Can you construct a cubic equation with a certain distance between its turning points?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Match the charts of these functions to the charts of their integrals.
Can you find the volumes of the mathematical vessels?
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 do you choose your planting levels to minimise the total loss at harvest time?
Which pdfs match the curves?
Which of these infinitely deep vessels will eventually full up?
Are these estimates of physical quantities accurate?
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?
How would you go about estimating populations of dolphins?
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.
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the properties of perspective drawing.
Go on a vector walk and determine which points on the walk are closest to the origin.
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 calulate various quantities in biological contexts.
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?
Use vectors and matrices to explore the symmetries of crystals.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Who will be the first investor to pay off their debt?
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
A problem about genetics and the transmission of disease.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little bit wrong?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Which line graph, equations and physical processes go together?
Invent scenarios which would give rise to these probability density functions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
This problem explores the biology behind Rudolph's glowing red nose.
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.
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?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Explore how matrices can fix vectors and vector directions.
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 your skill and judgement to match the sets of random data.
Can you match these equations to these graphs?
Get further into power series using the fascinating Bessel's equation.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
Estimate areas using random grids
Can you draw the height-time chart as this complicated vessel fills with water?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Formulate and investigate a simple mathematical model for the design of a table mat.