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Form 4 Mathematics Paper 2 Sample Revision Questions and Answers
Given that
sin
θ
=
√
3
2
, express as a fraction the value of
1
-
cos
2
θ
without using mathematical tables.
(1m 22s)
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1.
Solve for x in the equation Log(x-3) =log 24 –log(x-1)
2.
Solve the following quadratic equation by completing the square and giving your answer to 2 decimal places.
3
x
2
-
12
x
+
2
=
0
3.
Triangle A’B’C’ is the image of triangle ABC under a transformation represented by the matrix M =
(
2
1
3
5
)
.If the area of triangle ABC is
3.5
c
m
2
, determine the area of triangle A’ B’ C’.
4.
A radio manufacture sold a radio to wholesaler at a profit of 25% on the manufacturing cost of the radio. The wholesaler sold the same radio to a retailer at a retailer at a profit of 30%.A customer finally bought the radio from the retailer for sh.3640.If the retailer made a profit of 40%, calculate the manufacturing cost of the radio.
5.
Two points A and B are on the equator such that B is 2400 nautical miles to the west of A. Calculate a).The longitude difference between A and B. b).The local time at A if the local time at B is 11:30 a.m.
6.
A sphere of radius r has the same volume and radius as a cylinder of height h. Determine the ratio r:h
7.
Make y the subject of the formula
q
=
√
(
r
2
-
y
2
y
2
+
3
)
8.
Solve the simultaneous equations
x
2
+
y
2
=
29
x
+
y
=
3
9.
A room measuring 4m long and 3m wide is covered with a carpet in the middle leaving a path 25cm wide all around the room. This path is covered with a polythene material which costs sh 360 per square metre. Determine the cost of the polythene material used.
10.
Simplify by writing in the form log x
1
2
log
64
+
2
log
3
–
log
12
11.
Simplify the following surd by rationalizing the denominator
5
√
7
-
√
2
12.
In the year 2002 the population of a town was 324,000 out of this 55% were female and 2/5 of the town population were adults above 25 years. If a person was picked at random from this town during that year, find the probability that the person was a).below 25 years. b).male and above 25 years.
13.
Two similar cylindrical tanks are such that the larger one has a capacity of 810 litres and the smaller one a capacity of 240 litres .If the height of the smaller tank is 1.2 m, find the height of the larger tank.
14.
In the figure below O is the centre of the circle.Angle
O
Q
P
=
30
0
and angle
O
R
P
=
20
0
.Find the size of angle QPR and hence determine the size of reflex angle QOP.
15.
The figure below shows a circle, centre O and radius 14cm.PQR subtends an angle
α
at the centre of the circle as shown .If the length of the arc PQR Is 17.6cm.Calculate the size of the angle
α
.(
T
a
k
e
π
=
22
7
)
16.
The figure below is an equilateral triangle PQR of sides 2.5cm.Copy the triangle and on it construct the locus of point S such that angle
P
S
Q
=
15
0
given that S is always on the same side of PQ as R.
17.
A television set whose cash price is sh 30,000 can be bought by two method.The hire purchase method which requires the customer to pay one third of the HP price as deposit followed by ten equal monthly instalments.The HP price is 30% more than the cash price.The Tv can also be bought by paying half its cash price followed by three equal instalments together with interest rate of 5% per month on
18.
A Kenyan businessman imports wheat from the united States at an initial cost of 250 dollars per tonne.He then pays 20% of this amount as shipping costs,and 10% of the same amount as customs duty.When the wheat reaches Mombasa,the man has to pay 5% of the initial cost to transport it to Nairobi. a).Given that 1 US dollar = Ksh 78.20,calculate the total cost of importing one tonne of wheat in
19.
a).Using a ruler and a pair of compasses only, Construct triangle ABC such that AB = 8cm,BC =6cm and angle ABC =
30
0
. b).Measure line AC and angle ACB. c).Draw a circle that passes through A, B and d).A point P moves such that it is always equidistant from B and C. Construct the locus of P and define it.
20.
a).Complete the following table and use it to answer the questions that follow. b).On the same grid and using the same scale draw the graphs of y=sin(x+30) and y = cos(x-30). c).Use your graph to find the values of x for which sin (x+30) = cos(x-30). d).By what angle does the sine wave lead the cosine wave?
21.
The table below shows the masses of newly born babies at maternity home. a).Complete the table and use it to answer the questions below. b).Use the method of assumed mean to calculate to two decimal places i).The mean mass of the babies. ii).The standard deviation of the distribution.
