DARUBINI SERIES JOINT EXAMINATION
KENYA CERTIFICATE OF SECONDARY EDUCATION
KCSE TRIAL 4 ~ 2024
121/2 ~ MATHEMATICS
JULY/AUGUST ~ 2024 ~ TIME: 2½ Hours
NAME ________________________________________INDEX NO: ________________
CANDIDATE SIGN: _________________DATE __________________TIME:
___________
INSTRUCTIONS TO CANDIDATES
(a) Write your name and Admission number in the spaces provided at the top of this page.
(b) This paper consists of two sections: Section I and Section II.
(c) Answer ALL questions in section 1 and ONLY FIVE questions from section II
(d) All answers and workings must be written on the question paper in the spaces provided
below each question.
(e) Show all the steps in your calculation, giving your answer at each stage in the spaces
below each question.
(f) Non – Programmable silent electronic calculators and KNEC mathematical tables may be
used, except where stated otherwise.
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 GRAND TOTAL
17 18 19 20 21 22 23 24 TOTAL
D004 F4 PP2
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SECTION I (50 MARKS)
1. Use logarithm tables to solve; (4mks)
3
45.23 0.1122
6394
2. Solve for in the equation sin ( 4 + 10o)-cos(+70o) = 0 (3mks)
3. A quantity K is partly constant and partly varies as M. When K = 45, M = 20, and when
K = 87, M = 48
(a) Find the formulae connecting K and M (1mk)
(b) Find K when M = 36 (2mk)
2
4. (i) Expand 2 x 15 in ascending powers of x (1mk)
(ii) Hence use your expansion up to the third term to evaluate 0.98
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(2mks)
5. Find the equation of the normal to the curve y = x2 + 4x – 3 at point (1, 2). (3mks)
6. Using a ruler and a pair of compass only, construct triangle ABC in which BC is 6.6cm,
AC=3.8cm and AB= 5.6cm. Locate point E inside triangle ABC which is equidistant from
ponts A, and C such that angle AEC=900. (3mks)
3
7. Solve the following trigonometric equation 2 cos 2( x 30) 1 for 0 x 360 0 (3mks)
8. The position vectors of A and B are given as a= 2i-3j+4k and b= -2i-j+2k respectively.
⃗⃗⃗⃗⃗ .
Find to 2decimal places, the length of the vector 𝐴𝐵 (3mks)
9. A T.V set was bought on hire purchase. A down payment (deposit) of Ksh 5000 was paid
and a 15 monthly installment of Ksh: 1500 was required.
a) Calculate the total amount paid on hire purchase (1mks)
b) If the hire purchase payment is 20% than cash payment, find the cash price (2mks)
4
10. The figure below shows a triangle ABC inscribed in a circle. AC = 10cm, BC = 7cm and
AB = 10cm. Find the radius of the circle. (Leave your answer to the nearest 1 decimal
place) (3mks)
A
10cm
C
7cm 8cm
11. The floor of a rectangular room measures 4.8m by 3.2m. Estimate the percentage
error in the area. (3mks)
12. Simplify without using mathematical tables or a calculator (3mks)
log 16 + log 81
log 8 + log 27
5
13. Rationalize the denominator and simplify, leaving your answer in surd form (3mks)
2 5
5 3 7 6
14. The figure below shows the graph of logy against logX
If the law connecting x and y is of the form y = axb, where a and b are constants. Find the
values of a and b. (3mks)
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15. Solve the equation by completing square method 2𝑥 2 + 3x – 5 = 0 (3mks)
16. Find the area bounded by the curve y = x(x-1) (x+2) and the x-axis. (4mks)
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SECTION II (50 MARKS)
Answer any five questions from this section
17. Mr. Ouma is a civil servant on a basic salary of Kshs.18,000. On top of his salary, he
gets a monthly house allowance of Kshs.14,000, medical allowance of Kshs. 3080 and a
commuter allowance of Kshs. 4640. He has a life insurance policy for which he pays a
premium of Kshs.800 p.m and claims an insurance relief of Kshs 3 for every 20/= on the
monthly premiums. He is entitled to a personal relief of kshs.1056 p.m
(a) Using the tax table below calculate his PAYE
Income in K£ p.m Rate %
1 – 484 10
485 – 940 15
941 – 1396 20
1397 – 1852 25
over 1852 30
(b) In addition to PAYE the following deductions are made on his pay every month.
