Match the charts of these functions to the charts of their integrals.
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?
Match the descriptions of physical processes to these differential
Can you construct a cubic equation with a certain distance between
its turning points?
Can you sketch these difficult curves, which have uses in
Why MUST these statistical statements probably be at least a little
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?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you find the volumes of the mathematical vessels?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Was it possible that this dangerous driving penalty was issued in
How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Get further into power series using the fascinating Bessel's equation.
Which of these infinitely deep vessels will eventually full up?
Get some practice using big and small numbers in chemistry.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Which line graph, equations and physical processes go together?
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 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.
Estimate areas using random grids
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
When you change the units, do the numbers get bigger or smaller?
Use vectors and matrices to explore the symmetries of crystals.
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Go on a vector walk and determine which points on the walk are
closest to the origin.
A problem about genetics and the transmission of disease.
Simple models which help us to investigate how epidemics grow and die out.
Explore the relationship between resistance and temperature
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Explore the properties of perspective drawing.
This problem explores the biology behind Rudolph's glowing red nose.
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...
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.