May 2002, Stage 4&5

Problems

problem icon

Similarly So

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

problem icon

Approximating Pi

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

problem icon

Double Angle Triples

Stage: 5 Challenge Level: Challenge Level:1

Try out this geometry problem involving trigonometry and number theory

problem icon

30-60-90 Polypuzzle

Stage: 5 Challenge Level: Challenge Level:1

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

problem icon

Remainder Hunt

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What are the possible remainders when the 100-th power of an integer is divided by 125?

problem icon

Binary Squares

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

If a number N is expressed in binary by using only 'ones,' what can you say about its square (in binary)?