Quadratic equations

problem

Centre Square

Age

14 to 16

Challenge level

What does Pythagoras' Theorem tell you about the radius of these circles?
problem
Favourite

How Old Am I?

Age

14 to 16

Challenge level

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?
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Favourite

Quadratic Patterns

Age

14 to 16

Challenge level

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

A Third of the Area

Age

14 to 16

Challenge level

The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?
problem
Favourite

Golden Thoughts

Age

14 to 16

Challenge level

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.
problem
Favourite

Partly Circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?
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Favourite

Mega Quadratic Equations

Age

14 to 18

Challenge level

What do you get when you raise a quadratic to the power of a quadratic?
problem

Pentakite

Age

14 to 18

Challenge level

Given a regular pentagon, can you find the distance between two non-adjacent vertices?
problem

Xtra

Age

14 to 18

Challenge level

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.
problem
Favourite

Always Two

Age

14 to 18

Challenge level

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.