MASSSA JOINT TESTS

Kenya Certificate of Secondary Education

121/1 MATHEMATICS (Alt. A)
Paper 1
121 / 1 - Mathematics
Tuesday 21st May 2024
Time: 8.00 a.m  10.30 a.m

Name ……………………………………………… Adm. No……...……………Class ……………

School ……………….……………………….………….………Signature…………..……………...

Instructions to candidates
a) Write your name, admission number and class in the spaces provided above.
b) Write the name of your school and sign in the spaces provided above.
c) This paper consists of two sections; Section I and Section II.
d) Answer all the questions in Section I and only five questions from Section II.
e) Show all the steps in your calculations, giving your answers at each stage in the spaces provided
below each question.
f) Marks may be given for correct working even if the answer is wrong.
g) Non – programmable silent electronic calculators and KNEC Mathematical tables may be used, except
where stated otherwise.
h) This paper consists of 15 printed pages.
i) 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

MASSSA Joint Tests – 2024

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SECTION I (50 marks)

Answer all the questions in this section in the spaces provided.
1 Given that x  403217  321860  11 , find the total value of the second digit of x. (2 marks)

2 Mary sells goods worth Ksh 950 000. Her total commission was Ksh 45 000. If the commission on the
first Ksh 50 000 was half that earned on the rest, find the two rates of commission. (3 marks)

3 A restaurant serves tea from an urn that can fill cups of capacities 300 ml, 360 ml or 450 ml exact
number of times. Each cup of tea is sold at Ksh 100 for the 300 ml, Ksh 120 for the 360 ml and Ksh 150
for the 450 ml. Calculate the maximum revenue that can be collected if the urn is to have the least
capacity. (3 marks)

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4 An alloy of density 7 g/cm3 is made from two metals A and B by mixing them in the ratio 3:2 by
volume. Another alloy of density 5.5 g/cm3 is formed by mixing the same metals in the ratio 3:7 by
volume. Find the densities of A and B. (3 marks)

5 Solve the equation sin  5 x  15  cos  3x  33  0 hence find the exact value of tan  7 x  3 .

(3 marks)

6 The vectors x, y and z are represented on the grid below.

On the same grid, draw the vectors:

(a) x  y (2 marks)
(b) x  z (2 marks)

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7 The interior angles of a hexagon are 4 x ,  5 x  10  , 6 x ,  7 x  40  , 8 x and 9 x 10  . Find the

value of x hence determine the size of the largest interior angle. (3 marks)

8 Ali’s rectangular plot is represented by an area of 252 cm2 on map A and 700 cm2 on map B. If the scale
of map B is 1:30 000, find the scale of map A. (3 marks)

9 Solve the equation 32 x 1  9 x  36 . (3 marks)

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1 2 1
10 Kamau spends of his salary on school fees, of the remainder on food and of what is left on
4 3 5
transport. He saves the balance. In a certain month, he saved Ksh 8 500. Calculate his salary. (3 marks)

11 A translation T maps a point A  2,1 onto A 1, 3 . Given that a point B  4,9  is the image of B

under the translation T, find:

(a) The coordinates of B. (2 marks)

(b) The distance between A and B. (2 marks)

12 Solve the inequality x  3  3x  1  x  13 giving your answer as a combined inequality hence list all the
integral values of x. (3 marks)

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13 The figure below shows triangle PQR and a point R , the image of R, under reflection in the line MM.

(a) Draw the line of reflection MM. (1 mark)

(b) Construct triangle PQR  , the image of triangle PQR under reflection in the line MM. (2 marks)

14 A right – angled triangle has sides of lengths x cm,  x  2  cm and  x  2  cm . Calculate the value of x

hence determine the perimeter of the triangle. (4 marks)

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15 A solid comprises a cube ABCDEFGH of each side 2 cm and a square based pyramid EFGHV. The slant
edges of the pyramid EV = FV = GV = HV = 2 cm. Draw the net of the solid. (3 marks)

16 The length of a minor arc of a circle of radius 7 cm is 8.8 cm. Calculate the area of the minor sector.
22
Take  to be . (3 marks)
7

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SECTION II (50 marks)

Answer only five questions from this section in the spaces provided.
17 ABC is an isosceles triangle in which AB = BC. The coordinates of A and B are  2,1 and  6, 3

respectively and M is the mid-point of AB.

