Match the charts of these functions to the charts of their integrals.
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Look at the advanced way of viewing sin and cos through their power series.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you construct a cubic equation with a certain distance between its turning points?
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?
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?
Explore the relationship between resistance and temperature
Get further into power series using the fascinating Bessel's equation.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Can you match these equations to these graphs?
Which of these infinitely deep vessels will eventually full up?
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 error?
Can you draw the height-time chart as this complicated vessel fills with water?
Can you find the volumes of the mathematical vessels?
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?
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.
Work out the numerical values for these physical quantities.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
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 equations.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
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
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
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...
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.
A problem about genetics and the transmission of disease.
Explore how matrices can fix vectors and vector directions.
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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. . . .