# SPM Mathematics (Model Test Paper)

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.

 Point Latitude Longitude F 60° N 30° W G x° S 30° W H 60° N y° E I 25° S y° E
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]

(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]

(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
$=\frac{2100}{60×\mathrm{cos}{60}^{o}}$
= 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