Get some practice using big and small numbers in chemistry.
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How much energy has gone into warming the planet?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
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?
Which units would you choose best to fit these situations?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
When you change the units, do the numbers get bigger or smaller?
Build up the concept of the Taylor series
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Which dilutions can you make using only 10ml pipettes?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
This problem explores the biology behind Rudolph's glowing red nose.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Which line graph, equations and physical processes go together?
Match the descriptions of physical processes to these differential equations.
Analyse these beautiful biological images and attempt to rank them in size order.
Use vectors and matrices to explore the symmetries of crystals.
Is it really greener to go on the bus, or to buy local?
Why MUST these statistical statements probably be at least a little bit wrong?
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Have you ever wondered what it would be like to race against Usain Bolt?
Which pdfs match the curves?
Who will be the first investor to pay off their debt?
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Can you find the volumes of the mathematical vessels?
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.