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 from section I and ANY FIVE 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 A (50 marks)
 Without using a calculator or tables, evaluate: (3 marks)
 Solve the equation for x. 5^{2x+1}+5^{2x}750 =0 (3 marks)
 Simplify 8mn6m+8n^{2}6n (3 marks)
8n6  Use squares, square roots and reciprocals tables to evaluate the following giving your answer to 2 decimal places. (4 marks)
1 + 2
√20.52 (6.23)^{2}  Susan made a loss of 20% by selling a blender at sh. 2,400. What profit would she have made had she sold it at sh. 3300? (3 marks)
 Solve for x and y using substitution method:
^{1}/_{3}(x + y) – 2 = 0
^{1}/_{4}(x  y) = 1 (3 marks)  The number of sides of two regular polygons differs by one. If the sum of the interior angles of these polygons is in the ratio 2:3, calculate the number of sides of each polygon and name them. (3 marks)
 Solve for x in the following equation: Sin(½ x 10º)=Cos2x (3 marks)
 A vehicle moves at an initial speed of 20m/s with a constant acceleration of 2m/s2 for five seconds before breaks are applied. If the car comes to rest under constant deceleration 4 seconds, determine the total distance travelled during the 9 seconds (3 marks)
 Simplify completely the expression (4 marks)
 A point P divides the line AB shown below internally in the ratio 2:3. By construction, find the position P and measure AB.
A B (3 marks)  In the figure below, O is the centre of the circle and reflects angle AOC =1420. Find angle ABC. (3 marks)
 A tourist arrived in Kenya with 10,000 US dollars which he converted to Ksh on arrival. He spent Kshs.428,500 and converted the remaining amount to Sterling pounds. How much did he receive in Sterling pounds? The currency exchange rate of the day was as follows; (3 marks)
Currency Buying Selling 1 Sterling pound 135.50 135.97 1US dollar 72.23 72.65  Adam harvested 200 bags of wheat from 2 ha of his farm. How many bags of wheat would he harvest from 16 ha if he maintained the rate? (3 marks)
 Complete the solid below whose length is 7cm (3 marks)
 Write down three inequalities which fully describe the unshaded region R in the figure below (3 marks)
SECTION B (50 marks)
 Three points P, Q and S are pm the vertices of a triangular plain field. P is 400m from Q on a bearing of 3000 and R of 550m directly south of P.
 Using a scale of 1 cm to represent 100m on the ground, draw a diagram to show the position of the points. (3 marks)
 Use the scale drawing to determine;
 The distance and bearing of Q from R. (2 marks)
 The bearing and distance of point S from P given that point S is directly 600m East of R. (3 marks)
 The bearing and distance of Q from S. (2 marks)
 A bus travelling at a speed of 80km/hr left Mombasa at 8.00am for Nairobi. Two hours later, a car travelling at a speed of 100km/hr left Nairobi for Mombasa.
 Given that the distance between both cities is 500km, find the time of the day when the two vehicles met. (6 marks)
 After meeting, the speed of both vehicles dropped to 60km/hr due to traffic jam. At what time did each vehicle arrive at its destination? (4 marks)
 The figure below represents an histogram of heights against age brackets of members of a village.
Using the figure above, Develop a frequency distribution table (3marks)
 Using the table in (a) above find;
 The mean. (3marks)
 The median class (1mark)
 The median (3marks)
 The diagram below shows a container base made of a frustum of a square pyramid. The top is a solid frustum of a cone.
AB = BC = 12 cm
EF = 6
Height of 10 and 6 cm respectively. Calculate the surface area of the bottom solid. (5 marks)
 Calculate the surface area of the top side. (4 marks)
 Calculate the total area. (1 mark)

 Complete the table below for the function
y=x^{2}+10x (2marks)X 1 0 1 2 3 4 5 6 8 10 Y 9 24 0  On the grid provided draw the graph of y=x^{2}+10x (3marks)
 Using the graph above solves the equations:
 10xx^{2}=0 (2marks)
 x^{2}7x8=0 (3marks)
 Complete the table below for the function
 Two lines L_{1}=2y3x6 and L_{2}=3y+x20=0 intersect at point A.
 Find the coordinates of A (3marks)
 A third line L_{3} is perpendicular to L_{2} at point A. Find the equation of L_{3} in form of y=mx+c, where m and c are constants. (3marks)
 Another line L_{4} is parallel to l1 and passes through (1,3). Find the xintercept and the yintercept of L_{4}. (4marks)

 PQRS is a quadrilateral with vertices P(1,4), Q(2,1), R(2,3) and S(6,4). On the grid provided, plot the quadrilateral. (1 mark)
 Draw P’Q’R’S’ the image of PQRS under a positive quarter turn about the origin and write down its coordinates. (3 marks)
 Draw P”Q”R”S” the image of P’Q’R’S’ under an enlargement scale factor 1 and center (0,0) and write down its coordinates. (3 marks)
 Determine the matrix of a single transformation that maps PQRS onto P”Q”R”S (3 marks)
 PQRS is a quadrilateral with vertices P(1,4), Q(2,1), R(2,3) and S(6,4). On the grid provided, plot the quadrilateral. (1 mark)
 A curve whose equation is 3y=918x+^{27}/_{2} x^{2} 3x^{3} turns at points P and R.
