INSTRUCTIONS TO CANDIDATES
 Write your name and Admission number in the spaces provided at the top of this page.
 This paper consists of two sections: Section I and Section II.
 Answer ALL questions in section 1 and ONLY FIVE questions from section II
 All answers and workings must be written on the question paper in the spaces provided below each question.
 Show all the steps in your calculation, giving your answer at each stage in the spaces below each question.
 Non – Programmable silent electronic calculators and KNEC mathematical tables may be used, except where stated otherwise.
SECTION I (50 marks)
Answer all the questions in this section in the spaces provided.
 Without using mathematical tables or calculators, evaluateleaving your answer as a simplified fraction (3mks)
 Two similar solids have surface areas 48cm^{2} and 108cm^{2}respectively. Find the volume of the smaller solid if the bigger one has a volume of 162cm^{3}. (3mks)
 A triangle flower garden has an area of 28m^{2}. Two of its edges are 14 metres and 8 metres. Find the angle between the two edges. (2mks)
 A watch which looses a half a minute every hour.It was set read the correct time at 0445hr on Monday. Determine in twelve hour system the time the watch will show on Friday at 1845hr the same week. (3mks)
 Find the least whole number by which 2^{5}×5^{4}×7^{3} must be multiplied with to get a perfect cube. What is the cube root of the resulting number? (3mks )
 A woman went on a journey by walking, bus and matatu. She went by bus ^{4}/_{5 }of the distance, then by matatu for ^{2}/_{3} of the rest of the distance. The distance by bus was 55km more than the distance walked. Find the total distance. (3mks).
 Simplify the expression: (9t^{2} 25a^{2}) (3mks).
(6t^{2}+ 19at+15a^{2})  Solve the simultaneous equations
X y = 4 and x + y = 5 (4mks)  The size of an interior angle of regular polygon is 3xº. While its exterior angle is (x – 20)º. Find the number of sides of the polygon. (3mks)
 A Kenya company received US Dollars M. The money was converted into Kenya Shillings in a bank which buys and sells foreign currencies.
Buying (in Ksh) Selling (in (Ksh) 1 Sterling Pound 125.78 126.64 1 Us Dollar 75.66 75.86  If the company received Ksh.15, 132,000, calculate the amount, M received in US Dollar. (2mks)
 The company exchanged the above Kenya shillings into Sterling pounds to buy a car in Britain. Calculate the cost of the car to the nearest Sterling pound. (2mks)
 A plot in a shape of rectangle measurers 608m by 264m. Equidistance fencing posts are placed along its length and breadth as far apart as possible. Determine
 The maximum distance between the posts. (1mk)
 The number of posts used. (2mks)
 Given that sin (x – 30)º  Cos (4x) 0. Find the tan (2x+30)º (3mks)
 A trader sold a dress for Ksh 7200 allowing a discount of 10% on the marked price. If the discount had not been allowed the trader would have made a profit of 25% on the sale of the suit. Calculate the price at which the trader bought the dress. (3mks)
 In august, Joyce donated ^{1}/_{6 th }of her salary to a children’s home while Chui donated ^{1}/_{5 th }of his salary to the same children’s home. Their total donation for August was Kshs 14820. In September, Joyce donated ^{1}/_{8}_{ th }of her salary to the children’s home while Chui donated ^{1}/_{12}_{ th }of his salary to the children’s home. The total donation for September was Kshs 8675. Calculate Chui’s monthly salary. (4mks)
 Simplify completely 3^{n + 3}  3^{n + 1 }(3mks)
4 x 3^{n + 2 }  In what ratio should grade A tea costing Sh. 180 per kg be mixed with grade B tea costing Sh. 300 per kg to produce Nganomu Tea which when sold at Kshs 270 a profit of 20% is realized? (3mks)
SECTION II (50 MARKS)
Answer any five questions from this section in the spaces provided  Atambo poured spirit into a test tube which has hemispherical bottom of inner radius 1.5cm. He noted that the spirit is 8cm high.
 What is the area of surface in contact with spirit? (4mks)
 Calculate volume of spirit in the test tube. (4mks)
 If Atembo obtained the mass of the spirit as 10g. Calculate the density of the spirit. (2mks).
 A bus left Nairobi at 7.00 am and traveled towards Eldoret at an average speed of 80Km/hr. At 7.45am a car left Eldoret towards Nairobi at an average speed of 120Km/hr. The distance between Nairobi and Eldoret is 300 km. Calculate:
 The time the bus arrived at Eldoret. (2mks)
 The time of the day the two met. (4mks)
 The distance of the bus from Eldoret when the car arrived in Nairobi. (2mks)
 The distance from Nairobi when the two met. (2mks)
 The figure below C is a point on AB such that AC: CB=3:1 and D is the mid –point of OA. OC and BD intersect at X.
Given that OA = a and OB = b Write the vectors below in terms of a andb.
 AB (1mk)
 OC (2mks)
 BD (1mk)
 If BX = h BD, express OX in terms of a, b, and h. (1mk)
 If OX = KOL, find h and k. (4mks)
 Hence express OX in terms of a andb only. (1mk).
 Write the vectors below in terms of a andb.

