Can you find the volumes of the mathematical vessels?
Can you draw the height-time chart as this complicated vessel fills
Which of these infinitely deep vessels will eventually full up?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Can you construct a cubic equation with a certain distance between
its turning points?
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?
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?
Can you work out which processes are represented by the graphs?
Explore the relationship between resistance and temperature
Match the charts of these functions to the charts of their integrals.
Analyse these beautiful biological images and attempt to rank them in size order.
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?
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.
Use vectors and matrices to explore the symmetries of crystals.
Starting with two basic vector steps, which destinations can you
reach on a vector walk?
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little
How do you choose your planting levels to minimise the total loss
at harvest time?
Which pdfs match the curves?
Can you make matrices which will fix one lucky vector and crush another to zero?
Explore the properties of matrix transformations with these 10 stimulating questions.
Formulate and investigate a simple mathematical model for the design of a table mat.
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Explore the properties of perspective drawing.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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. . . .
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Invent scenarios which would give rise to these probability density functions.
Which countries have the most naturally athletic populations?
Go on a vector walk and determine which points on the walk are
closest to the origin.
Can you sketch these difficult curves, which have uses in
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?
Explore how matrices can fix vectors and vector directions.
Explore the meaning of the scalar and vector cross products and see
how the two are related.
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.
In this short problem, try to find the location of the roots of
some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential
Look at the advanced way of viewing sin and cos through their power series.
Explore the possibilities for reaction rates versus concentrations
with this non-linear differential equation
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Who will be the first investor to pay off their debt?