Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore how matrices can fix vectors and vector directions.
Can you make matrices which will fix one lucky vector and crush another to zero?
Who will be the first investor to pay off their debt?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Explore the properties of matrix transformations with these 10 stimulating questions.
Go on a vector walk and determine which points on the walk are closest to the origin.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
How would you go about estimating populations of dolphins?
Which of these infinitely deep vessels will eventually full up?
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?
Which pdfs match the curves?
How do you choose your planting levels to minimise the total loss at harvest time?
How much energy has gone into warming the planet?
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.
Explore the shape of a square after it is transformed by the action of a matrix.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Can you find the volumes of the mathematical vessels?
Are these estimates of physical quantities accurate?
This problem explores the biology behind Rudolph's glowing red nose.
Analyse these beautiful biological images and attempt to rank them in size order.
Explore the properties of perspective drawing.
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
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.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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.
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
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?
Can you construct a cubic equation with a certain distance between its turning points?
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?
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
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Can you match these equations to these graphs?
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.
Can you work out which processes are represented by the graphs?
A problem about genetics and the transmission of disease.
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Explore the relationship between resistance and temperature
How efficiently can you pack together disks?
Can you sketch these difficult curves, which have uses in mathematical modelling?
Can you draw the height-time chart as this complicated vessel fills with water?
Here are several equations from real life. Can you work out which measurements are possible from each equation?