What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you match the charts of these functions to the charts of their integrals?
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
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?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you match these equations to these graphs?
Can you find the volumes of the mathematical vessels?
How do you choose your planting levels to minimise the total loss at harvest time?
Which pdfs match the curves?
Which line graph, equations and physical processes go together?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Use vectors and matrices to explore the symmetries of crystals.
Can you make matrices which will fix one lucky vector and crush another to zero?
How efficiently can you pack together disks?
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.
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.
Explore how matrices can fix vectors and vector directions.
Can you work out which processes are represented by the graphs?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Which of these infinitely deep vessels will eventually full up?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Who will be the first investor to pay off their debt?
Match the descriptions of physical processes to these differential equations.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
This problem explores the biology behind Rudolph's glowing red nose.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Which units would you choose best to fit these situations?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Look at the advanced way of viewing sin and cos through their power series.
Was it possible that this dangerous driving penalty was issued in error?
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 biological contexts.
Get further into power series using the fascinating Bessel's equation.