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KCSE Mathematics Paper 2 Revision Questions and Answers Set 10
Find the value of 𝑥 in the logarithmic equation
log
10
(
7
x
+
3
)
−
log
10
(
2
−
x
)
=
1
.
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1.
The table below shows masses of 40 students in a form four class. a)State the modal class b)Calculate the median mass.
2.
Two quantities F and d are such that F varies with d and partly varies as the square of d. when d=2, F=60 and when d=3, F=105. a)Write down an equation connecting F and d. b)Find the value of F when d=5.
3.
A man working on a construction job is paid sh 12 an hour for the normal working hours and sh 15 for each hour worked overtime. In one week he worked a total of 81 hours and was paid sh 1 071 in wages. Determine the number of hours he worked overtime.
4.
In this figure ACD is an equilateral triangle and ABCD is a cyclic quadrilaterals. Given that angle ECD=
20
0
, determine the size of angle EBC.
5.
Solve the equation x-1=
12
x
.
6.
a)Simplify the following expression as afar as possible.
a
b
-
c
-
a
b
+
c
b)Hence leaving your answer in the form of a simplest surd, simplify
√
21
√
7
-
√
3
-
√
21
√
7
+
√
3
7.
A half-litre bottle is full of dilute suphuric acid solution which is 30% acid and 70% water. If 100ml of the solution is drawn off the bottle and replaced with water, find the new percentage of acid in the solution.
8.
Given that
2
x
2
-
5
x
+
k
is a perfect square, find the value of k.
9.
Find the value of ?? in the logarithmic equation
log
10
(
7
x
+
3
)
-
log
10
(
2
-
x
)
=
1
.
10.
Kimeu’s car covers 10km for every litre of petrol consumed. The car also uses engine oil at the rate of 1 litre for every 1 000km travelled. Petrol costs sh 33.50 per litre while oil cost four times as much per litre. Kimeu covers a total distance of 2 500km every month. Determine how much Kimeu’s pays for petrol and oil in a year.
11.
A bus can carry a maximum of 78 passengers when full. The bus has a total of 30 seats and some of which accommodate two passengers and others three passengers. Determine the number of three-passenger seats in the bus.
12.
Kimani sold a bicycle to Onyango at a profit of 30% on the cost price of the bicycle. Onyango sold the same bicycle to Rotich at a profit of 50%. Rotich then sold the same bicycle to Wambua at a loss of 20%. If Wambua paid sh 7 800 for the bicycle, determine how much Kimani had paid for the bicycle.
13.
A trader bought 360 bags of maize from a wholesaler. He later sold 300 bags to his customers making one and half times as much as he had spent in buying all the maize. If he sold all the maize at the same price, calculate his percentage profit.
14.
Given that
F
=
h
d
√
n
2
-
k
h
Find without using calculator, the value of F when h=1.5, d=2.25, n=25 and k=139.
15.
The difference in the capacity of two reservoirs is 12 000 litres. Given that two fifth of the larger reservoir equals half the smaller reservoir, determine the capacity of each reservoir.
16.
The position vectors of A and B are OA=7i+6j+5k and OB=9i-4j+3k. a)express vector AB in terms of i, j and k. b)Calculate the length of AB leaving your answer in simplified surd form.
17.
The population of a town in the 1989 was shown as 60 000 people with male to female ratio of 2 : 3. Another census had been taken 1979 and another one is due 1999. Statistics shows that the growth rate of the town population is 20% of the population at the preceding census. Determine a)the population of the town in 1979 b)the expected population in 1999 c)the expected number of males and females i
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