Cyber Students,

Here are 5 questions from the end of former finals (part C) .
The first one is extremely easy, can be done with a single calculation,
so don't believe that the hard ones are at the end.

Go to it:

1)The image represents the path of a dolphin both in water and out as it performs a trick.
The curves f (x) and g (x) are parabolas.

the rule represents the dolphin's path in the water.
The maximum height of the jump out of water is 4 meters.

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2)

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3)

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4)

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5)

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Solutions

1) g(x) = – (x – 8)² + 4

2) angle BPC = 65° (corresponding angles)
therefore (2x + 3x + 65)° = 180°, which makes x = 23°
so angle = 2x = 46°

3) Use the distance formula to find the lengths of the 3 sides,
then use Cosine law to find the angle.
you should get cos C = 0.7894 so C = 37.87°

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4) Use law of sines on triangle SMG to find SG = 9.97 meters
use trig definition of sine on right triangle SGN to find SN = h = 9.97(sin 70°) = 9.37 m.

A = ½bh = ½(2 m)(9.37 m) = 9.37 m² so answer is 9.4 m²

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5)

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