Can you match these equations to these graphs?
Can you sketch these difficult curves, which have uses in
Can you work out which processes are represented by the graphs?
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?
Here are several equations from real life. Can you work out which measurements are possible from each equation?
Can you construct a cubic equation with a certain distance between
its turning points?
By exploring the concept of scale invariance, find the probability
that a random piece of real data begins with a 1.
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?
Can you draw the height-time chart as this complicated vessel fills
Invent scenarios which would give rise to these probability density functions.
How efficiently can you pack together disks?
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. . . .
Can you find the volumes of the mathematical vessels?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Imagine different shaped vessels being filled. Can you work out
what the graphs of the water level should look like?
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.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
Which line graph, equations and physical processes go together?
Explore the relationship between resistance and temperature
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
This problem explores the biology behind Rudolph's glowing red
Explore the properties of matrix transformations with these 10 stimulating questions.
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.
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Go on a vector walk and determine which points on the walk are
closest to the origin.
Explore how matrices can fix vectors and vector directions.
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.
Explore the meaning of the scalar and vector cross products and see how the two are related.
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
Is it really greener to go on the bus, or to buy local?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
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.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Simple models which help us to investigate how epidemics grow and die out.
Looking at small values of functions. Motivating the existence of
the Taylor expansion.
Which dilutions can you make using only 10ml pipettes?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Formulate and investigate a simple mathematical model for the design of a table mat.
Use vectors and matrices to explore the symmetries of crystals.
A problem about genetics and the transmission of disease.
This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.