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