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.



Systematic Listing Strategies

Transum - Combinations resources

Transum – Combinations resources


5. apply systematic listing strategies including use of the product rule for counting

The UK GCSE specifications include systematic listing strategies.

Some resources for this topic:

Transum Combination Starters

Transum Combination Starters

Transum Mathematics has many excellent resources including a section on Combinations, where you will find Combinations starters, activities and investigations. The Transum site includes links to some videos includes The Counting Principle which provides a clear introduction. There is alao a whole section on Systematic Listing Strategies with activities from level 1 to level 7. Note Transum’s clear index for teachers and for students, Maths Map with numerous activities to support their learning.

On Corbett Maths, see Product Rule for Counting.

Nrich - Fraction Combinations

Nrich – Fraction Combinations

Nrich has a sophisticated problem, Fraction Combinations which not only asks students to systematically list possibilities but work with fractions too.

Ben Moss Area Problem

benmossmaths – area problem

Ben Moss has a rather nice area problem which it seems to me will involve students in some systematic listing! I tried this with Year 7 and it worked very well.

AQA have a very clear Teaching Guidance document with many useful examples, I use these a lot in class. If you use or are considering using AQA you can register here (there seems to be a problem with the link on the Teaching Guidance document page).

AQA Teaching Guidance

AQA Teaching Guidance

And finally (for now!) Don Steward has this bracelets or necklaces problem.

Don Steward - combinations

Don Steward – combinations

Have a look at this post on Just Maths: Product Rule for Counting which includes Pearson / Edexcel exam questions and solutions.

Just Maths

Just Maths

NCTM Illuminations – Bobbie Bear

Bobbie Bear – from NCTM Illuminations, whilst aimed at younger students, how many ways can you give Bobbie Bear a different outfit? An excellent example when thinking about systematic listing strategies!

By Colleen Young Posted in Number

Solving Linear Equations

A collection of resources to use to demonstrate and practise solving equations.

Student Exercises
I find Owen Elton’s worksheet, Balancing Equations on TES Resources very useful when introducing equations, the diagrams emphasise that we must do the same to both sides.
(See Diagrams in Mathematics, for more on the use of diagrams to help understanding).

Balancing Equations

Balancing Equations – Owen Elton

Linear Equations - Don Steward

Linear Equations – Don Steward

As an alternative to the balance approach, consider this doing / undoing approach, described here by Don Steward, this is an approach I use for finding inverse functions. The exercises Don refers to are here.

A2 - Mostly Algebra

A2 – Mostly Algebra

One of the Standards Unit resources, A2 Creating and solving equations (in Mostly Algebra) uses this approach, students create an equation and  then undo it; this is a great exercise for demonstrating notation. Another resource with this approach comes from the Mathematics Assessment Project (the design and development was led by the MARS Shell Center team at the University of Nottingham) Building and Solving Linear Equations lesson

For a superb collection of ideas and student exercises for solving linear equations see all Don Steward’s posts tagged linear equations. Many of these outstanding resources use a very visual approach with very clear diagrams to help students’ understanding.

Diagnostic Questions

Diagnostic Questions

There are numerous questions on linear equations on Diagnostic Questions.

WolframAlpha solve equationA simple way to check a solution to an equation of any type is to simply enter your equation as a WolframAlpha query. Note that WolframAlpha includes a graphical illustration; it is so important for students to understand how equations may be solved graphically; I always illustrate graphical solutions when we are working with Algebra to help students make these links. Desmos of course, is ideal here.
Desmos & solving equations

Centre for Innovation in Mathematics Teaching
CIMT Interactive Resources
have tutorials on equations: Linear Equations 1, Linear Equations 2, and Linear Equations with Brackets.

The following three resources work well for demonstrating the balance method of solving linear equations.

Duncan Keith’s Linear Equation Calculator is available on STEM Learning.

Choose the type of equation you require then the sequence of operations required to solve the equation.
Select Do it after each operation, for example -32 Do it were the keys selected to start the above problem.

The slideshow below shows how to use the calculator to solve equations where the unknown is on both sides.




Mathisfun has this very clear and easy to use interactive illustrating the solution of linear equations.