# Live Problems - Stage 4 & 5

Each time you visit the NRICH site there will be some activities which are 'live'. That means we are inviting you to send us your solutions and we will publish a selection of them, along with your name and school. If you'd like to read more about what we're looking for, read this short article.

### Stage 4 & 5 Toughnutslive

##### Stage: 5 Challenge Level:

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

### Discriminatinglive

##### Stage: 5

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

##### Stage: 5

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.

##### Stage: 5

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

### Picture the Process Ilive

##### Stage: 5

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.

### Approaching Asymptoteslive

##### Stage: 5

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.

### Two-way Functionslive

##### Stage: 5

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.

### Factorial Fragmentslive

##### Stage: 5 Challenge Level:

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

### The Quintessential Prooflive

##### Stage: 5 Challenge Level:

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

##### Stage: 5 Challenge Level:

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

### Finding Circleslive

##### Stage: 5 Challenge Level:

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?

### The Circle of Apollonius... Coordinate Editionlive

##### Stage: 5 Challenge Level:

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

### Can You Find... Trigonometry Editionlive

##### Stage: 5 Challenge Level:

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

### Equation or Identity (1)live

##### Stage: 5 Challenge Level:

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

### Equation or Identity (2)live

##### Stage: 5 Challenge Level:

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

### Have a Sinelive

##### Stage: 5 Challenge Level:

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