Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Who will be the first investor to pay off their debt?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
How much energy has gone into warming the planet?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Get some practice using big and small numbers in chemistry.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Use vectors and matrices to explore the symmetries of crystals.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work out the numerical values for these physical quantities.
Which pdfs match the curves?
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 biological contexts.
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the properties of matrix transformations with these 10 stimulating questions.
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?
Which line graph, equations and physical processes go together?
Explore how matrices can fix vectors and vector directions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore the relationship between resistance and temperature
Explore the properties of perspective drawing.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Analyse these beautiful biological images and attempt to rank them in size order.
Why MUST these statistical statements probably be at least a little bit wrong?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Invent scenarios which would give rise to these probability density functions.
Explore the shape of a square after it is transformed by the action of a matrix.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Was it possible that this dangerous driving penalty was issued in error?
When you change the units, do the numbers get bigger or smaller?
Match the charts of these functions to the charts of their integrals.
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?