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Form 4 Mathematics Paper 1 Solved Questions
Simplify as far as possible
(
2
x
−
y
)
2
−
(
y
+
2
x
)
2
(
y
−
x
)
2
−
(
y
+
x
)
2
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1.
To process tea, green tea leaves are dried and then ground to produce fine tea. In the process the mass of green tea leaves decreases in the ratio 2:15.Determine the mass of green tea which must be processed to produce 1.5 tonnes of fine tea.
2.
Expand the following expression and then factorize completely
(
2
a
+
b
)
2
–
(
a
-
2
b
)
2
3.
a).Find the gradient of the straight line joining the points A(1,-2) and B(4,-6). b).Hence find the equation of the straight line passing through A and perpendicular to AB.
4.
Solve for the value of x in the equation below
6
x
-
4
3
-
2
x
-
1
2
=
6
-
5
x
6
5.
A school bought 40 textbooks at a total cost of sh 9500.Some books cost sh 200 each while others cost sh 350 each. Find the number of text books which were bought at sh 200 each.
6.
You are given the points A (-2, 4), B(3,1) and C(13,-5).Express AB and AC as the column vectors and hence show that points A,B and C are collinear.
7.
A lorry driver travelled the first 130 km at an average speed at 65km/h. For the next 3 hours he travelled at an average speed of 50km/h. Find the average speed for the whole journey.
8.
Given that log 3 = 0.4771, log 5 =0.6990 and log 7 =0.8451, find without using logarithm tables or a calculator, the value of a).log 1575 b).log 2205
9.
A cylindrical tank of diameter 1.4m and height 1.2m is one-quarter full of water. This water is transferred to an empty rectangular container measuring 1.2 m long and 70cm wide. Calculate the height of the water in the container in centimeters.
10.
Factorize the expression
28
x
2
–
7
y
2
completely and hence or otherwise find its value when x =5 and y = 6
11.
Simplify the expression 2(2a - 3b-4c)-3(a-2b +2c) -4(b-2c-a)
12.
An article was sold to a customer for sh 510 after allowing him a 15% discount on the marked price. Find the price at which the article was marked.
13.
Evaluate
(
81
16
)
-
3
4
×
(
9
4
)
1
2
×
(
27
)
2
3
14.
Hamisi bought 3 shirts and 2 trousers at a total cost of sh 1575.If he had bought 2 shirts and 3 trousers he would have spent sh 225 more. Find the cost of 5 shirts and 2 trousers.
15.
Given that x = 2,y= 3 and z = - 2,find the value of
3
x
2
y
z
2
-
4
x
y
2
z
2
+
5
x
2
y
2
z
2
4
x
y
2
z
2
-
2
x
2
y
z
+
4
x
2
y
2
z
16.
The table below shows the heights to the nearest centimeter of 40 students in a form 2 class a) State the modal class b) Calculate the median height
17.
Giving your answer in the simplest terms possible, Express the expression
(
3
x
-
y
)
2
–
(
x
-
2
y
)
(
2
x
+
y
)
In terms of x only given that y = x-2
18.
The dimensions of a rectangle whose area is
104
c
m
2
are such that its width is 5cm shorter than its length. a).Taking l to be the length of the rectangle, write down a simplified quadratic equation for the area of the rectangle and hence find its dimensions. b).Calculate the perimeter of the rectangle.
19.
The straight line joining the points P(a,7) and Q(13,a) is parallel to the line whose equation is 3y+2x = 9.Find the value of a.
20.
Given that the ratio x:y = 3:5,find the ratio (x+y):(3x –y)
21.
Simplify the following expression by reducing it to a single fraction in its simplest form
3
x
-
2
2
-
2
x
-
3
3
-
3
-
x
6
22.
By writing your answer in the form ay simplify
(
3
5
x
×
5
2
x
×
3
-
x
÷
5
-
2
x
)
1
4
23.
Solve for x
27
x
×
3
2
x
-
2
=
9
x
+
2
24.
Form the quadratic equation whose roots are
x
=
-
5
2
and x = 3
25.
Solve the inequality
2
x
3
+
2
≥
5
x
2
-
9
26.
Factorize
2
x
2
–
x
-
3
27.
The sum of 4 consecutive odd numbers is 72.find the numbers.
