MASENO SCHOOL
2025 MOCK EXAMINATION
Kenya Certificate of Secondary Education
121 / 2 - Mathematics Paper 2 (Alt. A)
Thursday 19th July, 2025 Unique Identifier No...........................
8.00 a.m. - 10.30 a.m. Signature..............................................
Instructions to candidates
a) Write your Unique Identifier Number and sign in the spaces provided above.
b) This paper consists of two sections; Section I and Section II.
c) Answer all the questions in Section I and only five questions from Section II.
d) Show all the steps in your calculations, giving your answers at each stage in the spaces provided
below each question.
e) Marks may be given for correct working even if the answer is wrong.
f) Non – programmable silent electronic calculators and KNEC Mathematical tables may be used, except
where stated otherwise.
g) This paper consists of 15 printed pages.
h) Candidates should check the question paper to ascertain that all the pages are printed as indicated
and that no questions are missing.
For Examiner’s Use Only
Section I
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Total
Section II
17 18 19 20 21 22 23 24 Total
Grand Total
THE MASENO SCHOOL MOCK COMMITTEE – 2025
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SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
1 The dimensions of a rectangular floor are given to the nearest 10 cm as 12.5 m and 9.6 m. Calculate the
percentage error of the area of the floor. (3 marks)
5 2
2 Given that a 2 b 3 , find the values of a and b. (3 marks)
3 2 3 2
3 A hot water tap can fill a bath in 6 minutes while a cold water tap can fill the same bath in 4 minutes.
1
The drain pipe can empty the bath in 8 minutes. The two taps and the drain pipe are fully opened for 1
2
minutes after which the drain pipe is closed. Calculate the total time taken to fill the bath. (3 marks)
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4 Solve the following logarithmic equation. (3 marks)
2log4 x 2 log4 3x 2 1
5
1
5 (a) Expand 2 x in ascending powers of x leaving the coefficients as fraction in their simplest
3
form. (1 mark)
(b) Use the first four terms of the expansion in (a) to estimate the value of 1.9
5
(2 marks)
6 Solve the equation 6cos2 x sin x 4 for 0 x 360 . (3 marks)
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m
7 Make d the subject of the formula k (3 marks)
2
n
d
8 Point Q 1,5, 6 divides line AB externally in the ratio 3:5 where A is the point 2, 4,3 . Calculate
the coordinates of B. (3 marks)
9 A quantity P varies partly as the square of y and partly as the inverse of y. Given that P = 6 when y = 2
and P = 10 when y = 4, find P when y = 8. (3 marks)
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10 Using a ruler and a pair of compasses only, construct on the upper side of line AB = 6 cm, the locus P
such that APB 60 and the area of triangle APB = 12 cm2. (4 marks)
11 Sam bought a piece of land valued at Ksh 1 800 000 and a car valued at Ksh 4 500 000. The land
appreciated at the rate of 12% per annum while the car depreciated at the rate of 5% every 4 months.
Find the number of years it will take for the value of the land to be equal to the value of the car. Give
your answer correct to 1 decimal place. (3 marks)
2 1
12 Under a transformation T , triangle ABC is mapped onto triangle ABC whose vertices are
3 1
A 4, 2 , B 10, 2 and C 9,7 . Calculate the area of triangle ABC. (3 marks)
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13 In the figure below, R, T and S are points on the circle centre O. PQ is a tangent to the circle at T. POR
is a straight line. Angle QPR = 26o and RT = 12 cm.
Calculate the:
(a) Size of angle RST. (2 marks)
(b) Radius of the circle correct to 1 decimal place. (2 marks)
14 The equation of a circle is x 2 y 2 4x ky 12 . The radius of the circle is 5 units. Find the coordinates
of the two possible centres of the circle. (3 marks)
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15 The figure below is a model of a roof with a rectangular base ABCD. AB = 15 cm, BC = 26 cm. The
ridge EF = 14 cm and is centrally placed. The faces ABE and CDF are equilateral triangles.
Calculate the angle between lines CF and CE. (3 marks)
dy
16 The gradient function of a curve is given by 3x 2 4 x 5 . The curve passes through the point
dx
1, 4 . Find the equation of the curve. (3 marks)
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SECTION II (50 marks)
Answer only five questions from this section in the spaces provided.
17 A trader deals in two types of rice; type A and type B. Type A costs Ksh 600 per bag and type B costs
Ksh 420 per bag.
