Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Match the descriptions of physical processes to these differential equations.
Get further into power series using the fascinating Bessel's equation.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How would you go about estimating populations of dolphins?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Was it possible that this dangerous driving penalty was issued in error?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Which line graph, equations and physical processes go together?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Why MUST these statistical statements probably be at least a little bit wrong?
How much energy has gone into warming the planet?
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
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?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Estimate areas using random grids
Can you work out which processes are represented by the graphs?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Work out the numerical values for these physical quantities.
Formulate and investigate a simple mathematical model for the design of a table mat.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you make matrices which will fix one lucky vector and crush another to zero?
Use vectors and matrices to explore the symmetries of crystals.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
This problem explores the biology behind Rudolph's glowing red nose.
A problem about genetics and the transmission of disease.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Can you work out what this procedure is doing?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the meaning of the scalar and vector cross products and see how the two are related.