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KCSE Mathematics Paper 2 Revision Questions and Answers Set 6
Without using mathematical tables, solve for x in the equation.
9
2
x
-
4
×
27
x
-
1
2
=
729
x
+
1
3
(2m 51s)
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1.
The table below shows the rainfall recorded in a certain meteorological station during the first seven months of a particular year. The amount recorded for the months of a particular year. The amount recorded for the month of April is missing from the table. Given the mean rainfall for the seven months was 78.5mm, find the amount for the month of April.
2.
The length of a rectangle is increased by 25% while its width is decreased by 10%. Determine the percentage increase in the area of the rectangle.
3.
A quantity P is partially constant and partly varies as the square of r. when r=4, P=880 and when r=6, P=780. Find a)An equation which connect P and r. b)The value of P when r=8.
4.
Given the series 3+9+15+21+27…, find the number of terms that will give a sum of 243.
5.
Make T the subject of the formula
F
=
√
W
T
L
-
T
6.
Three football teams Awika, Baidoa and Chakata are playing in the national league. The propability that Awika will qualify for the finals is
2
3
,
3
5
and
1
4
respectively. Use a tree diagram to determine the probability that only two of the three teams qualify for the finals.
7.
In the figure PQRS is a cyclic quadrilateral and QRT is a straight line. Given the angle SRT=
100
0
and angle PSQ=
40
0
, find the size of angle PQS.
8.
Solve the quadratic equation
3
x
2
-
13
x
-
10
=
0
.
9.
Given the matrices A=
[
2
-
1
-
3
1
]
and B=
[
-
3
4
-
2
-
1
]
and that C=
A
2
-
B
, write down the converse of C.
10.
Two similar solid lead spheres of radius of 3.6cm each are melted down and recast into a solid cone of base radius r and height of 7.2cm. Calculate to one decimal place, the radius r of the cone.
11.
A lady started working on a job which paid a salary of Kenya pounds 8100 per annum. She received an increment of Kenya pounds 420 every year. Find the salary she received in the seventh year.
12.
Without using mathematical tables, solve for x in the equation.
9
2
x
-
4
×
27
x
-
1
2
=
729
x
+
1
3
13.
A boat sails from point A to a point B upstream a distance of 30km and back to A in 3hrs 12minutes. The current in the river is flowing at 5km/hr. determine the speed of boat in still water.
14.
The figure below shows triangle PQS in which PS=10cm, angle PSQ=
30
0
and angle PQS=
45
0
. Line PR is perpendicular to QS. Calculate the area of triangle PQS.
15.
The first four terms of GP are 81, m, n, 3. Find the values of m and n.
16.
Two towns P and Q are on the equator such that Q is 2100 nautical miles east of P. calculate a)the longitude difference between P and Q. b)the local time at P if the local time at Q is 1.00 pm.
17.
The figure below shows the position of a boat Q which is observed sailing directly towards the pier P at the base of a vertical cliff PT. the angle of elevation of the top of the cliff from Q is
25.4
0
. after 14seconds the boat is at point R and the angle for elevation of T is now
64.7
0
. If the cliff is 50m high, calculate a)the distance PQ b)the distance QR c)the speed of the boat in km/hr
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