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KCSE Mathematics Paper 2 Revision Questions and Answers Set 3
Given that
cos
(
90
-
β
)
=
√
3
2
, determine without using trigonometric tables the value of cos
β
.
(2m 18s)
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1.
Three angles are given in radius as follows:
θ
=
5
π
c
6
,
α
=
π
c
3
and
β
=
π
c
4
By converting to degrees or otherwise, find the value of
sin
θ
-
cos
α
+
tan
β
2.
The gradient function of a curve is given by
d
y
d
x
= 2x – 4. Determine a) The equation of the curve given the curve passes through the point (0,3). b) The coordinates of the turning point of the curve.
3.
Without using mathematical table, evaluate
log
10
20
+
log
10
40
-
log
10
8
.
4.
The number of bacteria in a colony was originally 3 million. This number double itself after every one hour. Calculate the number of bacteria generated in the colony during the
7
t
h
hour.
5.
A trader bought 360 trays of eggs at sh 120 per tray. He later discovered that 10% of the eggs were bad and he could not sell them. For how much must he sell the good eggs per dozen in order to make a profit of 50%
6.
The wheel of a bicycle has a diameter of 70 cm and is rotating at the rate of 200 revolutions per minute. Calculate the speed of the bicycle in km/h.
7.
Solve the equation
2
x
-
1
-
1
x
+
2
=
1
x
8.
Given that p=
n
+
1
n
-
1
express
3
p
-
1
3
p
+
1
in terms of n.
9.
A hall measures 12 m long and 8 m wide. A carpet is laid at the centre of the hall leaving a path of uniform width all around the hall. Given that the area of the carpet is
6
m
2
find the possible width of the path.
10.
Given the column vectors a=
(
1
-
2
1
)
,
b
=
(
6
-
3
9
)
,
c
=
(
-
3
2
3
)
and that p=2a-
1
3
a
+
c
express p as a column vector and hence calculate its magnitude to 3 significant figures.
11.
A quality P is partly constant and partly varies as the square of Q when Q = 2, P = 40 and when Q = 3, P = 65. Determine the value of P when Q = 4.
12.
Solve for x in the equation log(x - 1) = log12 - log(x - 2).
13.
The points A’(3 , -8) and B’(-5 , 4) are the images of A and B under a transformation whose matrix is T =
[
3
1
-
1
2
]
Find the coordinates of A and B.
14.
Given that
cos
(
90
-
β
)
=
√
3
2
, determine without using trigonometric tables the value of cos
β
.
15.
The cash price of a piece of furniture is sh 12 000. It can also be bought by hire purchase (HP) whose terms require the customer to pay one-third of the HP value as deposit and the balance in thirteen equal monthly instalments. If the HP value is 30% more than the cash price, determine the amount of each instalment.
16.
The angle of elevation of the top of a tree from a point P on the horizontal ground is 24.5°. From another point Q, five metres nearer to the base of the tree, the angle of elevation of the top of the tree is 33.2°. Calculate to one decimal place, the height of the tree.
17.
A bus can carry a maximum of 60 passengers. Each row of seats accommodates the same number of passengers. If two rows are added then each row would accommodate one passenger less for the bus to carry the maximum number of passengers. Determine the number of rows in the bus and the number of passengers each row can accommodate.
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