MOI GIRLS’ HIGH SCHOOL-ELDORET
−
𝟏𝟐𝟏/𝟐
−
MATHEMATICS
ALT A
𝐏𝐚𝐩𝐞𝐫 𝟐
𝟏
2025−𝟐 𝐡𝐨𝐮𝐫𝐬
𝟐
TRIAL EXAMINATION
Date: 30/09/2025
0800 − 1030 hours
Name……………………………….………………………………….. Adm. Number:…….……
Candidate’s Signature……………………… Date……………………….. Stream:…………….
Instructions to candidates
(a) Write your name and admission number in the spaces provided above.
(b) Sign and write the date of examination in the spaces provided.
(c) This paper consists of two sections: Section I and Section II.
(d) Answer all questions in section I and only five questions from section II.
(e) Show all the steps in your calculations, giving the 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 16 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.
(j) Candidates should answer the questions in English.
For Examiner’s Use Only
Section I
𝟏
𝟐
𝟑
𝟒
𝟓
𝟔
𝟏𝟗
𝟐𝟎
𝟐𝟏
𝟕
𝟖
𝟗
𝟏𝟎
𝟏𝟏
𝟏𝟐
𝟐𝟑
𝟐𝟒
𝐓𝐨𝐭𝐚𝐥
𝟏𝟑
𝟏𝟒
𝟏𝟓
𝟏𝟔
𝐓𝐨𝐭𝐚𝐥
Section II
𝟏𝟕
𝟏𝟖
𝟐𝟐
Grand Total
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Turn over
2
SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
1. A quantity P varies directly as the square root of Q and inversely as the square of R.
Determine the percentage change in P when Q is increased by 44% and R decreased by
28%.
(4 marks)
2. Solve the equation; 2log4  x  2  log 4 3x  2   1
1 5
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(3 marks)
3. (a) Using binomial expansion to expand (1 + x ) up to the term in x −3
(1 mark)
(b) Use the expansion above to evaluate (1.5)5
(2 marks)
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4. Make 𝑥 the subject of the formula.
𝑡=√
𝑦 (𝑥−𝑦)
𝑥−𝑘
(3 marks)
5. Calculate the shortest distance in nm between two points A(350N, 300E) and B (650N, 1500W)
on the earth surface.
(3 marks)
6. The gradient function of a curve is given by
through the point (−1, 6), find its equation.
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𝑑𝑦
𝑑𝑥
= 3𝑥 2 − 8𝑥 − 3. If the curve passes
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(3 marks)
4
7. Given that OA= 𝒂 , 𝑶𝑩 = 𝒃 and that P divides AB in the ratio 3: −1, express ⃗⃗⃗⃗⃗
𝑂𝑃 in terms of
vectors a and b.
(3 marks)
8. Two parallel chords AB = 4cm and CD =10cm lie on the same side of the centre O of a
circle. The perpendicular distance between the two chords is 2cm. Calculate the radius of the
circle giving your answer to two decimal places.
(3 marks)
9. Solve the equation 8𝑠𝑖𝑛2𝑥 +2sin𝑥 =3 for 0° ≤ 𝑥 ≤ 360°
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(3 marks)
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10. A teachers college can accommodate a maximum of 730 students. The number of male students
must be at least 450 while the number of female students must exceed 277.
Taking 𝑥 to represent the number of male students and 𝑦 the number of female students, write
down all the possible inequalities representing the information above.
(3 marks)
11. The cash price of a television is Ksh 45000. A customer decides to purchase it on hire
purchase by paying a deposit of Ksh 15000. Calculate the monthly rate of compound
interest charged on remaining balance if the customer is required to repay the television in
eight equal monthly instalments of Ksh 4000 each.
(3 marks)
12. The equation 𝑥2 − 6𝑥 + 𝑦2 + 14𝑦 + 22 = 0 represents a circle. Determine the equation
of its image under a reflection in the line 𝑥 = 0.
(4 marks)
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13. In the figure below, A, B, C and D are points on the circumference of the circle with the
centre O. The line EF is a tangent to the circle at point C. Angle BAD = 95o and angle
BDC = 72o.
Determine the size of angles;
(i)
BCD;
(1 mark)
(ii)
(2 marks)
DCF .
