LATITUDES AND LONGITUDES
KCSE 1989 – 2012 Form 4 Mathematics
Answer all the questions
1.
1989 Q18 P1
A globe representing the earth has a radius 0.5m. Points A(100W), B (00, 350E) P(600N, 1100E) and Q (600N,
1200W) are marked on the globe.
(a) Find the length of the arc AB, leaving your answer in terms of (3marks)
(b) If O is the centre of the latitude 600 N, find the area of the minor sector OPQ (5marks)
2.
1990 Q18 P1
(a) Calculate the distance round the latitude 600 N. (4marks)
(Take the radius of the earth, R = 6370 km and = 22/7)
(b) An aeroplane flew due south from a point
A (600N, 450E), to a point B. The distance covered by the aeroplane was 800km. Determine the position
of B. (4marks)
3.
1991 Q13 P2
The latitude and longitude of two stations A and B are (470N, 250 E) and (470N, 700 E). Calculate the distance
in nautical miles between A and B along latitude 470 N. (3marks)
4.
1992 Q11 P2
A point Q is 2000 nm to the west of P (600N, 00). Find the longitude of Q to the nearest degree.
(3marks)
5.
1994 Q18 P1
A and B are two points on the latitude 400 N. The two points lie on the longitudes 200 W and 1000E
respectively. Calculate
(i) The distance from A to B along a parallel of latitude (5marks)
(ii) The shortest distance from A to B along a great circle (Take Л = 22/ 7 and R = 6370 km)
(4marks)
6.
1995 Q24 P1
An aeroplane flies from a point A(1o 15’S, 37oE) to a point B directly north of A. The arc AB suspends an angle
of 45o at the centre of the earth. From B, the aeroplane flies due West to a point C on longitude 23o
W. (Take the value of л as 22/7 and radius of the earth as 6370)
a) (i)Find the latitude of B
(ii) Find the distance travelled by the aeroplane between Band C (5marks)
b) The aeroplane left B at 1.00 am local time. When the aeroplane was leaving B, what was the local time at
C? (2marks)
7.
1996 Q20 P1
The position of two A and B on the earth’s surface are ( 360 N, 490E) and ( 3600N, 1310 W) respectively.
(a) Find the difference in longitude between town A and town B ( 2 marks)
(b) Given that the radius of the earth is 6370, calculate the distance between town A and town B.
