Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you match the charts of these functions to the charts of their integrals?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Estimate areas using random grids
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?
Invent scenarios which would give rise to these probability density functions.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
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 write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
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.
Why MUST these statistical statements probably be at least a little bit wrong?
Can you construct a cubic equation with a certain distance between its turning points?
Work out the numerical values for these physical quantities.
Can you make matrices which will fix one lucky vector and crush another to zero?
Which line graph, equations and physical processes go together?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Use vectors and matrices to explore the symmetries of crystals.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Which pdfs match the curves?
Explore the properties of matrix transformations with these 10 stimulating questions.
Explore the meaning of the scalar and vector cross products and see how the two are related.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Formulate and investigate a simple mathematical model for the design of a table mat.
Can you work out which processes are represented by the graphs?
Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .
Get some practice using big and small numbers in chemistry.
Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
A problem about genetics and the transmission of disease.
Go on a vector walk and determine which points on the walk are closest to the origin.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Explore how matrices can fix vectors and vector directions.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the shape of a square after it is transformed by the action of a matrix.
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
How much energy has gone into warming the planet?
Can you find the volumes of the mathematical vessels?
How do you choose your planting levels to minimise the total loss at harvest time?
In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?
Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation
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.
Explore the properties of perspective drawing.