Estimate areas using random grids
Are these statistical statements sometimes, always or never true?
Or it is impossible to say?
Why MUST these statistical statements probably be at least a little
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
Invent scenarios which would give rise to these probability density functions.
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?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Can you sketch these difficult curves, which have uses in
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore the properties of perspective drawing.
Explore the shape of a square after it is transformed by the action
of a matrix.
Explore the properties of matrix transformations with these 10 stimulating questions.
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Which pdfs match the curves?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Use vectors and matrices to explore the symmetries of crystals.
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?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the meaning behind the algebra and geometry of matrices
with these 10 individual problems.
Explore how matrices can fix vectors and vector directions.
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
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 suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
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.
Which dilutions can you make using only 10ml pipettes?
How do you choose your planting levels to minimise the total loss
at harvest time?
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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...
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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 much energy has gone into warming the planet?
Use your skill and judgement to match the sets of random data.
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
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
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