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KCSE Mathematics Paper 2 Revision Questions and Answers Set 9
Solve for x in the equation
27
x
+
33
x
-
5
=
49
(2m 21s)
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1.
A singular matrix is given by M=
[
x
-
1
2
x
x
+
2
]
. Find two possible values of x and hence write down two possible matrices for M.
2.
The boot of the model of a car measures 5cm by 5cm. the area of the boot of the actual car is
0.4225
m
2
.if the actual car is 2.86 metres long ,find the length of the model in centimetres
3.
A trader bought two brands of sugar labelled Grade A and Grade B. Grade A sugar costs sh 60 per kg and Grade B sugar costs sh 50 per kg. He mixed them in a ratio such that after selling the mixture at sh. 81 per kg, he made a profit of 50%. Determine the ratio in which he mixed Grade A to Grade B sugar.
4.
A carpenter made a sofa set and decided to sell it at sh 3200.if he had sold it for sh 3600, he would have gained half as much again as he did. Determine how much it had cost the carpenter to make the set.
5.
A box contains 6 yellow balls, 4 white balls and 2 blue balls all balls being similar in shape. A ball is picked at a radom without replacement and its colour noted. Use a tree diagram to determine the probability that at least one of the first two balls picked is blue.
6.
A transformation whose matrix is M=
[
1
-
2
1
-
1
]
maps the points A and B onto A’(6,5) and B’(-4,-3) respectively .Write down the coordinates of A and B
7.
Find the value of log3 58.47
8.
A farmer originally stored water in a cylindrical tank of diameter 8m and height 3m .This tank has since then been replaced by similar tank of diameter 12m and 2.4m.Find the ratio of the capacity of the first tank to that of the second.
9.
The length and breath of metal sheet are measured to the nearest centimeter and recorded as 25cm and 16cm respectively. (a) Determine the lower and upper limit for each measurement. (b) Find the maximum possible error in the area of the sheet. (c) Calculate to one decimal place the percentage error in the area of the sheet.
10.
A farmer intends to fence off 3.24 hectares of his shamba for grazing. The enclosure which is rectangular in shape is to be fenced on all sides. Determine the dimensions of the enclosure which will require minimum length of fencing wire.
11.
In the figure O is the centre of the circle .The diameter AOB is produced to D and PC is the tangent to the circle at point C. Given that angle CBD=
140
0
,determine the size of angle ACP.
12.
A cone of base radius r and vertical height h has its slant height l twice as long as its vertical height .A cylinder has the same radius and volume as the cone. Determine the ratio of the curved surface area of the cylinder to that of the cone.
13.
Solve for x in the equation
27
x
+
33
x
-
5
=
49
14.
The height h metres above the ground of a projectile fired into the air is given by the formula h=
3
t
2
-13t where t seconds is the time elapsed since the projectile was fired. Determine after how many seconds the projectile will be exactly 10 metres above the ground.
15.
From a balcony 16m above the ground an observer notices that the angle of depression of the foot of a multi-storeyed building is
18.6
o
.The angle of the elevation of the same building from the balcony is observed to be
50.5
o
.Calculate to the nearest metre the height of the building.
16.
Kasilu and Nthenge contributed sh 60,000 and 90,000 respectively in order to start a business. They employed a manager and agreed to pay him a salary of 4,500 a month from the profit made each year. They also agreed that 20% of the profits made each year would be put back to the business. The remaining profit would be shared among the patners in the ratio of their contributions. During the first y
17.
A farmer uses two harvesters to harvest wheat on his farm. One of the harvesters is Ferguson and the other is a Honda. It normally takes both harvesters working together 3 hours and 20 minutes to complete the job. On one occasion both harvesters started working together, but after 40 minutes the Ferguson broke down and the Honda had to complete the job alone. It took a further 4 hours to complete
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