SPM Mathematics (Model Test Paper)Section B [48 marks]
Answer any
four questions from this section.16. Table 3 shows the latitudes and longitudes of four points F, G, H and I, on the surface of the earth.
Table 3
(a)
J is a point on the surface of the earth such that FJ is the diameter of the earth. State the position of J. [2 marks] |
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(b) Calculate (i) the value of x, if the distance from F to G measured along the meridian is 5 400 nautical miles,(i) the value of
y, if the distance from F due east to H measured along the common parallel of latitude is 2 100 nautical miles. [7 marks](c) An aeroplane took off from
F and flew due east to H along the common parallel of latitude and then due south to I.If the average speed for the whole flight is 460 knots, calculate the time taken for the whole flight. [3 marks] Answer and solution:(a)Position of
J = (60° S, 180° – 30° E) = (60° S, 150° E)(b)(i) Difference in latitude between
F and G$=\frac{5400}{60}$ = 90° Latitude of G= 90° – 60° = 30° x = 30(b)(ii) Difference in longitude between
F and H$=\frac{2100}{60\times \mathrm{cos}{60}^{o}}$
= 70° Latitude of G= 70° – 30° = 40° E
y = 40(c) Distance of
HI= (60 + 25) × 60 = 5 100 n.m. Distance of the whole flight
= 2 100 + 5 100 = 7 200 n.m. Time taken for the whole flight
$=\frac{7200}{460}$ = 15.65 hours |