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KCSE Mathematics Paper 1 Revision Questions and Answers Set 9
Solve the equation
2
x
+
1
3
-
x
-
3
2
=
4
x
-
1
6
(2m 6s)
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1.
Factorise completely
6
x
2
-
5
x
y
-
6
y
2
2
x
2
-
x
y
-
3
y
2
2.
Thirty men working at the rate of 10 hours a day can complete a job in 14 days. Find how long it would take 40 men working at the rate of 7 hours a day to complete the same job.
3.
Solve the equation
2
x
+
1
3
-
x
-
3
2
=
4
x
-
1
6
4.
Solve the equation
49
2
x
+
74
x
=
98
5.
Evaluate
5
3
5
×
1
3
4
+
8
1
3
÷
5
9
5
1
6
×
1
1
5
6.
The figure on the right shows a circle Centre O and radius 6 cm. Sector AOB subtends an angle of 1000 at the centre of the circle as shown. Calculate to two decimal places the area of the shaded region (take
π
=3.142)
7.
The sum of ages of three brothers Temu, Juma, and Abdul is 65 years. Juma is twice as old as Abdul and one and half times as old as temu. Determine their present ages
8.
Two similar containers are such that the radius of the smaller container is two thirds that of the larger one. The capacity of the smaller container is 760
c
m
3
. Calculate to 2 decimal places the capacity of the larger container in litres.
9.
The cost of 2 dresses and 3 trousers is sh 3 450. The cost of 3 dresses and 4 trousers is sh 4 800. Find the cost of each item
10.
Awour uses one third of her farm for coffee, one quarter for tea and two fifths of the remainder for mixed farming. She still has 6 hectares of unused land. Find the size of the farm
11.
A straight line passing through the point P(4,5) also passes through the origin and makes an acute angle ? with the x-axis. Calculate to 2 decimal places the size of angle ?
12.
The length of a rectangle is increased by 25% while its width is decreased by 5%. Determine the percentage increase in the area of the rectangle.
13.
The angle of elevation to the top of a tree from a point P is
22.6
0
. from another point Q which is 12m from the base of the tree, the angle of elevation of the top of the tree is
47.5
0
Calculate to one decimal palce a)the height of the tree b)the distance between P and Q
14.
Three towns A,B and C are situated such that town B is 50km on a bearing of 0600 from town A. Town C is 120km on a bearing of 1500 from town B. a) Draw a sketch showing the positions of towns A,B and C b) calculate i)the size of angle ABC ii)the distance of C from A
15.
The diagram below shows a wooden structure comprising of two blocks. The bottom block measures 1m long, 50cm wide and 20cm high. A circular hole of radius 10cm is drilled right through the bottom block as shown. The top block measures 40cm long, 20cm wide and 30cm high. a)Calculate i)the cross-sectional area of wood in the bottom block.(take ?=3.142) ii)the volume of wood in the bottom block
16.
Solve the following inequalities and represent the solution on a number line in each case i)
2
x
-
9
≥
4
x
+
3
3x-5<7-x ii)4x+5>x-4
x
-
2
≥
3
x
-
10
17.
A sector of a circle of radius 42 cm subtends an angle of 1200 at the centre of the circle a) Calculate i)the area of the sector ii)the length of the arc b)The sector is folded into an inverted right cone. Calculate i)the base radius of the cone ii)to one decimal place the vertical height of the cone c)Determine to 2 decimal places the capacity of the cone in litres (Take
π
=
22
7
)
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