QUESTIONS
SECTION 1 (50 MARKS)
Answer all the questions in the space provided below each question
 Without using mathematical tables or calculator evaluate (3marks)
 Find the equation of a straight line that passes through the points A (2,3) and B5,1). Express your answer in the form ax + by = c where a, b and care integers. (3marks)
 Solve for θ if (3marks)
 A Swimming pool can be emptied by 3 pipes P, Q and working together in 3^{3}/_{4} hours. Pipe P and working alone takes 7^{1}/_{2} hours and 11^{1}/_{4} respectively. Determine how long pipe R working alone would take to empty the swimming pool. (3marks)
 In the figure below PQ  RS.PS and RQ intersect at T. If PT: PS = 2:5 and QT = 3.5 cm, calculate correct to 2 decimal place RQ. (3 marks)
 A is the point (2, 3, 4) and B is the point (X, 6, 8).Determine the possible values of X if AB =13 (4 marks)
 A metal hemisphere of radius 16 cm is melted down and cast into a cone of radius 8cm.Calculate the volume of the cone. (3marks)
 Five of the iterior angles in a nonagon are 160° and the remaining are each x^{0}. Find the possible values of x. (3marks)
 Calculate the quartile deviation of the following set of data (4marks)
Marks 2130 3140 4150 5160 6170 7180 8190 91100 No. of students 3 5 8 12 15 11 9 4  A metallic pipe which is 21 meters long has an internal radius of 13 cm and an external radius of 15 cm. if the density of the metal is 8000 kg/m^{3}, find its mass. (Take π = 22/7). (4 marks)
 Muthoni, Chebet and Amina contributed ksh 50,000, ksh 40,000 and ksh 25,000 respectively to start a business. After some time they realized a profit which was shared in the ratio of their contribution. If Aminas share was ksh 10,000, by how much was Muthoni's share more than that of Chebet's. (3marks)
 The cost of two jackets and 3 shirts was 1800. After the cost of a jacket and that of a shirt were increased by 20%, the cost of 6 jackets and 2 shirts was ksh 4,800. Calculate new total cost of 5 jackets and 4 shirts. (3 marks)
 Without using mathematical tables evaluate (3marks)
 Using a ruler and a pair of compass only, construct a rhombus AB< CD such that AC = 10 cm and ∠BAD = 60° (3marks)
 Without using a calculator or mathematical tables, evaluate (3marks)
 A point P divides a line AB externally in the ratio 4:3. Given that A is (2, 4) and point B (2,3). Find the coordinates of T. (3marks)
SECTION II (50MARKS)
Answer only five questions from this section.
 In the figure below, AC=14 cm, AD = 16 cm, DC = 11 cm, and B is a point on AC
 Calculate, correct to 2d.p
 ∠BAD (3marks)
 The size of obtuse ∠ABD (3marks)
 Calculate correct to 1 decimal place:
 The length of AB (2marks)
 The area of triangle BCD (2marks)
 Calculate, correct to 2d.p
 The following table shows heights of 100 seedlings each measured to the nearest cm.
Height (cm) Frequency 70  79 14 80  84 16 85  89 18 90  94 20 95  99 17 100  109 15  Calculate the differences between the mean and the median. (6marks)
 Draw a frequency polygon to illustrate the above information (4marks)
 Two towns P and Q are 280 km apart. A bus left town P at 9.30 am and travelled to Q at an average speed of 80 km/h. After 30 minutes, a car left town p for Q and travelled at an average speed of 100 km/h.
 Determine:
 The time when the car caught up with the bus. (3marks)
 The distance of the car from town Q when it overtook the bus. (3marks)
 After the car overtook the bus, it accelerated for 6 minutes to a speed of 120 km/h. It moved with that speed for 30 minutes after which breaks are applied and came to rest at town T after 3 minutes. Determine the distance travelled by the car in 39 minutes. (4marks)
 Determine:

 Complete the table of values for the equation y .2x^{2} + 3x + 6. (2 marks)
x 3 2 1 0 1 2 3 4 y  Use the values above to draw the graph of y = 2x^{2} + 3x + 6. (3marks)
 Using the graph drawn above Solve the oquations:
 2x^{2} = 3x +6 (2 marks)
 2x^{2} + x + 9 = 0 (3marks)
 Complete the table of values for the equation y .2x^{2} + 3x + 6. (2 marks)
 A trader deals with two types of Millet, type A and type B. type A costs ksh 400 per bag and type B costs ksh 350 per bag.
