Can you find out what numbers divide these expressions? Can you prove that they are always divisors?
Explore some of the different types of network, and prove a result about network trees.
What happens when you find the powers of this matrix?
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.
The nth term of a sequence is given by the formula n^3 + 11n. Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.
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.
If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?
Which numbers cannot be written as the sum of two or more consecutive numbers?
$40$ can be written as $7^2 - 3^2.$ Which other numbers can be written as the difference of squares of odd numbers?
Can you prove that triangles are right-angled when $a^2+b^2=c^2$?
