Mathematical Miscellany #29

With Exam season already started, an exam themed miscellany this week…

Command Words GCSE EdexcelFrom Edexcel – I do like this recently added Teacher’s Guide to Command Words, not only do we have commentary on what is expected from students when a particular commonly used command word is used but examples of questions to exemplify the use of the word.

All the examination boards have very clear resources illustrating command words, something we can incorporate into our teaching.

On Naikermaths you will find four new A Level Pure Mathematics Practice Papers. These papers are based on legacy Edexcel Exam Papers, but they have been edited to reflect the new A Level Specifications and include new questions to make them suitable for the new specification. Full solutions are provided.

What a treasure trove Edexcel’s Emporium is, log in and look for example at the themed practice papers for GCSE. This includes one mark questions and mark schemes (scroll down the alphabetical list), a good idea for any final revision sessions. Talking of one mark questions has given me an idea for Maths and Further Maths A Level revision sessions;  the very old Multiple choice papers I began my career with could be a very useful source of questions. Scroll down this post for an example.
Multiple Choice Example

Note the comment from Graham Cummings below, papers are available in 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.

A recent post from The Calculator Guide blog has very useful advice from AQA on the use of calculators in A Level Maths. I have recommended the Calculator Guide before and have shown many of the very helpful videos in both Maths and Further Maths classes. Check the resources here. Certainly, calculator use at A level needs to be taught explicitly. Note section 3 on Calculator Use from AQA’s excellent A-Level Maths The thinking behind great assessment.
Note my page here on Classwiz tutorials.

Crashmaths AS Countdown
With common content for all the examination boards at A Level, we have many resources for our students. On Crashmaths, see the AS and A Level Countdowns. With the first AS exam on 15th May – all 10 worksheets are available. The A Level countdown leads up to the first A Level Maths Exam on 5th June 2019 with the first worksheet available on 26th May. Each question sheet has 5  pure questions and 2 applied, one Mechanics and one Statistics; I like the way the pure section includes a mix of basic, problem and modelling questions.


From Crashmaths I have successfully used all the AS key skills checks this year with Year 13 and will do so again; they make great lesson starters. I see a section on End of Unit Tests under development, with a good set of Proof questions available now; certainly a space to watch.



Mathematical Miscellany #28

MEI Calculator Crunch

MEI – Calculator Crunch

This coming June MEI’ summer challenge, the Calculator Crunch will be helping Year 6s get ‘calculator-ready’ for secondary school, and additionally provide extra practice for Year 7s.

Note the dates – from 10 to 20 June, on each school day, MEIMaths will tweet a question a day for students to work on. PDFs of the questions will also be available from MEI’s page for display on whiteboards and to print as hand-outs. MEI has designed the problems not only to practise using a basic or scientific calculator but to develop mathematical thinking skills. Lesson plans will also be provided.

On the subject of MEI and Primary Maths, don’t forget their latest wonderful Sumaze! Primary app, one of a series of three apps in the series. All highly recommended, these problem-solving games cover a wide range of ages. Sumaze! which explores arithmetic, inequalities, the modulus function, logarithms, powers and primes is a problem-solving puzzle game suitable for A level mathematicians and above. Its sequel, Sumaze! 2, which explores fractions, decimals, percentages, primes and digits is suitable for those studying GCSE Mathematics and above.

For some more practise with calculators, perhaps try this calculator exercise from ADA Maths. Students can check that they can key in all the calculations correctly by answering the questions and checking their answers. ADA Maths is a free Mathematics Question Bank with no login required. The creator is Sam Powell, a mathematics teacher from the UK, working in Australia. All questions have answers, some have a fuller solution and a video explanation. Several categories of questions are available; look at Algebra for example and we see some nice use of colour in presenting a solution to a problem expanding double brackets (select Show Solutions) These examples could be helpful for students when revising.
ADA Project Algebra

Desmos AQA LDS Cars
In February of this year, I was very pleased to see that we can use Desmos for Statistics. Tom Bennison has written a large data set (AQA-Cars) resource using the Desmos statistics visualisation functions. It really is very easy to copy and paste into Desmos and display boxplots. Tom’s resource includes questions for students. It strikes me we should use the large data sets with younger year groups, using Desmos (or GeoGebra) makes it very easy to investigate such data when we are teaching boxplots and other Statistics topics.

Tom Bennison A Level Question a day

Tom Bennison – Year 13 Exam Question a Day

Tom has been busy, see also his Year 13 Exam Question a Day with questions up to June 13th. Tom has used Sample Assessment Materials from the awarding bodies’ websites so students can find mark schemes using the reference for any question. This will be a very useful resource for revision now and also in future. I do like the way we can easily see the topic for each question.

TeachItMaths Proof review

TeachitMaths Proof review sheet

Following my post on Proof resources, looking further through TeachIt Maths proof resources, I see many gems. Rather good for year 11 Higher GCSE students is this Higher Level Proof review sheet.

Maths Week London
In June we have for London teachers, Maths Week London. You can still register for this event, there are a limited number of welcome packs remaining.

Coming in November 2019, we have Maths Week England.

Mathematical Miscellany #27

From Access Maths, a brilliant selection of 90 Algebra Questions, Progressive Overload-Algebra is ideal for revision.

Have a look at all the other Access Maths revision resources too.