Given that the equation of AC is x  3 y  5  0 , find:
(a) The equation of CM in the form y  mx  c where m and c are constants. (4 marks)

(b) The coordinates of C. (3 marks)

(c) The x and y intercepts of BC. (3 marks)

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18 A conical flask comprises of a bottom in the shape of a frustum of a cone and a top in the shape of a
cylinder. The base and top diameters of the frustum are 8.4 cm and 3.5 cm and the height of the frustum
is 8.4 cm. The height of the cylindrical part is 5 cm.
22
Taking  to be ,
7
(a) Calculate volume of water in the flask when filled to a height of 12.4 cm. (5 marks)

(b) Calculate surface of the flask in contact with water when the flask is filled to a height of 7.2 cm.
(5 marks)

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19 In the figure below ABCD is a quadrilateral. AB = 72 cm, BC = 17 cm, CD = 10 cm and AD = 75 cm.

The size of angle ABD  90 .

(a) Calculate correct to 1 decimal place:

(i) The size of angle BCD. (4 marks)

(ii) The size of angle ABC. (3 marks)

(b) Calculate the area of the quadrilateral ABCD. (3 marks)

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20 ABCD is a trapezium in which AB = 10 cm, AD = 5 cm, DAB  60 , ABC  75 and AB is parallel

to DC.
(a) Using a ruler and a pair of compasses only;
(i) Construct the trapezium. (4 marks)
(ii) Construct a circle centre O such that AB, AD and DC are its tangents. Measure the radius of
the circle. (3 marks)

(b) Calculate to 1 decimal place, the area of the trapezium that lies outside the circle. Take  to be
3.142. (3 marks)

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21 A school investigated how much space on its computers’ hard drives is used for data storage. The results
are shown below. It is given that 16 hard drives use less than 5GB for data storage.

(a) Find the total number of hard drives represented. (3 marks)

(b) Calculate the average space on its computers’ hard drives. (4 marks)

(c) Use the histogram above to estimate the median. (3 marks)

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22 The distance between Nairobi and Mombasa is 500 km. A bus left Nairobi at 10.45 a.m. and travelled
towards Mombasa at an average speed of 60 km/h. A matatu left Nairobi for Mombasa at 1.15 p.m.
using the same route and on the same day at an average speed of 100 km/h.
(a) Calculate:
(i) The time of the day when the matatu overtook the bus. (3 marks)

(ii) The distance of the matatu from Mombasa when it overtook the bus. (2 marks)

(b) Both vehicles continue towards Mombasa at their original speeds.

(i) How far was the bus from Mombasa when the matatu arrived? (2 marks)

(ii) For how long did the matatu wait in Mombasa before the bus arrived? (3 marks)

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2 5  4 6 1
23 (a) Given that A    and B    , find the determinant of A B . (4 marks)
 1 3 1 1

(b) The cost of a Mathematics book in shop A is Ksh x and that of a Chemistry book is Ksh y. In shop B,
the cost of a Mathematics book is 6% less of that in shop A while the cost of a Chemistry book is 5%
more than that in shop A. Jane bought 5 Mathematics books and 4 Chemistry books from shop A and
paid a total of Ksh 6 630. Dan bought 5 Mathematics books and 4 Chemistry books from shop B and
paid a total of Ksh 6 549.
(i) Form a matrix equation to represent the above information. (2 marks)

(ii) Use matrix method to find the cost of a Mathematics book and that of a Chemistry book in
shop A. (4 marks)

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24 The shape shown below is a wire frame in the form of a large rectangle split by parallel lengths of wire
into 12 smaller equal – sized rectangles.

(a) Given that the total length of wire used to complete the whole frame is 1512 mm, find an expression
in x for the area of the whole shape, A mm2. (4 marks)

(b) Hence find:

(i) The values of x and y for which the area of the whole shape is a maximum. (4 marks)

(ii) The maximum area of the whole shape. (2 marks)

THIS IS THE LAST PRINTED PAGE.

121/1 Mathematics Paper 1