Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
This problem explores the biology behind Rudolph's glowing red nose.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
Can you match these equations to these graphs?
How would you go about estimating populations of dolphins?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
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?
Was it possible that this dangerous driving penalty was issued in error?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Explore how matrices can fix vectors and vector directions.
Which units would you choose best to fit these situations?
Can you find the volumes of the mathematical vessels?
How much energy has gone into warming the planet?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Which line graph, equations and physical processes go together?
Work out the numerical values for these physical quantities.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Explore the meaning of the scalar and vector cross products and see how the two are related.
Can you make matrices which will fix one lucky vector and crush another to zero?
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Which dilutions can you make using only 10ml pipettes?
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.
Get some practice using big and small numbers in chemistry.
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.
Analyse these beautiful biological images and attempt to rank them in size order.
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.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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?
Build up the concept of the Taylor series
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Go on a vector walk and determine which points on the walk are closest to the origin.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
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.