KCSE PREDICTION EXAMS SERIES, 2024

Kenya Certificate of Secondary Education

121/1 - MATHEMATICS - Paper 1

T- 2024 – Time 2 ½ hours KCSE TRIAL
EXAMS, 2024

Name …………………………………………….……… Adm Number…………………………..

Candidate’s Signature ………………….…...……….. Date ……………………………………

INSTRUCTIONS TO CANDIDATES
1. Write your name, index number and class in the spaces provided above.
2. The paper contains two sections: Section I and Section II.
3. This paper contains 14 PRINTED pages make sure all PAGES ARE PRINTED and NON IS
MISSING
4. Answer ALL the questions in Section I and ANY FIVE questions from Section II.
5. All working and answers must be written on the question paper in the spaces provided below each
question.
6. Marks may be awarded for correct working even if the answer is wrong.
7. Negligent and slovenly work will be penalized.
8. Non-programmable silent electronic calculators and mathematical tables are allowed for use.

For examiners 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

TURN OVER
T3MATHS2024 1
 121/1 Mathematics Paper 1
SECTION I (50 MARKS)
Answer ALL questions in this section
1. Evaluate. (3 marks)
[28 − (−18)] [15 − (−2)(−6)]
−
−2 3

2. Simplify p2 – 2pq + q2 (3mrks)

2p2 -3pq + q2

3. Solve for X in the equation. (3mrks)

16 1.5 x
( ) = 0.75
9

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 121/1 Mathematics Paper 1
4. In the figure below PQRS is a trapezium with QR parallel to PS.QR=6cm, RS=4cm, QS=9cm and
PS=10cm
Q 6cm R

9cm 4cm

P 10cm S

Calculate

(a). The size of angle SQR (2marks)

(b). The area of triangle PQS (2marks)

5. Find the value of x in the equation. (3marks)

√3
COS (3x – 180o ) = in the range 0o≤ x ≤ 180o
2

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 121/1 Mathematics Paper 1
6. A famer has a piece of land measuring 840m by 396m. He divides it into square plots of equal sizes.
Find the maximum area of one plot. (3marks)

7. A liquid spray of 384g is packed in a cylindrical container of internal radius 3.2cm.

Given that the density of the liquid is 0.6g/cm3, calculate to 2 decimal places the height of the liquid in
the container. (3marks)

8. ( a ) Find the inverse of the matrix. (1mark)

 
4 3
 
3 5


(b) Hence solve the simultaneous equation using the matrix method. (2marks)

4𝑥 + 3𝑦 = 6

3𝑥 + 5𝑦 = 5

9. Two pipes A and B can fill an empty tank in 3hrs and 5hrs respectively. Pipe C can empty the tank in
4hrs. If the three pipes A, B and C are opened at the same time find how long it will take for the tank to
be full. (3marks)

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 121/1 Mathematics Paper 1

10. A tourist arrived in Kenya with sterling pound (£) 4680 all of which he exchanged into Kenyan money.
He spent Ksh.51790 while in Kenya and converted the rest of the money into US dollars. Calculate the
amount he received in US dollars. The. Exchange rates were as follows. (4marks)

Buying Selling
US dollars $ 65.20 69.10

Sterling pounds £ 123.40 131.80

-3/
11. The gradient of a straight line L1, passing through the point P (3, 4) and Q (a, b) is 2. A line L2 is
perpendicular to L1 through Q and R (2, -1). Determine the values of a and b. (3marks)

12. Find the number of sides of a regular polygon whose interior angel is 5 times the exterior angle.
(3marks)

13. The points A, B and C lie on a straight line. The position vectors of A and C are
2 i + 3j + 9k and 5i - 3j + 4k respectively; B divides AC internally in the ratio 2:1 Find the:
˜ ˜ ˜ ˜ ˜ ˜
( a ) Position vector of B (2marks)

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 121/1 Mathematics Paper 1

(b )distance of B from the Origin (1mark)

14. The sum of digits in a two digit number is 16. When the number is subtracted from the number formed
by reversing the digits the difference is 18. Find the number. (3marks)

15. In Blessed Church Choir the ratio of males to females is 2:3. On one Sunday service ten male members
were absent and six new female members joined the choir as guests for the day. If on this day the ratio of
males to females was 1:3, how many regular members does the choir have? (3marks)

16. A businessman makes a profit of 20% when he sells a carpet for Ksh. 36000. In a trade fair he sold one
such carpet for Ksh. 33600. Calculate the percentage profit made on the sale of the carpet during the
trade fair. (3marks)

SECTION II (50 MARKS)

