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## 'Maths Filler 2' printed from http://nrich.maths.org/

The first 6 marks are filled one every half minute.

Then for mark 7 we first fill up to 6 completely:

$M+ = 1+3+1 = 5$

$A+ = \frac{3.5+4}{2} \times 2 +4 - \frac{1+2}{2} \times 2 +2 =
10.5$

$T+ = 6+2 = 8$

$H+ = 3+3+3+1 = 10$

$S = 4+1+1+1+1+0.5 = 8.5$

42 total

And then fill up to 7:

$M = 2$

$A = \frac{3.5 + 3.375}{2} \times 0.5 -1 \times 0.5 =
\frac{39}{32}$

$T = 2$

$H = 2$

$S = 2 \times \frac{1}{2} + \frac{1}{8} = \frac{9}{8}$

$\frac{267}{32}$ total (sum to this point =
$\frac{1707}{32}$)

And following the same process for the rest of the levels:

Level 8: $\frac{225}{32}$ total (sum to this point =
$\frac{1932}{32}$)

level 9: $\frac{267}{32}$ total (sum to this point =
$\frac{2199}{32}$)

Level 10: $\frac{249}{32}$ total (sum to this point = 76.5)

The sum of all these is 76.5.

Now if we check the total size to check it's the same: $24 \times 5
- 23.5 \textrm{ spaces} = 76.5$ check!

So we can plot these points on a graph! Joining them up is another
matter...