TES Resources
From one of my favourite resource authors, try Building Blocks from Andy Lutwyche.

Building Blocks for Bearings

A great idea, Andy!

A Level Practice Papers

CrashMaths gold

CrashMaths Edexcel Practice AS paper – gold

A recent addition from CrashMaths, Gold Edexcel AS Practice papers.

ATM Open Resources
For, activities, videos and more, have a look at ATM’s Open Resources. ATM provides many free resources on their website for teachers to download or use online in the classroom. There are many free resources available, note the menu on the right, these are excellent in their own right and also provide an excellent way of seeing what ATM has to offer. I do like GeoBoard tasks, try for example Board Task 3B.

If you like GeoBoards, see GeoBoard Activities, where I have given information on free online GeoBoards and resources.

Try ATM’s Puzzle Page, where you will find many examples of their puzzles, or get some free posters for your walls.

On the subject of Geometry, have a look at Don Stewards great slides from his recent London ATM/MA session.

I’m looking forward to attending the next session, Jonny Griffiths on Further Maths RISPS,

A Level (16+) Examination Materials
A very popular page is the Edexcel page in the A Level reform series; this has been updated and checked.

Edexcel new teaching materials

Edexcel frequently publishes new material, keep an eye on new publications by changing the Sort By filter to ‘Latest’. Check Teaching and Learning materials.
also Exam Materials and Specification and Sample Assessments.

Edexcel Model Answers for Sample Assessment materials

Edexcel Model Answers – Core Pure Further Mathematics

Looking at the latest Teaching and Learning materials we see for example recent February and March publications including very welcome Model answers for Further Mathematics Sample assessment materials. The content of Core Pure for Further Mathematics is common to all the examination boards, so a very useful document for any Further Mathematics teacher.

The latest Exam Materials include, for teachers, A Level Mathematics Mock papers and with common content for all examination boards, a very useful source of questions. (The same is true of course for AQA and OCRA and OCRB).

GeoGebra Scientific Calculator App
See the Calculators page for further information on Casio and Texas Instruments calculators.

Geogebra Scientific Calculator

GeoGebra has announced the release of their new free GeoGebra Scientific Calculator apps for tablets and phones.

The online calculator is here and you can get apps for iPhone & iPad: Scientific Calculator in App Store and Android: Scientific Calculator in Play Store.

There are several Scientific Calculator tutorials available.

Have you seen…?#5

From MEI, the latest in the Sumaze series, this time a fun educational puzzle game aimed at 4-7-year-olds. This has been added to my Apps page which includes some personal favourites. Visit for more information and links to all the apps in the series.

Dr Frost Full Coverage A level

Dr Frost – full coverage revision worksheets

From Dr Frost, additional really useful A Level Full Coverage Revision Worksheets.
Adding to his GCSE and IGCSE collections, Dr Frost now has an A Level series intended to “provide a single example of each of the variants of a type of question within a particular topic, rather than to provide multiple questions of exactly the same type to practise a single concept; the emphasis is broad coverage, collated from a huge database of past paper exam questions.”

#Have you seen…? is one of a series of short posts, simply to quickly provide links to interesting information and/or resources; a subset of the Mathematical Miscellany series.


Mathematical Miscellany #26

Chalkface Classwiz Simulator
From The Chalkface comes a brilliant spreadsheet that emulates the statistical functions of the Casio ClassWiz. The spreadsheet includes details which allow students to interpret each of the different modes, the List function is also included.
Direct link to the calculator. I have added this to the ClassWiz page, one of the Lesson Planning series.

Jack Brown teaching vdeosJack Brown has now completed teaching videos for all three papers of Edexcel’s sample assessment material. A very busy man – thank you, Jack! The easiest way to navigate Jack’s thousands of videos covering the complete A Level specification is through his website,

Jack is also creating Further Maths teaching videos; you can use this link to take you directly to his live Google Doc that has the new A-Level Further Maths specification and the teaching videos Jack has made so far. I see many useful videos on Proof, including the use of Induction for proofs of divisibility. I have added these resources to the Further Maths series of pages, see Teaching Resources.

On the subject of Further Maths teaching resources, thank you to Tom Button for sharing MEI GeoGebra Tasks for AS/A Level Further Maths
From The GeoGebra Institute of MEI, Use of GeoGebra in Further Maths: examples.
MEI GeoGebra Institute Further Maths
These can also be found on the Teaching Resources page for Further Maths (still a work in progress, this is being updated regularly.) Note also the addition of AMSP ResourcesYou can register your school free with AMSP for many benefits and resources. A free student account will enable students to access a comprehensive set of short videos to support the learning of AS/A level Further Mathematics.

David Morse has announced his new website. This is an outstanding and comprehensive set of resources for Primary and Secondary. Note What’s New at the top of the site where you can keep an eye on the latest additions to the collection. The Click-to-zoom feature of the Worksheet collection works so well for display on screen.
Maths4Everyone David Morse

OCR Check-in testOCR has several new Check in test resources for both GCSE and AS and A Level Further Maths (Specification A). Check in tests are also available for A Level Mathematics and for Further Maths Syllabus B. For Further Maths, scroll down the page to see the comprehensive set of Delivery Guides and Check in tests. These resources are included in the Further Maths teaching resources collection.