3 out of 3
Can you use the diagram to prove the AM-GM inequality?
3 out of 3
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
3 out of 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.
3 out of 3
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
3 out of 3
Show that all pentagonal numbers are one third of a triangular number.
3 out of 3
You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
3 out of 3
Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?
3 out of 3
Drawing a triangle is not always as easy as you might think!
3 out of 3
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
3 out of 3
When the numbers from 1 to 1000 are written on a blackboard, which digit appears the most number of times?