 Find the coordinates of P and R (5 marks)
 Determine the nature of points P and R (3 marks)
 Sketch the curve (2 marks)
MARKING SCHEME
SECTION A (50 marks)
 Without using a calculator or tables, evaluate: (3 marks)
(^{203}/_{135} ÷ ^{429}/_{56})^{2}
(^{203}/_{135} ÷ ^{56}/_{429})^{2 }
(135x  429)^{2}
203 x 56  Solve the equation for x. 5^{2x+1}+5^{2x}750 =0 (3 marks)
5^{2x+1} + 5^{2x} = 750
5^{2x}.51+5^{2x} = 75
5^{2x}(5 + 1)= 750
5^{2x}(6) = 750
5^{2x}=5^{3}
2x = 3
x = 1.5  Simplify 8mn6m+8n^{2}6n (3 marks)
8n6
2m(4n  3)+2n(4n  3) = (4n  3)(2m + 2n)
2(4n  3) 2(4n  3)
=2(m + n)
2
= m + n  Use squares, square roots and reciprocals tables to evaluate the following giving your answer to 2 decimal places. (4 marks)
1 + 2
√20.52 (6.23)^{2}
√20.56 = 4.5299
(6.23)^{2} = 38.81
1(rec 4.530) + 2(rec 38.81)
0.2208 + 2 x 0.02576
= 0.2208 + 0.05152
= 0.27232  Susan made a loss of 20% by selling a blender at sh. 2,400. What profit would she have made had she sold it at sh. 3300? (3 marks)
80% = 2400
100% = ?
100% x 2400
80
= 3000  Solve for x and y using substitution method:
^{1}/_{3}(x + y) – 2 = 0
^{1}/_{4}(x  y) = 1 (3 marks)
x + y  6 = 0
x  y  4 = 0
x = y + 4
(y + 4)+ y = 6
2y = 2
y = 1
x = 1 + 4
= 5  The number of sides of two regular polygons differs by one. If the sum of the interior angles of these polygons is in the ratio 2:3, calculate the number of sides of each polygon and name them. (3 marks)
180 (n  2) = ^{2}/_{3}
180(n + 1  2)
3(n  2) = 2(n  1)
3n  6 = 2n  2
3(n  2) = 6  2
n = 4  Quadrilateral
n + 1 = 5  Pentagon  Solve for x in the following equation: Sin(½ x 10º)=Cos2x (3 marks)
(½x  10)+ 2x = 90
2.5x = 100
x = 40  A vehicle moves at an initial speed of 20m/s with a constant acceleration of 2m/s2 for five seconds before breaks are applied. If the car comes to rest under constant deceleration 4 seconds, determine the total distance travelled during the 9 seconds (3 marks)
D=(30 + 20)5 + ½ x 30 x 4
2
= 125 + 60
= 185m  Simplify completely the expression (4 marks)
1 (25x^{2}  9y^{2})
225
1 (25x^{2} + 30xy + 9y^{2})
225
(5x  3y)(5x + 3y)
25x^{2} + 15xy + 15xy + 9y^{2}
(5x  3y)(5x + 3y)
5x(5x  3y)+3y(5x + 3y)
(5x  3y)(5x + 3y)
(5x  3y)(5x + 3y
= 5x  3y
5x + 3y  A point P divides the line AB shown below internally in the ratio 2:3. By construction, find the position P and measure AB.
