What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Invent scenarios which would give rise to these probability density functions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Look at the advanced way of viewing sin and cos through their power series.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Why MUST these statistical statements probably be at least a little bit wrong?
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?
Explore the relationship between resistance and temperature
Match the charts of these functions to the charts of their integrals.
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Can you match these equations to these graphs?
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Was it possible that this dangerous driving penalty was issued in error?
Can you construct a cubic equation with a certain distance between its turning points?
Can you draw the height-time chart as this complicated vessel fills with water?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Get some practice using big and small numbers in chemistry.
Can you work out what this procedure is doing?
Can you work out which processes are represented by the graphs?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Work out the numerical values for these physical quantities.
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Build up the concept of the Taylor series
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Estimate areas using random grids
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.
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
A problem about genetics and the transmission of disease.
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.
Go on a vector walk and determine which points on the walk are closest to the origin.
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
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.
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.
Explore how matrices can fix vectors and vector directions.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Investigate circuits and record your findings in this simple introduction to truth tables and logic.