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
Monthly Archives: November 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.
