An annual job – I have checked and updated both my Maths Advent Calendars and Christmas Mathematics resources collections. Both collections are easily accessible from the Featured Posts menu on the right-hand side.
Advent & Christmas 2024
‘Hidden’ Quadratic Equations
Having had several student queries on solving ‘hidden’ quadratic equations, I thought I would note some great resources available.
Firstly two videos on TL Maths, 3.15 and 3.16
From Dr Austin Maths try this practice exercise of 7 questions.
The resources on Dr Frost Maths are so good; I love the new slideshow format with the slide types, each created for specific pedagogical purposes.
Scroll down to Factorising and Solving Hidden Quadratics.
From Exam Solutions, a tutorial, Solving quadratic equations in some function of x is available.
Try this Hidden Quadratics activity from Swinton Maths:
A fill in the blank activity for hidden quadratics. All the quadratics are monic and factorisable, and the index equations have integer solutions (so no logarithms needed).
And finally, we could use a favourite Underground Maths task to spot the hidden quadratics!
To log or not to log – Underground Maths
A favourite Underground Maths resource I have used many times – To log or not to log? This has worked really well every time I have used it. The activity requires students to think about the methods which could be used to solve the various equations. In addition to working on indices and logarithms, I have always found that this task has exposed some misconceptions, with students trying to invent some new and invalid laws of logarithms!
This problem is classified as a Problem Requiring Decisions.
For more favourite Underground Maths tasks, see the Underground Maths series of pages.
We could, of course, illustrate these equations graphically; I looked at the solutions of the equation 4x4 −13x2 + 9 = 0 with a student on Desmos.
November 2024 – Paper 3
We now have suggestions for priority topics for revision (Edexcel Foundation and Higher) from both 1st Class Maths and On Maths. From OnMaths, we also have topic revision questions and complete practice to try online where each question is marked as students try it. (Subscribers can download pdf files).
There are many revision resources available in this collection.
From 1st Class Maths, Key topic suggestions are available for Paper 3 revision.
At the time of writing, these are for Edexcel Foundation and Edexcel Higher.
Suggested topics for revision for Edexcel Paper 3 Foundation and Higher are also available from on maths. Practice questions are available for each suggested topic. Subscribers can download pdf files, but free access is available for all to practice online. For example, choose the Topic paper, Accuracy Error Intervals for a short paper.
Practice Papers and video walkthroughs from OnMaths for Paper 3 are available for Foundation and higher.
Graph Sketching
Students need to be familiar with the behaviour of all the functions they meet and for older students be able to sketch those functions.
To start, a look at the various functions students meet for GCSE.
On Dr Austin Maths, we have plenty of her lovely exercises on Graphs, under Algebra, we have Coordinates and Linear Graphs and Non-Linear Graphs which includes transformations of graphs.
Third Space Learning has a selection of clear examples on sketching graphs.
Third Space Learning has a selection of clear examples on sketching graphs.
From AMSP, see Teaching and learning resources for 11-16 maths: Algebra. Scroll down to Graphs for resources 9 – 16.
For GCSE (age14-16) on Transum Mathematics, there is an extensive library of self-checking exercises including Name that Graph which offers great practice in recognising functions.
Desmos is ideal for exploration; students can add sliders to explore the possible shapes of functions.
Nrich have several problems on Graph sketching, offering a variety of challenge levels.
This post, Transformations of Functions includes many excellent resources to help with understanding the effect of transformations and graphs.
For A Level students, on MadAsMaths, you will find great resources for lots of practice with graph sketching, all with answers provided. Hover on Maths Booklets from the top menu for a dropdown menu of questions available by topic. These are pdf files; increase the magnification to view the solutions.
Maths Booklets Basic Topics – Various includes:
And under Standard Topics – Various, we have
- Curve Sketching Exam Questions
- Transformation of Graphs – Student version
- Transformation of Graphs Practice- solutions
- Transformations of Graphs Exam Questions
For A Level students on TL Maths, this very useful video shows students graphs they must know how to sketch.
