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?
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Why MUST these statistical statements probably be at least a little bit wrong?
Invent scenarios which would give rise to these probability density functions.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
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.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
How do you choose your planting levels to minimise the total loss at harvest time?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you match the charts of these functions to the charts of their integrals?
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Can you match these equations to these graphs?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Who will be the first investor to pay off their debt?
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 sketch these difficult curves, which have uses in mathematical modelling?
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.
Was it possible that this dangerous driving penalty was issued in error?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Use vectors and matrices to explore the symmetries of crystals.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
Which of these infinitely deep vessels will eventually full up?
Work out the numerical values for these physical quantities.
Can you find the volumes of the mathematical vessels?
Explore how matrices can fix vectors and vector directions.
How much energy has gone into warming the planet?
Explore the properties of matrix transformations with these 10 stimulating questions.
Look at the advanced way of viewing sin and cos through their power series.
When you change the units, do the numbers get bigger or smaller?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Get further into power series using the fascinating Bessel's equation.
This problem explores the biology behind Rudolph's glowing red nose.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Build up the concept of the Taylor series
Which units would you choose best to fit these situations?
How efficiently can you pack together disks?
Formulate and investigate a simple mathematical model for the design of a table mat.
Explore the shape of a square after it is transformed by the action of a matrix.