Can you construct a cubic equation with a certain distance between
its turning points?
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 sketch these difficult curves, which have uses in
Can you work out which processes are represented by the graphs?
Can you match these equations to these graphs?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Match the charts of these functions to the charts of their integrals.
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?
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?
Invent scenarios which would give rise to these probability density functions.
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Why MUST these statistical statements probably be at least a little
Explore the relationship between resistance and temperature
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.
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Can you draw the height-time chart as this complicated vessel fills
Which of these infinitely deep vessels will eventually full up?
Which line graph, equations and physical processes go together?
Can you find the volumes of the mathematical vessels?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Go on a vector walk and determine which points on the walk are
closest to the origin.
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.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Use vectors and matrices to explore the symmetries of crystals.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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?
Simple models which help us to investigate how epidemics grow and die out.
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Explore the properties of perspective drawing.
Which dilutions can you make using only 10ml pipettes?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore the shape of a square after it is transformed by the action
of a matrix.
Which pdfs match the curves?
A problem about genetics and the transmission of disease.
Get some practice using big and small numbers in chemistry.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Explore the properties of matrix transformations with these 10 stimulating questions.
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.