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+.

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 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.