(a) The trader mixes 50 bags of type A rice with 30 bags of type B rice and sells the mixture at a profit
of 20%. Calculate the selling price of 1 bag of the mixture. (4 marks)
(b) The trader now mixes type A rice with type B rice in the ratio x : y respectively. The cost of the
mixture is Ksh 528 per bag. Determine the ratio x : y . (3 marks)
(c) One bag of the mixture in (a) is mixed with 1 bag of the mixture in (b) above. Calculate the
percentage of type A rice in this new mixture. (3 marks)
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18 The marks scored by 50 students in a mathematics test were as shown in the table below.
Marks 50 54 55 59 60 64 65 69 70 74 75 79
No. of students 5 8 15 10 8 4
(a) Using an assumed mean of 62, calculate the:
(i) Mean mark. (3 marks)
(ii) Standard deviation. (3 marks)
(b) Calculate the number of students who scored more than 68 marks. (4 marks)
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19 The 5th and 10th terms of an arithmetic progression (A.P) are 60 and 45 respectively.
(a) Find the common difference and the first term. (3 marks)
(b) Determine the least number of terms of the A.P which must be added together so that the sum of the
progression is negative. Hence find the sum. (5 marks)
(c) The 5th and the 10th terms of the A.P above form the first two consecutive terms of a geometric
progression (G.P). Determine the 6th term of the G.P. (2 marks)
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20 A farmer wishes to grow two crops; potatoes and beans. He has 70 hectares of land available for this
purpose. He has 240 man – days of labour available to work the land and he can spend up to
Ksh 180 000 shillings. The requirements for the crops are as follows:
Potatoes Beans
Minimum number of hectares to be sown 10 20
Man - days per hectare 2 4
Cost per hectare in Ksh 3000 2000
Profit per hectare in Ksh 15000 10000
(a) Taking x to be the number of hectares for potatoes and y to be the number of hectares for beans, form
all the inequalities in x and y to represent this information. (4 marks)
(b) On the grid provided below, draw all the inequalities and shade the unwanted region. (4 marks)
(c) Determine the maximum profit. (2 marks)
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21 A bag contains 6 red, 4 white and 5 blue balls. Two balls are drawn at random from the bag, one at a
time and without replacement.
(a) Represent this information in a tree diagram. (2 marks)
(b) Use the tree diagram to find the probability that:
(i) The second ball drawn is red. (2 marks)
(ii) The two balls are of the same colour. (2 marks)
(iii) No white ball is drawn. (2 marks)
(iv) At least one ball is blue. (2 marks)
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22 (a) Complete the table below giving the values correct to 2 decimal places. (2 marks)
x 0 15 30 45 60 75 90 105 120 135 150 165 180
sin 2 x 0 0.50 0.87 1.00 0.50 0 0.87 0.87 0.50
2cos x 30 1.73 2.00 1.93 1.42 1.00 0 1.00 1.42 1.73
(b) On the grid provided, draw the graphs of y sin 2 x and y 2 cos x 30 for 0 x 180 .
Use the scale 1 cm to represent 15 on the x – axis and 2 cm to represent 1 unit on the y – axis.
(4 marks)
(c) Using the graphs in (b) above to:
(i) Solve the equation sin 2 x 2 cos x 30 . (1 mark)
(ii) Determine the difference in the amplitude of the graphs y sin 2 x and y 2 cos x 30 .
(1 mark)
(iii) Solve the equation cos x 30 0.4 . (2 marks)
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23 A point A is 8008 km south of B 12 N,110 W . Another point C lies on longitude 160 E and is on the
22
same latitude as A. Take and the radius of the earth to be 6370 km.
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(a) Determine:
(i) The position of A. (3 marks)
(ii) The shorter distance in kilometres between A and C along the parallel of latitude. (3 marks)
(b) An aeroplane left point A on Monday 0730 hours local time for C along the parallel of latitude using
the shorter route at an average speed of 550 km/h. Determine:
(i) The local time at C when the aeroplane left point A. (2 marks)
(ii) The local time at C when the aeroplane arrived. (2 marks)
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24 Triangle ABC with vertices at A 2,3 , B 5, 2 and C 4, 1 is mapped onto triangle ABC by a shear
with x – axis invariant and A is mapped onto A 8,3 .
(a) Find:
(i) The matrix representing the shear. (2 marks)
(ii) The coordinates of B and C . (2 marks)
(b) Triangle ABC is the image of triangle ABC under a transformation represented by the matrix
2 0
M .
0 1
(i) Find the coordinates of triangle ABC . (2 marks)
(ii) Describe the transformation M fully. (2 marks)
(c) Determine a single matrix that maps triangle ABC onto triangle ABC. (2 marks)
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