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

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

Which of these infinitely deep vessels will eventually full up?

Use vectors and matrices to explore the symmetries of crystals.

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

Get further into power series using the fascinating Bessel's equation.

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

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

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

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

Build up the concept of the Taylor series

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

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

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

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

Which line graph, equations and physical processes go together?

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

Work out the numerical values for these physical quantities.

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

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

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?

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

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

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

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

Explore the relationship between resistance and temperature

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?

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

Get some practice using big and small numbers in chemistry.

Match the descriptions of physical processes to these differential equations.

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

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

When you change the units, do the numbers get bigger or smaller?

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

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

Which units would you choose best to fit these situations?