3 out of 3
Can you explain why a sequence of operations always gives you perfect squares?
3 out of 3
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
3 out of 3
Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?
3 out of 3
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
3 out of 3
Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.
3 out of 3
Can you use the diagram to prove the AM-GM inequality?
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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
Can you explain what's happening with these numbers?
3 out of 3
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
3 out of 3
Show that all pentagonal numbers are one third of a triangular number.