2 1
14. A point 𝐴(𝑥, 𝑦) is mapped onto 𝐴1 (𝑥1 , 𝑦1 ) by successive transformation 𝐾 = (
) folllowed
0 1
1 −2
by 𝑇 = (
).Determine the single transformation matrix that would map 𝐴1 (𝑥1 , 𝑦1 )
3 0
onto 𝐴(𝑥, 𝑦).
(3 marks)
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15. A carpenter wishes to cut a 2 m long piece of wood into 9 equal parts. He approximates the
length of each piece to 0.22 m. Calculate the percentage error due to this approximation.
(3 marks)
16. The population of a colony of bacteria was recorded at intervals of 5 seconds as shown in the
table below.
Time, t (s)
0 5 10 15 20 25
Number of bacteria 5 7 11 16 24 36
(a) On the grid provided, draw the graph of population of bacteria against time.
(2 marks)
(b) Determine the average rate of change between t = 5 seconds and t = 20 seconds correct to 2
decimal places.
(1 mark)
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SECTION II (50 marks)
Answer only five questions from this section in the spaces provided
17. Tap A can fill a tank 3 times faster than tap B and takes 28 minutes less than tap B to fill the tank.
Both taps were opened simultaneously for 7.2 minutes.
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(a)
Determine the fraction of the tank that was still empty at the end of the 7.2 minutes.
(4 marks)
(b)
Tap A was later opened alone to completely fill the tank. Determine the time it took tap A
to fill the remaining fraction of the tank.
(2 marks)
(c)
The two taps A and B are operated by different proprietors. Water from the full tank
was sold for Ksh 15 750.The money was shared between the two proprietors in the
ratio of the quantity of water supplied by each. Determine the amount of money
received by the proprietor of tank A.
(4 marks)
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18. 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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19. The table below shows the values of x and some values of y for the curve y = x 3 − 7x + 6 in
the range −3 ≤ x ≤ 3.
(a) Complete the table by filling in the missing values of y.
(2 marks)
𝑥
−3
−2
−1
0
1
2
3
𝑦
(b) On the grid provided, draw the graph of y = x 3 − 7x + 6 for the range −3 ≤ x ≤ 3. (3 marks)
(c) Use your graph to estimate the roots of the following.
i.
x 3 − 7x − 6 = 0.
ii.
−x 3 + 8x − 2 = 0.
(1 mark)
(2 marks)
(d) By drawing a tangent, estimate the gradient of the curve y = x 3 − 7x + 6 at 𝑥 = −2. (2 marks)
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20. The table below shows monthly income tax rates for a certain year.
Monthly taxable income (ksh) Rate of tax (%) in each shilling
0
to
10166
to
19741
to
29317
to
Over 38892
10165
19740
29316
38892
10%
15%
20%
25%
30%
An employee earns a monthly basic salary of ksh 𝑥 and he is entitled to a house
allowance of ksh.10480 per month. The employee is also entitled to a monthly
personal relief of ksh.1162. His employer deducts ksh.6075.75 as income tax per
month.
Calculate;
(a) The monthly gross tax
(2 marks)
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(b) His taxable income per month.
(6 marks)
(c) The value of 𝑥
(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 without replacement.
(a) Represent this information in a tree diagram.
(2 marks)
(b) Use the tree diagram to find the probability that:
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(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. In the figure below, OP = p and OQ = q. R is the mid-point of PQ and OM:MQ = 2:3. OR and
PM intersect at X.
(a) Express the following vectors in terms of p and q.
(i) OR
(ii) PM
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(1 mark)
(1 mark)
(b) If PX = tPM and OX = sOR, find the values of s and t.
(6 marks)
(c) Show that O, X and R are collinear.
(2 marks)
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23. The figure below represents cuboid ABCDEFGH. M is the midpoint of AD. AB = 50cm,
AD = 30cm and BG = 20cm.
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Calculate correct to one decimal place;
(a) The length of BE
(3 marks)
(b) The angle between line AF and the plane ABCD
(2 marks)
(c) The angle between the planes ABFE and ABCD
(2 marks)
(d) The angle between the line MC and the line FG
(3 marks)
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24. The data below shows the masses in kg of 50 calves in a dairy farm.
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Mass (kg)
25  34
35  44
no. of calves
x
2x
45  54 55  64
16
4x
65  74
8
75  84 85  94
4
1
(a) Determine the value of x
(2 marks)
(b) On the grid provided draw a cumulative frequency curve for the data
(4 marks)
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(c) Use the graph in (b) above to determine:
(i) The median mass.
(1 mark)
(ii) The quartile deviation.
(3 marks)
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