Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Invent scenarios which would give rise to these probability density functions.
Why MUST these statistical statements probably be at least a little bit wrong?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which line graph, equations and physical processes go together?
Was it possible that this dangerous driving penalty was issued in error?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
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.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Get further into power series using the fascinating Bessel's equation.
Match the charts of these functions to the charts of their integrals.
Look at the advanced way of viewing sin and cos through their power series.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
How much energy has gone into warming the planet?
Match the descriptions of physical processes to these differential equations.
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.
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.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Build up the concept of the Taylor series
Explore the relationship between resistance and temperature
Simple models which help us to investigate how epidemics grow and die out.
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.
Analyse these beautiful biological images and attempt to rank them in size order.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Work out the numerical values for these physical quantities.
Get some practice using big and small numbers in chemistry.
Can you work out what this procedure is doing?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which of these infinitely deep vessels will eventually full up?
Formulate and investigate a simple mathematical model for the design of a table mat.
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. . . .
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Can you sketch these difficult curves, which have uses in mathematical modelling?
How would you go about estimating populations of dolphins?
How efficiently can you pack together disks?
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.
Which units would you choose best to fit these situations?
Explore the shape of a square after it is transformed by the action of a matrix.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
A problem about genetics and the transmission of disease.