Quadratic equations

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.

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

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel lines are 1 unit and 2 units.

Find the equation from which to calculate the resistance of an infinite network of resistances.