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 121/1 Mathematics Paper 1
Answer ANY FIVE questions in the section.
17. Tickets for a football match cost 100 shillings and 50 shillings and tickets to the value of
Ksh.100,000 were sold. If 30% more tickets of sh.50 and 40% fewer tickets of sh.100 had been sold,
the income would have increased to Ksh.112, 500. How many tickets of each category were sold?
(10 marks)

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 121/1 Mathematics Paper 1
18. Given that A(-7, 2), B(-3, 3), C(-3, 6), D(-7, 8) are the vertices of a trapezium.
a) Draw the trapezium on the grid provided. (1 mark)

b) Rotate ABCD through -900 about the origin to be mapped onto A1B1C1D1. (2 marks)
c) Reflect A1B1C1D1 along y = -x to be mapped onto A11B11C11D11. (2 marks)
11 11 11 11 111 111 111 111
d) A certain transformation maps A B C D to A (-7, -9) B (-3, -6) C (-3, -9) D (-7, -15).
i) Plot A111B111C111D111 on the same axis. (1 mark)

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 121/1 Mathematics Paper 1
ii) Find the matrix and describe fully the transformation that maps A11B11C11D11 onto A111B111C111D111.
(3 marks)

iii) Find the area of A111B111C111D111 (1 mark)

19. The field book below gives measurement of a field. The distances are given in metres. AF= 100m.
F
100
E40 80
60 D50
C40 40
20 B30
A
a) Using a scale of 1cm represents 10m draw a map of the field with straight boundary edges. (4 marks)

b) i) Find the area of the field in square metres. (5 marks)

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 121/1 Mathematics Paper 1

ii) Determine the area of the field in hectares. (1 mark)

20. Use a ruler and compass only for all the constructions in this question.
a) Construct a triangle XYZ in which XY= 6cm, YZ =5cm and angle XYZ= 1200. (2 marks)

b) Measure XZ and angle YXZ. (2 marks)

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 121/1 Mathematics Paper 1
c) Construct the perpendicular bisector of XZ and let it meet XZ at N. (1 mark)

d) Locate a point W on the opposite of XZ as Y and that XW = ZW and YW =9cm and hence complete
triangle XZW. (2 marks)

e) Measure WM and hence calculate the area of triangle XZW. (3 marks)

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 121/1 Mathematics Paper 1
21. The table below shows the masses of newly born babies at a maternity home.
a) Complete the table and use it to answer the questions below. Take A = 3.7 (6 marks)
Mass (kg) X f d= X - A fd d2 fd2
2.0 – 2.4 2.2 5 -1.5 -7.5
2.5 – 2.9 2.7 15
3.0 – 3.4 3.2 24
3.5 – 3.9 3.7 40 0 0
4.0 – 4.4 4.2 10
4.5 – 4.9 4.7 4
5.0 – 5.4 5.2 2 1.5 3.0
f= 100 fd= fd2=

b) Use the method of assumed mean to calculate to two decimal places.

i) The mean mass of the babies. (2 marks)

ii) The standard deviation of the distribution. (2 marks)

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22. a) Complete the table below, for the function y =2x2 + 4x - 3. (2 marks)
x -4 -3 -2 -1 0 1 2
2x2 32 8 2 0 2
4x-3 -11 -3 5
y -3 3 13

b) On the grid provided, draw the graph of y=2x2 + 4x - 3 for -4≤ x≤ 2 and use the graph to estimate
the roots of the equation to 1 decimal place. (4 marks)

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 121/1 Mathematics Paper 1

c) In order to solve graphically 2x2 + x – 5 = 0, a straight line must be drawn to intersect the curve
y = 2x2 + 4x – 3.
Determine the equation of the straight line and draw it, hence obtain the roots of the equation
2x2 + x  5 = 0 to 1 decimal place. (4 marks)

23. a) A carpet measuring (x+4)m by (x-1)m laid down in a rectangular room measuring 2x m by x m
leaving out uncovered floor near the walls round the room. If the carpet is 36m2, calculate the area
of the uncarpeted floor. (6 marks)

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 121/1 Mathematics Paper 1

b) If 20cm square tiles were to be used to carpet the uncarpeted section of the floor in (a) above,
calculate the cost of carpeting the whole floor if the carpet costs sh.300 per square metre and each
tile costs sh.100 per square metre. (4 marks)

24. Mwikali is standing at a point P, 160m South of a hill H on a level ground. From point P she observes
the angle of elevation of the top of the hill to be 670.
a) Calculate the height of the hill. (3 marks)

b) After walking 420m due East to the point Q, Mwikali proceeds to point R due East of Q where the angle
of elevation of the top of the hill is 350. Calculate the angle of elevation of the top of the hill from Q.
(3 marks)

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 121/1 Mathematics Paper 1

c) Calculate the distance from P to R. (4 marks)

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