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KCSE Mathematics Paper 1 Revision Exercise Set 2
Expand the following expression and then factorise as far as possible.
(
3
x
+
y
)
2
–
(
x
-
3
y
)
2
.
(6m 54s)
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1.
Evaluate
8
×
1
3
o
f
9
÷
2
-
2
3
o
f
144
÷
12
+
2
×
3
3
4
o
f
36
÷
3
-
4
÷
2
5
o
f
10
+
3
×
-
2
2.
A man is now three times as old as his daughter. In twelve years’ time, he will be twice as old as his daughter. Find their present years.
3.
When coffee beans are dried to become
m
b
u
n
i
, the mass decreases in the ratio 5:13. Find the mass of green coffee beans which must be dried to give 650kg of
m
b
u
n
i
.
4.
Expand the following expression and then factorise as far as possible.
(
3
x
+
y
)
2
–
(
x
-
3
y
)
2
.
5.
(a) Find the gradient of the straight line joining the points P (2, 3) and Q (8,-6). (b) Hence find the equation of the line through P perpendicular to line PQ.
6.
Starting from noon the minute hand of a clock moved so that the clock is showing 21 minutes past noon. (a) Find the angle through which the minute hand has moved. (b) Given that the minute hand is 8cm long, calculate the length of the arc it describes in that time.
(
T
a
k
e
π
=
22
7
)
7.
A rectangular container measuring 1.2 m long, 70cm wide and 55cm high is half full of water. All this water is poured into an empty cylindrical tank of diameter 1.4 metres. Find the height to which the water rises.
8.
Given that log 3=0.477 1 and log 5=0.699 0, evaluate the following without using logarithm tables or a calculator. (a) Log 135 (b) Log 1 125
9.
In the figure below, ABCD is a cyclic quadrilateral in which AD=DC and AB is parallel to CD. Given that angle ABC=
80
0
, find the size of: (a) Angle DAC (b) Angle BAC (c) Angle BCD
10.
A motorist travelled the first 90km at an average speed of 60km/h and for the next
3
1
2
hours he travelled at an average speed of 80km/h. find the average speed for the whole journey.
11.
Given that points P (-6, -3), Q (-2, -1) and R (6, 3), express vectors PQ and QR as column vectors and hence show that points P, Q and R are collinear.
12.
An artisan working on a construction job is paid sh30 for every normal working hour and sh 50 for each hour worked over time. During one week he worked for a total of 65 hours and was paid sh 2,450 in wages. Determine the number of hours he worked overtime.
13.
Solve the equation
x
-
2
3
-
3
-
x
4
=
x
-
2
2
14.
On a certain map, an estate is represented by an area of
48
c
m
2
. If the actual area of the estate is 1 200 hectares, find the scale of the map in the form 1: n.
15.
The number
5
.
..
81
contains an integral part and a recurring decimal. Convert the number into an improper fraction and hence into a mixed number.
16.
In the figure, ABCD is a trapezium in which AD is parallel to BC. Given that AD=25cm, BC=15cm, AB=12.8cm and angle DAB=
40
o
Calculate the area of the trapezium.
17.
A trader bought some eggs at sh 64 per dozen and sold two-thirds of them at sh 240 per tray and the other one third at sh 225 per tray. In so doing, she made a profit of sh 450. Given that one tray holds 30 eggs,determine: (a) The number of eggs she bought. (b) The percentage profit she made giving your answer to one decimal place. (c) The percentage profit she would have made if she sold all the
18.
A hollow metal pipe whose internal and external diameters are 5.0cm and 5.6cm respectively is 2.4m long. The pipe is melted down and recast into a solid sphere. (a) Calculate to one decimal place (i) The volume of the metal in the pipe leaving
π
in your answer. (ii) The radius of the sphere obtained. (b) A similar pipe is melted down and recast into a solid cone of height 20cm. If in the
19.
The length of a room is 3m longer than its width. A carpet whose area is
18
m
2
is laid in the middle of the room leaving a margin 50cm wide between the wall and the carpet all around the room. (a) Taking w to represent the width of the room, express the dimensions of the carpet in terms of w. (b) Write down the area of the carpet in terms of w. (c) Determine the dimensions of the room. (d) The
20.
In the figure below, ABCD is a quadrilateral in which AB=10cm and angle DAB=angle ABC=
90
0
. P is a point on AB such that AP=3cm and PB=7cm. AB produced meets DC produced at Q. Given that APD=
70
0
and BPC = BQC=
30
0
, calculate to one decimal place: (a) The length of AD. (b) The length of BC. (c) The area of quadrilateral ABCD. (d) The length of BQ and hence find the area of triangle ADQ.
21.
A jua kali artisan made an article and sold it to a wholesaler at a profit of 20%. The wholesaler sold the article to a retailer at a profit of 30%. The retailer finally sold the article to a customer at a profit of 50%. (a) If it cost the artisan sh.500 to make the article,find how much the customer paid for it. (b) A customer paid sh. 1,560 for another article. Determine how much the wholesaler
22.
A model of a cylindrical tank is made in such a way that it is similar in shape to the actual tank to be constructed. The curved surface area of the model is
440
c
m
2
and that of the proposed tank is
110
m
2
.
(a) Given that the height of the model is 4cm,calculate the height of the actual tank in metres. (b) Calculate the volume of the model given that the diameter of the actual tank is 7m.
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