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KCSE Mathematics Paper 2 Revision Exercise Set 2
Given the matrices A =
[
3
2
4
1
]
and B =
[
1
-
1
2
3
]
and that C = AB, find the inverse of C.
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1.
The figure below shows a triangle ABC in which AB= 20cm, angle BAC=110° and angle ACB = 30°. Calculate to one decimal place the length of Ab and hence the area of the triangle ABC.
2.
Mueni bought maize and beans at sh 20 per kg and 50 per kg respectively. She mixed in a ratio such that after selling the mixture at sh 39 per kg, she made a profit of 50%. Find the ratio in which she mixed them
3.
The velocity v meters per second of a particle in motion is given by the equation v =
2
t
2
-4t+10 where t is time in seconds. Determine the total distance moved by the particle in the first 3 seconds.
4.
Given that the expression
9
x
2
-30x+k is a perfect square, find the value of k.
5.
Solve the following quadratic equation by completing the square.
2
x
2
-5x+3=0
6.
Given the matrices A =
[
3
2
4
1
]
and B =
[
1
-
1
2
3
]
and that C = AB, find the inverse of C.
7.
On the above figure PQR and PT are tangents to the circle at Q and T respectively. Angle RPT = 30° and angle RQS = 50°. Giving reasons for your answer find the size of angle PTS.
8.
a) Using the binomial expansion, expand and simplify
(
1
-
2
x
)
5
up to the term
x
3
b) Use the simplified expression in (a) above to calculate to 4 decimal places the approximate value of
(
0.98
)
5
.
9.
The speed of bout in calm water is 25 km/h. The bout moves from point A to a point B upstream and back to a point A in 6 hours 15minutes. If the river current is flowing at speed of 5km/h, calculate the distance between A and B.
10.
Two points have the coordinates P (6, -3,9) and Q (3, -6, -3). A point R divides line PQ internally in the ratio 1:2. The position vectors of P, Q and Rare p, q and r respectively. (a) Express the position vector of p and q. i. In terms of p and q. ii. In terms of i, j and k (b) Hence state the coordinates of R.
11.
Grade A sugar costs sh 75 per kg and grade B sugar costs sh 50 per kg. Angela mixed the two grades and sold the mixture at sh 72 per kg. In so doing she made a profit of 20%. In what ratio did she mix them?
12.
The map of a district is drawn to the scale of 1: n on this map an estate is represented by a rectangle measuring 7.5 mm long and 2.4 mm wide. If the actual area of the estate is 72 hectares, find the value of n.
13.
Two qualities X and Y are such that Y varies inversely as the square of X. Given that y= 8 when X= 2, find the value of X when Y= 18.
14.
The hire purchase value of a sewing machine is 25% more than its cash price. The HP terms require a customer to pay 32.5% of the HP price as deposit followed by 9 monthly instalments of sh.1 500 each. Calculate the cash price of the sewing machine.
15.
The equation of circle is
X
2
-
8
x
+
y
2
+
12
+
16
=
0
.
Determine the coordinates of the Centre of the circle and its radius.
16.
A cylindrical water tank of diameter 7 metres and height 2.4 metres is to be filled by a pipe P of internal radius 3.5 cm. Water flows through the pipe at the rate of 50 metres per minute. A drainage pipe Q can empty the tank in 12 hours. a) Calculate the time in hours pipe P would take to fill the empty tank. b) Starting with the empty tank water flows into this tank through pipe P for 6 hours.
17.
In the figure OPQ is a triangle in which OS =
1
3
OP and OR =
1
3
O
Q
.
T is a point on QS such that QT =
3
4
QS. a) Given that OP = p and OQ = q, express the following vectors in terms of p and q: i. SR ii. QS iii. PT iv. TR b) Hence or otherwise show that the points P, T, and R are collinear.
18.
A sales man is paid a basic salary of sh 4 500 and a house allowance of sh 1 800 per month. On top of this he is paid commission at the rate of 5% on the first sh 10 000 worth of goods sold and further commission of
7
1
2
%
on anything above this. At the end of the first month he received a gross income of sh 7 595 while at the end of the second month he received a commission of sh 1 445.
19.
You are given a matrix M =
[
7
25
4
50
]
. a) Find
M
-
1
the inverse of M. b) Two slaughter houses Masho and Jasho bought bulls at sh b per bull and goats at sh g per goat. Masho bought 7 bulls and 25 goats at a total cost of sh 135 000. Jasho bought 4 bulls and 50 goats at a total cost of sh 120 000. i. Form a matrix equation to represent the information. ii. Use the inverse M-1 in (a) above
20.
The figure above shows a circle in which chords AD and BC intersect at E. Chords AB and CD produced meet at X. a) Giving reason for your answer, show that triangle XDA and XBC are similar. b) Given that XB= 3 cm, XC= 9cm and XD= 4cm, determine the length of XA.
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