There are **55** NRICH Mathematical resources connected to **Investigations**, you may find related items under Thinking Mathematically.

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Where should runners start the 200m race so that they have all run the same distance by the finish?

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How fast would you have to throw a ball upwards so that it would never land?

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

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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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Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

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Which parts of these framework bridges are in tension and which parts are in compression?

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Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

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What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Formulate and investigate a simple mathematical model for the design of a table mat.

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Investigate constructible images which contain rational areas.

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Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

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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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Get some practice using big and small numbers in chemistry.

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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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Explore the properties of this different sort of differential equation.

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What's the chance of a pair of lists of numbers having sample correlation exactly equal to zero?

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

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

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Explore the properties of combinations of trig functions in this open investigation.

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

Read about the mathematics behind the measuring devices used in quantitative chemistry

Dip your toe into the fascinating topic of genetics. From Mendel's theories to some cutting edge experimental techniques, this article gives an insight into some of the processes underlying. . . .

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Unearth the beautiful mathematics of symmetry whilst investigating the properties of crystal lattices

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...

An introduction to a useful tool to check the validity of an equation.

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Ever wondered what it would be like to vaporise a diamond? Find out inside...

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We all know that smoking poses a long term health risk and has the potential to cause cancer. But what actually happens when you light up a cigarette, place it to your mouth, take a tidal breath. . . .

An article demonstrating mathematically how various physical modelling assumptions affect the solution to the seemingly simple problem of the projectile.

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Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

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There has been a murder on the Stevenson estate. Use your analytical chemistry skills to assess the crime scene and identify the cause of death...

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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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Is it really greener to go on the bus, or to buy local?

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Work out the numerical values for these physical quantities.

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

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Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

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Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

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Build up the concept of the Taylor series

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

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Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

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A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?