Expanding and factorising quadratics

problem
Always perfect

Age

14 to 18

Challenge level

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

Age

14 to 16

Challenge level

There are unexpected discoveries to be made about square numbers...
problem
Quadratic patterns

Age

14 to 16

Challenge level

Surprising numerical patterns can be explained using algebra and diagrams...
problem
Pythagoras perimeters

Age

14 to 16

Challenge level

If you know the perimeter of a right angled triangle, what can you say about the area?
problem
Hollow squares

Age

14 to 16

Challenge level

Which armies can be arranged in hollow square fighting formations?
problem
Difference of two squares

Age

14 to 16

Challenge level

What is special about the difference between squares of numbers adjacent to multiples of three?
problem
Factorising with multilink

Age

14 to 16

Challenge level

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
Finding factors

Age

14 to 16

Challenge level

Can you find the hidden factors which multiply together to produce each quadratic expression?
problem
Unit interval

Age

16 to 18

Challenge level

Can you prove our inequality holds for all values of x and y between 0 and 1?
problem
Geometric parabola

Age

14 to 16

Challenge level

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.