Quadratic equations

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

Centre Square

Age

14 to 16

Challenge level

3 out of 3

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

Pentakite

Age

14 to 18

Challenge level

1 out of 3

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

Xtra

Age

14 to 18

Challenge level

1 out of 3

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.
interactivity

Proof Sorter - Quadratic Equation

Age

14 to 18

Challenge level

2 out of 3

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.
problem

Pent

Age

14 to 18

Challenge level

2 out of 3

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.
problem

How Many Balls?

Age

16 to 18

Challenge level

1 out of 3

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.
problem

Halving the Triangle

Age

16 to 18

Challenge level

1 out of 3

Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.
problem

Golden Eggs

Age

16 to 18

Challenge level

2 out of 3

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

Implicitly

Age

16 to 18

Challenge level

2 out of 3

Can you find the maximum value of the curve defined by this expression?