A B (3 marks) for a line forming <with AB
 for parallel line
 for point P
 In the figure below, O is the centre of the circle and reflects angle AOC =1420. Find angle ABC. (3 marks)
<ABC= 180º  ½(142)
= 180º  71
= 109º
Alt<ABC = 360  142
3
=218
2
=109º
2  A tourist arrived in Kenya with 10,000 US dollars which he converted to Ksh on arrival. He spent Kshs.428,500 and converted the remaining amount to Sterling pounds. How much did he receive in Sterling pounds? The currency exchange rate of the day was as follows; (3 marks)
Currency Buying Selling 1 Sterling pound 135.50 135.97 1US dollar 72.23 72.65
(10000 x 72.23)
sh.722300
spend 428500
(722300  428500)
=sh 293800
1 sterling pound = sh135.97
sh293800
=293800 = 2160.8 sterling pounds
135.97  Adam harvested 200 bags of wheat from 2 ha of his farm. How many bags of wheat would he harvest from 16 ha if he maintained the rate? (3 marks)
16 x 200
2
= 1600bags  Complete the solid below whose length is 7cm (3 marks)
showing hidden side
complete solid  Write down three inequalities which fully describe the unshaded region R in the figure below (3 marks)
L1
^{x}/_{4} + ^{y}/4 = 1_{ }
^{x}/_{3}(12) + ^{y}/_{4}(12) =1(12)
4x + 3y = 12
8 + 0 = 12
8 < 12
4x + 3y ≤ 12
L2
^{x}/_{4} + ^{y}/_{4} = 1 (6,0)
^{6}/_{4}  ¼
^{5}/_{4} > 1
L3
^{x}/_{4} + ^{y}/_{4} ≥1
or
x + y ≥ 4
or
x  y ≥ 4
y ≥ 3
SECTION B (50 marks)
 Three points P, Q and S are pm the vertices of a triangular plain field. P is 400m from Q on a bearing of 3000 and R of 550m directly south of P.
 Using a scale of 1 cm to represent 100m on the ground, draw a diagram to show the position of the points. (3 marks)
 Use the scale drawing to determine;
 The distance and bearing of Q from R. (2 marks)
 The bearing and distance of point S from P given that point S is directly 600m East of R. (3 marks)
 The bearing and distance of Q from S. (2 marks)
 A bus travelling at a speed of 80km/hr left Mombasa at 8.00am for Nairobi. Two hours later, a car travelling at a speed of 100km/hr left Nairobi for Mombasa.
 Given that the distance between both cities is 500km, find the time of the day when the two vehicles met. (6 marks)
D = t x s
= 2 x 80
= 160km
500  160 = 340km
A.S = 80 + 100
= 180km/hr
t = ^{d}/_{s}
T =340
180
= ^{17}/_{9} hrs
= 1^{8}/_{9}hrs →1hr . 53^{1}/_{3}
10:00:00
1 53 20
11:53:20 am  After meeting, the speed of both vehicles dropped to 60km/hr due to traffic jam. At what time did each vehicle arrive at its destination? (4 marks)
d = t x s
= ^{17}/_{9} x 100
Distance covered at the time of meeting
1^{8}/_{9} x 80 = 151^{1}/_{9}km
Bus = 160 + 151^{1}/_{9} = 311^{1}/_{9}km
Car = 151^{1}/_{9}km
remaining distance
Bus = 500  311^{1}/_{9 }= 188^{8}/_{9}km
Car = 500  151^{1}/_{9} = 348^{8}/_{9}km
Time taken by
Bus =188^{8}/_{9} = 3hr 9mins
60
Car = 348^{8}/_{9} = 5hrs 49mins
60
Arrival time
Bus 11:53
3 09
15.20hrs
Car 11:53
5 49
17:42 hrs
 Given that the distance between both cities is 500km, find the time of the day when the two vehicles met. (6 marks)
 The figure below represents an histogram of heights against age brackets of members of a village.
Using the figure above, Develop a frequency distribution table (3marks)
x f x xf cf 015
1520
2055
5565120
50
560
60
8507.5
17.5
47.5
60900
875
26600
3600
31975120
170
730
790  Using the table in (a) above find;
 The mean. (3marks)
x =31975
790
= 40.475  The median class (1mark)
790 = 395
2  The median (3marks)
20 +(395  170)35
730
= 30.788
 The mean. (3marks)
 Develop a frequency distribution table (3marks)
 The diagram below shows a container base made of a frustum of a square pyramid. The top is a solid frustum of a cone.
