Instructions to candidates
 This paper consists of two sections I, II.
 Answer all the questions in section 1 and any five questions from section II.
 Show all steps in your calculations, giving answers at each stage in the spaces provided below each question.
 Marks may be given for correct working even if the answer is wrong.
 Nonprogrammable silent electronic calculators and KNEC mathematical tables may be used.
For Examiner’s Use Only.
SECTION I
Questions 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
Total 
marks 
SECTION II
Questions 
17 
18 
19 
20 
21 
22 
23 
24 
Total 
Marks 
QUESTIONS
 Evaluate (3mks)
 Use square roots, reciprocal and square tables to evaluate to 4 significant figures the expression (4mks)
 Three similar 21inch television sets and five similar 17inch television cost Ksh.129, 250. The difference between the cost of two 21inch television sets and four 17inch television sets is Ksh. 22,000. Calculate the price of a 21inch television set and that of 17inch television set. (3mks)
 Three numbers, 1400, 1960 and n, have a G.C.D and L.C.M of 70 and 2^{2} x 5^{2} x 7^{2} x 1^{1} respectively. Find the least possible value of n (3mks)
 Find the equation of a straight line which is equidistant from the points A (2,3) and B (6,1) (3mks)
 Solve for x in the equation. (3mks)
9^{(2x1)} x 3^{(2x+1)} = 243  An open rectangular box measures externally 32cm long, 27cm wide and 15cm deep. The box is made up of metal 1cm thick. If it has a mass of 1.5kg, what is the density of the box to 4 significant figures? (3mks)
 Using the three quadratic identities only factorize and simplify: (3mks)
(xy)^{2 } (x+y)^{2 }
(x^{2}+ y^{2})^{2} (x^{2} y^{2} )^{2}  An airplane leaves point A (60^{0}S, 10^{0}W) and travels due East for a distance of 960 nautical miles to point B. determine the position of B and the time difference between points A and B. (3mks)
 A salesman earns 3% commission for selling a chair and 4% commission for selling a table. A chair fetches K£ 75. One time, he sold ten more chairs than tables and earned seven thousand, two hundred Kenya shillings as commission. Find the number of tables and chairs sold. (3mks)
 A Kenyan company received US Dollars 200,000. The money was converted into Kenya shillings in a bank which buys and sells foreign currencies as follows:
Buying Selling
(in Kenya shillings) (in Kenya shillings)
1 US Dollar 77.24 77.44
Sterling Pound 121.93 122.27 Calculate the amount of money, in Kenya shillings, the company received. (1 marks)
 The company exchanged the Kenya shillings calculated in (a) above, into sterling pounds to buy a car from Britain. Calculate the cost of the car to the nearest sterling pound. (2 marks)
 Tap A fills a tank in 6 hours, tap B fills it in 8 hours and tap C empties it in10 hours. Starting with an empty tank and all the three taps are opened at the same time, how long will it take to fill the tank? (3 marks)
 The length of a rectangle is increased by 20% while the width is decreased by 10% . Find the percentage change in area. (3 marks)
 In the figure below, AC is an arc of a circle centre D. Angle ADC = 600, AD = DC = 7cm and CB = 5cm.
Calculate The area of triangle ADB (2 marks)
 The area of the shaded region. (2 marks)
 Solve 4 ≤ 3x – 2 < 9 + x , hence list the integral values that satisfies the inequality. (3 marks)
 A transformation whose matrix is given by (2x1  32x) maps a triangle with area 8 cm2 onto another triangle with area 72 cm2, calculate the value of x (3 marks )
SECTION II
 The distance between two towns A and B is 760 km. A minibus left town A at 8:15a.m and traveled towards B at an average speed of 90km/h. A matatu left B at 10:35a.m and on the same day and travelled towards A at an average speed of 110km/h.

 How far from A did they meet? (4mks)
 At what time did they meet? (2mks)
 A motorist starts from his home at 10:30 a.m on the same day and traveled at an average speed of 100km/h. He arrived at B at the same time as the minibus. Calculate the distance from B to his home. (4mks)

