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Take a look at these recently solved problems.
Try out some calculations. Are you surprised by the results?
Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
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.
What is the remainder if you divide a square number by $8$?
Can you show that $n^5-n^3$ is always divisible by $24$?
Can you find the smallest integer which has exactly 426 proper factors?
Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form 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?
Can you justify this equation involving three angles?
In this short challenge, can you use angle properties in a circle to figure out some trig identities?
Can you find a way to prove the trig identities using a diagram?
Draw graphs of the sine and modulus functions and explain the humps.
Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?
Can you find the sum of the squared sine values?
Submit your solutions to the latest problems and our toughnuts.
Why not get your creative juices flowing by trying out some of the tasks on our new website Wild Maths?
A collection of short problems for Stages 3 and 4.