Can you match these equations to these graphs?
Can you find the volumes of the mathematical vessels?
Can you work out which processes are represented by the graphs?
Can you sketch these difficult curves, which have uses in mathematical modelling?
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?
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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?
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.
How do you choose your planting levels to minimise the total loss at harvest time?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Which pdfs match the curves?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Get further into power series using the fascinating Bessel's equation.
Which line graph, equations and physical processes go together?
Which of these infinitely deep vessels will eventually full up?
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.
Who will be the first investor to pay off their debt?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Look at the advanced way of viewing sin and cos through their power series.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Match the descriptions of physical processes to these differential equations.
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Build up the concept of the Taylor series
Explore the shape of a square after it is transformed by the action of a matrix.
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Explore how matrices can fix vectors and vector directions.
Get some practice using big and small numbers in chemistry.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
A problem about genetics and the transmission of disease.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Invent scenarios which would give rise to these probability density functions.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Work out the numerical values for these physical quantities.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
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.
How much energy has gone into warming the planet?
When you change the units, do the numbers get bigger or smaller?
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
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.
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?
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?