Which line graph, equations and physical processes go together?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Was it possible that this dangerous driving penalty was issued in error?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Why MUST these statistical statements probably be at least a little bit wrong?
Match the descriptions of physical processes to these differential equations.
Build up the concept of the Taylor series
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use vectors and matrices to explore the symmetries of crystals.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
This problem explores the biology behind Rudolph's glowing red nose.
Work out the numerical values for these physical quantities.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
Can you find the volumes of the mathematical vessels?
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you match these equations to these graphs?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Get some practice using big and small numbers in chemistry.
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Which units would you choose best to fit these situations?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
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?
When you change the units, do the numbers get bigger or smaller?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
How would you go about estimating populations of dolphins?
Explore the shape of a square after it is transformed by the action of a matrix.
How do you choose your planting levels to minimise the total loss at harvest time?