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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

22/5/2023

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A forest is enclosed by four straight boundaries AB, BC, CD and DA. Point B is 25 km on a bearing of 315° from A, C is directly south of B on a bearing of 260° from A and D is 30 km on a bearing of 210° from C.

​​KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 20
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Three Jets MN and P are coming to airport A which is on the bearing 3400 from an adjacent airport B. N is East of airport A and 600km from airport B, on the bearing of 0400. M is on a bearing 0450 from A . P and M are due north of B. P is on the bearing

11/5/2023

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​Three Jets MN and P are coming to airport A which is on the bearing 3400 from an adjacent airport B. N is East of airport A and 600km from airport B, on the bearing of 0400. M is on a bearing 0450 from A . P and M are due north of B. P is on the bearing of 2500 from N 
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​Four towns PQR and S are located such that town Q is 70km on a bearing of 050° from P. Town R is 50km on a bearing of 145° from Q and town S is 55km on a bearing of S35°W of R.

29/4/2023

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​Four towns PQR and S are located such that town Q is 70km on a bearing of 050° from P. 
Town R is 50km on a bearing of 145° from Q and town S is 55km on a bearing of S35°W of R.
(a)By scale drawing, show the relative position of the four towns.
(Use a scale of 1cm to represent 10km).     (3mks)
(b) Use your diagram to determine
    (i)        the distance and bearing of P from S.  (3mks)
    (ii)       how far R is from P.   (2mks)
 (c)       Determine by the diagram or otherwise how far north town P is from town S.   (2mks)

​ANSWER

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Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60degreesE from Q. Point D is equidistant from B, Q and C.

23/11/2021

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Four points B, C, Q and D lie on the same plane. Point B is 42km due southwest point Q. Point C is 50 km on a bearing of S60oE from Q. Point D is equidistant from B, Q and C.

(a) Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. (5mks)

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(b) Determine the 
(i) Distance between B and C           (1mk)

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(ii) Bearing of D from B                      (2mks)

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(c) Find the distance and bearing of D from C.  (2mks)

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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.22

23/9/2020

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Form 1 Mathematics



A boat at point x is 200 m to the south of point Y. The boat sails X to another point Z. Point Z is 200m on a bearing of 3100 from X, Y and Z are on the same horizontal plane.

(a) Calculate the bearing and the distance of Z from Y ( 3 marks)

(b) W is the point on the path of the boat nearest to Y. Calculate the distance WY ( 2 marks)

(c) A vertical tower stands at point Y. The angle of point X from the top of the tower is 60 calculate the angle of elevation of the top of the tower from W (3 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2019PP1QN07

22/9/2020

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Form 1 Mathematics


Three villages A, B and C rife Such that B is 53 km on a bearing of 295° from A and C is 75 km east of B.
(a) Using a scale of 1 cm to represent 10 km, draw a diagram to show the relative positions of villages A, B and C.
(b) Determine the distance, in km, of C from A.
answer
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K.C.S.E Mathematics Q & A - MODEL 2005.PP1.QN.23

18/9/2020

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Form 2 Mathematics



A boat which travels at 5 km/h in still water is set to cross a river which flows from the north at 6km/h. The boat is set on a course of x0 with the north.

(a) Given that cos x0 = 3/5 , calculate

(i) The resultant speed of the boat ( 2 marks)

(ii) The angle which the track makes with the north ( 2 marks)

(b) If the boat is to sail on a bearing of 1350, calculate the bearing of possible course on which it can be set ( 4 marks)

Answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP1QN21

16/9/2020

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Form 1 Mathematics


​The comer points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D.
(b) Use the scale drawing to determine:
(i) the bearing of A from D; 
(ii) the distance BD in kilometres.
answers
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.19

16/9/2020

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Form 1 Mathematics



For electricity posts, A,B,C, and D stand on a level ground such that B is 21 m on a bearing of 0600 from A, C, is 15 m to the south of B and D is 12 m on a bearing of 1400 from A.

