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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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A vertical electric pole was erected 6.4 m from the foot of a vertical fencing pole on the same horizontal level. The fencing pole is 2 m high. The angle of elevation of the top of the electric pole from the top of the fencing pole is 30°. Determine the

22/5/2023

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A vertical electric pole was erected 6.4 m from the foot of a vertical fencing pole on the same horizontal level. The fencing pole is 2 m high. The angle of elevation of the top of the electric pole from the top of the fencing pole is 30°. Determine the height of the electric pole correct to 1 decimal place. (2 marks)

KCSE 2020 MATHEMATICS ALT A PAPER 1 QUESTION 14
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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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Transfer the measurement of the reap below to a field book (2mks)

11/5/2023

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​Transfer the measurement of the reap below to a field book (2mks) 

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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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The scale of a map is 1: 200.Calculate the actual area of a triangular coffee field whose sides are 6cm, 8cm and 10cm on the map. (3 marks)

27/12/2022

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The scale of a map is 1: 200.Calculate the actual area of a triangular coffee field whose sides are 6cm, 8cm and 10cm on the map.    (3 marks)                        
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A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm-square. Calculate the actual area in hectares of the land.

26/11/2021

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​A map has a scale of 1 : 2500 and on it is square plot of land which has an area of 4cm². Calculate the actual area in hectares of the land. (3mks)

​​​Worked Answer:

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A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below.

23/11/2021

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(a) A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below. ​

A small field was surveyed and the measurements recorded in a surveyor’s field book as in the table below.

​(i) Using a scale of 1cm to 10m make an accurate drawing of the map of the field.         (4mks)

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​(ii) Find the area of the field. (3mks)

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(iii) Assuming that the baseline in (a) runs in a northern direction give the position of D relative to A using bearing and distance.    (3mks)

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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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From a point 20m away on a level ground the angle of elevation to the lower window line is 25° and the angle of elevation to the top line of the window is 34°.  Calculate the height of the window.

19/11/2021

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From a point 20m away on a level ground the angle of elevation to the lower window line is 25° and the angle of elevation to the top line of the window is 34°.  Calculate the height of the window.   [3 marks]

Worked solution

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From a point 20m away on a level ground the angle of elevation to the lower window line is 27degrees and the angle of elevation to the top of the window is 32degrees. calculate the height of the window.

24/10/2021

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From a point 20m away on a level ground the angle of elevation to the lower window line is 270 and the angle of elevation to the top of the window is 320. calculate the height of the window (3mks)

Worked Answer:

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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 2018PP1QN07

18/9/2020

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Form 1 Mathematics


(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle. 
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres.
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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 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 2015PP1QN07

10/9/2020

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Form 1 Mathematics


Below is part of a sketch of a solid cuboid ABCDEFGH. Complete the sketch
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answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.6

9/9/2020

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Form 1 Mathematics



Point C divide line AB given below externally in the ratio 5:2
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By construction, determine the position of point c
Answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP1QN23

7/9/2020

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Form 1 Mathematics


​The figure below represents a piece of land in the shape of a quadrilateral in which AB =240M, BC = 70m CD = 200m ˂BCD = 1500 ˂ABC = 900
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Calculate
(a) The size of ˂BAC correct to 2decimal places 
(b) The length AD correct to one decimal place 
(c) The area of the piece of land, in hectares, correct to 2 decimal places

answers
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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 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 2008PP1QN05

16/8/2020

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Form 1 Mathematics


The figure below shows a net of a solid
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Below is a part of the sketch of the solid whose net is shown above.
Complete the sketch of the solid, showing the hidden edges with broken lines.
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answer
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K.C.S.E Mathematics Q & A - MODEL 2007PP1QN18

12/8/2020

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Form 2 Mathematics


In the diagram below PA represents an electricity post of height 9.6 m. BB and RC represents two storey buildings of heights 15.4 m and 33.4 m respectively.
The angle of depression of A from B is 5.50 While the angle of elevation of C from B is 30.50 and BC = 35m.
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(a) Calculate, to the nearest metre, the distance AB 
(b) By scale drawing find,
(i) The distance AC in metres 
(ii) Angle BCA and hence determine the angle of depression of A from C 
answers
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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN13

10/8/2020

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Form 1 Mathematics


The figure below is drawn to scale. It represents a field in the shape of an equilateral triangle of side 80m
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The owner wants to plant some flowers in the field. The flowers must be at most, 60m from A and nearer to B than to C. If no flower is to be more than 40m from BC, show by shading, the exact region where the flowers may be planted
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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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN18

14/7/2020

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Form 1 Mathematics



A rally car traveled from point R to point S. S is 128 km on a bearing 0600 from R. The car then set off S at 9.30 am towards T at an average of 150 km/h. It was expected at T at 11.30 am. After traveling for I hour and 20 minutes it broke down at point P. The bearing of T and P from S is 3000.

Calculate the:
  • (a)
    • (i) Distance from R to P
    • (ii) Bearing of P and R
  • (b) The repair took 10 minutes and the car set off to complete its journey to T. Find the speed at which car must now move to reach T  on time.
Answer
K.C.S.E Mathematics Q & A - MODEL 2000PP2QN18

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