Underground Mathematics

exponentials
For many challenging questions to really get you thinking, try the brilliant Underground Mathematics site. You can follow them on Facebook or Twitter too.

underground-mathematics

thinkig-about-algebraYou can search by Station, suppose you want to practise your Algebra – try the Thinking About Algebra Station for example where you will find everything from Equation Sudoku to some challenging Surd manipulations.
nested-surds

On the subject of surds – try Scary Sum!
scary-sum

If you create a (free) account you can save and categorise your favourite resources.

There are many Underground Mathematics Resource Types. Try the Review Questions for example, which in the words of the Underground Maths Team:

These are questions designed to test students’ understanding of one or more topics and to exercise their problem-solving skills. In many cases they can also be used as a classroom resource to help teach concepts and methods. They are mostly drawn from past examination questions and have been chosen as ones that are interesting in nature and require non-routine thinking. The hints and solutions are designed to explain the reasoning and highlight connections as well as giving the answer. In many cases, alternative methods or solutions are presented.

review-question-types

Note the various question types available; these include very challenging questions for students age 16+.

oxford-mat-example

Select image for question & solution


The Oxford MAT collection includes an extensive selection of Multiple Choice Questions.

O/AO-level questions are included. These questions provide excellent challenge for sudents aspiring to the top grades for examinations taken at age 15-16 and beyond..

Can we fully factorise x4+4y4?
Starts with a Show that….
We could get very sophisticated and look at those quadratic factors too; useful for those studying the Level 2 Further Mathematics Qualification.

Can we simplify these algebraic fractions?
Review algebraic fractions

Can we simplify these simultaneous equations of degree 1 and 2?
Solve simultaneous equations. We will need to factorise a quadratic in this problem with a coefficient which is not 1 for the square term. My students and I are fans of the Box Method where a factorisation cannot easily be done by inspection.

 

Brilliant

Signing up to Brilliant (including an easy option for sign in for Facebook users) will allow you to join an international community and get free weekly, personalised problems. Questions at various levels are available, from problems suitable for younger students:

Brilliant problem

To improve your problem solving skills you could try the Techniques Trainer. For those of you who participate in Mathematics challenges you may well find this a valuable resource.

NRICH – new look

I have recommended Nrich who publish new problems to really make you think every month on the Challenges page here. The site has been updated recently and now has a great new look and is easy to navigate. There is a clear guide for studentsYou can sign up for an Nrich student newsletter if you want to be notified of new developments on the site. If you have not tried Nrich problems before you may find their recommended starter problems good to try.

On the new site just select your chosen home under the Student list. You could then for example search for activities by curriculum topic, for example look at this collection for Lower Secondary. (Note the collections available on the top right of each student home).

Why not try a problem and send in your solution to NRICH?