  • (a)
    • (i) Using  scale of  1 cm of I cm to represents 3 metres, draw a diagram to show the relative positions of the posts
    • (ii) Find the distances and the  bearing of C from D
  • (b) The height of the post at A IS 8.4m. On a separate scale drawing,  mark and determine the  angle of depression of the foot of  the post at C from the top of the top of the post at A.
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K.C.S.E Mathematics Q & A - MODEL 2016PP1QN12

13/9/2020

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Form 1 Mathematics


Points L and M are equidistant from another point K.; The bearing of L form K is 330. The bearing of M from K is 220.
Calculate the bearing of M from L

answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN09

7/9/2020

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Form 1 Mathematics


A plane leaves an airstrip L and flies on a bearing of 0400 to airstrip M, 500km away. The plane then leaves on a bearing of 3160 to airstrip N. The bearing ofN from L is 3500. By scale drawing, determine the distance between airstrips M and N.
answer
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K.C.S.E Mathematics Q & A - MODEL 2003PP1QN015

3/9/2020

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Form 2 Mathematics



Three points O, A and B are on the same horizontal ground. Point A is 80 metres to the north of O. Point B is located 70 metres on a bearing of 0600 from A. A vertical mast stands at point B. The angle of elevation of the top of the mast from o is 200.

Calculate:

a) The distance of B from O. (2mks)

b) The height of the mast in metres (2mks)

aNSWERS
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN23

31/8/2020

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Form 1 Mathematics


Three pegs R, S and T are on the vertices of a triangular plain field. R is 300 m from S on a bearing of 300° and T is 450 m directly south of R.
(a) Using a scale of 1 cm to represent 60 m, draw a diagram to show the positions of the pegs. 
(b) Use the scale drawing to determine:
(i) the distance between T and S in metres: 
(ii) the bearing of T from S. 
(c) Find the area of the field, in hectares, correct to one decimal place.
answers
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN022

30/8/2020

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Form 1 Mathematics



Four points B,C,Q and D lie on the same plane. Point B is 42km due South – West of point Q. Point C is 50km on a bearing of S 600 E from Q.
Point D is equidistant B, Q and C.
  • a)    Using the scale: 1cm represents 10km, construct a diagram showing the positions of B, C, Q and D. 
              Determines the:
  • i)    Distance between B and C
  • ii)    Bearing of D from B.
aNSWER
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K.C.S.E Mathematics Q & A - MODEL 2011PP1QN15

26/8/2020

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Form 1 Mathematics


Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060° from X while Z is 70 km from Y and on a bearing of 300° from X.
(a) Using a suitable scale, draw a diagram to represent the above situation. 
(b) Determine the distance, in km, of Z from X.

answer
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K.C.S.E Mathematics Q & A - MODEL 2010PP1QN20

25/8/2020

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Form 1 Mathematics


The boundaries PQ, QR, RS and SP of a ranch are straight lines such that: Q is 16 km on a bearing of 040° from P; R is directly south of Q and east of P and S is 12 km on a bearing of 1200 from R.
(a) Using a scale of 1cm to represent 2 km, show the above information in a scale drawing.
(b) From the scale drawing determine:
(i) the distance, in kilometers, of P from S;
(ii) the bearing of P from S.
(c) Calculate the area of the ranch PQRS in square kilometres.
answers
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K.C.S.E Mathematics Q & A - MODEL 2009PP1QN23

20/8/2020

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Form 1 Mathematics


Three points P, Q and R are on a level ground. Q is 240 m from P on a bearing of 2300 . R is 120 m to the east of P
a) Using a scale of 1 cm to represent 40 m, draw a diagram to show the positions of P, Q and R in the space provided below.
b) Determine i) The distance of R from Q ii) The bearing of R from Q
c) A vertical post stands at P and another one at Q. A bird takes 18 seconds to fly directly from the top of the post at q to the top of the post at P. Given that the angle of depression of the top of the post at P from the top of the post at Q is 90, Calculate:
i) The distance to the nearest metre, the bird covers;
ii)The speed of the bird in Km/h
answers
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K.C.S.E Mathematics Q & A - MODEL 2007PP1QN15

12/8/2020

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Form 1 Mathematics


Points L and M are equidistant from another point K. The bearing of L from K is 3300.
The bearing of M from K is 2200.Calculate the bearing of M from L
answer
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K.C.S.E Mathematics Q & A - MODEL 2001PP2QN017

10/8/2020

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Form 1 Mathematics


A helicopter is stationed at an airport H on a bearing 060o and 800km from another airport P.A third airport is J is on bearing of 1400 and 1,200km from H. 

Determine:

  • i) Value of P
  • ii)The bearing of P from J
Answer
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