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KCSE Mathematics Paper 2 Revision Questions and Answers Set 7
Solve the simultaneous equations
x
-
1
y
+
1
=
1
4
and
x
+
1
y
-
1
=
2
3
(3m 29s)
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1.
For the last 5 years the value of a car has been depreciating at a constant rate of 12% per annum. The present value of the car is sh316 640. Calculate the value of the car at the beginning of the 5 year period.
2.
Simplify the following surds by rationalizing the denominator
2
√
5
+
√
3
3.
In the figure above PB is a tangent to the circle at B. AC is a chord of the circle which is produced to meet PB at P. given that PB=12cm and PC=10cm, calculate the length of AC.
4.
Two cartons P and Q each contains a mixture of red and blue pens. Carton P contains 9 red pens and 11 blue pens while carton Q contains 15 red pens and 10 blue pens. A carton is selected at random a pen is picked at random from it. a)draw probability tree diagram to illustrate this information. b)find the probability that the pen picked is blue.
5.
Given the transformation matrices
T
1
=
(
1
-
2
-
1
3
)
and
(
2
0
0
2
)
And that T=T1T2, determine the coordinates of A’ and B’ the images of points A(-2,-1) and B(5 ,3) under transformation T.
6.
Solve for T in the equation sin(3T+1200)=
√
32
in the range
0
≤
T
≤
180
0
.
7.
The volume V of a cone of radius r and height h is given by the formula V=
1
3
π
r
2
h
Find the percentage increase in the volume when the radius increases by 20% and the height decreases by 25%.
8.
Solve the simultaneous equations
x
-
1
y
+
1
=
1
4
and
x
+
1
y
-
1
=
2
3
9.
In the figure alongside O is the centre of the circle with POQ and ROS as the diameters. PT and PQ are chords of the circle. Given that angle POR=
28
0
, determine the size of the angle PTS.
10.
Kamau invested sh6 400 at 15% per annum compound interest for 3 years. Salim invested twice that amount at
12
1
2
% per annum simple interest for the same period of time. Find whose investment earned more interest and by how much.
11.
The cost of one textbook is sh t and the cost of one pen is sh p. Nyongesa spent sh 970 to buy 3 textbooks and 5 pens while Ouma spent sh 880 to buy 2 textbooks and 8 pens. a)Form two simultaneous equations to represent the above information. b)hence use the matrix method to the above simultaneous equations.
12.
Given the function ??=
3
x
2
-
6
x
+
7
, determine a)the coordinates of the turning point of the curve. b)the gradient of the tangent to the curve at point (2 , 3).
13.
Patel bought some articles at sh 3 060 per dozen and sold them all making a profit of 20% on the cost price. When selling this articles he had allowed his customers a discount of 10% on the marked price of each article. Find the marked price of each article.
14.
The middle angle of a triangle exceeds the smallest angle by 20%. If the largest angle is twice the middle angle, determine the size of the largest angle.
15.
The figure above shows a trough which is 40cm wide at the top and 25cm wide at the bottom. The trough is 20cm deep and 4.5m long. Calculate the capacity of the trough in litres.
16.
A radio dealer had planned to buy some radios from a wholesaler for sh 340 000. Before he could buy the price of each radio was increased by sh 300. He now discovers that he can only afford to buy 30 radios less than he had planned to buy with the same amount of money. Determine the number of radios he had originally planned to buy and the new price of each radio.
17.
A dam is constructed with the intentions of supplying a town with fresh water. The dam, which is cylindrical in shape, has a diameter of 2.8km and a depth of 10.5m3tres. After completion the dam is filled with water from a river which is 3.6 metres wide and 2.5 metres deep at the point of entry into the dam. The speed of the current in the river is 2.4km/h. Calculate the time to the nearest day,
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