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Can you work out which processes are represented by the graphs?

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Can you sketch these difficult curves, which have uses in mathematical modelling?

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Can you match the charts of these functions to the charts of their integrals?

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What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

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Here are several equations from real life. Can you work out which measurements are possible from each equation?

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Which of these infinitely deep vessels will eventually full up?

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Which line graph, equations and physical processes go together?

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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?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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Use vectors and matrices to explore the symmetries of crystals.

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Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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Explore the meaning of the scalar and vector cross products and see how the two are related.

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Explore the properties of matrix transformations with these 10 stimulating questions.

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Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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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.

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This is our collection of tasks on the mathematical theme of 'Population Dynamics' for advanced students and those interested in mathematical modelling.

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Explore the shape of a square after it is transformed by the action of a matrix.

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How do you choose your planting levels to minimise the total loss at harvest time?

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Match the descriptions of physical processes to these differential equations.

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In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

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Starting with two basic vector steps, which destinations can you reach on a vector walk?

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In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

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Get some practice using big and small numbers in chemistry.

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Work with numbers big and small to estimate and calculate various quantities in biological contexts.

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To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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Work out the numerical values for these physical quantities.

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See how enormously large quantities can cancel out to give a good approximation to the factorial function.

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Invent scenarios which would give rise to these probability density functions.

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Can you make matrices which will fix one lucky vector and crush another to zero?

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.

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Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

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Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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Why MUST these statistical statements probably be at least a little bit wrong?

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Various solids are lowered into a beaker of water. How does the water level rise in each case?

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Work with numbers big and small to estimate and calulate various quantities in biological contexts.

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Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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This problem explores the biology behind Rudolph's glowing red nose.

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Analyse these beautiful biological images and attempt to rank them in size order.

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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.

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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?

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Build up the concept of the Taylor series