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