Can you construct a cubic equation with a certain distance between its turning points?
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 find the volumes of the mathematical vessels?
Can you match the charts of these functions to the charts of their integrals?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
Was it possible that this dangerous driving penalty was issued in error?
Go on a vector walk and determine which points on the walk are closest to the origin.
Which pdfs match the curves?
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?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Explore how matrices can fix vectors and vector directions.
Use vectors and matrices to explore the symmetries of crystals.
Match the descriptions of physical processes to these differential equations.
This problem explores the biology behind Rudolph's glowing red nose.
Are these estimates of physical quantities accurate?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
Analyse these beautiful biological images and attempt to rank them in size order.
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?
Explore the properties of perspective drawing.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Explore the relationship between resistance and temperature
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.
Can you work out which processes are represented by the 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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you draw the height-time chart as this complicated vessel fills with water?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Get further into power series using the fascinating Bessel's equation.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
A problem about genetics and the transmission of disease.
Invent scenarios which would give rise to these probability density functions.
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?