For students taking STEP examinations, from the University of Cambridge Curve STEP Support Programme, see STEP 2 Curve Sketching.
Mechanics
Many resources for teaching Mechanics can be found on my A Level teaching resources page, this post highlights just some of the useful Mechanics examples and notes.
- Notes and Examples
- Knowledge Organisers
- Erica’s Errors – Mechanics
- Dr Frost Maths – Mechanics
- Dr Austin Maths A Level
- Stoke Maths
- PhET Simulations
- Mechanics Calculators
- Edexcel Scheme of work and use of Technology
- Further Maths – Dimensional Analysis
Notes and Examples
From the excellent MathsBox site, see: A Level Maths Mechanics Revision Notes. The notes have a very comprehensive set of clear and well-explained examples.
Also available are Pure and Statistics notes.
Mathsbox has many free samples to try, easily one of the best value subscription sites around in my opinion.
Resources for Mechanics from mathcentre.
Forces and Newton’s Laws of Motion
Hodder My Revision Notes
You might find these free Hodder Revision Resources useful; questions and fully worked solutions for each section of the book are provided, and whilst the documents refer to the books, they are complete in themselves. The free document pdf file) has questions with fully worked answers.
Hodder – My Revision Notes series
- AQA A Level Maths (Pure)
- AQA A Level Maths (Applied)
- Edexcel A Level Maths (Pure)
- Edexcel A Level Maths (Applied)
- OCR B (MEI) A Level Mathematics (Pure)
- OCR B (MEI) A Level Mathematics (Applied)
- OCR (A) A Level Mathematics (Applied)
From CIMT, the A Level Mathematics course material includes a section on Mechanics. These topics are mostly aimed at the Mechanics found in Further Maths specifications.
A Level Knowledge Organisers
This page includes a set of knowledge organisers from Lucyjc. These resources are available free on TES Resources: Mechanics. All include Key Words and Definitions and What Do I Need to Know sections.
From an absolute favourite resource Author – Andy Lutwyche, (search his resources by newest on TES). Have a look at his excellent Erica’s Errors series which included Mechanics.
Dr Frost Maths – Key Skills
You will find an excellent collection of practice questions – try these key skills for Mechanics.
Select All Skills, and see the Mechanics menu. The resources for each section include key skills.
Dr Frost Teaching resources (see Mechanics index)
Select All Skills, and see the Mechanics menu. The resources for each section include teaching resources.
The latest resources are so good. Look at this PowePoint on Displacement-Time & Velocity-Time Graphs, for example. Animations help to explain the concepts.
There is now an A Level section on Dr Austin Maths with a growing collection of resources. We see some useful introductory resources for Mechanics.
From Stoke Maths comes very attractively presented high-quality resources. Look under A Level on the Padlet and we can see several sets of resources including A Level Starters and Revision questions, and Spot the Mistake resources for Year 1 and Year 2 content. Looking at the Spot the Mistake PowerPoints for example, as you can see in the image there is a great collection of questions that include full answers. It’s brilliant to see a Mechanics collection.
The revision question starters provide very useful question sets.
This can be also be found in my Starters collection under Advanced Starters.
PhET Simulations
PhET Sims Forces and Motion: Basics
From PhET Interactive Simulations, see
PhET Balancing Act working nicely on my phone!
Staying with Mechanics, one of my favourites available in the HTML5 collection: Projectile Motion.
Calculators
Elastic Collisions Calculators, Projectiles, Periodic Motion
Projectile Motion Calculator from Mr Mont.com
Edexcel’s latest Scheme of Work document now includes many links for the use of technology as well as all the very useful notes for teachers. A link from the Mechanics notes led to these CG50 Mechanics resources.
Edexcel’s GeoGebra resources include a small number for Mechanics at A level, and more for Further Maths.
It is good to see all the GeoGebra resources for Further Mathematics, for example, check Explore toppling and sliding using GeoGebra.
Dimensional Analysis
AQA: Optional application 1 – mechanics Assessed at AS and A Level
My post on Dimensional Analysis for Further Maths includes many resources for teaching this topic.