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?
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 equations.
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?
Why MUST these statistical statements probably be at least a little bit wrong?
Can you sketch these difficult curves, which have uses in mathematical modelling?
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.
How would you go about estimating populations of dolphins?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in error?
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.
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?
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.
Get some practice using big and small numbers in chemistry.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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.
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?
How much energy has gone into warming the planet?
Are these estimates of physical quantities accurate?
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
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
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?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the properties of matrix transformations with these 10 stimulating questions.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the shape of a square after it is transformed by the action of a matrix.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the relationship between resistance and temperature
Simple models which help us to investigate how epidemics grow and die out.
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
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.