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PhET – Collision Lab
Category Mechanics
Technology in Mathematics
An update has been made to the Use of Technology page.
In particular note the GeoGebra resources from Edexcel (and also OCR).
From Edexcel you can use A Guide to using GeoGebra when teaching AS and A Level Mathematics which links to numerous GeoGebra files clearly mapped to the specification content. You can also access an excellent collection relating to the Pearson books (see table below). Whilst linked to the books many of these GeoGebra resources do stand alone, for example check this equations and inequalities example from the Pearson Maths A Level Pure 1 collection.
It is good to see all the GeoGebra resources for Further Mathematics, for example, check Explore toppling and sliding using GeoGebra.
For exploring the Large Data, on AQA’s All About Maths see AQA Large Data Set – Guidance and Worksheets including a tool to help support teaching the statistics content of the specification. This is an amended version of the large data set spreadsheet, the first three sheets are as on the AQA large data set but there are many additional sheets which allow students to explore the large data set. The tools are all provided for students, they do not need knowledge of Excel, meaning time can be spent on interpreting the data rather than learning about Excel. The worksheet on Exploring the Large Data Set could I think be usefully used lower down the school to get students used to working with more data.
A separate page is available on Statistics.
Mechanics – Dimensional Analysis
For UK Examination Boards AQA, OCR A, OCR B MEI Further Mathematics.
This posts gives details of the specifications and teaching resources for Dimensional Analysis.
First a look at the specifications and we see a similarity between all three specifications. For AQA see the first image below. OCR A and B (MEI) additionally mention the relationship between the units of a quantity and its dimensions, with OCR B MEI adding ‘be able to change the units in which a quantity is given’.
Specifications
AQA: Optional application 1 – mechanics Assessed at AS and A Level
AQA have a very helpful Teaching Guidance document for Mechanics, explaining how AQA have interpreted the content of the specification, the guide provides examples of how the content of the specification may be assessed.
The guidance is available on AQA’s free Maths portal for teachers, All about Maths. The resources are for teachers who offer, or are considering offering AQA maths qualifications. See this page for how to register.
OCR A Mechanics (Optional paper Y543) Assessed at AS and A Level
OCR B MEI
Note that mapping documents from the legacy specifications to the new specifications are available on this page in the Further Maths series.
Examination Questions
New Specifications
AQA Specimen questions paper and mark scheme. The only question on Dimensional Analysis is question 2, a multiple choice question on dimensional consistency.
AS Practice Papers and A Level are available on All About Maths
For some Legacy questions and mark schemes see the paragraph on MathedUp below.
The Legacy Mechanics 3 papers which included Dimensional Analysis are available on All About Maths.
OCR A Sample Question paper and mark scheme. Question 3 is on Dimensional Analysis.
OCR B Mechanics Minor (question 3) and Mechanics Major (question 6)
OCR also have practice papers – these require an Interchange log-in.
The Legacy M3 OCR MEI questions are very useful indeed for this topic. (No log-in required.
A Level Maths Revision very usefully provides Further Maths exam questions by topic (scroll down). Legacy questions from OCR MEI and mark schemes are available for Dimensional Analysis.
Further Resources
From amsp this brilliant collection of short videos produced by the legacy Further Mathematics Support Program supports the Further Maths Specification. I have used many of these successfully in class and recommended them to students to support their studies. Look at any of the examination boards to see the coverage for the course. Check the list for your examination board and you can find the videos on Dimensional Analysis for AQA, OCR A and OCR B MEI.
OCR Section Check In Tests and Delivery Guides
OCR have very useful check in tests on Dimensional Analysis with fully worked solutions for OCR A and OCR B MEI. These both seem to use the same questions.
Each check in has 10 questions, the first four questions are are routine procedural questions which primarily assess ‘Use and apply standard techniques (AO1)’ The remaining questions primarily assess ‘Reason, interpret and communicate mathematically (AO2)’ and ‘Solve problems within maths and in other contexts (AO3)’
At least half of the questions are appropriate for the AS course.
OCR A Delivery Guide Dimensional Analysis
OCR B MEI Delivery Guide Dimensional Analysis
These Delivery Guides discuss general approaches to the delivery of the topic, common difficulties and common misconceptions. A good approach, whenever a formula is taught, a dimensional analysis can be performed to check the validity. Both guides have the same suggested list of Further Resources including some good Nrich resources such as this article. The Springer notes are helpful, with clearly explained examples. The University of Guelph resource seems to have an unwanted full stop at the end of the address – the resource is here.
MathedUp – Mohammed Ladak
On Mohammed Ladak’s ‘MathedUp’ see his A Level Further Maths Takeaway, a wonderful source of exam questions by topic with mark schemes. AQA questions have been used here.
A video of a legacy AQA question is provided, also four challenge questions with mark schemes.
For a very comprehensive set of notes with many fully worked examples and exercises, have a look at Section 47 of the HELM Project which was designed to support the mathematical education of engineering students and includes an extensive collection of notes which include very clear worked examples. For easy access to these resources, the HELM Project Workbooks are hosted by Loughborough University’s Mathematics Learning Support Centre. Alternatively, the complete set is hosted by the Open University. To access the Open University resources you will need to create an account (easy and free), this will also give you access to the numerous free online courses.