 The trader mixes 30 bags of type A and 50 bags of type B. If she sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. (4 marks)
 The trader now mixes type A and type B in the ratio x: y respectively. If the cost of the mixture is ksh 383.50 per bag, find the ratio x:y. (4marks)
 The trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b) above. Calculate the ratio of type A millet to type B millet in this mixture. (2marks)
 The equation of a line L_{1} is 3y + 2x = 10
 Find in form of y=mx+c,where m and care constants:
 The equation of line L_{2} passing through N (5,2) and parallel to L_{1} (2 marks)
 The equation of line L_{3} perpendicular to L_{2} at M (1,8) (3marks)
 Find the angle of inclination of the line L, with the horizontal. (2marks)
 Find the magnitude of MN. (3marks)
 Find in form of y=mx+c,where m and care constants:
 In the figure below A, B, C and D are points on the circle Centre O. ACF and EDFG are straight lines. Line EG is a tangent to the circle at D. ∠CDF = 35° and ∠CFG = 130°
 Calculate the Size of
 ∠OCD (2 marks)
 ∠EDA (1 mark)
 ∠ABC (2 marks)
 Given that CF_{o} 6.7 cm and DF = 8.5 cm, Calculate to 3 significant figures:
 The length of DC. (3marks)
 The radius of the circle. (3marks)
 Calculate the Size of
 The product of the first three terms of a geometric progression is 64.If the first term is a and the common ratio is r,
 Express r in terms of a. (3marks)
 Given that the sum of the three terms is 14
 Find the value of a and r and hence write down two possible sequence up to the 4th term. (5 marks)
 Find the product of the 50th terms of the two sequence. (2marks)
MARKING SCHEME
SECTION 1 (50 MARKS)
Answer all the questions in the space provided below each question
 Without using mathematical tables or calculator evaluate (3marks)
11/3  7/3 x 5/6 x 3/2
11/3  35/12
44  35
12
9/12
3/4
Denominator
1/8  1/4
 1  2
8
3/8
3/4 x 8/3
= 2  Find the equation of a straight line that passes through the points A (2,3) and B5,1). Express your answer in the form ax + by = c where a, b and care integers. (3marks)
gradient =
1  3 = 1
 5  2 7
y + 3 = 4
x  2 7
4 (x  2) = 7 (y + 3)
4x + 8 = 7y + 21
4x  7y = 13
4x + 7y = 13  Solve for θ if (3marks)
sin(2θ  50º) = cos (θ + 10º)
sin (2θ  50º) = sin 90  (θ + 10º)
20 50 = 90  θ  10
3θ = 130
θ = 43^{1}/_{3} or 43.33º  A Swimming pool can be emptied by 3 pipes P, Q and working together in 3^{3}/_{4} hours. Pipe P and working alone takes 7^{1}/_{2} hours and 11^{1}/_{4} respectively. Determine how long pipe R working alone would take to empty the swimming pool. (3marks)
ans = 22^{1}/_{2} hrs  In the figure below PQ  RS.PS and RQ intersect at T. If PT: PS = 2:5 and QT = 3.5 cm, calculate correct to 2 decimal place RQ. (3 marks)
RT/3.5 = 3/2
RT = 3/2 x 3.5
= 5.25
RQ = 5.25 + 3.5
= 8.75  A is the point (2, 3, 4) and B is the point (X, 6, 8).Determine the possible values of X if AB =13 (4 marks)
(x  2)^{2} + (6  3)^{2} + (8  4)^{2} = 169
x^{2}  4x + 4 + 9 + 16 = 169
x^{2}  4x  140 = 0  A metal hemisphere of radius 16 cm is melted down and cast into a cone of radius 8cm.Calculate the volume of the cone. (3marks)
1/2 x 4/3 x 22/7 x 16^{3} = 1/3 x 22/7 x 64 x h
h = 1/2 x 4/3 x 3 x 7 x 22/7 x 16^{3}
64 x 22
h = 128
volume of cone = 1/3 x 22/7 x 64 x 128
= 8,582  Five of the interior angles in a nonagon are 160° and the remaining are each x^{0}. Find the possible values of x. (3marks)
sum of interior angles of nonagon = 180(9  2)
= 1260
160 x 5 + 4x = 1260
4x = 1260  800
x = 460
4
x = 115  Calculate the quartile deviation of the following set of data (4marks)
