QUESTIONS
SECTION A (50MKS)
Instructions.
Answer all questions in this section in the spaces provided.
 Use logarithms to evaluate. (4mks)
 Three similar bars of length 200 cm , 300cm and 360 cm are cut into equal pieces. Find the largest possible area of square which can be made from any of the three pieces.(3mks)
 A triangle has vertices A(2,5), B(1, 2) and C(5,1). Determine:
 The equation of the line BC. (3mks)
 The equation of the perpendicular line from A to BC. (3mks)
 The ratio of the radii of two spheres is 2:3. Calculate the volume of the first sphere if the volume of the second is 20cm^{3}. (3mks)
 Without using a mathematical table or calculator solve the following. (3mks)
 Three boys shared some money, the youngest boy got ½ of it and the next got 1/9, and the eldest got the remainder. What fraction of money did the eldest receive? If the eldest got sh 330, what was the original sum of money? (4mks)
 Ten men working 6 hours a day take 12 days to complete a job. How long will it take 8 men working 12 hours a day to complete the same job? (3mks)
 An electric pole is supported to stand vertically by a tight wire as shown below. Find the height of the pole and leave to 2 decimal places. (3mks)
 From a window 25m above a street, the angle of elevation of the top of a wall on the opposite side is 15º. If the angle of depression of the base of the wall from the window is 35º find:
 The width of the street. (2mks)
 The height of the wall on the opposite side. (2mks)
 Simplify: (2mks)
 Solve the in equality: (3mks)
2x – 1 ≤ 3x + 4 < 7 – x  Solve the following: (3mks)
x^{2} + 3x – 54 = 0  The figure below shows a circle with centre O and radius 5cm. if ON= 3cm, AB = 8cm and <AOB= 106.3º. Find the area of shaded region. (3mks)
 Expand and simplify: (2mks)
4(q + 6 ) + 7 (q – 3) 
 The length of a rectangle is three times its breadth. If its perimeter is 24cm what is the length of the rectangle. (2mks)
 Area of rectangle. (2mk)
SECTION B
Answer any two questions.
 A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is filled with milk.
 Calculate the volume of milk in the tank in cubic metres. (2mks)

 The milk is to be packed in small packets. Each packet is in the shape of a right pyramid on an equilateral triangular base of side 16cm. The height of each packet is 13.6cm. Calculate the volume of milk contained in each packet. (3mks)
 If each packet was to be sold at sh 25 per packet, what is the sale realized from the sale of all exact packets of milk. (5mks)
 A triangle ABC with vertices A(2,2), B (1, 4) and C(1, 4) is mapped on to triangle A’B’C’ by a reflection in the line y=x+1.
 On the grid provided draw:
 Triangle ABC (1mk)
 The line y=x+1 (2mks)
 Triangle A’B’C’ (3mks)
 Triangle A’’B’’C’’ is the image of triangle A’B’C’ under a negative quater turn, with the centre of rotation as origin (0, 0). On the same grid draw triangle A”B”C” (4mks)
 On the grid provided draw:
 The following measurements were obtained while measuring a coffee field. The measurements were entered in a field book as follows:
Y 360 80 to Q 280 To R 80 200 To S 160 80 200 to P X  Taking the baseline XY = 400 m. draw the map of the coffee field using a scale of 1cm represents 40m.
 Calculate the area of the coffee field. (5mks)
 The figure below represents a right pyramid. On a square base of side 3cm. the slant edge of the pyramid is 4cm.
 Draw the net of the pyramid. (2mks)
 Calculate the surface area of the pyramid. (4mks)
 Calculate the volume of the pyramid to 2 decimal places. (4mks)
MARKING SCHEME
SECTION A (50MKS)
Instructions.
Answer all questions in this section in the spaces provided.
 Use logarithms to evaluate. (4mks)
No Log 415.2 2.6182 0.0761 2.8814 1.4996 2.1303 135 3.3693
2= 4 + 1.3693
2 2
0.48378 < antilog
1.6847
Ans = 0.48378  Three similar bars of length 200 cm , 300cm and 360 cm are cut into equal pieces. Find the largest possible area of square which can be made from any of the three pieces.(3mks)
10 200 300 360 2 20 30 36 10 15 18
area = 20 x 20 = 400 cm^{2}  A triangle has vertices A(2,5), B(1, 2) and C(5,1). Determine:
 The equation of the line BC. (3mks)
y1  y2 = 1 + 2 = 3 = 1
x1  x2 5  1 6 2
y + 2 = 1
x  1 2
2 (y + 2) = 1(x  1)
2y  4 = x  1
2y = x +3
2y = x + 3 or y = x/2  3/2  The equation of the perpendicular line from A to BC. (3mks)
m1m2 = 1
1/2 m2 = 1 m2 = 2
x1 + x2 y1 + y2
2 2
1  5 = 4 2 + 1 = 1
2 2 2 2
(2, 1/2)
y + 1/2 = 2
x + 2
y + 1/2 = 2(x + 2)
y = 2x + (4  1/2)
y = 2x + 31/2
y = 2x + 7/2 or 2y = 4x + 7
 The equation of the line BC. (3mks)
 The ratio of the radii of two spheres is 2:3. Calculate the volume of the first sphere if the volume of the second is 20cm^{3}. (3mks)
LSF: 2:3
vsf:(lsf)^{3}
vsf = (2:3)^{3} = 8:27
27  20cm3
20 x 8 = 5.926 cm3
27  Without using a mathematical table or calculator solve the following. (3mks)
