These Stage 4 and 5 problems haven't been solved yet. Can you be the first?

You're invited to decide whether statements about the number of solutions of a quadratic equation is always, sometimes or never true.

This will encourage you to think about whether all quadratics can be factorised and to develop a better understanding of the effect that changing the coefficients has on the factorised form.

In this activity you will need to work in a group to connect different representations of quadratics.

What can you say about this graph? A number of questions have been suggested to help you look at the graph in different ways. Use these to help you make sense of this and similar graphs.

How does the temperature of a cup of tea behave over time? What is the radius of a spherical balloon as it is inflated? What is the distance fallen by a parachutist after jumping out of a plane? After sketching graphs for these and other real-world processes, you are offered a selection of equations to match to these graphs and processes.

Can you describe what an asymptote is? This resource includes a list of statements about asymptotes and a collection of graphs, some of which have asymptotes. Use the graphs to help you decide whether you agree with the statements about asymptotes.

This gives you an opportunity to explore roots and asymptotes of functions, both by identifying properties that functions have in common and also by trying to find functions that have particular properties. You may like to use the list of functions in the Hint, which includes enough functions to complete the table plus some extras.You might like to work on this problem in a pair or small group, or to compare your table to someone else's to see where you have used the same functions and where not.

Here you have an expression containing logs and factorials! What can you do with it?

In this resource, the aim is to understand a fundamental proof of Pythagoras's Theorem.

A lune is the area left when part of a circle is cut off by another circle. Can you work out the area?

Can you find the centre and equation of a circle given a number of points on the circle? When is it possible and when is it not?

Can you sketch and then find an equation for the locus of a point based on its distance from two fixed points?

What graphs can you make by transforming sine, cosine and tangent graphs?

Which of these equations concerning the angles of triangles are always true?

Here are some more triangle equations. Which are always true?

There's much more to trigonometry than sin, cos and tan...