Marks 2130 3140 4150 5160 6170 7180 8190 91100 No. of students 3 5 8 12 15 11 9 4 cf 3 8 16 28 43 54 63 67
50.5 + (16.75  16)10
12
50.5 + 0.625
∠ 1.125
Q3 = 3/4 x 67 = 50.25
70.5 + (50.25  43) x 10
11
70.5 + 6.591
= 77.09
Quartile deviation =
77.09  51.125 = 25.965
2 2
= 12.98  A metallic pipe which is 21 meters long has an internal radius of 13 cm and an external radius of 15 cm. if the density of the metal is 8000 kg/m^{3}, find its mass. (Take π = 22/7). (4 marks)
external volume = 22/7 x 7.5^{2} x 2100 = 371,250
internal volume = 22/7 x 6.5^{2} x 2100 = 278,850
volume of material = 371,250  278,250 = 92,400cm^{3}
= 0.924m^{3}
8000 = mass
0.924
mass = 7,392 kg  Muthoni, Chebet and Amina contributed ksh 50,000, ksh 40,000 and ksh 25,000 respectively to start a business. After some time they realized a profit which was shared in the ratio of their contribution. If Aminas share was ksh 10,000, by how much was Muthoni's share more than that of Chebet's. (3marks)
M:C:A = 50000:40000:25000
=10:8:5
5/23 x 10000
x = 10000 x 23
5
= 46000
muthoni = 10/23 x 46000 = 20000
chebet = 8/23 x 46000 = 8000
20000 8000
= 12000  The cost of two jackets and 3 shirts was 1800. After the cost of a jacket and that of a shirt were increased by 20%, the cost of 6 jackets and 2 shirts was ksh 4,800. Calculate new total cost of 5 jackets and 4 shirts. (3 marks)
(2J + 3S = 1800)8
(7.2J + 2.4S = 4800)10
16J + 24S = 14400
72J + 24S = 48000
56J = 33600
= 600
shrt = 1800  1600 = 200
3
1.2 x 600 = 720
1.2 x 200 = 240
5 x 720 + 4 x 240
3600 + 960
= 4560  Without using mathematical tables evaluate (3marks)
 Using a ruler and a pair of compass only, construct a rhombus ABCD such that AC = 10 cm and ∠BAD = 60° (3marks)
 Without using a calculator or mathematical tables, evaluate (3marks)
 A point P divides a line AB externally in the ratio 4:3. Given that A is (2, 4) and point B (2,3). Find the coordinates of T. (3marks)
T(14, 24)
SECTION II (50MARKS)
Answer only five questions from this section.
 In the figure below, AC=14 cm, AD = 16 cm, DC = 11 cm, and B is a point on AC
 Calculate, correct to 2d.p
 ∠BAD (3marks)
11^{2} = 14^{2}+ 16^{2}  2 x 14 x 16 x cosA
121 = 196 + 256  448 cos A
448 cos A = 331
cos A = 0.7388
A = 42.37
 ∠BAD (3marks)
 The size of obtuse ∠ABD (3marks)
16/sin B = 12/sin 42.37
sin B = 0.8986
B = 63.97
obtuse angle B = 116.03
 Calculate correct to 1 decimal place:
 The length of AB (2marks)
ADB = 180  (42.37 + 116.03)
= 21.6º
AB = 16
sin 21.6 sin 116.03
AB = 6.555
AB = 6.6  The area of triangle BCD (2marks)
DBC = 180  116.03 = 63.97, BC = 14  6.555
= 7.445
1/2 x 7.445 x 12 x sin 63.97
40.14
40.1
 The length of AB (2marks)
 Calculate, correct to 2d.p
 The following table shows heights of 100 seedlings each measured to the nearest cm.
Height (cm) Frequency x fx cf frequency class 70  79 14 74.5 1043 14 1.4 80  84 16 82 1312 30 3.2 85  89 18 87 1566 48 3.6 90  94 20 92 1840 68 4.0 95  99 17 97 1649 85 3.4 100  109 15 104.5 1567.5 100 1.5 Σf = 100 Σfx = 89775  Calculate the differences between the mean and the median. (6marks)
x = 8977.5 = 89.78
100
median = 89.5 + (50  48) x 5
20
= 89.5 + 0.5
= 90
differences = 90  89.78
= 0.22  Draw a frequency polygon to illustrate the above information (4marks)
 Calculate the differences between the mean and the median. (6marks)
 Two towns P and Q are 280 km apart. A bus left town P at 9.30 am and travelled to Q at an average speed of 80 km/h. After 30 minutes, a car left town p for Q and travelled at an average speed of 100 km/h.
