Quadratic equations

article
Continued fractions II

In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
article
Golden mathematics

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.
problem
Two cubes

Age

14 to 16

Challenge level

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.]
problem
Good approximations

Age

16 to 18

Challenge level

Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
problem
Darts and kites

Age

14 to 16

Challenge level

Explore the geometry of these dart and kite shapes!
problem
Power quady

Age

16 to 18

Challenge level

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
problem
Golden construction

Age

16 to 18

Challenge level

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
problem
Symmetrically so

Age

16 to 18

Challenge level

Exploit the symmetry and turn this quartic into a quadratic.
problem
Bird-brained

Age

16 to 18

Challenge level

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
interactivity
Proof sorter - quadratic equation

Age

14 to 18

Challenge level

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.