Quadratic equations

problem

Golden Eggs

Age

16 to 18

Challenge level

Find a connection between the shape of a special ellipse and an infinite string of nested square roots.
problem

Target Six

Age

16 to 18

Challenge level

Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
problem

Pareq Calc

Age

14 to 16

Challenge level

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

Plus or Minus

Age

16 to 18

Challenge level

Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
problem

Resistance

Age

16 to 18

Challenge level

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

Centre Square

Age

14 to 16

Challenge level

What does Pythagoras' Theorem tell you about the radius of these circles?
problem

A Third of the Area

Age

14 to 16

Challenge level

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

Pentakite

Age

14 to 18

Challenge level

Given a regular pentagon, can you find the distance between two non-adjacent vertices?
problem

Xtra

Age

14 to 18

Challenge level

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
problem

How Many Balls?

Age

16 to 18

Challenge level

A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.