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KCSE Mathematics Paper 2 Revision Questions and Answers Set 8
Without using logarithms or calculator evaluate.
2
log
10
5
-
3
log
10
2
+
log
10
32
(2m 31s)
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1.
Make x the subject of the formula p=
1
d
โ
g
+
x
2
1
-
x
2
.
2.
Given that
5
x
2
-
7
x
y
+
2
y
2
=0, express x in terms of y.
3.
A cone of base radius r and slant height l has the same curved surface area as a sphere of radius r. Determine the ratio r:l.
4.
John bought two shirts and two pairs of trousers at sh. 1 750. If he had bought three shirts and two pairs of trousers he would have saved sh. 250. On another occasion John bought four shirts and three pairs of trousers at the same price as before. How much money did he spend this time?
5.
a) Expand and simplify the binomial expression
(
2
-
4
x
)
5
up to the fourth term. b) Hence estimate the value of
(
1.96
)
5
.
6.
A metal sheet measuring 1.2m long, 50cm wide and 2.5mm thick is melted down and recast into a new sheet with a square base. If the new sheet is four times as thick as the original sheet, find to the nearest centimeter, the length of the base of the new sheet.
7.
A form IV math teacher originally worked out the mean mark of her 30 students to be 41. After the correction of the test, she added some marks to Amina, Nduku and Karim in the ratio 2 :3 :4. If the new mean mark for the class is 42.5,determine how many more marks Karim was added than Nduku.
8.
The radius of a cylinder is increased by 50% while its height is decreased by 25%. The curved surface area of the new cylinder is
135
c
m
2
. Determine the curved surface area of the old cylinder.
9.
A passenger train travelling at 15km/h completely passes a goods train travelling at 25km/h in the opposite direction in 10.8 seconds. If the passenger is twice as long as the goods train, find the length of each train.
10.
a nail factory starts producing nails at the rate of 10,000 per hour. This rate of production decreases by 20% every hour. a)Find the number of nails produced during the third hour. b)Calculate the total number of nails produced in the first four hours.
11.
Solve the equation
4
x
-
1
=
3
-
x
x
+
3
12.
The equation of a circle is
x
2
+
y
2
+
6
x
-
10
y
-
2
=
0
. Determine the coordinates of the centre of the circle and state its radius.
13.
Solve the quadratic expression
3
x
2
-
11
x
+
6
=
0
14.
Without using logarithms or calculator evaluate.
2
log
10
5
-
3
log
10
2
+
log
10
32
15.
The value of a new tractor is sh. 800 000. For the time the tractor has been in use its value has been depreciating at a uniform rate of 7 percent per annum. If its present value is sh. 556 550, calculate the number of years it has been in use.
16.
The cost of manufacturing a car is divided into the cost of materials, labour and other expenses in the ratio 5:2:1. In a certain year the cost of materials increased by 30%, the cost of labour increased by 40% and other expenses decreased by 10%. Determine the percentage increase in the cost of manufacturing the car.
17.
Kanja invested sh. 15 000 at r% per annum and sh 20 000 at s% per annum both simple interest. His investments earned him a total of sh. 11 400 after three years. If he had invested all his money at the average rate (
r
+
s
2
)% per annum simple interest, his investment would have earned him sh. 150 more than it did. Determine the values of r and s.
ร
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