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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

A and B are two points on earth’s surface and on latitude 400 N. The two points are on the longitude 500W and 1300E respectively. Calculate the distance from A to B along a parallel of latitude in kilometers. (2mks)

13/5/2023

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(a) A and B are two points on earth’s surface and on latitude 400 N. The two points are on the longitude 500W and 1300E 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)

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find the distance between two points A(50 degrees N, 20 degrees E) and (50 degrees N, 50 degrees E) in;i) Kilometers (2 Marks)ii) Nautical miles (Take R = 6400km and  (2 Marks)

10/4/2023

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QUESTION ON LONGITUDES AND LATITUDES MODEL06012023001

5/1/2023

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TAKING THE RADIUS OF THE EARTH R=6370 KM AND PIE=22/7, CALCULATE THE SHORTEST DISTANCE BETWEEN THE TWO CITIES P(60]0 N,29]0 E) ALONG THE PARALLEL OF LATITUDE.

29/11/2021

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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(60oN, 29oW) and Q(60oN, 31oE) along the parallel of latitude.          (3mks)

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(ii) If it is 1200hrs at P, what is the local time at Q.      (3mks)

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(b)    An aeroplane flew due south from a point A (60oN, 45oE) to a point B. the distance covered by the aeroplane was 8000km. determine the position of B.  (4mks)

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN20

24/9/2020

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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.

answers
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K.C.S.E Mathematics Q & A - MODEL 2018PP2QN12

21/9/2020

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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. 
answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN10

17/9/2020

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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.
answer
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K.C.S.E Mathematics Q & A - MODEL 2016PP2QN21

15/9/2020

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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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN14

10/9/2020

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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.
answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN13

8/9/2020

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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 ).
answer
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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN019

8/9/2020

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Form 4 Mathematics



A ship leaves port p for port R though port Q.Q is 200 km on a bearing of 2200 from P.R is 420 km on the bearing of 1400 from from Q.
  • a) Using the scale 1:4,000,000, draw a diagram, showing the relative positions of the three ports P,Q, and R.
  • b) By further drawing on the same diagram, determine how far R is to the east of p Distance = 3.5 x40
  • c) If the ship has sailed directly from P to R at an average speed of 40 knots, find how long it would have taken to arrive at R.(Take 1 nautical mile = 1.853 km)
Answer
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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN024

4/9/2020

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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.
  • a) Given that the longitude of A is 150 E find the longitude of B. (2mks)
  • b) A plane leaves A for B and takes 3 1/2 hours to arrive at B traveling along a parallel of latitude at 850km/h. Find:
    • (i) The radius of the circle of latitude on which towns A and B lie. (3mks)
    • (ii) The latitude of the two towns (take radius of the earth to be 6371km) (3mks)
aNSWER
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN15

3/9/2020

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Form 4 Mathematics


The position of two towns are (20 S,300 E) and 20S, 37.4 0E) calculate , to the nearest km, the shortest distance between the two towns.(take the radius ofthe earth to be 6370 km)
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN22

2/9/2020

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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.
answers
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K.C.S.E Mathematics Q & A - MODEL 2011PP2QN14

28/8/2020

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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.
answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP2QN19

26/8/2020

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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. 
answers
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K.C.S.E Mathematics Q & A - MODEL 2009PP2QN13

21/8/2020

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Form 4 Mathematics


Point P (400S, 450E) and point Q (400S, 600W) are on the surface of the Earth.
Calculate the shortest distance along a circle of latitude between the two points.
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K.C.S.E Mathematics Q & A - MODEL 2008PP2QN07

17/8/2020

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Form 4 Mathematics


An aero plane flies at an average speed of 500 knots due East from a point p (53.40e) 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
answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP2QN13

13/8/2020

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Form 4 Mathematics


Two places A and B are on the same circle of latitude north of the equator. The longitude of A is 1180W and the longitude of B is 1330E. 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
answer
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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN16

11/8/2020

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Form 4 Mathematics


Two places P and Q are at ( 360N, 1250W) and 360N, 1250W) and 360 N, 1250W) and 360 N, 550E) respectively. Calculate the distance in nautical miles between P and Q measured along the great circle through the North pole.
answer
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K.C.S.E Mathematics Q & A - MODEL 2000PP1QN22

8/7/2020

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Form 4 Mathematics



A plane leaves an airport A (38.50, 37.050W) and flies dues North to a point B on latitude 520N.
  • (a) Find the distance covered by the plane
  • (b) The plane then flies due east to a point C, 2400km from B. Determine the position of C  

Take the value Π of as 22 ⁄ 7 and radius of the earth as 6370 km
Answer
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Related Questions on Longitudes and Latitudes


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K.C.S.E Mathematics Q & A - MODEL 1998PP2QN15

13/6/2020

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Free 1998 K.C.S.E Mathematics Topical Question & Answers Paper 2

​A river is flowing at uniform speed of 6 km/ h. A canoeist who can paddle at 10 km/h through still water wishes to go straight across the river.
Find the direction, relative to the bank in which he should steer.
answers
K.C.S.E Mathematics Q & A - MODEL 1998PP2QN15
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K.C.S.E Mathematics Q & A - MODEL 1998PP1QN20

7/6/2020

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K.C.S.E Mathematics Q & A - MODEL 1998PP1QN20

The position of two towns X and Y are given to the nearest degree as X (450N, 100W) and Y ( 450N, 700W)

​Find
  • (a)The distance between the two towns in
    • (i)  Kilometres ( take the radius of the earth as 6371)
    • (ii) Nautical miles  ( take I nautical mile to be 1.85 km)
  • (c) The local time at X when the local time at Y is 2.00 pm.

answer
K.C.S.E Mathematics Q & A - MODEL 1998PP1QN20
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K.C.S.E Mathematics Q & A-MODEL 1997PP1QN18

20/5/2020

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A ship leaves an island ( 50N, 450E) and sails due east for 120 hours to another island. The average speed of the ship is 27 knots.

  • (a) Calculate the distance between the two islands
    • (i) in nautical miles
    • (ii) in kilometres
  • (b) Calculate the speed of the ship in kilometres per hour
  • (c) Find the position of the second island
(take 1 nautical mile to be 1.853 Km and the radius of the earth to be 6370 Km)

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