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KCSE MATHEMATICS QUESTIONS AND SOLUTIONS


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Form 3
Form 2
Form 4
Form 1

K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.24

16/9/2020

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Form 2 Mathematics



The figure below shows a model of a roof with a rectangular base PQRS PQ = 32 cm and QR = 14 cm. The ridge XY = 12 cm and is centrally placed. The faces PSX and QRY are equilateral triangles M is the midpoint of QR.

Picture

Calculate 

(a) 

(i) the length of YM 

(ii) The height of Y above the base PQRS 

(b) The angle between the planes RSXY and PQRS 

(c) The acute angle between the lines XY and QS

Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.23

16/9/2020

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Form 3 Mathematics



Three quantities P,Q and R are sure that P varies directly as the square of Q and inversely as the square root of R. 

(a) Given that P = 20 when Q = 5 and R = 9, find P when Q and R = 25 

(b) If Q increases by 20% and decreases by 36%, find the percentage increase in P.

Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.22

16/9/2020

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Form 4 Mathematics



A particle moves in a straight line. It passes though point O at t = O with velocity v= 5m/s. The acceleration a m/s2 of the particle at time t seconds after passing through O is given by a = 6t + 4
(a) Express the velocity v of the particle at time t seconds in terms of t
(b) Calculate
(i) The velocity of the particle when t = 3
(ii) The distance covered by the particle between t = 2 and t = 4

Answer
Picture
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.21

16/9/2020

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Form 3 Mathematics



Triangle ABC is the image of triangle PQR under the transformation

Picture
Picture

(b) Triangle ABC in part (a) above is to be enlarged scale factor 2 with centre at (11, -6) to map onto A’B’C. Construct and label triangle A’B’C’ on the grid above.

(c) By construction find the coordinates of the centre and the angle of rotation which can be used to rotate triangle A’B’C’ onto triangle A” B” C”, shown on the grid above.

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.20

16/9/2020

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Form 3 Mathematics



(a)  Given that the  matrix
Picture

Find A-1 the inverse of A

(b) Kimtai bought 200 bags of sugar and 300 bags of rice for a total of Kshs. 850,000. Buya bought 90 bags of sugar and 120 bags of rice for a total of Kshs. 360,000. If the price of a bag of sugar is Kshs x and that of rice is Kshs. Y, 

(i) Form two equations to represent the information above 

(ii) Use the matrix A-1 to find the prices of one bag of each item.

(c) Kali bought 225 bags of sugar and 360 bags of rice. He was given a total discount of Kshs. 33, 300. If the discount on the price of a bag of rice was 2%, calculate the percentage discount on the price of a bag of sugar.

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.
Answer

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.18

15/9/2020

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Form 3 Mathematics



The table below shows the ages in years of 60 people who attended a conference.
Picture
Calculate
(a)The  inter-quartile range of the data
(b)The percentage of the people in the conference whose ages were 54.5 years and below.
Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.17

15/9/2020

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Form 3 Mathematics



Farmer has two tractors A and B. The tractors, working together can plough a farm in 2 1/2h. One day, the tractors started to plough the farm together. After 1 h 10  min tractor  B broke down but A continued alone and completed the  job after a  further 4 h.
Find:
  • (a) The fraction of the job done by the tractors, working together for  one  hour
  • (b) The fraction  of the job done  by  tractor A and B broke down
  • (c) The time each tractor working alone would have  taken to plough the farm.
Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.16

15/9/2020

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Form 3 Mathematics



Without using mathematical tables, simplify
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.15

15/9/2020

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Form 2 Mathematics



Form the three inequalities that satisfy the given  region R
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.14

15/9/2020

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Form 1 Mathematics



In this questions, mathematical tables should not be used
At Kenya bank buys sells foreign currencies as shown below:
Picture
A Japanese traveling from France arrives in Kenya with 5000 Euros; he converts all the 5000 Euros to Kenya Shillings at the bank.
Calculate the amount in Japanese yen, than he receives.

Answers
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.13

15/9/2020

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Form 4 Mathematics



The gradient function of a curve is given
Picture
If the curve passes through the point, (0, 2), find its  equation.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.12

14/9/2020

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Form 1 Mathematics



An industrialist has 450 litres of a chemical which is 70% pure.  He mixes it with a chemical of the same type but 90%  pure  so as to obtain a mixture  which is 75% pure.
Find the amount of the 90% pure chemical used

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.11

14/9/2020

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In the figure below ABCDE is a cross- section of a sold. The solid has uniform cross- section. Given that BG is a base edge of the solid, complete the sketch, showing the hidden edges with broken lines.
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.10

14/9/2020

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Form 3 Mathematics



A group of 5 people can do a piece of work in 6 hours. Calculate the time a group of people. Working at half the rate of the first group would take to complete the same work.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.9

14/9/2020

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Form 3 Mathematics



Make b the subject 
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.8

14/9/2020

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Form 3 Mathematics



(a) Expand (1 + x)5
(b) Use the first three terms of the expansion in (a) to find the approximate value of (0.98)5

Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.7

14/9/2020

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Form 3 Mathematics



Use matrices to solve the simultaneous equations
   4x + 3 y = 18
   5x – 2y = 11
Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.6

13/9/2020

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Form 2 Mathematics



A students obtained the following marks in four tests during a school term: 60%, 75%, 48% and 66%. The tests were weighted as follows: 2,1, 4 and 3 respectively.
Calculate the students weighed mean mark of the tests

Answer
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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.5

13/9/2020

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Form 2 Mathematics



Evaluate without using mathematical tables, the expression
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.4

13/9/2020

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Form 2 Mathematics



Two trains T1 and T2 traveling in the opposite directions, on parallel tracks are just beginning to pass one another. Train T1 is 72 m long and traveling at 108 km/h. T2 is 78 m long and is traveling at 72 km/h.
answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.3

13/9/2020

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Form 3 Mathematics



Find the number of terms of the series 2 + 6 + 10 + 14 + 18 + ……….. that will give a sum of 800.
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.2

13/9/2020

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Form 1 Mathematics



The marked price of a car in a dealer’s shop was Kshs 400,000. Wekesa bought the car at 8% discount. The dealer still made a profit of 15%.
Calculate the amount of money the dealer had paid for the car.

Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP2.QN.1

13/9/2020

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Form 2 Mathematics



Use logarithms to evaluate
Picture
Answer
Picture

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K.C.S.E Mathematics Q & A - MODEL 2004.PP1.QN.24

12/9/2020

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Form 2 Mathematics



A man who can swim at 5km/h in still water swims towards the east to cross a river. If the river flows from north to south at the rate of 3km/h
a) Calculate:
    i)          The resultant speed
    ii)         The drift
b) If the width of the river is 30m, find the time taken, in seconds, for the man to cross the river.      

Answer
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