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A Different Differential Equation

Stage: 5 Challenge Level:

Explore the properties of this different sort of differential equation.

Taking Trigonometry Series-ly

Stage: 5 Challenge Level:

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

Bessel's Equation

Stage: 5 Challenge Level:

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

Scale Invariance

Stage: 5 Challenge Level:

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

Making More Tracks

Stage: 5 Challenge Level:

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?

Building Approximations for Sin(x)

Stage: 5 Challenge Level:

Build up the concept of the Taylor series

Stirling Work

Stage: 5 Challenge Level:

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

Global Warming

Stage: 4 Challenge Level:

How much energy has gone into warming the planet?

Big and Small Numbers in the Physical World

Stage: 4 Challenge Level:

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

Big and Small Numbers in the Living World

Stage: 3 and 4 Challenge Level:

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

Genetic Intrigue

Stage: 5

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. . . .

A Rational Search

Stage: 4 and 5 Challenge Level:

Investigate constructible images which contain rational areas.

9 Hole Light Golf

Stage: 1, 2, 3, 4 and 5 Challenge Level:

We think this 3x3 version of the game is often harder than the 5x5 version. Do you agree? If so, why do you think that might be?

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level:

Get some practice using big and small numbers in chemistry.

Trig-trig

Stage: 4 and 5 Challenge Level:

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

The Power of Dimensional Analysis

Stage: 4 and 5

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

Powerfully Fast

Stage: 5 Challenge Level:

Explore the power of aeroplanes, spaceships and horses.

More Bridge Building

Stage: 5 Challenge Level:

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

Escape from Planet Earth

Stage: 5 Challenge Level:

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

Peeling the Apple or the Cone That Lost Its Head

Stage: 4 Challenge Level:

How much peel does an apple have?

Stage: 4 and 5 Challenge Level:

Some of our more advanced investigations

The Invertible Trefoil

Stage: 4 Challenge Level:

When is a knot invertible ?

Problem Solving: Opening up Problems

Stage: 1, 2, 3 and 4

All types of mathematical problems serve a useful purpose in mathematics teaching, but different types of problem will achieve different learning objectives. In generalmore open-ended problems have. . . .

Chance of That

Stage: 4 and 5 Challenge Level:

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

Two Regular Polygons

Stage: 4 Challenge Level:

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?

Eight Ratios

Stage: 4 Challenge Level:

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.

Smoke and Daggers

Stage: 5 Challenge Level:

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. . . .

Mach Attack

Stage: 5 Challenge Level:

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

Diamonds Aren't Forever

Stage: 5 Challenge Level:

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

What Salt?

Stage: 5 Challenge Level:

Can you deduce why common salt isn't NaCl_2?

Clear as Crystal

Stage: 5 Challenge Level:

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

Big and Small Numbers in Physics

Stage: 4 Challenge Level:

Work out the numerical values for these physical quantities.

Reaction Rates!

Stage: 5

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

Stage: 5

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

Modelling Assumptions in Mechanics

Stage: 5

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

Sextet

Stage: 5 Challenge Level:

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

What Do Functions Do for Tiny X?

Stage: 5 Challenge Level:

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

Which Twin Is Older?

Stage: 5

A simplified account of special relativity and the twins paradox.

Geometry and Gravity 1

Stage: 3, 4 and 5

This article (the first of two) contains ideas for investigations. Space-time, the curvature of space and topology are introduced with some fascinating problems to explore.

Few and Far Between?

Stage: 4 and 5 Challenge Level:

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

Snookered

Stage: 4 and 5 Challenge Level:

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Twizzles Venture Forth

Stage: 4 Challenge Level:

Where we follow twizzles to places that no number has been before.

CSI: Chemical Scene Investigation

Stage: 5 Challenge Level:

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...

Robot Camera

Stage: 4 Challenge Level:

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

Very Old Man

Stage: 5 Challenge Level:

Is the age of this very old man statistically believable?

Designing Table Mats

Stage: 3 and 4 Challenge Level:

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

Operating Machines

Stage: 5 Challenge Level:

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

Odd Stones

Stage: 4 Challenge Level:

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

Spokes

Stage: 5 Challenge Level:

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