Mathematical Miscellany #80

A compilation post, featuring:

New on BBC Bitesize are GCSE exam-style quizzes; the quizzes have been designed for students working on GCSE maths, biology, chemistry, physics, combined science, computer science and geography studying any awarding body specification. For each subject, you will find 50 exam-style questions, these are arranged over five activities of ten questions each. The questions are multiple-choice and students can see a fully worked solution for each question.

Rob Southern

Rob Southern has created a very useful document linking sections from the Pearson A level textbooks to his videos, where they exist. Rob’s YouTube channel is Maths in an empty classroom. Do check Rob’s site for his collection of A Level Maths and Further Maths resources. I mentioned his Coordinate Geometry exercise, part of the A Level Pure 1 Year 1 collection in this Fill in the blanks post. Note Rob’s questions to consider to get students thinking hard. You can also find a version on Transum, Coordinate Geometry Table which allows answers to be checked.

Rob Southern Coordinate Geometry Table – on Transum

I do like Amanda Austin’s latest inequalities resources, these linear programming style resources would be very helpful for Decision Maths.

For resources for Linear Programming, see these pages in the A Level Further Mathematics series.

From MEI, comes excellent support for investigating the A Level large data sets. You will find help videos with useful techniques for using Excel and GeoGebra for statistics in GCSE and A level, also, from The Advanced Mathematics Support Programme (AMSP) look at these workbooks that show how to use Desmos to investigate the large data sets. Desmos could be used to support Statistics at GCSE also.

Desmos classroom activity

Here’s a Desmos activity on Interpreting Box Plots.

Staying with Statistics, an activity I have always liked is S4 Understanding Mean, Median, Mode and Range.
(All Standards Unit resources).


GCSE content

Looking at some favourite resource websites, some recommended resources for teaching functions …

For an excellent introduction the PhET Simulation, Function Builder provides a very visually appealing resource. Using the pattern option even very young students could explore important concepts. This is very intuitive to use, the slides in the following slideshow demonstrate examples of its use. Note that teachers can register with PhET and gain access to supporting documentation.

Desmos can be used very simply to illustrate function notation and note the use of Desmos as a calculator to evaluate the value of a function for a given input.

Functions - Desmos. Select image for graph page
Functions – Desmos. Select image for graph page

From White Rose Maths, we have Year 7 work on algebraic thinking, including function machines, and in Year 11, Functions.

White Rose Maths – Year 7, Algebraic Thinking, understand and use algebraic notation

Dr Austin Maths

Dr Austin Maths on Functions

As always CIMT is worth a search; we find:

CIMT Interactive Materials - Functions
CIMT Interactive Materials – Functions

In the interactive materials for year 7: Unit 16 Section 2: Function Machines and there is also a section in the associated text (16.2). All CIMT resources are free to access, a small number of documents such as text answers are password protected, you can obtain the CIMT password. These exercises could be used as an introduction and students also shown function notation. They could write the functions described by the function machines using f(x) notation.

AQA Bridging the Gap

The AQA Bridging the Gap resources includes a resource on introducing function notation; These resources were originally designed to support teaching and learning for students who studied the 2007 Key Stage 3 Programme of Study and were preparing for the then new Mathematics GCSE. The resources are still very useful. 

On Transum, try this online exercise on function notation, inverse functions and composite functions.

Functions - Transum
Transum – Functions

There are also many more activities on functions on Transum.

For a challenging problem on Function Notation, try this from Open Middle.

Andy Lutwyche – Building Blocks, Function Notations

From Andy Lutwyche, a resource I have always liked is one of his excellent Building Blocks series on Function Notation. We can also search his site on functions. (I am so pleased to see Andy’s resources on his own site,

Or we could help Clumsy Clive with his homework on Function Notation.

From CorbettMaths try the Practice Questions.


On DrFrostMaths, try the Functions Key Skills.

From Don Steward, try these lovely questions on Compound Functions.

Maths HKO

From MathsHKO see Function Machines, and also Functions.

We could simplify expressions on Graspable Math

On Starting Points Maths, a search on Functions returns several tasks, including work on Graphs and Transformations.

On Maths Genie, under Grade 7, we have Inverse and Composite Functions. You will find some revision examples and also exam questions with solutions.

Maths Genie Functions
Maths Genie – Inverse and Composite Functions

For a compilation of GCSE questions, William Neill’s GCSE Maths Questions site is so useful. Under Algebra, we see A7 Function Machines and A65-68 (H) Functions.

On MathsBot we could use GCSE Exam Style Questions for higher questions on Composite functions.

Or use a GCSE Revision Grid.

TES Functions
TES Resources – Functions

On TES, this Crossnumber from cbarthur is an ideal resource for becoming familiar with function notation. Also on TES from Owen134866 we have a set PowerPoint resources including an introduction to f(x) notation for GCSE students.

OCR GCSE 9-1 Check in tests

From OCR, Check in tests can be very useful, consider the language of functions for example, the first questions could be used for students as young as Year 7 (age 11-12).

Functions – Plymouth University

See also these very clear notes with exercises from Plymouth University including Functions..

Mathematical Miscellany #79

Looking ahead to summer examinations, this year there will not be advance infomation as there was last year, but in GCSE Mathenatics students will again have formaule sheets; the exam boards have now published these. This page, Examinations 2023, includes links to infomation and the formulae sheets for each exam board. The page also includes the series of revision pages with many ideas and resources for revision.

Formulae sheets 2023

OCR formulae test

OCR additionally have formulae sheets top tips, and GCSE formulae tests.

Mathsbot – Directed Number

I often use Jonathan Hall’s wonderful Completion Tables so was delighted to see that these are all in one place on MathsBot, a personal favorite is his Directed Number.

(See Fill in the Blanks for many such exercises, and Negative Numbers for more resources on Negative Numbers.)

Regular readers will be aware a favourite website of mine is Transum, two recent additions are Algebraic HCF with Algebraic HCF and LCM exercises over 5 levels and Gradients now with a new level 2 which features straight lines drawn on axes where the vertical scale is different from the horizontal scale, soe labels are obscured for an additional challenge.

From Chris McGrane on Starting Points Maths, have a look at this lovely task on Integration which provides much needed practice on deciding on the integration required to determine the areas shown. Students are required only to write down the integrals with limits.  

It struck me that the questions could be checked and illustrated on WolframAlpha.

Both MathsBot and Transum featured in my Enduring Websites collection, websites started between 1997 and 2013, and still there! MathsBot and Transum are regularly producing such excellent resources after many years. I believe Starting Points Maths will be included in the next Enduring websites collection!

These slides are from a session I presented at last year’s MA Conference.

Mathematics Revision

Seeing that my earlier posts on revision resources including papers for the 2022 GCSE examinations are still popular I have created a page to include the resources from those collections, whilst some of these are based on the advance information for the June and November 2022 exam series they still provide very useful revision. We are fortunate in Maths that the subject content is the same for all the UK exam boards. The collection of pages brings together many varied revision resources.

The page, GCSE Revision 2022 is one of the Revision series of pages:

Jake Gordon – featured in Custom Maths Revision Starters
GCSE Show that…