Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work out the numerical values for these physical quantities.
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.
Which line graph, equations and physical processes go together?
Get further into power series using the fascinating Bessel's equation.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Formulate and investigate a simple mathematical model for the design of a table mat.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the shape of a square after it is transformed by the action of a matrix.
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 much energy has gone into warming the planet?
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
When you change the units, do the numbers get bigger or smaller?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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?
Invent scenarios which would give rise to these probability density functions.
Explore how matrices can fix vectors and vector directions.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Can you sketch these difficult curves, which have uses in mathematical modelling?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How would you design the tiering of seats in a stadium so that all spectators have a good view?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
This problem explores the biology behind Rudolph's glowing red nose.
Which dilutions can you make using only 10ml pipettes?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Explore the relationship between resistance and temperature
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?