Challenge Level

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Challenge Level

Where should runners start the 200m race so that they have all run the same distance by the finish?

Challenge Level

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Challenge Level

How do you choose your planting levels to minimise the total loss at harvest time?

Challenge Level

Was it possible that this dangerous driving penalty was issued in error?

Challenge Level

How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?

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

Here are several equations from real life. Can you work out which measurements are possible from each equation?

Challenge Level

Are these statistical statements sometimes, always or never true? Or it is impossible to say?

Challenge Level

Look at the advanced way of viewing sin and cos through their power series.

Challenge Level

By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

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

Match the descriptions of physical processes to these differential equations.

Challenge Level

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Challenge Level

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

Challenge Level

Can Jo make a gym bag for her trainers from the piece of fabric she has?

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

Challenge Level

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Challenge Level

Simple models which help us to investigate how epidemics grow and die out.

Challenge Level

Formulate and investigate a simple mathematical model for the design of a table mat.

Challenge Level

This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

Challenge Level

Invent scenarios which would give rise to these probability density functions.

Challenge Level

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Challenge Level

Can you work out which processes are represented by the graphs?

Challenge Level

How would you design the tiering of seats in a stadium so that all spectators have a good view?

Challenge Level

Explore the relationship between resistance and temperature

Challenge Level

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

This problem explores the biology behind Rudolph's glowing red nose.

Challenge Level

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

Challenge Level

How would you go about estimating populations of dolphins?

Challenge Level

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

Challenge Level

Work with numbers big and small to estimate and calculate various quantities in physical contexts.

Challenge Level

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

Challenge Level

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Challenge Level

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Challenge Level

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Challenge Level

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Challenge Level

Explore the shape of a square after it is transformed by the action of a matrix.

Challenge Level

Explore the properties of matrix transformations with these 10 stimulating questions.

Challenge Level

Use trigonometry to determine whether solar eclipses on earth can be perfect.