Quadratic equations

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.]

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

Explore the geometry of these dart and kite shapes!

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

Exploit the symmetry and turn this quartic into a quadratic.

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

Sketch the graphs for this implicitly defined family of functions.

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!