729 x 4096
1728
3 = √1728
= 12  Three boys shared some money, the youngest boy got ½ of it and the next got 1/9, and the eldest got the remainder. What fraction of money did the eldest receive? If the eldest got sh 330, what was the original sum of money? (4mks)
x
youngest  1/12x
middle  1/9x
1/12x + 1/9x = 7/36
36/36  7/36 = 29/36 oldest
29/36 = 330
original = 330 x 36
29
= 409.65  Ten men working 6 hours a day take 12 days to complete a job. How long will it take 8 men working 12 hours a day to complete the same job? (3mks)
No of men decreases 8:10
no of days increase 10:8
no of hours increase 12:6
no of days taken = 12 x 10/8 x 6/12
= 7^{1}/_{2} days  An electric pole is supported to stand vertically by a tight wire as shown below. Find the height of the pole and leave to 2 decimal places. (3mks)
a^{2} + b^{2} = c^{2}
85^{2}  3^{2} = b^{2}
b^{2} = 63.25
b = 7.95 + 1 = 8.59 m  From a window 25m above a street, the angle of elevation of the top of a wall on the opposite side is 15º. If the angle of depression of the base of the wall from the window is 35º find:
 The width of the street. (2mks)
cos 35 = x/25
x = 25 cos 35
= 20.48m  The height of the wall on the opposite side. (2mks)
Tan 5 = x/20.48
x = 20.48 Tan 15
= 5.49 + 25
= 30.49m
 The width of the street. (2mks)
 Simplify: (2mks)
5^{2} x 3 x 4 = 4
5^{2} x 3^{2} 3  Solve the in equality: (3mks)
2x – 1 ≤ 3x + 4 < 7 – x
2x  1 = 3x + 4
2x  3x = 4 + 1
x = 5
4 1
3x + 4 < 7  x
3x + x = 7  4
4x = 3
4 3
x < 3 5 ≤ x < 3/4  Solve the following: (3mks)
x^{2} + 3x – 54 = 0
x(x  6) + 9(x  6) = 0
(x  6)(x + 9) = 0
x = 9 or x = 6  The figure below shows a circle with centre O and radius 5cm. if ON= 3cm, AB = 8cm and <AOB= 106.3º. Find the area of shaded region. (3mks)
area = area of sector  area of triangle
106.3 x 3.142 x 5^{2}
360
= 1/2 x 8 x 3
= 23.19  12
= 11.19 cm^{2}  Expand and simplify: (2mks)
4(q + 6 ) + 7 (q – 3)
4q + 24 + 7q  21
11q + 3 
 The length of a rectangle is three times its breadth. If its perimeter is 24cm what is the length of the rectangle. (2mks)
2(3x + x) = 24
8x = 24
x = 3
3x = 3 x 3 = 9 cm  Area of rectangle. (2mk)
l x w = A
9 x 3 = 27
= 27cm^{2}
 The length of a rectangle is three times its breadth. If its perimeter is 24cm what is the length of the rectangle. (2mks)
SECTION B
Answer any two questions.
 A rectangular tank whose internal dimensions are 1.7m by 1.4m by 2.2m is filled with milk.
 Calculate the volume of milk in the tank in cubic metres. (2mks)
v = l x w x h
1.7 x 1.4 x 2.2
= 5.236m^{3} 
 The milk is to be packed in small packets. Each packet is in the shape of a right pyramid on an equilateral triangular base of side 16cm. The height of each packet is 13.6cm. Calculate the volume of milk contained in each packet. (3mks)
v = 1/3 bah
16 x 16 = 256 cm^{2} x 13.6 x 1/3
= 1160.5cm^{3}  If each packet was to be sold at sh 25 per packet, what is the sale realized from the sale of all exact packets of milk. (5mks)
1000000cm^{3}  1m^{3}
x 5.236m^{3}
5236000
1160.5
= 4511.848
= 4511 packets
4511 x 25
= sh 112775
 The milk is to be packed in small packets. Each packet is in the shape of a right pyramid on an equilateral triangular base of side 16cm. The height of each packet is 13.6cm. Calculate the volume of milk contained in each packet. (3mks)
 Calculate the volume of milk in the tank in cubic metres. (2mks)
 A triangle ABC with vertices A(2,2), B (1, 4) and C(1, 4) is mapped on to triangle A’B’C’ by a reflection in the line y=x+1.
 On the grid provided draw:
 Triangle ABC (1mk)
 The line y=x+1 (2mks)
 Triangle A’B’C’ (3mks)
 Triangle A’’B’’C’’ is the image of triangle A’B’C’ under a negative quater turn, with the centre of rotation as origin (0, 0). On the same grid draw triangle A”B”C” (4mks)
 On the grid provided draw:
 The following measurements were obtained while measuring a coffee field. The measurements were entered in a field book as follows:
Y 360 80 to Q 280 To R 80 200 To S 160 80 200 to P X  Taking the baseline XY = 400 m. draw the map of the coffee field using a scale of 1cm represents 40m.
 Calculate the area of the coffee field. (5mks)
XP = 1/2 x 80 x 100 = 4000
PQ = 1/2 x (80 + 200)280 = 39200
PY = 1/2 x 40 x 80 = 1600
YR = 1/2 x 80 x 120 = 4800
RS = 1/2 x 80x (80 + 160) = 9600
SX = 1/2 x 200 x 160 = 16000
75200
10000
= 7.52 ha
 Taking the baseline XY = 400 m. draw the map of the coffee field using a scale of 1cm represents 40m.
 The figure below represents a right pyramid. On a square base of side 3cm. the slant edge of the pyramid is 4cm.
 Draw the net of the pyramid. (2mks)
 Calculate the surface area of the pyramid. (4mks)
1/2 x 3 x 3.708 = 5.562
5.562 x 4 = 22.25
3 x = 9 9 +
31.25 cm^{2}  Calculate the volume of the pyramid to 2 decimal places. (4mks)
 Draw the net of the pyramid. (2mks)
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