An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
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.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Where should runners start the 200m race so that they have all run the same distance by the finish?
Which pdfs match the curves?
Get further into power series using the fascinating Bessel's equation.
How efficiently can you pack together disks?
Are these estimates of physical quantities accurate?
Look at the advanced way of viewing sin and cos through their power series.
Explore the shape of a square after it is transformed by the action of a matrix.
Use vectors and matrices to explore the symmetries of crystals.
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?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Build up the concept of the Taylor series
Analyse these beautiful biological images and attempt to rank them in size order.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Explore the properties of matrix transformations with these 10 stimulating questions.
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Is it really greener to go on the bus, or to buy local?
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?
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.
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 make matrices which will fix one lucky vector and crush another to zero?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
A problem about genetics and the transmission of disease.
Work out the numerical values for these physical quantities.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
Can you work out what this procedure is doing?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you work out which processes are represented by the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Explore the properties of perspective drawing.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Have you ever wondered what it would be like to race against Usain Bolt?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the relationship between resistance and temperature