Build up the concept of the Taylor series
Look at the advanced way of viewing sin and cos through their power 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.
Use vectors and matrices to explore the symmetries of crystals.
Explore the properties of matrix transformations with these 10 stimulating questions.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
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. . . .
Explore the shape of a square after it is transformed by the action of a matrix.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
How efficiently can you pack together disks?
How would you go about estimating populations of dolphins?
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Explore the meaning of the scalar and vector cross products and see how the two are related.
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.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Is it really greener to go on the bus, or to buy local?
Which line graph, equations and physical processes go together?
Why MUST these statistical statements probably be at least a little bit wrong?
Which pdfs match the curves?
Work out the numerical values for these physical quantities.
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?
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.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Can you make matrices which will fix one lucky vector and crush another to zero?
Invent scenarios which would give rise to these probability density functions.
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?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Explore the properties of perspective drawing.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.
Can you work out what this procedure is doing?
Have you ever wondered what it would be like to race against Usain Bolt?
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.
A problem about genetics and the transmission of disease.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
How much energy has gone into warming the planet?
Use your skill and judgement to match the sets of random data.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
Match the descriptions of physical processes to these differential equations.