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Can you match these equations to these graphs?
Can you work out which processes are represented by the graphs?
Can you draw the height-time chart as this complicated vessel fills with water?
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
Various solids are lowered into a beaker of water. How does the water level rise in each case?
Explore the relationship between resistance and temperature
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?
Can you find the volumes of the mathematical vessels?
How efficiently can you pack together disks?
Can you sketch these difficult curves, which have uses in mathematical modelling?
This problem explores the biology behind Rudolph's glowing red nose.
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?
Which line graph, equations and physical processes go together?
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?
Use vectors and matrices to explore the symmetries of crystals.
Which of these infinitely deep vessels will eventually full up?
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.
How do you choose your planting levels to minimise the total loss at harvest time?
Which pdfs match the curves?
Starting with two basic vector steps, which destinations can you reach on a vector walk?
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
Why MUST these statistical statements probably be at least a little bit wrong?
Go on a vector walk and determine which points on the walk are closest to the origin.
Formulate and investigate a simple mathematical model for the design of a table mat.
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
A problem about genetics and the transmission of disease.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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 properties of perspective drawing.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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.
Explore the properties of matrix transformations with these 10 stimulating questions.
Which countries have the most naturally athletic populations?
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.
Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.
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.
Can you make matrices which will fix one lucky vector and crush another to zero?
How much energy has gone into warming the planet?
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Use your skill and judgement to match the sets of random data.
Match the descriptions of physical processes to these differential equations.
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
Who will be the first investor to pay off their debt?
Estimate areas using random grids