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Where will the spaceman go when he falls through these strange planetary systems?

Things are roughened up and friction is now added to the approximate simple pendulum

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

A series of activities to build up intuition on the mathematics of friction.

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

Show that even a very powerful spaceship would eventually run out of overtaking power

We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.

Can you work out the means of these distributions using numerical methods?

Can you work through these direct proofs, using our interactive proof sorters?
This article explores the process of making and testing hypotheses.

Investigate the mathematics behind blood buffers and derive the form of a titration curve.

See how the motion of the simple pendulum is not-so-simple after all.

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

Get into the exponential distribution through an exploration of its pdf.

How high will a ball taking a million seconds to fall travel?

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

What will happen when you switch on these circular circuits?

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

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

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?

Match the descriptions of physical processes to these differential equations.

Solve these differential equations to see how a minus sign can change the answer

This short question asks if you can work out the most precarious way to balance four tiles.

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

Can you work out which of the equations models a bouncing bomb? Will you be able to hit the target?

At what positions and speeds can the bomb be dropped to destroy the dam?

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

When is 7^n + 3^n a multiple of 10? Can you prove the result by two different methods?

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

Change one equation in this pair of simultaneous equations very slightly and there is a big change in the solution. Why?

Given the products of diagonally opposite cells - can you complete this Sudoku?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Whirl a conker around in a horizontal circle on a piece of string. What is the smallest angular speed with which it can whirl?

A ball whooshes down a slide and hits another ball which flies off the slide horizontally as a projectile. How far does it go?

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?

Draw graphs of the sine and modulus functions and explain the humps.

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
An account of multiplication of vectors, both scalar products and vector products.
The article provides a summary of the elementary ideas about vectors usually met in school mathematics, describes what vectors are and how to add, subtract and multiply them by scalars and indicates. . . .

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?