Challenge Level

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Challenge Level

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Challenge Level

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Challenge Level

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Challenge Level

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

Challenge Level

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Challenge Level

Get some practice using big and small numbers in chemistry.

Challenge Level

Analyse these beautiful biological images and attempt to rank them in size order.

Challenge Level

See how the motion of the simple pendulum is not-so-simple after all.

Challenge Level

Work in groups to try to create the best approximations to these physical quantities.

Challenge Level

Work out the numerical values for these physical quantities.

Challenge Level

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Challenge Level

Build up the concept of the Taylor series

Challenge Level

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Challenge Level

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Challenge Level

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Challenge Level

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Challenge Level

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

Challenge Level

How many generations would link an evolutionist to a very distant ancestor?

Challenge Level

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

Challenge Level

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Challenge Level

Have you ever wondered what it would be like to race against Usain Bolt?

Challenge Level

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?