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

You 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.**

On the subject of surds – try **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.

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

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 x ^{4}+4y^{4}?**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.