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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

QUESTION AND ANSWER ON LOCI MODEL06012023006

5/1/2023

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K.C.S.E Mathematics Q & A - MODEL 2019PP2QN19

24/9/2020

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Form 4 Mathematics


The figure KLMN below is a scale drawing of a rectangular piece of land of length KL = 80m
Picture
(a) On the figure, construct
(i) The locus of a point P which is both equidistant from points L and M It and from lines KL and LM. 
(ii) the locus of a point Q such that ∠KQL = 90°. 
(b) (i) Shade the region R bounded by the locus of Q and the Locus of points equidistant from KL and LM. 
(ii) Find the area of the region R in m². (Take ℼ= 3.142).

answers
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K.C.S.E Mathematics Q & A - MODEL 2005.PP2.QN.20

22/9/2020

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Form 4 Mathematics



(a) BCD is a rectangle in which AB = 7.6 cm and AD = 5.2 cm. draw the rectangle and construct the lucus of a point P within the rectangle such that P is equidistant from CB and CD ( 3 marks)

(b) Q is a variable point within the rectangle ABCD drawn in (a) above such that 600 ≤ AQB≤ 900 On the same diagram, construct and show the locus of point Q, by leaving unshaded, the region in which point Q lies

Answer
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K.C.S.E Mathematics Q & A - MODEL 2017PP2QN09

17/9/2020

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Form 4 Mathematics


​The figure below is a triangle ABC.
Picture
(a) On the triangle, locate the locus of points equidistant from AC and AB and 5 cm from B.
(b) Shade the region R, inside the triangle, which is less than 5 cm from B and nearer to AC than AB.
answer
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K.C.S.E Mathematics Q & A - MODEL 2015PP2QN10

10/9/2020

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Form 4 Mathematics


Below is a lien AB and a point X. Determine the locus of a point P equidistant from points A and B and 4 cm from X.
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answer
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K.C.S.E Mathematics Q & A - MODEL 2014PP2QN23

8/9/2020

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Form 4 Mathematics


Figure ABCD below is a scale drawing representing a square plot of side 80 metres.
Picture
On the drawing, construct:
(i) the locus of a point P, such that it is equidistant from AD and BC. 
(ii) the locus of a point Q such that <AQB = 60°. 
(i) Mark on the drawing the point Q , the intersection of the locus of Q and line AD.
Determine the length of BQ1 in metres.
(ii) Calculate, correct to the nearest m2, the area of the region bounded by the locus of P, the locus of Q and the line BQ1
answers
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K.C.S.E Mathematics Q & A - MODEL 2003PP2QN022

8/9/2020

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Form 4 Mathematics



The line PQ below is 8cm long and L is its midpoint
  • a)
    • i) Draw the locus of point R above line PQ such that the area of triangle PQR is 12cm2.
    • ii) Given that point R is equidistant from P and Q,show the position of point R..
  • b) Draw all the possible loci of a point T such that ∠RQL = ∠RTL. (4mks)
Answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP2QN12

3/9/2020

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Form 4 Mathematics


A point P moves inside a sector of a circle, centre O, and chord AB such that 2cm < OP ≤ 3cm and angle APB = 65 Draw the locus of P
answer
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K.C.S.E Mathematics Q & A - MODEL 2013PP1QN06

2/9/2020

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Form 4 Mathematics


A point P on the line AB shown below is such that AP = 2/7 AB. By construction locate P.
Picture
answer
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K.C.S.E Mathematics Q & A - MODEL 2011PP2QN12

28/8/2020

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Form 4 Mathematics


The figure below represents a scale drawing of a rectangular piece of land, RSTU. RS = 9 cm and ST = 7 cm.
Picture
An electric post P, is to be erected inside the piece of land. On the scale drawing, shade the possible region in which P would lie such that PU > PT and PS ≤ 7 cm
answer
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K.C.S.E Mathematics Q & A - MODEL 2006PP2QN07

10/8/2020

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Form 4 Mathematics


The figure below shows a circle centre O and a point Q which is outside the circle
Picture
Using a ruler and a pair of compasses, only locate a point on the circle such that angle OPQ = 90o
answer
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K.C.S.E Mathematics Q & A - MODEL 2001PP2QN014

10/8/2020

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Form 4 Mathematics



The diagram below represents a field PQR
Picture
  • a) ​Draw the locus of points equidistant from sides PQ and PR.
  • b) Draw the locus of points equidistant from points P and R.
  • c) a coin is lost within a region which is nearest to point P than to R and closer to side Pr than to side P,q, shade the region where the coin can be located.
Answer
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K.C.S.E Mathematics Q & A - MODEL 2000PP2QN22

14/7/2020

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Form 4 Mathematics



The line segment BC given below is one side of triangle ABC

  • (a) Use a ruler and compasses to complete the construction of a triangle ABC in which ∠ABC = 450. AC = 5.6 cm and ∠BAC is obtuse 
  • (b) Draw the locus of point P such that P is equidistant from a point O and passes though the vertices of triangle. 
  • (c) Locate point D on the locus of P equidistant from lines BC and BO. Q lies in the region enclosed by lines BD, BO extended and the locus of P. Shade the locus of Q.
Answer
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K.C.S.E Mathematics Q & A - MODEL 1998PP1QN23

7/6/2020

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​Use a ruler and a pair of compasses only for all constructions in this question

(a) On the line BC given below, construct triangle ABC such that ∠ABC = 300 and BA = 12 cm

  • (b) Construct a perpendicular from A to meet BC produced at D. Measure CD
  • (c) Construct  triangle A’B’C’ such that the area of triangle A’B’C is the three quarters of the area  of triangle ABC and on the same side  of BC as triangle ABC.
  • (d) Describe the lucus of A’
K.C.S.E Mathematics Q & A - MODEL 1998PP1QN23

ANSWER
K.C.S.E Mathematics Q & A - MODEL 1998PP1QN23
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K.C.S.E Mathematics Q & A - MODEL 1997PP2QN04

26/5/2020

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K.C.S.E Mathematics Q & A

On the figure below construct

  • (i) The perpendicular bisector of BC

  • (ii) The locus of a point P which moves such a way that
    ∠APB = ∠AVB and P is on the same side of AB on the same side of AB as C
Picture

K.N.E.C Marking Scheme
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K.C.S.E Mathematics Q & A-MODEL 1996PP1QN23

14/5/2020

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Use ruler and compasses only in this question 

The diagram below shows three points A, B and D

  • (a) Construct the angle bisector of acute angle BAD (1 mark)
  • (b) A point P, on the same side of AB and D, moves in such a way that ∠APB = 22 ½0 construct the locus of P (6 marks)
  • (c) The locus of P meets the angle bisector of < BAD at C measure ∠ABC (1 mark)
  • (d) Hence find area of the image A” B” C” (2 marks)

MARKING SCHEME
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K.C.S.E Mathematics Q & A-MODEL 1995PP2QN22

12/5/2020

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Using ruler and compasses only, construct a parallelogram ABCD such that AB = 10cm, BC = 7cm and ∠ABC = 1050. Also construct the loci of P and Q within the parallel such that AP ≤ 4 cm, and BC ≤ 6 cm. Calculate the area within the parallelogram and outside the regions bounded by the loci.


MARKING SCHEME
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