 Determine:
 The time when the car caught up with the bus. (3marks)
distance moved by bus
30/60 x 80 = 40 km
R.s = 100  80 = 20km/h
Time = 40/20 = 2hrs
9:30
2:00
11:30 am  The distance of the car from town Q when it overtook the bus. (3marks)
distance = 2 x 100 = 200 km
dixtance frm Q = 280  200
= 80 km
 The time when the car caught up with the bus. (3marks)
 After the car overtook the bus, it accelerated for 6 minutes to a speed of 120 km/h. It moved with that speed for 30 minutes after which breaks are applied and came to rest at town T after 3 minutes. Determine the distance travelled by the car in 39 minutes. (4marks)
1/2 x 6/60(100 + 120) + 30/60 x 120 + 1/2 x 3/60 x 120
11 km + 60 km + 3 km
= 74 km
 Determine:

 Complete the table of values for the equation y .2x^{2} + 3x + 6. (2 marks)
x 3 2 1 0 1 2 3 4 y 21 8 1 6 7 4 3 14  Use the values above to draw the graph of y = 2x^{2} + 3x + 6. (3marks)
 Using the graph drawn above Solve the oquations:
 2x^{2} = 3x +6 (2 marks)
2x^{2} + 3x + 6 = 0
at point of intersection of curve with xaxis
x = 1.15 or x = 2.1  2x^{2} + x + 9 = 0 (3marks)
x = 1.85 or 2.35
 2x^{2} = 3x +6 (2 marks)
 Complete the table of values for the equation y .2x^{2} + 3x + 6. (2 marks)
 A trader deals with two types of Millet, type A and type B. type A costs ksh 400 per bag and type B costs ksh 350 per bag.
 The trader mixes 30 bags of type A and 50 bags of type B. If she sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. (4 marks)
30 x 400 + 50 x 350
80
29500
80
368.75
100%  368.75
120%  120 x 368.75
100
= 442.50  The trader now mixes type A and type B in the ratio x: y respectively. If the cost of the mixture is ksh 383.50 per bag, find the ratio x:y. (4marks)
400x + 350y = 383.50
x + y
400x + 350y = 383.50x + 383.50y
16.5x = 33.5y
x/y = 33.5/16.5
x/y = 2^{1}/_{33}
x:y = 67:33  The trader mixes one bag of the mixture in part (a) with one bag of the mixture in part (b) above. Calculate the ratio of type A millet to type B millet in this mixture. (2marks)
A:B = 3:5 A:B = 67:33
A 3/8 A 67/100
B 5/8 B 33/100
3/8 + 67/100 : 5/8 + 33/100
1^{9}/_{200} : 191/200
209/200: 191/200
209:191
 The trader mixes 30 bags of type A and 50 bags of type B. If she sells the mixture at a profit of 20%, calculate the selling price of one bag of the mixture. (4 marks)
 The equation of a line L_{1} is 3y + 2x = 10
 Find in form of y=mx+c,where m and care constants:
 The equation of line L_{2} passing through N (5,2) and parallel to L_{1} (2 marks)
3y = 2x + 10
y = 2x/3 + 10/3
Q1 = 2/3 = a2
y  2 = 2
x + 5 3
2x  10 = 3y  6
2x  4 = 3y
y = 2x/3  4/3  The equation of line L_{3} perpendicular to L_{2} at M (1,8) (3marks)
y = 3/2x  19/2
 The equation of line L_{2} passing through N (5,2) and parallel to L_{1} (2 marks)
 Find the angle of inclination of the line L, with the horizontal. (2marks)
tan θ = 2/3
θ = 33.69
but tan is ve
therefore θ = 146.3  Find the magnitude of MN. (3marks)
 Find in form of y=mx+c,where m and care constants:
 In the figure below A, B, C and D are points on the circle Centre O. ACF and EDFG are straight lines. Line EG is a tangent to the circle at D. ∠CDF = 35° and ∠CFG = 130°
 Calculate the Size of
 ∠OCD (2 marks)
1/2(180  70) = 55º  ∠EDA (1 mark)
ACD = EDA = 30 + 55 = 85º  ∠ABC (2 marks)
∠ ADC = 55 + 5 = 60º
∠ABC = 180  60 = 120º
 ∠OCD (2 marks)
 Given that CF_{o} 6.7 cm and DF = 8.5 cm, Calculate to 3 significant figures:
 The length of DC. (3marks)
DC^{2} = 8.5^{2} + 6.7^{2}  2 x 6.7 x 8.5 x cos 50
= √43.93
= 6.628
= 6.63  The radius of the circle. (3marks)
r = 5.78
 The length of DC. (3marks)
 Calculate the Size of
 The product of the first three terms of a geometric progression is 64.If the first term is a and the common ratio is r,
 Express r in terms of a. (3marks)
 Given that the sum of the three terms is 14
 Find the value of a and r and hence write down two possible sequence up to the 4th term. (5 marks)
 Find the product of the 50th terms of the two sequence. (2marks)
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