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KCSE Mathematics Paper 2 Revision Questions and Answers Set 4
Solve the simultaneous equations
X
2
+
y
2
= 10
X – y = 2
(0m 0s)
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1.
The figure below shows a circle centre O and a radius 7 cm. The minor arc ABC subtends an angle
θ
at the centre as shown. Given that the length of arc ABC is 13.2 cm, calculate the size of angle
θ
(take
π
=
22
7
)
2.
A plane figure P has an area of 12.5
c
m
2
.This figure is mapped onto its image figure P’ by a transformation given by the matrix. T =
[
3
-
2
-
4
4
]
Find a) The determinant of matrix T. b) The area of the image figure P’
3.
Make y the subject of the formula p=
√
(
x
y
2
x
2
-
y
2
)
4.
A man has 140 m of mesh wire with which he intends to fence a rectangular enclosure for rearing hens. Find the length of the enclosure which will give the maximum area and hence calculate this area.
5.
Kariuki deposited sh 20 000 in a fixed deposit account for a period of 18 months. The bank pays compound interest on quarterly basis (i.e. after every 3 months) At the end of this period Kariuki’s account had sh 46 200. Determine the rate at which interest was paid.
6.
Under a transformation whose matrix is T =
[
a
-
2
-
2
a
a
]
A figure whose area is 2.5
c
m
2
is mapped onto a figure whose area is 10
c
m
2
. Find two possible values of a and hence write down two possible matrices for T.
7.
The position vector of A is
(
-
3
5
-
1
)
and vector AB =
(
8
-
3
5
)
Determine the coordinates of B.
8.
Solve the simultaneous equations
X
2
+
y
2
= 10 X – y = 2
9.
The figure below shows a circle centre O and AOC is a straight line. PB is a tangent to the circle at B and angle PBC = 35°. Giving reasons for each answer, find the size of a) angle BDC. b) angle ACB.
10.
The vector p = 6i + (n -10)j + (3n – 5)k and its length |p| = 11. Find two possible values of n.
11.
The equation of a curve is y =
x
2
–
4
x
+
5
Find the coordinate of the turning point of the curve.
12.
Use the formula to solve the quadratic equation
2
x
2
+
3
x
–
35
=
0
13.
Two fair dice are tossed and the outcome on each dice recorded. Find the probability that the sum shown on both dice is greater than or equal to 7.
14.
a) Expand and simplify the binomial expression
(
2
-
1
2
y
)
5
b) Use the first four terms of the simplified expression in (a) above to evaluate to 5 significant figures
(
1.98
)
5
15.
A solid metal cuboid measuring 7.2 cm long, 4.8 cm wide and 2.4 cm high is melted down and recast into a spherical ball. Calculate to two decimal places the radius of the ball. ( Take
π
= 3.142)
16.
Casual labourers in a certain factory are paid per hour for a fixed number of hours per week. In order to increase production, the company decided to increase each man’s weekly working hours by 18%. This is called for a 15% increase in each man’s pay per hour. Determine the percentage increase in each man’s weekly wages.
17.
Water is pumped into two similar cylindrical tanks of height 1.4 metres each at the rate of 69.6 litres per minute by a diesel pump. The pump started pumping water into the empty tanks at 9.30 am and both tanks were full by 2.30 pm. Diesel costs sh 55.50 per litre and the pump consumes it at the rate of 4 litres per hour. A school uses all the water in these tanks in 6 days. Calculate
18.
Mwenga bought a plot of land at sh 300 000 per hectare in a town where land value appreciates at a constant rate of 10% per annum. After two years he sold the whole plot to a customer who was willing too pay sh 500 000 per hectare. In the transaction Mwenga received sh 274 000 more than the present value of the plot. Determine a) The present land value per hectare. b) The size of mwenge’s plot in
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