Wcps at 2% of his basic salary
NHIF of Kshs.400
Loan repayment of kshs. 4000
Co-op shares of Kshs. 800
(i) Calculate his total monthly deductions in Kshs. (7mks)
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(ii) Calculate his net monthly pay in Kshs. (3mks)
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18. The points A1B1C1 are images of ABC A (1, 4), B (-2, 0), C (4, -2) respectively under a
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transformation N presented by the matrix N = ( ).
4 0
(a) Write down the co-ordinates of A1B1C1 (3mks)
(b)A11B11C11 are the images of A1B1C1 under a transformation represented by matrix
2 −2
M=( ). Write down the co-ordinates of A11B11C11 . (3mks)
1 0
(c)A transformation N followed by M can be represented by a single transformation K.
Determine the matrix K (4mks)
10
19. The figure below shows a solid frustum of a pyramid with a rectangular top of side 6cm
by 4 cm and a rectangular base of side 10cm by 8 cm. The slant edge of the frustum is
8cm.
D C
4cm
A 6cm
B 8cm
E H
8cm
F 10cm G
a) Calculate the height of the frustrum (3mks)
b) Calculate the volume of the solid frustum. (3mks)
c) Calculate the angle between the line FC and the plane FGHE (2mks)
d) Calculate the angle between the planes BCHG and the base EFGH. (2mks)
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20. The 2nd and 5th terms of an arithmetic progression are 8 and 17 respectively. The 2nd,
10th and 42nd terms of the A.P. form the first three terms of a geometric progression.
Find
(a) The 1st term and the common difference. (3mks)
(b) The first three terms of the G.P and the 10th term of the G.P. (4mks)
(c) The sum of the first 10 terms of the G.P. (3mks)
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21. Hospital records indicating the maternity patients that stayed in a hospital for a
number of days are as shown in the table below.
No of days stayed Frequency (No of patients)
3 15
4 32
5 56
6 19
7 5
Find the probability that
a) A patient stayed exactly 5 days (2mks)
b) A patient stayed less than 6 days (2mks)
c) A patient stayed at most 4 days (2mks)
d) A patient stayed at least 5 days (2mks)
e) A patient stayed less than 7 days but more than 4days (2mks)
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22. The position of two towns X and Y are given to the nearest degree as X (450 N, 1100 W)
and Y (450 N, 700 E). Take = 3.142, R = 6370km.Find:
(a) The distance between the two towns along the parallel of latitude in km. (3mks)
(b) The distance between the towns along a parallel of latitude in nautical miles. (3mks)
(c) A plane flew from X to Y taking the shortest distance possible. It took the plane 15hrs to
move from X and Y. Calculate its speed in Knots. (4mks)
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23. A transporter has a van and a pick-up available for trips to the nearest town. He can
allow atmost 120 litres of petrol and 4 litres of oil to be used each day. Each trip, the
van uses 10litres of petrol and 0.2 litres of oil. Each trip the pick-up uses 6 litres of
petrol and 0.8 litres of oil. The profit made on each trip by the van is shs. 60 and on
each trip by the pick-up is shs. 80. If he makes x trips in the van and y trips in the pick-
up;
(a) Write down four inequalities which must be satisfied by x and y (4mks)
(b) Represent the inequalities above graphically using a scale of 1cm to represent 2 units in
both axes, and then determine the number of trips made by each vehicle to give maximum
profit by use of a search line. Then give the maximum profit. (6mks)
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24. A stone is thrown straight up from the edge of a roof, 80m above the ground, at a
speed of 10m/s. Given that the acceleration due to gravity is 10m/s2
(a) How far is the stone 3 seconds later? (5mks)
(b) What time does it hit the ground? (3mks)
(c) What is the velocity of the stone when it hits the ground? (2mks)
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