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?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Which line graph, equations and physical processes go together?
Can you construct a cubic equation with a certain distance between its turning points?
Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power series.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Work out the numerical values for these physical quantities.
Use vectors and matrices to explore the symmetries of crystals.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in error?
Which of these infinitely deep vessels will eventually full up?
Which pdfs match the curves?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you work out which processes are represented by the graphs?
Can you make matrices which will fix one lucky vector and crush another to zero?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the properties of perspective drawing.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Get further into power series using the fascinating Bessel's equation.
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Can you work out what this procedure is doing?
How much energy has gone into warming the planet?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Who will be the first investor to pay off their debt?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Are these estimates of physical quantities accurate?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Explore the relationship between resistance and temperature
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.