Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
Which dilutions can you make using only 10ml pipettes?
Explore the properties of matrix transformations with these 10 stimulating questions.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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 physical contexts.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
How much energy has gone into warming the planet?
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Get further into power series using the fascinating Bessel's equation.
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?
Which line graph, equations and physical processes go together?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Formulate and investigate a simple mathematical model for the design of a table mat.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Is it really greener to go on the bus, or to buy local?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Work out the numerical values for these physical quantities.
When you change the units, do the numbers get bigger or smaller?
Explore the relationship between resistance and temperature
Are these estimates of physical quantities accurate?
Analyse these beautiful biological images and attempt to rank them in size order.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Which units would you choose best to fit these situations?
Build up the concept of the Taylor series
Use vectors and matrices to explore the symmetries of crystals.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore the shape of a square after it is transformed by the action of a matrix.
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 meaning behind the algebra and geometry of matrices with these 10 individual problems.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Go on a vector walk and determine which points on the walk are closest to the origin.
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.
Which pdfs match the curves?
Was it possible that this dangerous driving penalty was issued in error?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
How do you choose your planting levels to minimise the total loss at harvest time?