Estimate areas using random grids
A problem about genetics and the transmission of disease.
Use your skill and judgement to match the sets of random data.
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
How do you choose your planting levels to minimise the total loss
at harvest time?
Match the charts of these functions to the charts of their integrals.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you find the volumes of the mathematical vessels?
Use vectors and matrices to explore the symmetries of crystals.
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?
Which line graph, equations and physical processes go together?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Which of these infinitely deep vessels will eventually full up?
Can you construct a cubic equation with a certain distance between
its turning points?
Which pdfs match the curves?
Why MUST these statistical statements probably be at least a little
Which countries have the most naturally athletic populations?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
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?
Simple models which help us to investigate how epidemics grow and die out.
Explore the properties of perspective drawing.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you draw the height-time chart as this complicated vessel fills
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Invent scenarios which would give rise to these probability density functions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Can you sketch these difficult curves, which have uses in
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
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?
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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.