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

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Looking at small values of functions. Motivating the existence of the Taylor expansion.

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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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Get further into power series using the fascinating Bessel's equation.

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Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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How would you go about estimating populations of dolphins?

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Which units would you choose best to fit these situations?

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

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When you change the units, do the numbers get bigger or smaller?

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

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

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Look at the advanced way of viewing sin and cos through their power series.

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

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Get some practice using big and small numbers in chemistry.

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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?

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

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Which dilutions can you make using only 10ml pipettes?

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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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Build up the concept of the Taylor series

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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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Use vectors and matrices to explore the symmetries of crystals.

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Which line graph, equations and physical processes go together?

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Which of these infinitely deep vessels will eventually full up?

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Can you draw the height-time chart as this complicated vessel fills with water?

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

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Was it possible that this dangerous driving penalty was issued in error?

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

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

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Explore the relationship between resistance and temperature

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

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Match the descriptions of physical processes to these differential equations.

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By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.

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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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Are these statistical statements sometimes, always or never true? Or it is impossible to say?

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

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Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

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

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Use trigonometry to determine whether solar eclipses on earth can be perfect.