Quadratic equations

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Favourite

How Old Am I?

Age

14 to 16

Challenge level

1 out of 3

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

1 out of 3

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

Interactive Number Patterns

Age

14 to 16

Challenge level

2 out of 3

How good are you at finding the formula for a number pattern ?
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Favourite

Golden Thoughts

Age

14 to 16

Challenge level

3 out of 3

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.
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Favourite

Square Mean

Age

14 to 16

Challenge level

3 out of 3

Is the mean of the squares of two numbers greater than, or less than, the square of their means?
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Favourite

Partly Circles

Age

14 to 16

Challenge level

3 out of 3

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

1 out of 3

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

Always Two

Age

14 to 18

Challenge level

2 out of 3

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.
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Favourite

In Between

Age

16 to 18

Challenge level

2 out of 3

Can you find the solution to this algebraic inequality?
problem

Two Cubes

Age

14 to 16

Challenge level

1 out of 3

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.]