Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you construct a cubic equation with a certain distance between its turning points?
Can you 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.
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.
Invent scenarios which would give rise to these probability density functions.
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?
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.
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 match these equations to these graphs?
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
Work out the numerical values for these physical quantities.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
How much energy has gone into warming the planet?
How do you choose your planting levels to minimise the total loss at harvest time?
Which of these infinitely deep vessels will eventually full up?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
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?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Simple models which help us to investigate how epidemics grow and die out.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
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.
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?
Explore how matrices can fix vectors and vector directions.
Formulate and investigate a simple mathematical model for the design of a table mat.
A problem about genetics and the transmission of disease.
Can you work out which processes are represented by the graphs?
Can you find the volumes of the mathematical vessels?
Was it possible that this dangerous driving penalty was issued in error?
Can you draw the height-time chart as this complicated vessel fills with water?
Who will be the first investor to pay off their debt?
Explore the relationship between resistance and temperature
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.
Build up the concept of the Taylor series
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Match the descriptions of physical processes to these differential equations.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Look at the advanced way of viewing sin and cos through their power series.