Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Which line graph, equations and physical processes go together?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How much energy has gone into warming the planet?
Was it possible that this dangerous driving penalty was issued in error?
This problem explores the biology behind Rudolph's glowing red nose.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Get further into power series using the fascinating Bessel's equation.
Explore how matrices can fix vectors and vector directions.
Which pdfs match the curves?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work out the numerical values for these physical quantities.
Can you match these equations to these graphs?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you find the volumes of the mathematical vessels?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Use vectors and matrices to explore the symmetries of crystals.
When you change the units, do the numbers get bigger or smaller?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you make matrices which will fix one lucky vector and crush another to zero?
Get some practice using big and small numbers in chemistry.
Build up the concept of the Taylor series
Match the descriptions of physical processes to these differential equations.
Invent scenarios which would give rise to these probability density functions.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.
Who will be the first investor to pay off their debt?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which of these infinitely deep vessels will eventually full up?
Can you construct a cubic equation with a certain distance between its turning points?
Explore the relationship between resistance and temperature
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
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?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?