AB = BC = 12 cm
EF = 6
Height of 10 and 6 cm respectively. Calculate the surface area of the bottom solid. (5 marks)
AC^{2} = 144 + 144
AC^{2} = 288
AC = √288
OC = √288
2
(VC^{2}) = 16^{2} + (√288)^{2}
2
= 256 + 72
VC = √328
H^{12} = (√328)^{2}  6^{2}
= 328  36
(H^{1}) = √292
h ^{1} = h
H^{1} H
h ^{1} = 6
√292 16
h^{1} = ^{3}/_{8} (√292)
A = [½ x 12 x √292 ½ x 6 x ^{3}/_{8} √292]4
=[√292(6  ^{9}/_{8})]4
=[83.304cm^{2}]4
= 333.216cm^{2}_{2} = 12 x 12 = 144cmcm^{3 }
A_{2} = 12 x 12 = 144cm^{2}^{ }
A_{3} = (6 x 6)  ^{22}/_{7} x 3 x 3
= 36  28^{2}/_{7}
= 7.7142cm2
Total = 333.216 + 144 + 7.7142
= 484.93cm  Calculate the surface area of the top side. (4 marks)
A_{1} = ^{22}/_{7} x 2 x 2
= 12.5714cm^{2}^{ }
^{h}/_{H} = ^{r}/_{R}
h = ^{2}/_{3}
6+h
3h = 12 + 2h
h = 12
L^{2} = 12^{2} + 2^{2}
L = 12.166
12.166 = ^{2}/_{3}
L
2L = 36.4966
L = 18.248
A_{2} = πRL  πrl
=π x 30.412
=95.581
total area = 12.57N + 95.581
=108.152  Calculate the total area. (1 mark)
484.93 + 108.15
= 593.082cm^{2}
 Calculate the surface area of the bottom solid. (5 marks)

 Complete the table below for the function
y=x^{2}+10x (2marks)X 1 0 1 2 3 4 5 6 8 10 Y 11 0 9 16 21 24 25 24 16 0  On the grid provided draw the graph of y=x^{2}+10x (3marks)
 Using the graph above solves the equations:
 10xx^{2}=0 (2marks)
x = 0 or x = 0  x^{2}7x8=0 (3marks)
y = x^{2} + 10x + 0
+
0 = x^{2}  7x  8
y = 3x + 8
x = 0, y = 8, (0,8)
x = 2, y = 2, (2,2)
x = 1 or x = 8
 10xx^{2}=0 (2marks)
 Complete the table below for the function
 Two lines L_{1}=2y3x6 and L_{2}=3y+x20=0 intersect at point A.
 Find the coordinates of A (3marks)
(2y  3x = 6) 3
(3y + x = 20) 2
6y  9x = 18
6y + 2x = 40
11x = 22
x = 2
2y  3(2) = 6
2y = 12
y = 6
A(2,6)  A third line L_{3} is perpendicular to L_{2} at point A. Find the equation of L_{3} in form of y=mx+c, where m and c are constants. (3marks)
3y = x + 20
y = ^{1}/_{3} x + ^{20}/_{3}
m = 3
y  6 = ^{3}/_{1}
x  2
y  6 = 3x  6
y = 3x + 0  Another line L_{4} is parallel to l1 and passes through (1,3). Find the xintercept and the yintercept of L_{4}. (4marks)
2y = 3x + 6
y = ^{3}/_{2} x + 3
y  3 = ^{3}/_{2}
x + 1
2(y  3) = 3(x + 1)
2y  6 = 3x + 3
2y = 3x + 9
y = ^{3}/_{2} x + ^{9}/_{2}
x intercept y = 0
^{2}/_{3} x ^{3}/_{2}x = ^{9}/_{2}x ^{x}/_{3}
x = 3
y intercept x =0
y = ^{9}/_{2},
y = 4.5
 Find the coordinates of A (3marks)

 PQRS is a quadrilateral with vertices P(1,4), Q(2,1), R(2,3) and S(6,4). On the grid provided, plot the quadrilateral. (1 mark)
 Draw P’Q’R’S’ the image of PQRS under a positive quarter turn about the origin and write down its coordinates. (3 marks)
P'(4,1) Q'(1,2) R'(3,2) S'(4,6)  Draw P”Q”R”S” the image of P’Q’R’S’ under an enlargement scale factor 1 and center (0,0) and write down its coordinates. (3 marks)
P"(4,1) Q"(1,2) R"(3,2) S"(4,2)  Determine the matrix of a single transformation that maps PQRS onto P”Q”R”S (3 marks)
The transformation of +90º about the origin
for constructions
 PQRS is a quadrilateral with vertices P(1,4), Q(2,1), R(2,3) and S(6,4). On the grid provided, plot the quadrilateral. (1 mark)
 A curve whose equation is 3y=918x+^{27}/_{2} x^{2} 3x^{3} turns at points P and R.
 Find the coordinates of P and R (5 marks)
[3y = 9  18x + ^{22}/_{2}x^{2}  3x^{3}]x ^{1}/_{3}
y = 3  6x + 4.5x^{2}  x^{3}^{dy}/_{dx} = 6 + 9x  3x^{2}
at st.p ^{dy}/_{dx} = 0
6 + 9x 3x^{2} = 0
x^{2}  3x + 2 = 0
x(x1) 2(x  1) = 0
x = 1, y = 3  6 + 4.5 + 1
y = ½
when x = 2
y = 3  12 + 18  8
y = 1
p_{1}(1,½) P_{2}(2,1)  Determine the nature of points P and R (3 marks)
y" = 9  6x
at x = 1
y = 9  6 = 3
p_{1}(1,½) min point
y" = 9  6x at x = 2
y" = 9  6(2) = 3
P_{2}(2,1) max point  Sketch the curve (2 marks)
 Find the coordinates of P and R (5 marks)
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