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

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?

Derive an equation which describes satellite dynamics.

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

A task which depends on members of the group noticing the needs of others and responding.

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?

Can you find a rule which relates triangular numbers to square numbers?

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

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Can you find the value of this function involving algebraic fractions for x=2000?

115^2 = (110 x 120) + 25, that is 13225 895^2 = (890 x 900) + 25, that is 801025 Can you explain what is happening and generalise?

Find the five distinct digits N, R, I, C and H in the following nomogram

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?

This pattern of six circles contains three unit circles. Work out the radii of the other three circles and the relationship between them.

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Attach weights of 1, 2, 4, and 8 units to the four attachment points on the bar. Move the bar from side to side until you find a balance point. Is it possible to predict that position?

Can you find a rule which connects consecutive triangular numbers?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Take a complicated fraction with the product of five quartics top and bottom and reduce this to a whole number. This is a numerical example involving some clever algebra.

By proving these particular identities, prove the existence of general cases.

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Show that all pentagonal numbers are one third of a triangular number.

If x + y = -1 find the largest value of xy by coordinate geometry, by calculus and by algebra.

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Given any two polynomials in a single variable it is always possible to eliminate the variable and obtain a formula showing the relationship between the two polynomials. Try this one.

By considering powers of (1+x), show that the sum of the squares of the binomial coefficients from 0 to n is 2nCn

Find relationships between the polynomials a, b and c which are polynomials in n giving the sums of the first n natural numbers, squares and cubes respectively.

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

For which values of n is the Fibonacci number fn even? Which Fibonnaci numbers are divisible by 3?

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

The sum of any two of the numbers 2, 34 and 47 is a perfect square. Choose three square numbers and find sets of three integers with this property. Generalise to four integers.

What is the total number of squares that can be made on a 5 by 5 geoboard?

If a sum invested gains 10% each year how long before it has doubled its value?