Match the charts of these functions to the charts of their integrals.
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
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?
Invent scenarios which would give rise to these probability density functions.
Can you sketch these difficult curves, which have uses in
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which of these infinitely deep vessels will eventually full up?
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in
Get further into power series using the fascinating Bessel's equation.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
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.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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?
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential
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
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.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Go on a vector walk and determine which points on the walk are
closest to the origin.
When you change the units, do the numbers get bigger or smaller?
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 meaning of the scalar and vector cross products and see how the two are related.
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.
A problem about genetics and the transmission of disease.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Simple models which help us to investigate how epidemics grow and die out.
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.
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.
Explore the relationship between resistance and temperature
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...