General Mathematics Paper 2,Nov/Dec. 2010
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Question 5

(a) The diagonals of a rhombus are 14em and gem. Calculate, correct to the nearest centimetre, the perimeter of the rhombus.
(b) The cross section of a rectangular tank measures l.2m by 0.9m. It contains water to a depth of O.4m. If a cubical block of side 50em is lowered into the tank, calculate, correct to 2 significant figures, the rise in the water level (in metres).

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Observation

Part(a) of the question required the knowledge of the properties of the rhombus. It has equal sides and the diagonals intersect at right angles to each other. Many candidates demonstrated poor knowledge of these properties.
Candidates were expected to divide each diagonal by 2 and apply the Pythagoras theorem to obtain the length of the rhombus, x, as x = .../72+ 4.52 = 8.32 cm. Perimeter of the rhombus is . given by 4 x length of one side = 4 x 8.32 = 33 cm to the nearest centimetre.
In part (b), majority of the candidates who attempted this question performed well in it however, many of them who did not convert the dimensions to the same unit did not get the full marks for this question.
Candidates were expected to recall that volume of a cube = 13 while that of a cuboid is I x b X h, where I = length, b = breadth (width) and h = height.
Volume of the tank before the block was lowered into it = (1.2 x 0.9 x 0.4)m3 = 0.432m3•
Volume of cubical block = (0.5m)3 = 0.125m3• Therefore total volume = (0.432 + 0.125)m3
= 0.557m3• New height of water = 0.557m = 0.5157m. Difference in height = (0.5157 - 0.4)
1.2 XO.9
= 0.12m, correct to two Significant figures.