Match the charts of these functions to the charts of their integrals.
Match the descriptions of physical processes to these differential
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?
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 sketch these difficult curves, which have uses in
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?
Why MUST these statistical statements probably be at least a little
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?
Get further into power series using the fascinating Bessel's equation.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Was it possible that this dangerous driving penalty was issued in
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which of these infinitely deep vessels will eventually full up?
How much energy has gone into warming the planet?
Estimate areas using random grids
Look at the advanced way of viewing sin and cos through their power series.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
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.
If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.
Are these estimates of physical quantities accurate?
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 make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of perspective drawing.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Analyse these beautiful biological images and attempt to rank them in size order.
This problem explores the biology behind Rudolph's glowing red
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?
Explore the relationship between resistance and temperature
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.
Simple models which help us to investigate how epidemics grow and die out.
Can you work out what this procedure is doing?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...