### Powerful Quadratics

This comes in two parts, with the first being less fiendish than the second. Itâ€™s great for practising both quadratics and laws of indices, and you can get a lot from making sure that you find all the solutions. For a real challenge (requiring a bit more knowledge), you could consider finding the complex solutions.

### Discriminating

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

### Factorisable Quadratics

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.

# A Big Power

##### Age 16 to 18Challenge Level

This resource is from the Underground Mathematics team.

$2^{2000}$ is a big number!

Here are three questions about it.

1.  Without using a calculator, estimate the size of $2^{2000}$.

You might like to give your answer as a power of $10$.

2.  The first two digits of $2^{16}=65536$ are $65$.

What are the first five digits of $2^{2000}$?

You are welcome to use your calculator to help you for this one!

3.  The final digit of $2^{16}=65536$ is $6$, and the final two digits
are $36$.

What is the final digit of $2^{2000}$?

And what are the final two digits?

This is an Underground Mathematics resource.

Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.

Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.