 The income tax rates in a certain year are as shown below.
Income (k₤ – p.a
Rate (KSh. per ₤)
1 – 4200
2
4201 – 8000
3
8001 – 12600
5
12601 – 16800
6
16801 and above
7
 his gross tax per annum in Kshs (2 Marks)
 his taxable income in K₤ per annum (2 marks)
 his basic salary in Ksh. per month (2marks)
 his net salary per month (2 mark
 The parents of a certain mixed secondary school decided to buy a school van worth Ksh. 900,000. Each student was to contribute the same amount of money. 50 students were transferred from the school; as a result, each if the remaining students had to pay Ksh. 600 more.
 Find the original number of the students in the school. (5mks)
 Find the percentage change in contributions per student. (3mks)
 If the ratio of boys to girl in the school was 11: 7 find the amount money contributed by boys alone. (2mks)
 Using a ruler and a pair of compasses only construct triangle ABC such that angle BAC= 90^{0}, AC= 5 cm and BC = 10 cm. (3 marks)
 Circumscribe a circle on the triangle ABC constructed above (3 marks)
 Measure the radius of the circle (1 mark)
 Find the difference in the area of the circumcircle and the triangle. (3 marks)
 The coordinates of a triangle ABC are A(1, 1) B(3, 1) and C (1, 3).
 Plot the triangle ABC. (1 mark)
 Triangle ABC undergoes a translation vector (2 , 2 ). Obtain the image of A' B' C ' under the transformation, write the coordinates of A' B' C'. (2 marks)
 A' B' C' undergoes a reflection along the line X = 0, obtain the coordinates and plot on the graph points A" B" C", under the transformation (2 marks)
 The triangle A" B" C" , undergoes an enlargement scale factor 1, centre origin. Obtain the coordinates of the image A'" B"' C"'. (2 marks)
 The triangle A"' B"' C"' undergoes a rotation centre (1, 2) angle 1200. Obtain the coordinates of the image Aiv Biv Civ. (2 marks)
 Which triangles are directly congruent. (1 mark)
 The figure below shows triangle OPQ in which OS = ^{1}/_{3} OP and OR = ^{1}/_{3} OQ. T is a point on QS such that QT = ^{3}/_{4} QS
 Given that OP = p and OQ = q, express the following vectors in terms of p and q.
 SR (1 Mark)
 QS (2 Marks)
 PT (2 Marks)
 TR (2 Marks)
 show that point PTR are collinear. (3mks)
 Given that OP = p and OQ = q, express the following vectors in terms of p and q.


 Fill the table below for the function.
y = 2x^{2} + 5x – 12 for 8 ≤ x ≤ 4 (2 marks)
X
8
7
6
5
4
3
2
1
0
1
2
3
4
2x^{2}
128
18
2
32
5x
40
15
5
20
12
12
12
12
12
Y
76
9
5
40
 Using the table, draw the graph of the function y = 2x2 + 5x – 12. Use the scale 1cm to 1 unit on the xaxis and 1cm for 10 units for the y – axis (4 mark
 Fill the table below for the function.
 Use the graph drawn above to solve the following equations.
 2x^{2} + 5x – 12 = 0 (2 marks)
 3 – 7x – 3x^{2} = 0 (2 marks)

 The displacement, S meters of a moving particle after t seconds is given by S=2t^{3}5t^{2}+4t+3
Determine: The velocity of the particle when t=4 seconds (3marks)
 The value of t when the particle is momentarily at rest (3 marks)
 The displacement when the particle is momentarily at rest (2 marks)
 The acceleration of the particle when t=10 seconds (2 marks)
MARKING SCHEME
 N: 2^{1}/_{4}  ^{3}/_{4} = 9  3 = 6 = 3
4 4 2
^{3}/_{2} x ^{11}/_{3} ÷ ^{11}/_{5} = ^{3}/_{2} x ^{11}/_{3} x^{ 5}/_{11} = ^{5}/_{2}
D: ^{10}/_{6} ÷ ^{5}/_{4} = ^{10}/_{6} x ^{4}/_{5} = ^{4}/_{3}
^{5/2} / _{4/3} = ^{5}/_{2} x ^{3}/_{4} = ^{15}/_{8} = 1^{7}/_{8}  (0.06458)1/2 = √6.458 x 10^{2} = 2.5413 x 10^{1}
(2/0.4327)^{2} = [2(^{1}/_{4.327} x 10^{1}]^{2} = {2(0.2311 x 10)}^{2}
= (2 x 2.311)^{2} = 4
0.25413 + 21.363 = 21.61713
= 21.62  3x + 5y = 129250
2x  4y = 22000
6x + 10y = 258500
6x  12y = 66000
22y = 192500
y = 8750
2x  4(8750) = 22000
2x  35000 = 22000
2x = 57000
x = 28500
17 inch TV = sh 8750 ; 21 inch tv = sh 28500  gcd = 70 = 2 x 5 x 7
l.c.m = 23 x 52 x 7
1960 = 23 x 5 x 72
oter number = 2 x 5 x 7 x11
= 770  midpoint = (2 + 6 , 3 + 1) = (4, 2)
2 2
m^{1} = 1  3 = 2 = 1
6  2 4 2
m^{2} = 2
y  2 = 2
x  4
y  2 = 2x  8
y = 2x  6  32(2x  1) x 3(2x+1) = 3^{5}
34x  2 + 2x + 1 = 3^{5}
36x  1 = 3^{5}
6x  1 = 5
6x = 6
x = 1  volume of materias ofte box = external  internal volume
= (32 x 27 x 15)  (30 x 25 x 14) = 2460cm^{3}
mass of te box = 1.5 = 1.5 = 1500
density = mass/volume = 1500/2460
=0.6098 g/cm^{3}  = (2x)(2y) = 4xy = 1
(2x^{2})(2y^{2}) 4x^{2}y^{2} xy  didstance = ∅ x 60 cos 60
∅ x 60 x 0.5 = 960
∅ = 960/30 = 32  lonitude difference
B(60ºS, 22ºE)
total difference in time = 32 x 4 min = 128 minutes
= 2 hours 8 minutes  a chair = 30 = 30 x 20 = 600
a table = 75 = 75 x 20 = 1500
no of chairs = x
no of tables = x  10
3/100 x 600x + 4/100 x 1500(x  10) = 7200
18x + 60(x  10) = 7200
18x + 60x  600
78x = 7800
x = 100 chairs
x  10 = 90 tables 
 200000 us dollars
1 US dollars = s 7724
200000 = 200000 x 77.24 = 15 448 000
1  1 sterling pound = ks 122.27
? = 15448000
1 x 15448000 = 126343
122.27
 200000 us dollars
 new lengths = 120%L = 1.2L
new month = 90%W = 0.9W
New area = 1.2L x 0.9W = 1.08LW
Original area = LW
% change = 1.08LW  LW x 100
LW
= 8% increase 
 area of a triangle = 1/2 ab sin
1/2 x 7 x 12 sin 60°
1/2 x 7 x 12 x 0.866 = 36.372 cm^{2}  shaded area = area of triangle  area of sector
= 36.372  (60/360 x 22/7 x 7 x 7)
= 36.372  25.667 = 10.705 cm^{2}
 area of a triangle = 1/2 ab sin
 4 ≤ 3x  2 3x  2 < 9 + x
6 ≤ 3x 2x < 11
2 ≤ x x < 5.5
2 ≤ x < 5.5
integral values 2,3,4,5  ASF = determinant of transformation matrix
72/8 = (2x  1)x  2(3)
9 = 2x^{2}  x + 6
2x^{2}  x  3 = 0
(2x  3) (x + 1) = 0
x = 1.5 or x = 1 

