Explore the relationship between resistance and temperature
Can you draw the height-time chart as this complicated vessel fills with water?
Can you match these equations to these graphs?
Can you work out which processes are represented by the graphs?
Build up the concept of the Taylor series
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Look at the advanced way of viewing sin and cos through their power series.
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Can you work out what this procedure is doing?
Get some practice using big and small numbers in chemistry.
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
See how enormously large quantities can cancel out to give a good approximation to the factorial function.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Here are several equations from real life. Can you work out which measurements are possible from each equation?
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.
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?
How much energy has gone into warming the planet?
Which line graph, equations and physical processes go together?
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Why MUST these statistical statements probably be at least a little bit wrong?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Looking at small values of functions. Motivating the existence of the Taylor expansion.
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?
Use simple trigonometry to calculate the distance along the flight path from London to Sydney.
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.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Work out the numerical values for these physical quantities.
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Go on a vector walk and determine which points on the walk are closest to the origin.
Explore the properties of matrix transformations with these 10 stimulating questions.
Can you sketch these difficult curves, which have uses in mathematical modelling?
Explore the meaning of the scalar and vector cross products and see how the two are related.
Explore the shape of a square after it is transformed by the action of a matrix.
Have you ever wondered what it would be like to race against Usain Bolt?
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
Simple models which help us to investigate how epidemics grow and die out.
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.
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.
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. . . .
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Explore how matrices can fix vectors and vector directions.