Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Invent scenarios which would give rise to these probability density functions.
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you match these equations to these graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
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?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Get further into power series using the fascinating Bessel's equation.
Can you match the charts of these functions to the charts of their integrals?
Can you work out which processes are represented by the graphs?
Can you draw the height-time chart as this complicated vessel fills with water?
Can you find the volumes of the mathematical vessels?
Can you construct a cubic equation with a certain distance between its turning points?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Which units would you choose best to fit these situations?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
When you change the units, do the numbers get bigger or smaller?
Are these estimates of physical quantities accurate?
Which dilutions can you make using only 10ml pipettes?
Build up the concept of the Taylor series
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore the relationship between resistance and temperature
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 meaning of the scalar and vector cross products and see how the two are related.
Get some practice using big and small numbers in chemistry.
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?
Simple models which help us to investigate how epidemics grow and die out.
Go on a vector walk and determine which points on the walk are closest to the origin.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
This problem explores the biology behind Rudolph's glowing red nose.