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?
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
Invent scenarios which would give rise to these probability density functions.
Can you find the volumes of the mathematical vessels?
Can you sketch these difficult curves, which have uses in
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?
Can you construct a cubic equation with a certain distance between
its turning points?
Explore the relationship between resistance and temperature
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?
Get further into power series using the fascinating Bessel's equation.
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.
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Can you draw the height-time chart as this complicated vessel fills
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?
Was it possible that this dangerous driving penalty was issued in
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
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.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which line graph, equations and physical processes go together?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Build up the concept of the Taylor series
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.
A problem about genetics and the transmission of disease.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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 meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore the properties of matrix transformations with these 10 stimulating questions.
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
Explore the shape of a square after it is transformed by the action
of a matrix.
Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.
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?
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. . . .
How would you design the tiering of seats in a stadium so that all spectators have a good view?