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KCSE Mathematics Paper 2 Revision Exercise Set 1
Given the matrices
A
=
[
1
-
1
3
-
2
]
and
B
=
[
2
-
1
1
1
]
, find matrix c such that
B
2
= C + AB.
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1.
Use the method of completing the square to solve the quadratic equation
2
x
2
– 13x + 15 = 0
2.
The figure below shows an isosceles triangle ABC in which AB = 12 cm, AC = x cm and triangle ACB = 120°. (a) Find to 2 decimal places the value of x (b) Calculate to 3 significant figures the area of the triangle
3.
Solve for
Θ
in the question
6
cos
2
Θ
-
sin
Θ
-
4
= 0 in the range
0
°
≤
Θ
≤
180
°
.
4.
The figure below represents the map of an estate drawn to scale on a grid of 1cm square (a) Estimate the area of map. (b) If the area of the estate is 560 hectares, calculate the linear scale of the map.
5.
Three types of cofee A, B and C are mixed in the ratio 2:3:5 by mass. Type A coffee costs sh 210 per kg, Type B sh 160 per kg and Type C sh 120 per kg. The blend is then sold at a profit of 30%. Determine the selling price of the per kilogram.
6.
Make A the subject of the formula T =
2
m
n
√
L
-
A
3
k
7.
A cold water tap can fill a bath in 6 minutes while a hot water tap can fill it in 12 minutes. The drainage pipe can empty the bath in 8 minutes. All three are opened fully for 3 minutes and then the hot water tap is closed. How many more minutes will it take to fill the bath?
8.
Juma deposited sh 16 000 in a bank which paid compound interest at the rate of 12% per annum. At the end of five years, he withdrew all his money. Determine how much money he withdrew.
9.
The coordinates of the points A, B and C are (1, -2), (-1, 2) and (4, 3) respectively. Find the coordinates of A’, B’ and C’, the image of A, b and C under transformation represented by the matrix
[
2
-
3
-
1
1
]
10.
A mixed day an boarding secondary school has a student population of 630. The ratio of girls to boys is 3:4. The school has 350 borders some of whom are boys, others girls. A student is picked at random from the school. Find the probability that the student is a) a border b) a girl and not a border.
11.
Given the matrices
A
=
[
1
-
1
3
-
2
]
and
B
=
[
2
-
1
1
1
]
, find matrix c such that
B
2
= C + AB.
12.
A train whose length is 86 meters is traveling at 28 km/h in the same direction as a truck whose length is 10 meters. If the speed of the truck is 60km/h and is moving parallel to the train, calculate the time it takes the truck to overtake the train completely.
13.
The sum of the first 8 terms of an AP is 236 and the sum of the first 6 terms of the same series is 147. Find the sum of the first 12 terms of the series.
14.
The data below represents the heights, taken to the nearest centimeter, of 40 orange trees in a garden. (Assumed mean A=165.5 and m = calculated mean) (a) Complete the table (b) Using the method of assumed mean, calculate the mean height. (c) Calculate the standard deviation of the distribution.
15.
The model of aircraft is designed such that the volume of its interior airspace is
125
c
m
3
.
The volume of the airspace of the actual aircraft is 3.375 liters. (a) Given that the wing span of the actual aircraft is 7.44 m, find the wingspan of the model in centimeters. (b) If the total surface area of the model is
2420
c
m
2
, find the total surface area of the actual aircraft in square meters.
16.
Two businessmen Karega and Motema contributed sh 90 000 and sh 12 000 respectively in order to start a business. They agreed that 25% of the profit made at end of each year will be put back in the business. They also agreed that 40% of the profit will cover salaries and other expenses for that year. The remainder would then be shared between the partners in the ratio of their contributions. At the
17.
The above diagram represents a swimming pool which measures 50m long, 20 m wide and 2.5m deep at the deepest end. The shallow end is 1.2m deep and 10m long. The remaining part tappers gently to the deepest end of the pool as shown. (a) Calculate the volume of the water in the pool when full (b) The pool which is initially one quarter full, is filled by four similar pipes of diameter 8.0 cm each.
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