Which line graph, equations and physical processes go together?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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?
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.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Can you match these equations to these graphs?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Can you work out which processes are represented by the graphs?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Estimate areas using random grids
Can you find the volumes of the mathematical vessels?
Can you construct a cubic equation with a certain distance between its turning points?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Get some practice using big and small numbers in chemistry.
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
How much energy has gone into warming the planet?
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.
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.
Explore the shape of a square after it is transformed by the action of a matrix.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Is it really greener to go on the bus, or to buy local?
Can you make matrices which will fix one lucky vector and crush another to zero?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Use vectors and matrices to explore the symmetries of crystals.
Which pdfs match the curves?
Can you draw the height-time chart as this complicated vessel fills with water?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Which dilutions can you make using only 10ml pipettes?
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Formulate and investigate a simple mathematical model for the design of a table mat.
Use your skill and judgement to match the sets of random data.