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KCSE Mathematics Paper 1 Revision Questions and Answers Set 5
Simplify
x
-
2
x
+
2
-
2
x
-
4
x
2
-
4
(2m 26s)
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1.
Factorise
3
x
2
-
11
x
+
6
2.
On a day when the currency exchange rate was: 100 Japanese yen=Ksh 72.50 A Japanese tourist exchanged all his money for Ksh 28 130. If the bank charged him a commission of 3% on the transaction, calculate the number of Japanese yen he exchanged.
3.
The radius of a cylinder is increased by 20% while its height is reduced by 15%. Find the percentage increase in the volume of the cylinder.
4.
The line passing through the point A(1,2) is parallel to the line whose equation is 3y=2x+5. Find the equation of the line and hence determine the coordinate P where this line cuts the x-axis.
5.
In form one class there are 5 more boys than girls. On a certain day one-quarter of the boys and one-fifth of the girls went for a music festival. If 8 students from this class went to the music festival, find the number of students in the class.
6.
Without using mathematical tables evaluate
sin
60
0
.
tan
30
0
.
tan
45
0
-
cos
45
0
.
cos
60
0
cos
30
0
.
tan
60
0
.
sin
30
0
-
cos
60
0
.
sin
60
0
.
cos
30
0
7.
Syengo spend one-third of his salary on food, one-quarter on rent, three-fifth of the remainder on transport and saves the rest. If he spend sh 1 800 on transport, find how much he saves.
8.
The sum of four consecutive even numbers is 108. Find the numbers.
9.
A cylindrical container of diameter 42 cm and height 30cm is one-third full of water. The container is filled using a smaller cylindrical can of radius 4.2 and height 10cm. Determine the number of full cans required to fill the container.
10.
Kambo bought a suit for sh 1 200 and marked it at a price such that after allowing his customer a 10% discount, he would make a profit at 20%. Calculate the marked price of the suit.
11.
The figure shows a solid cone of the base radius 7cm and height 10cm. Calculate to one decimal place a)the slant height of the cone b)the total surface area of the cone
12.
Factorise the expression
2
x
2
-
3
x
-
5
and hence solve the quadratic equation
2
x
2
-
3
x
-
5
=
0
13.
Sixteen men working at the rate of 9 hours a day can complete a piece of work in 14days. How many more men working at the rate of 7 hours a day would take to complete the same job in 12day?
14.
Simplify
x
-
2
x
+
2
-
2
x
-
4
x
2
-
4
15.
The figure shows a circle centre O and radius 6cm. AOBC is a sector of the circle and AOB is a triangle in which angle AOB is equal 700. Calculate to 2 decimal places the area of the shaded region. (take pi=227 )
16.
A piece of wire can be folded into a rectangle whose dimensions are such that its length is 3cm longer than its width, the area of the rectangle so formed is 28
c
m
2
a)Determine i)the dimensions of the rectangle ii)the perimeter of the rectangle b)The wire can also be folded into a circle. Taking pi=
22
7
find the radius of the circle and hence area of the circle.
17.
Solve the inequalities i)
1
4
x
-
1
2
>
1
3
x
-
2
3
ii)3x+4=-2 5x-11<4
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