 10.35
8.15
2.20 = 2 hours 20 minutes = 2^{1}/_{3} hrs
distance covered in that time = 2^{1}/_{3} x 90 210 km
distance remainin = 760  210 = 550km
relative speed = 90 + 110 = 200km/h
time taken to meet D/R.S = 550/200 = 2.75hr
distance covered by minibus in 2.75 hr
= 2.7 x 9 = 247.5k
distance from A = 210 + 247.5 = 457.5 km 10.35 am + 2 hours 45 min
10:35
2:45
13.20
12:00
1.20 pm
 10.35 am + 2 hours 45 min
 10.35
 time taken by minibus from A to B = 760/90 = 8^{4}/_{9} hrs
time A arrived at B
8:15 am + 8:27 min
8:15
8:27
16:42
12:00
4:42 pm
time taaaken by motorist from ome to B
1642
10:30
6:12
6^{1}/_{5} hrs
distance covered by motorists from home to B
100 x 6^{1}/_{5} = 100 x 6.2 = 620 km


 his ross tax p.a in ksh
(4000 x 12) + (1100 x 12)
48000 + 13200 = 61200  1 slab = 4200 x 2
2 slab = 3800 x 3
3 slab = 4600 x 5
4 slab = y x 6 = 61200  42800
y = kf 3066.67
taxable income = (12600 + 3066.67) = kf 15 666.67  15666.67 x 20  10800 = 15311.12
1.2
26111.12  10800  26111.12  4000 = 22111.12
 his ross tax p.a in ksh
 900000  900000 = 600
x  50 x 900000x  (900000)(x  50) = 60 (x^{2}  50x)
45000000 = 600x^{2}  30000x
ans = 300 students  900000/300 = 3000
600 x 100
3000
= 20%  total ratio = 18
11/18 x 900000
= 550000
 900000x  (900000)(x  50) = 60 (x^{2}  50x)


 R  50 cm
 (22/7 x 5^{2})  (1/2 x 5 x 8.6)
 78.5714  21.5 = 57.0714 cm ^{2}





 2x^{2} + 5x  12 = y
2x^{2} + 5x  12 = 0
0 = y
x = 4 or 1.5  2x^{2} + 5x  12 = y^{3}
y = 1/3x  10 x = 2.8 or o.4
 2x^{2} + 5x  12 = y


 v = ds/dt
v = 64^{2}  104 + 4
v at 4
v = 6(4)^{2}  10(4) + 4
= 96  40 + 4
= 60 m/s  at rest
6t^{2}  10t + 4 = 0
6t^{2}  6t  4t + 4 = 0
6t(t  1)  4(t  1) = 0
6t = 4
t = 4/6s = 2/5 (S)
t = 1s  displacement of t = 1
ans = 2^{25}/_{27} m  a = dv/dt
= 12t  10
a at t = 10
120  10
= 110 m/s^{2}
 v = ds/dt
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