Can you sketch these difficult curves, which have uses in mathematical modelling?
Build up the concept of the Taylor series
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?
Use vectors and matrices to explore the symmetries of crystals.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Look at the advanced way of viewing sin and cos through their power series.
Can you work out which processes are represented by the graphs?
Can you match these equations to these graphs?
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.
Can you construct a cubic equation with a certain distance between its turning points?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which line graph, equations and physical processes go together?
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Is it really greener to go on the bus, or to buy local?
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.
Work out the numerical values for these physical quantities.
Explore how matrices can fix vectors and vector directions.
Formulate and investigate a simple mathematical model for the design of a table mat.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you work out what this procedure is doing?
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the properties of perspective drawing.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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?
Invent scenarios which would give rise to these probability density functions.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
A problem about genetics and the transmission of disease.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Explore the properties of matrix transformations with these 10 stimulating questions.
How much energy has gone into warming the planet?
Use your skill and judgement to match the sets of random data.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
How do you choose your planting levels to minimise the total loss at harvest time?