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Candidate’s Signature……………………… Date……………………….. Stream:…………….
For Examiner’s Use Only
Section I
Section II
Grand Total
@2025 The Moi Girls’ High School-Eldoret
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SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
1. Without using mathematical tables or a calculator, evaluate
3 6 2 12 9 5 5 .
7 3 6 3 2 3
(3 marks)
2. Simplify 3 2 x 1 4 3x 1 .
2
(3 marks)
3. A rectangular floor of a hall measures by . The floor is to be carpeted using square
tiles leaving a uniform margin of all round. Calculate the least number of tiles used.
(4 marks)
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4. Solve for in the equation 52 x 1 25 x 2500 . (3 marks)
5. A Kenyan bank bought and sold foreign currencies on two different days as shown below.
A businessman arrived in Kenya on with Sterling pound. He changed the whole
amount to Kenya shillings at a commission of While in Kenya, he spent of the money and
changed the balance to South African Rands before leaving for South African on . If he
was charged a commission of for the last transaction, determine, to the nearest Rand, the amount he
obtained. (3 marks)
6. The masses of two similar solid spheres are and . If the surface area of the smaller
sphere is , find the surface area of the larger sphere. (3 marks)
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7. Given that 2sin 2m 30 4sin 120 2m and is an acute angle, find the value of .
(4 marks)
8. The current ages of Nyikuri and Simiyu are in the ratio . The ages of Simiyu and Ronald are in
the ratio . If in years’ time the ratio of Nyikuri’s age to Ronald’s age will be , determine
the current age of Nyikuri. (3 marks)
9. The figure below is a rhombus ABCD of sides . BD is an arc of circle centre C. Given that
ABC 138 .
22
Find the area of the shaded region correct to 3 significant figures. Take π= . (3 marks)
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10. The figure below is a part of the sketch of a triangular prism ABCDEF.
Complete the sketch by drawing the hidden edges using broken lines. (3 marks)
11. From a viewing tower metres above the ground, the angle of depression of an object on the
ground is and the angle of elevation of an aircraft vertically above the object is . Calculate
the height of the aircraft above the object on the ground. (4 marks)
12. A salesman is paid a salary of per month. He also paid a commission on sales above
. In one month he sold goods worth . If his total earning that month was
calculate the rate of commission. (3 marks)
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13. The figure below is such that , and are parallel lines. BMN 50 and CNM 80 .
Giving reasons, find DCN . (2 marks)
14. Three of the exterior angle of an sided polygon are , and , and the remaining exterior
angles are each. Find the value of . (3 marks)
15. The average lap time for athletes in a long distance race is seconds, seconds and seconds
respectively. If they all start the race at the same time, find the number of times the slowest runner
will have been overlapped by the fastest athlete at the time they all cross the starting point together
again. (3 marks)
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16. Solve the pair of simultaneous equations using graphing method. (3 marks)
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SECTION II (50 marks)
Answer all questions from this section in the spaces provided.
17. Line AB drawn below is a side of a triangle .
(a) Using a pair of compasses and a ruler only, construct;
(i) Triangle ABC in which BC=10 cm and CAB 90 . (2 marks)
(ii) A rhombus BCDE such that CBE 120 . (2 marks)
(iii) A perpendicular from F, the point of intersection of the diagonals of a rhombus to meet
BE at G. Measure FG. (2 marks)
(iv) A circle to touch all the sides of the rhombus. (1 mark)
(b) Determine the area of the region in the rhombus that lies outside the circle. (3 marks)
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18. The equation of line is 2 x 3 y 12 . Line is perpendicular to and meets at a point where
x 3.
(a) Find the:
(i) Equation of in the form y mx c where m and c are constants. (3 marks)
(ii) A point on which is equidistant from x and y axes. (2 marks)
(b) Another line is parallel to and passes through 6,5 . Find the:
(i) Equation of in the form ax by c where a, b and c are integers. (2 marks)
(ii) Coordinates of the point where lines and intersect. (3 marks)
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19. A solid below comprise of a cylindrical solid and a base which is a frustum of a pyramid. A
hemispherical hole is drilled at the top of the cylinder along a dotted line as shown. Radius of the
cylinder is and height .
Given that the original pyramid had slant edge of and , ,
and . Find to decimal place;
(a) The total surface area of the solid. (6 marks)
(b) The volume of the solid. (4 marks)
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20. Five points , , , and T lie on the same plane. Point Q is on a bearing of from .
Point lies from at a distance of . Given that point is west of and from
and is directly south of P and from .
(a) Using a scale of , show the above information in a scale drawing. (4 marks)
(b) From the scale drawing, determine;
(i) The distance in km of point from . (2 marks)
(ii) The compass bearing of from . (1 marks)
(c) Calculate the area enclosed by the points in square kilometers. (3 marks)
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21. Triangle drawn is the image of triangle under a negative quarter turn about .
(a) On the grid provided below, draw the triangle.
(i) . (3 mark)
(ii) , the image of triangle , under reflection in the line .
(2 marks)
(b) Triangle with vertices is the
image of triangle under a transformation T.
(i) Draw triangle . (1 mark)
(ii) Describe fully the transformation T. (2 marks)
(c) State any pair of triangles which are;
(i) Directly congruent. (1 mark)
(ii) Oppositely congruent. (1 mark)
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