 Using a ruler and a pair of compasses only, draw a triangle ABC such that AB = 5cm,BC = 8cm and <ABC = 60º. Measure AC and <CAB.(4mks)
 Find a point O in ΔABC such that OA = OB = OC. (2mks)
 Construct a perpendicular from A to BC to meet BC at D. Measure AD. Hence calculate the area of the ΔABC (4mks)
 A boy started walking due East from a dormitory 100m South of a borehole. He walked to the school library from which the bearing of the borehole is 315º. He then walked on a bearing of 030º to the water tank. From the water tank he went west to the borehole.
 Using a scale of 1cm to represent 20m, construct a diagram to show the positions of the tank, borehole, dormitory and library. (5mks).
 Find the distance and bearing of the borehole from the water tank. (3mks)
 Calculate the total distance covered by the boy. (2mks).
 The table below shows the amount in shillings of pocket money given to students in a particular school.
Pocket Money (Ksh) 210 – 219 220229 230239 240249 250259 260269 270279 280289 290299 No. of Students 5 13 23 32 26 20 15 12 4  State the modal class. (1mk)
 Calculate the mean amount of pocket money given to these students to the nearest shilling. (4mks).
 Use the same axes to draw a histogram and a frequency polygon on the grid provided(5mks)

 Given that y = 7 + 3χ  χ², complete the table below. (2mks)
χ 3 2 1 0 1 2 3 4 5 6 y 11 7 11  On the grid provided and using a suitable scale draw the graph of y = 7 + 3χ  χ².(3mks)
On the same grid draw the straight line and use your graph to solve the equation χ²  4χ– 3 = 0. (3mks)  Determine the coordinates of the turning point of the curve. (2mks)
 Given that y = 7 + 3χ  χ², complete the table below. (2mks)
 A straight line L_{1} has a gradient ˉ½ and passes through point P (1, 3). Another line L_{2} passes through the points Q (1, 3) and R (4, 5). Find.
 The equation of L_{1}. (2mks)
 The gradient of L_{2}. (1mk)
 The equation of L_{2}. (2mks)
 The equation of a line passing through a point S (0, 5) and is perpendicular to L2. (3mks)
 The equation of a line through R parallel to L_{1}.(2mks)
MARKING SCHEME
SNO:  WORKING  MARKS  
1  √1408X594X12 √128X54X12 √[128X9X2X3X3X2 625  M1 M1 A1  
03  