28.
Simplify
x
+
4
x
-
4
-
5
x
+
20
x
2
-
16
29.
After allowing his customer a
12
1
2
%
discount a trader sold an article at sh 350.Find the price at which the article was marked.
30.
Simplify as far as possible
(
2
x
-
y
)
2
-
(
y
+
2
x
)
2
(
y
-
x
)
2
-
(
y
+
x
)
2
31.
The position vectors of points A,B and C are a,b and c respectively and C is the mid-point of AB a).Find a relationship between vectors a,b and c b).Given that a =( -2,7 ) and b = ( -4,1) ,Find c and hence state the coordinates of point C.
32.
A car which consumes 1 litre of petrol for every 12 km uses 48 litres of petrol for a certain journey. Find how many litres of petrol a matatu which consumes 1 litre for every 8 km uses for the same journey.
33.
A truck left town A at 9:35a.m and travelled towards town B at an average speed of x km/h. At the same time a lorry left town B and travelled towards town A along the same road. The distance between the two towns is 322km and the two vehicles met at 2:11p.m.Given that the lorry travelled 20km/h faster than the truck, find the value of x.
34.
Two coils which are made by winding aluminium wire of different gauges and length have the same mass.The first coil is made by winding 270 metres of wire with cross-sectional diameter 2.8mm while the second coil is made by winding a certain length of wire with cross-sectional diameter 2.1mm.Find the length of the wire in the second coil.
35.
The wheel of a racing bicycle has a diameter of 80cm and rotates at the rate of 2.5 revolutions per second. Calculate to one decimal place the speed in km/h at which the bicycle is moving.
(
T
a
k
e
π
=
3.142
)
36.
The straight line whose double intercept equation is
x
a
+
y
b
=
1
Passes through the points A(6,-4) and B(-3, 8).Find the equation of the line in the form y =mx +c and determine the values of a and b.
37.
Pipe A can fill a drum in 6 minutes while pipe B can fill it in 10minutes.A drainage pipe C can empty the full drum in 5 minutes. Pipes A and B are opened and left running for 3 minutes. The drainage pipe C is then opened and all three left running. Find how many more minutes it takes to fill the drum.
38.
On arrival to Kenya a Canadian tourist exchanged his Canadian dollars for ksh 199690.Given that the currency exchange rate was 1 Canadian dollar = ksh 52.55 and that the bank charged him 5% commission, find the number of dollars he exchanged.
39.
The radius of a cylinder is increased by 15% while its height is decreased by 20%.Find the percentage increase in the volume of the cylinder.
40.
The straight line passing through the point A (-3,-4) is perpendicular to the line whose equation is 2y +3x = 8.The line passing through A cuts the x-axis and the y-axis at P and Q respectively. Find the equation of the line and hence determine the coordinates of P and Q.
41.
In a school there are 30 more boys than girls. One-quarter of the boys and two-thirds of the girls are boarders. If there are 255 boarders, find the number of students in the school.
42.
Without using mathematical tables evaluate
sin
60
.
tan
30
.
cos
60
+
sin
30
.
cos
45
.
sin
45
sin
90
.
cos
45
.
sin
45
-
sin
60
.
cos
30
.
sin
30
43.
Omare uses one half of his farm for planting maize, one-fifth for tea, one-third of the remainder for mixed farming and the rest for grazing. If he uses 3.5 hectares for grazing, Calculate how many hectares he puts under maize.
44.
A cylindrical container of diameter 35cm and height 20cm is two-fifths full of water. The container is filled using a smaller cylindrical can of diameter 7cm and height 10cm.Find the number of cans that must be drawn in order to fill the container.
45.
A trader bought an article at sh 600 and marked it at a price such that after allowing his customer a 10% discount he would make a profit of 35%.Find the marked price of the article.
46.
Factorize the expression
5
x
2
+
x
-
4
and hence solve the quadratic equation
5
x
2
+
x
-
4
=
0
47.
In order to complete building a house in 30 days, a contractor employs 18 men to work at the rate of 8 hours a day. Find how many more days it would take 12 men working at the rate of 10 hours a day to complete the house.
48.
Without using mathematical tables or a calculator, Evaluate
41.58
×
4.095
1.365
×
20.79
×
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