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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
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 how matrices can fix vectors and vector directions.
Which of these infinitely deep vessels will eventually full up?
How do you choose your planting levels to minimise the total loss at harvest time?
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
Match the charts of these functions to the charts of their integrals.
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Can you find the volumes of the mathematical vessels?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
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?
Invent scenarios which would give rise to these probability density functions.
Explore the properties of perspective drawing.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
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.
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Are these estimates of physical quantities accurate?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
This problem explores the biology behind Rudolph's glowing red nose.
Work out the numerical values for these physical quantities.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
Formulate and investigate a simple mathematical model for the design of a table mat.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Build up the concept of the Taylor series
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the relationship between resistance and temperature
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...