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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


Topically Analysed


Form 3
Form 2
Form 4
Form 1

K.C.S.E Mathematics Q & A - MODEL 2012PP2QN02

31/8/2020

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Form 3 Mathematics


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K.C.S.E Mathematics Q & A - MODEL 2012PP2QN01

31/8/2020

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Form 2 Mathematics


Evaluate;
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giving the answer to 4 significant figures.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN24

31/8/2020

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Form 2 Mathematics


In the figure below, PQ is parallel to RS. The lines PS and RQ intersect at T. RQ = 10 cm, RT:TQ = 3:2, angle PQT = 40° and angle RTS - 80°.
Picture
(a) Find the length of RT.
(b) Determine, correct to 2 significant figures:
(i) the perpendicular distance between PQ and RS; 
(ii) the length of TS. 
(c) Using the cosine rule, find the length of RS correct to 2 significant figures. 
(d) Calculate, correct to one decimal place, the area of triangle RST.
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 2012PP1QN22

31/8/2020

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Form 4 Mathematics


The equation of a curve is y = 2x3 + 3x2.
(a) Find:
(i) the x - intercept of the curve;
(ii) the y - intercept of the curve.
(b) (i) Determine the stationery points of the curve.
(ii) For each point in (b) (i) above, determine whether it is a maximum or a minimum.
(c) Sketch the curve.
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN21

31/8/2020

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Form 2 Mathematics


The vertices of quadrilateral OPQR are O (0,0), P(2,0), Q(4,2) and R(0,3).
The vertices of its image under a rotation are O'(l, -1), P'(l, -3), Q'(3, -5) and R'(4, -1).
(a) (i) On the grid provided, draw OPQR and its image O'P'Q'R'.
(ii) By construction, determine the centre and angle of rotation. 
(b) On the same grid as (a) (i) above, draw O"P"Q"R", the image of O'P'Q'R' under a reflection in the line y = x. 
(i) directly congruent;
(ii) oppositely congruent.
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN20

31/8/2020

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Form 3 Mathematics


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(b) Neema did y tests and scored a total of 120 mks. She did two more tests which she scored 14 and 13 mks. The mean score of the first y tests was 3 mks more than
the mean score for all the tests she did. Find the total number of tests that she did.

answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN19

31/8/2020

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Form 1 Mathematics


Two alloys, A and B, are each made up of copper, zinc and tin. In alloy A, the ratio of copper to zinc is 3:2 and the ratio of zinc to tin is 3:5.
(a) Determine the ratio, copper: zinc: tin, in alloy A. 
(b) The mass of alloy A is 250 kg. Alloy B has the same mass as alloy A but the amount of copper is 30% less than that of alloy A.
Calculate:
(i) the mass of tin in alloy A;
(ii) the total mass of zinc and tin in alloy B. 
(c) Given that the ratio of zinc to tin in alloy B is 3:8, determine the amount of tin in alloy B than in alloy A.
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN18

31/8/2020

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Form 2 Mathematics


The figure below represents a solid cuboid ABCDEFGH with a rectangular base, AC= 13cm, BC = 5 cm and CH = 15cm.
Picture
(a) Determine the length of AB, 
(b) Calculate the surface area of the cuboid. 
(c) Given that the density of the material used to make the cuboid is 7.6 g/cm3, calculate its mass in kilograms. 
(d) Determine the number of such cuboids that can fit exactly in a container measuring 1.5 m by 1.2 m by 1 m.
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN17

31/8/2020

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Form 2 Mathematics


The table below shows the height, measured to the nearest cm, of 101 pawpaw trees.
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(a) State the modal class.
(b) Calculate to 2 decimal places:
(i) the mean height; 
(ii) the difference between the median height and the mean height.
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN16

