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KCSE Mathematics Paper 1 Revision Questions and Answers Set 6
Factorise and Simplify
15
x
2
+
11
x
-
12
12
x
2
+
x
-
20
(7m 10s)
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1.
Factorise and Simplify
15
x
2
+
11
x
-
12
12
x
2
+
x
-
20
2.
In order to complete a job in 10 days a company employs 30 men to work at the rate of 8 hours a day. Determine how long it would take 20 men working at the rate of 12 hours a day to complete the same job.
3.
Solve the equation:
1
2
x
=
2
3
x
+
1
4.
Solve for x in the equation
9
x
+
32
x
=
162
5.
A cylindrical tank of diameter 2.1m and height 150cm initially contains water to a height of 35 cm. water flows into this tank at the rate of 33 litres per minute fro 21 minutes. Determine the new height of water in the tank.(take ?=22/7).
6.
The line which passes through the points P(4,a) and Q(2a,2) is parallel to the line whose equation is 2y-3x=6. Find the value of a
7.
Amina deposited sh 25,000 in a bank which paid compoubd interest at the rate of 12% per annum for a period of 18 months.Juma invested sh 30,000 at 15% per annum simple interest for the same period. Determine whose investment earned more interest and by how much.
8.
a)Find the greast common divisor for the terms
9
x
3
y
2
and
4
x
y
4
b) hence factorise completely the expression
9
x
3
y
2
-
4
x
y
4
9.
Evaluate
14
÷
1
3
o
f
5
1
4
-
3
3
4
×
1
1
3
10.
Sales lady sold goods whose marked price was sh 340,000 at a discount of 3%. She was paid sh.16, 490 as commission for this sale. Calculate the percentage rate of commission she was paid.
11.
Two containers have base areas of 750
c
m
2
and 120
c
m
2
respectively. Calculate the volume of the larger container in litres given that the volume of the smaller container is 400
c
m
3
12.
The longer parallel side of a trapezium is twice as long as the shorter parallel side.. the perpendicular distance between the two parallel sides is 10cm. if the area of the trapezium is 225
c
m
2
, find the length of the longer parallel side.
13.
Three boats P,Q, and R are situate in such a way that boat Q is 450 m on the bearing of
120
0
from boat P. Boat R is 600m on a bearing of
030
0
from boat Q a)Draw a sketch showing the positions of P,Q and R b) Calculate the distance of boat R from P
14.
During the year 2001 Samora had forty more goats than sheep and half as many cows as sheep. In a year 2002 his goats increased by 50%, his cows decreased by 10% and his sheep increased by 20%. At the end of 2002 all his animals were 690. Calculate to the nearest whole number the percentage increase in the number of animals during the year 2002.
15.
The external measurements of a closed wooden box are 1.5m long, 0.8m wide and 0.3m high. The wood used in making the box is 0.1cm thick and has a density of 0.75g/
c
m
3
. The box contains 30 packets of 12 similar tools and each tool has a mass of 125g. calculate : a) the volume of wood used for making the box b) b)the mass of the empty box in Kg c) c)The gross mass of the box in Kg
16.
In the year 2003 Wananchi Cooperative society received a gross income of sh. 12.5 million. after deducting all expenses the society had a balance of sh. 6.5million. each year 50% of the balance is paid to members as dividends which is calculated per share. In the year 2004 the society gross income increased by 20%, expenses increased by 25% while member shares remained the same at 50,000. Calculat
17.
An open cylindrical reservoir of internal diameter 42m and height 4m is constructed using reinforced concrete for walls and foundation. The walls are 1.4m thick while the foundation is laid to a depth of 2m a)calculate to the nearest cubic metre i)the volume of the concrete used to construct the reservoir ii)the capacity of the reservoir b)Starting with the full reservoir, water is consumed at the
18.
The young Farmers club hired a number of buses and matatus to transport its members for a trip to Kisumu. The number of matatus hired were twice as many as buses and no vehicle made a double trip. Each matatu can carry a maximum of 14 students and a bus can carry four times as many. The hiree charges were sh.5 200 per bus and sh. 2 800 per matatu. A total of sh. 21 600 was spent on transport for
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