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?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Can you match the charts of these functions to the charts of their integrals?
Can you find the volumes of the mathematical vessels?
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?
Which pdfs match the curves?
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.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Are these estimates of physical quantities accurate?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the shape of a square after it is transformed by the action of a matrix.
How would you go about estimating populations of dolphins?
How much energy has gone into warming the planet?
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.
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
Who will be the first investor to pay off their debt?
Match the descriptions of physical processes to these differential equations.
Explore the properties of perspective drawing.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you match these equations to these graphs?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Invent scenarios which would give rise to these probability density functions.
Can you construct a cubic equation with a certain distance between its turning points?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Was it possible that this dangerous driving penalty was issued in error?
Get further into power series using the fascinating Bessel's equation.
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?
A problem about genetics and the transmission of disease.
Can you work out which processes are represented by the graphs?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the relationship between resistance and temperature
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Build up the concept of the Taylor series
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.
Here are several equations from real life. Can you work out which measurements are possible from each equation?