Quadratic equations

problem

Bird-Brained

Age

16 to 18

Challenge level

1 out of 3

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

Kissing

Age

16 to 18

Challenge level

2 out of 3

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?
problem

Cocked Hat

Age

16 to 18

Challenge level

2 out of 3

Sketch the graphs for this implicitly defined family of functions.
problem

Golden Fibs

Age

16 to 18

Challenge level

2 out of 3

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

Pareq Calc

Age

14 to 16

Challenge level

3 out of 3

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.
problem

Resistance

Age

16 to 18

Challenge level

3 out of 3

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

Two Cubes

Age

14 to 16

Challenge level

2 out of 3

Two cubes have a combined volume equal to the total of the lengths of their edges. How big are the cubes?
problem

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 ?
problem

A Third of the Area

Age

14 to 16

Challenge level

3 out of 3

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

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.