2  ASF = 48 = 4 LSF = √ ^{4}/_{9} = ^{2}/_{3} VSF= (^{2}/_{3})^{3} = ^{8}/_{27} Vol=^{8}/_{27} x162 =48cm^{3 }  M1 M1 A1  
03  
3  0.5 x14x8 sin θ=28m^{2} Sin θ=0.5 θ=Sin^{1} (0.5) θ =30º  M1 A1  
02  
4  TuesdayThursday=24x3=72hours  B1 M1 A1  
03  
5  2^{5}X5^{4}X7^{3}X(2X5^{2})  M1 M1 A1  
03  
6  Bus═> 4x  M1 M1 A1  
03  
7  N=9t^{2}25a^{2}=(3t5a)(3t+5a) D=6t^{2}+19at+15a^{2}=6t^{2}+9at+10at+15a^{2}  M1 M1 A1  
03  
8  x = 4 y 4 + y = 5 y 4 + y^{2} = 5y y^{2}  5y + 4 = 0 y^{2}  y  4y + 4 = 0 y(y  1) 4(y  1) = 0 (y  4)(y  1) = y = 4 ; y = 1 x = 1 x = 4  M1 M1 M1 A1  
04  
9  3x+x20=180º 4x=200º X=50º n=360º=360º 12sides  M1 M1 A1  
03  
10(a)
(b)  M = 15,132,000 75.66 = 200,000 USDollars 15,132,000 126.64 11944 Sterling pounds  M1 A1 M1 A1  
04  
11(a)
(b)  HCF of 608 and 264 HCF = 2^{3} = 8 Maximum distance between the posts = 8m Number of posts=2(608+264)÷8  A1
 
03  
12  x  3 + 4x = 90º 5x = 120º x = 24º tan/92 x 24 + 30)º = tan 78º = 4.705  M1 M1 A1  
03  
13  Marked Price = 100 x 7200 =sh6400  M1 M1 A1  
03  
14  ^{1}/_{6} x + ^{1}/_{5}y = 14820 x= 45 000 Chui’s salary =Kshs 36,600  M1 M1 A1 A1  
04  
15  = 27(3^{n}) 3(3^{n}) 36(3^{n}) = 24(3^{n}) 36(3^{n}) = ^{2}/_{3}  M1 M1 A1  
16  cost price = 270 x 100= 225 120 180x + 300y = 225 x + y 180x + 300y = 225 + 225y 45x = 75y x = 75 = 5 y 45 3 ratio 5:3  M1 M1 A1  
03  
17(a)
(b)
(c)  Surface area of hemisphere=2πr^{2} S.A= 2xπ x1.52 T.S.A=14.14+61.29 Density=M/v
 M1 M1
A1 M1 A1 M1 A1
 
10  
18(a
(b)
(d)  Time = D = 300 Distance covered by bus at 7.45am Time taken by car =  M1 A1 M1 M1 M1 A1 M1 A1
 
10  
19(a) (ii)
(iii)
(b)
(c)
 AB = b  a
OX=b(1h)+½ ah OX=b(1h)+½ ah OX=¼ ak+¾ bk ½ah =¼ak 2h = k ^{1}/_{5} a+ ^{3}/_{5} b 
A2
M1
A1 A1  
10  
20  AB=5cm, BC=8cm ABC=60º AC=7.0 ± 0.1cm BAC=83±1º Bisectors of any 2 sides centre o marked Bisector of BC from A AD measured 4.3±0.1 Area=½ x 8 x 4.3 =17.2cm^{2}  B1 B1
B1
M1 A1  
10  
21(a)

Distance=20x8 =160km Bearing =270º± 2º Total distance walked = 100+120+160 =380km  B1
A1
 
10  
22(a)
 Modal class=240249
Mean=∑fx =37825 = ksh 252  B1
L1  
10  
23(a)
(b)

(1.5, 9.8)  B2 S1 C1 P1 M1 L1 A1 B2  
10  
24(a)
(b)
(c)
(d)
(e)  y  3= ½ g = 5   3 y  5 = ^{8}/_{3} y  5 =  3  M1 A1
M1
M1 M1 A1  
10 
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