1. The radius of a semicircle is 10 metres. A square is
inscribed in the semicircle, with one side on the diameter, as shown in the
diagram. Find the area of the square (in

*m*^{2}).
2. The human body has (on average) 114 trillion cells (114×10

^{12}) . The weight of each cell (on average) is 55×10^{−}^{11}grams. What is the average weight of the human body (in kilograms)? Give your answer as a decimal, correct to one decimal place
3. What is the remainder when 10

^{24}is divided by 9997?
4. Aziz wrote all of the ten thousand integers from the number
1 to the number 10000, one by one, in increasing order. The beginning of his
sequence looks like this:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, ...

Note that he wrote the digit 0 for the first time when he
wrote the number "10", and he wrote it for the second time when he wrote
the number "20". In what number N, of his sequence, did he write the
digit 0 for the 2007-th time?

5. In the diagram, BCED is a trapezoid. The length of DE is
10. The line segment AG is a height of the large triangle, and it intersects DE
at F. Also given: AF=5, and FG=3. Find the area of the trapezoid.

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