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Partly Circles

Age 14 to 16Challenge Level

What is the same and what is different about these circle questions? What connections can you make?

Pareq Calc

Age 14 to 16Challenge 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. . . .

Square Mean

Age 14 to 16Challenge Level

Is the mean of the squares of two numbers greater than, or less than, the square of their means?

Xtra

Age 14 to 18Challenge 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.

Pent

Age 14 to 18Challenge Level

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.

Golden Thoughts

Age 14 to 16Challenge Level

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.

A Third of the Area

Age 14 to 16 ShortChallenge Level

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

Age 11 to 14Challenge Level

Surprising numerical patterns can be explained using algebra and diagrams...

Pentakite

Age 14 to 18Challenge Level

ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.

Darts and Kites

Age 14 to 16Challenge Level

Explore the geometry of these dart and kite shapes!

Age 14 to 18Challenge Level

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.

How Old Am I?

Age 14 to 16Challenge Level

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Interactive Number Patterns

Age 14 to 16Challenge Level

How good are you at finding the formula for a number pattern ?

Always Two

Age 14 to 18Challenge Level

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Two Cubes

Age 14 to 16Challenge Level

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. . . .