if they wished.

This is certainly a feature I will be experimenting more with. Happily I have excellent students who like to be given further resources which enable them to help themselves.

Another thank you to Craig Barton and Simon Woodhead for creating and developing this outstanding resource. Talking of further developments Craig tells me that a Quiz Preview function (currently an easy way to preview a quiz is to download a worksheet) and a newly improved Data Quiz page will be available very soon.