What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Match the charts of these functions to the charts of their integrals.
How do you choose your planting levels to minimise the total loss
at harvest time?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
Can you sketch these difficult curves, which have uses in
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.
Estimate areas using random grids
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Can you find the volumes of the mathematical vessels?
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. . . .
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Why MUST these statistical statements probably be at least a little
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.
Which dilutions can you make using only 10ml pipettes?
Invent scenarios which would give rise to these probability density functions.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Explore the shape of a square after it is transformed by the action
of a matrix.
Go on a vector walk and determine which points on the walk are
closest to the origin.
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.
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?
Is it really greener to go on the bus, or to buy local?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you make matrices which will fix one lucky vector and crush another to zero?
See how enormously large quantities can cancel out to give a good
approximation to the factorial function.
Explore the meaning of the scalar and vector cross products and see how the two are related.
A problem about genetics and the transmission of disease.
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 would you design the tiering of seats in a stadium so that all spectators have a good view?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Simple models which help us to investigate how epidemics grow and die out.
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?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Explore the properties of perspective drawing.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Get some practice using big and small numbers in chemistry.
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?