Or search by topic
Surprising numerical patterns can be explained using algebra and diagrams...
What is the same and what is different about these circle questions? What connections can you make?
How good are you at finding the formula for a number pattern ?
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?
What do you get when you raise a quadratic to the power of a quadratic?
Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
Given a regular pentagon, can you find the distance between two non-adjacent vertices?
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.
Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to prove you have found all possible solutions.]