KCSE MATHEMATICS QUESTIONS AND SOLUTIONS ~ Topically Analyzed
ALT B  LONGITUDES AND LATITUDES   FORM 4 LEVEL  SECTION 1  PAPER 2  KCSE 2010  QUESTION 14The positions of two points A and B on the surface of the earth are A(32.8°N, 26°E) and B(21.2°S, 26°E).
Calculate in kilometres the shortest distance between A and B. (Take the radius of the earth to be 6370 km and π = 22/7) (3 marks)
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LONGITUDES & LATITUDES  KCSE 1997  PAPER 1  SECTION B  FORM 4 LEVELA ship leaves an island (5°N, 45°E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.
(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km) QUESTION 5  KCSE 2023  LONGITUDES & LATITUDES  PAPER 2  FORM 4 LEVELA plane took 3 hours to fly from P(66.42°N, 30°E) to Q(66.42°N, 52.5°E). Determine the speed of the plane in knots correct to one decimal place. (3 marks)
QUESTION 11  KCSE 2021  LONGITUDES  PAPER 2  FORM 4 LEVELA point Q is 2000 nm to the West of a point P(40°N, 155°W). Find the longitude of Q to the nearest degree. (3 marks)
QUESTION 15  KCSE 2022  LONGITUDES  PAPER 2  FORM 4 LEVELAn aircraft took off from an airport A(0°, 40°W) at 1100 h local time. The aircraft landed at airport B(0°, 65°W) at 1200 h local time.
Determine the speed of the aircraft in knots. (4 marks) An aircraft took off from point A (x degrees North, 15 degrees east) at 0720h, local time. It flew due west to another point B (x degrees North, 75 degrees West) a distance of 5005 km from A.KCSE 2020 MATHEMATICS ALT A PAPER 2 QUESTION 20(a) A and B are two points on earthâ€™s surface and on latitude 40^{0} N. The two points are on the longitude 50^{0}W and 130^{0}E respectively. Calculate the distance from A to B along a parallel of latitude in kilometers. (2mks)(b) The shortest distance from A to B along a great circle in kilometres (Take p = ^{22}/_{7} and radius of the earth = 6370km) (2mks)LONGITUDES AND LATITUDES  Distance between two points along the small and great circles in nautical miles and kilometres.  FORM 4 LEVEL  PAPER 2 QUESTIONS  SECTION B(a) (i) Taking the radius of the earth, R= 6370km and π = 22/7, calculate the shortest distance between the two cities P(60^{o}N, 29^{o}W) and Q(60^{o}N, 31^{o}E) along the parallel of latitude. (3mks)(ii) If it is 1200hrs at P, what is the local time at Q. (3mks)(b) An aeroplane flew due south from a point A (60^{o}N, 45^{o}E) to a point B. the distance covered by the aeroplane was 8000km. determine the position of B. (4mks)
Form 4 Mathematics
A ship left point P(10°S, 40°E) and sailed due East for 90 hours at an average speed of 24 knots to a point R.(Take 1 nautical mile (nm) to be 1.853 km and radius of the earth to be 6370 km)
(a) Calculate the distance between P and R in: (i) nm; (ii) km. (b) Determine the position of point R. (c) Find the local time, to the nearest minute, at point R when the time at P is 11:00a.m. Form 4 Mathematics
The position of two points C and D on the earth’s surface are (θ°N, l0°E) and (θ°N, 30°E)
respectively. The distance between the two points is 600 nm. Determine the latitude on which C and D lie. Form 4 Mathematics
An aircraft took off from a point P (65° S, 76° W) and flew due North to a point Q. The distance between P and Q is 5400 nm.
Determine the position of Q. Form 4 Mathematics
A tourist took 1 hour 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E, ). (Take the radius of the earth to be 6370km and π = 22/7)
(a) Find the average speed of the aircraft. (a) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E), The average speed of the second aircraft was 90% that of the first aircraft Determine the time, to the nearest minute, the aircraft took to travel from U to V. (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 4 Mathematics
The positions of two points P and Q, on the surface of the earth are P(45 °N, 36°E) and Q(45 °N, 71°E). Calculate the distance, in nautical miles, between P and Q, correct to 1 decimal place.
Form 4 Mathematics
The shortest distance between two points A (40°N, 20°W) and B (0°S, 20°W) on the surface of y the earth is 8008km. Given that the radius of the earth is 6370km,
determine the position of B. (Take n = 22/7 ). Form 4 Mathematics
A ship leaves port p for port R though port Q.Q is 200 km on a bearing of 220^{0} from P.R is 420 km on the bearing of 140^{0} from from Q.
Form 4 Mathematics
Two towns A and B lie on the same latitude in the northern hemisphere. When its 8am at A, the time at B is 11.00am.
Form 4 Mathematics
The position of two towns are (2^{0} S,30^{0} E) and 2^{0}S, 37.4 ^{0}E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
Form 4 Mathematics
A tourist took 1 h 20 minutes to travel by an aircraft from town T(3°S, 35°E) to town U(9°N, 35°E). (Take the radius of the earth to be 6370km and π =22/7
(a) Find the average speed of the aircraft. (b) After staying at town U for 30 minutes, the tourist took a second aircraft to town V(9°N, 5°E). The average speed of the second aircraft was 90% that of the first aircraft. Determine the time, to the nearest minute, the aircraft took to travel from U to V (c) When the journey started at town T, the local time was 0700h. Find the local time at V when the tourist arrived. Form 4 Mathematics
A point M (60°N, 18°E) is on the surface of the earth. Another point N is situated at a distance of 630 nautical miles east of M.
Find: (a) the longitude difference between M and N; (b) The position of N. Form 4 Mathematics
The positions of three ports A, B and C are (34°N, 16°W), (34°N. 24°E) and (26°S, 16°W) respectively.
(a) Find the distance in nautical miles between: (i) Ports A and B to the nearest nautical miles; (ii) Ports A and C. (b) A ship left Port A on Monday at 1330 h and sailed to Port B at 40 knots. Calculate: (i) the local time at Port B when the ship left Port A; (ii) the day and the time the ship arrived at port B. Form 4 Mathematics
Point P (40^{0}S, 45^{0}E) and point Q (40^{0}S, 60^{0}W) are on the surface of the Earth.
Calculate the shortest distance along a circle of latitude between the two points. Form 4 Mathematics
An aero plane flies at an average speed of 500 knots due East from a point p (53.4^{0}e) to another point Q. It takes 2 ¼ hours to reach point Q. Calculate:
(i) The distance in nautical miles it traveled; (ii) The longitude of point Q to 2 decimal places Form 4 Mathematics
Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 118^{0}W and the longitude of B is 133^{0}E. The shorter distance between A and B measured along the circle of latitude is 5422 nautical miles.Find, to the nearest degree, the latitude on which A and B lie

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