Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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?
Invent scenarios which would give rise to these probability density functions.
How is the length of time between the birth of an animal and the birth of its great great ... great grandparent distributed?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Was it possible that this dangerous driving penalty was issued in error?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Who will be the first investor to pay off their debt?
Get some practice using big and small numbers in chemistry.
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
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.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
Use vectors and matrices to explore the symmetries of crystals.
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
A problem about genetics and the transmission of disease.
Get further into power series using the fascinating Bessel's equation.
Can you match the charts of these functions to the charts of their integrals?
Can you draw the height-time chart as this complicated vessel fills with water?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
How do you choose your planting levels to minimise the total loss at harvest time?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
Which pdfs match the curves?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you match these equations to these graphs?
Explore the properties of perspective drawing.
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.
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.
Simple models which help us to investigate how epidemics grow and die out.
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.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Are these estimates of physical quantities accurate?
When you change the units, do the numbers get bigger or smaller?
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which units would you choose best to fit these situations?
Formulate and investigate a simple mathematical model for the design of a table mat.
Looking at small values of functions. Motivating the existence of the Taylor expansion.