31/8/2020

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Form 1 Mathematics


Bukra had two bags A and B, containing sugar. If he removed 2 kg of sugar from bag A and added it to bag B, the mass of sugar in bag B would be four times the
mass of the sugar in bag A. If he added 10 kg of sugar to the original amount of sugar in each bag, the mass of sugar in bag B would be twice the mass of the
sugar in bag A. Calculate the original mass of sugar in each bag.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN15

31/8/2020

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Form 2 Mathematics


The figure below represents a solid cone with a cylindrical hole drilled into it. The radius of the cone is 10.5 cm and its vertical height is 15 cm. The hole has a diameter of 7 cm and
depth of 8 cm. 
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Calculate the volume of the solid.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN14

31/8/2020

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Form 1 Mathematics


A Forex Bureau in Kenya buys and sells foreign currencies as shown below:
                                        Buying                       Selling
     Currency                   (Ksh)                         (Ksh)
Chinese Yuan                 12.34                         12.38
South African Rand      11.28                         11.37
A businesswoman from China converted 195 250 Chinese Yuan into Kenya shillings.
(a) Calculate the amount of money, in Kenya shillings, that she received. 
(b) While in Kenya, the businesswoman spent Ksh 1 258 000 and then converted the balance into South African Rand. Calculate the amount of money, to the nearest Rand, that she received. 
answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN13

31/8/2020

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Form 2 Mathematics


A line L passes through point (3,1) and is perpendicular to the line 2y = 4x + 5.
Determine the equation of line L.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN12

31/8/2020

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Form 3 Mathematics


Without using mathematical tables or a calculator, solve the equation,
 2log10x – 3log102 + log1032 = 2
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN11

31/8/2020

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Form 4 Mathematics


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answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN10

31/8/2020

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Form 3 Mathematics


Given that tan x° = 3/7 find cos (90 - x)° giving the answer to 4 significant figures.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN09

31/8/2020

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Form 2 Mathematics


Given that OA = 2i + 3j and OB = 3i - 2j
Find the magnitude of AB to one decimal place.

answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN08

31/8/2020

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Form 1 Mathematics


Using a pair of compasses and ruler only, construct a quadrilateral ABCD in which AB = 4cm, BC = 6 cm, AD = 3 cm, angle ABC = 135° and angle
DAB = 60°.
Measure the size of angle BCD.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN07

31/8/2020

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Form 1 Mathematics


Koech left home to a shopping centre 12 km away, running at 8 km/h. Fifteen minutes later, Mutua left the same home and cycled to the shopping centre at 20 km/h. Calculate the distance to the shopping centre at which Mutua caught
up with Koech.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN06

31/8/2020

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Form 1 Mathematics


Three bells ring at intervals of 9 minutes, 15 minutes and 21 minutes. The bells will next ring together at 11.00 pm. Find the time the bells had last rang together.
answer
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN024

31/8/2020

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Form 4 Mathematics



The displacement s metre of a particle moving along straight line after t seconds is given by. S = 3t + 3/2 t2 – 2t3
  • a) Find its initial acceleration
  • b) Calculate:
    • i) The time when the particle was momentarily at rest.
    • ii) Its displacement by the time it comes to rest momentarily
  • c) Calculate the maximum speed attained.
Answer
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K.C.S.E Mathematics Q & A - MODEL 2002PP2QN023

31/8/2020

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Form 4 Mathematics



​a) Complete the table below, giving your values correct to 2 decimal place.
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b) Using the grid provided and the table in part (a) draw the graphs of Y = tan Ө and y = sin 2Ө.
c) Using your graphs, determine the range of values for which tan Ө>Sin 2Ө for 00 ≤ Ө ≤ 900.
Answers
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN05

30/8/2020

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Form 2 Mathematics


Given that 92y x 2 x = 72, find the values of x and y.
answer
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K.C.S.E Mathematics Q & A - MODEL 2012PP1QN04

30/8/2020

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Form 1 Mathematics


In the parallelogram PQRS shown below, PQ = 8 cm and angle SPQ = 30°.
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If the area of the parallelogram is 24 cm2, find its perimeter
answer
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