Can you sketch these difficult curves, which have uses in mathematical modelling?

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

Which line graph, equations and physical processes go together?

Can you make matrices which will fix one lucky vector and crush another to zero?

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

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?

Use vectors and matrices to explore the symmetries of crystals.

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

Can you construct a cubic equation with a certain distance between its turning points?

Explore the meaning of the scalar and vector cross products and see how the two are related.

Build up the concept of the Taylor series

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

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

Why MUST these statistical statements probably be at least a little bit wrong?

Which of these infinitely deep vessels will eventually full up?

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

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

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

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

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

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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

Work out the numerical values for these physical quantities.

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

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

Get some practice using big and small numbers in chemistry.

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

Go on a vector walk and determine which points on the walk are closest to the origin.

See how enormously large quantities can cancel out to give a good approximation to the factorial function.

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

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

Can you match the charts of these functions to the charts of their integrals?

Can you draw the height-time chart as this complicated vessel fills with water?

Explore the relationship between resistance and temperature

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

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

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

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

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?

Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.

Match the descriptions of physical processes to these differential equations.

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