Mathematics and Mathematical Literacy - Thutong

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Mathematics(NSC)/Grade 11/ P2 24 ExemplarQUESTION 7You go down to the beach for a few days. As an experiment you place a metre stick in thesand to measure the height of the water. As the tide comes in, the height rises and thenfalls as the tide goes out. You record the heights for 48 hours – the height fluctuatesbetween 0 cm and 50 cm. This is shown in the graph below:50y(5;50) (25;50) (45;50)(48;a)25x5 10 15 20 25 30 35 40 45 50The equation for the height of the water is: y = 25 sin18x+ 25 where y is the height of thewater and x is the time in hours from the beginning of the experiment.7.1 Calculate the height of the water when x = 48. (1)7.2 Calculate the times when the height of the water is 10 cm by solving the equation25 sin18x + 25 = 10 for the 48 hour interval rounded off to the nearest hour.(6)[7]Copyright reserved
Mathematics(NSC)/Grade 11/ P2 25 ExemplarQUESTION 8While you are on the beach you stand at the base of a life-guards’ tower, B, and measurethe angle of elevation of a lighthouse, PT, to be y. From the top of the 5 m high lifeguards’tower, A, the angle of elevation of P is x.PA5mBxyT8.1 Find the size of APˆ B in terms of x and y. (2)8.2 Show thatPB =5cos xsin( y − x)(3)8.3 Hence show thatPT=5cos x.sinysin( y − x)(2)[7]Copyright reserved
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Mathematics and Mathematical Literacy - Thutong

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