22.
a).Given the matrix Q =
(
5
24
4
30
)
,Find its inverse matrix
Q
-
1
b).Two friends, Kamara and Teso, bought bulls at sh b per bull and goats at sh g per goat. Kamara spent sh 96000 in buying 5 bulls and 24 goats while Teso spent sh 93000 in buying 4 bulls and 30 goats. i).Form a matrix equation to represent this information. ii).Use the inverse matrix
Q
-
1
in (a) above to find the cost of
23.
a).Given the transformation matrices T1 =
(
2
1
-
1
-
2
)
and T2 =
(
3
1
1
3
)
And that transformation T1 followed by T2 can be replaced by a single transformation T, write down the matrix for T. b).Find the inverse of matrix T. c).The points A”(7,-11), B”(-7,-13),C”(-8,16) and D”(8,8) are the images, of points A,B,C and D respectively under transformation T1 followed by T2 ..Write down th
24.
The sketch below shows the curve
y
=
x
2
+
5
and the line y = 8-2x.The line intersects the curve at points C and D as shown. Line AC and BD are parallel to the y-axis. a).Determine the coordinates of C and D. b).Use integration to calculate the area bounded by the curve and the x-axis between C and D. c).Calculate the area enclosed by line CD and the x-axis between points A and B. d).
25.
Use the method of completing the square to solve the quadratic equation.
4
x
2
–
9
x
+
5
=
0
26.
The velocity V of a particle in motion is given by the equation
V
=
3
t
2
+
2
t
-
5
where t is time in seconds. Determine the total distance moved by the particle in the first 5 seconds of motion.
27.
Make F the subject of the formula
W
=
√
H
-
2
F
L
3
F
28.
Three quantities X,Y and Z are such that X varies directly as the square of Y and inversely as Z. Given that X=3 when Y =6 and Z=15,find a).An equation which connects X,Y and Z. b).The value of X when Y =4 and Z=5
29.
The surface are S of a sphere is directly proportional to the square of its radius r.The volume V of the sphere is directly proportional to the cube of its radius r.Find the percentage increase in V when S increases by 25%.
30.
The points A’ (4,-7) B’(5,5) and C’(3,1) are the images of the points A,B and C respectively under a transformation represented by the matrix M=
(
2
-
3
-
1
4
)
Write down the coordinates of A,B and C.
31.
Given the vectors a = 6i + 8j – 2k b = 3i – 9j +9k c = 4i + j +2k Find the values of h and k such that ha + kb = c.
32.
Given the series 4 + 12 +20 +28 +... Find the number of the terms that will give the sum of 324.
33.
Solve the equation
5
y
2
-
2
y
-
5
2
=
y
4
34.
Find the value of x in the equation.
10
sin
2
x
–
7
cos
x
+
2
=
0
For the range
0
≤
x
≤
360
0
.
35.
Three darts players Musa, Nyongesa and Obanda are contesting to qualify for the National Darts Finals.The probability that Musa,Nyongesa and Obanda will qualify for the finals is
2
5
,
3
4
and
2
3
respectively. Use a tree diagram to determine the probability that only two of three players reach the finals.
36.
A water pump can be bought by cash or by hire purchase. The HP price of the water pump is 30% higher than its cash price. Under the HP terms a customer pays
33
1
3
%
of the HP price as deposit followed by monthly instalments of sh 1625 each. Calculate the cash price of the water pump.
37.
Solve for x in the equation
2
3
x
-
1
×
8
x
-
1
=
256
38.
Given the matrices P =
(
3
-
1
2
1
)
and Q =
(
2
3
-
1
1
)
,find matrix R such that
P
2
=
P
Q
–
R
.
39.
Find the equation of a circle centre (4,-3) and radius 6 units.
40.
A bus and a matatu start from Nairobi at the same time and travel to Meru a distance of 280km.The matatu averages 20km/h faster than the bus and reaches there 1 hour and 36 minutes earlier. Determine the speed of each vehicle.
41.
Two friends, Safari and Temu, contributed sh 200000 and sh 300000 respectively to start a business. They decided that 15% of the profits made each year would be put back into the business. They also estimated that 33% of the profit would cover salaries and other expenses for that year. The rest would be shared between the two in the ratio of their contributions. At the end of the first year sh 330
42.
Given that the expression
16
x
2
–
72
x
+
m
is a perfect square, find the value of m.
43.
The points P and Q have the co-ordinates P (6, 4, 2) and Q (10,-5, 3). a).Express the position vectors of P and Q in terms of i ,j and k. b).Express vector PQ in terms of i , j and k and hence find its length leaving your answer in simplified surd form.
44.
Find the values of x which make the following inequality true.
5
-
2
x
>
x
-
7
45.
Solve the equation
2
x
3
=
x
-
1
3
x
-
4
46.
Form 3 students measured the length and width of their classroom and recorded these measurements as 8.4m and 4.5 m respectively. a).Find the limits of these measurements. b).Find the absolute error in the area of the classroom. c).Calculate to 2 decimal places the percentage error in area.
47.
Given that
sin
θ
=
√
3
2
, express as a fraction the value of
1
-
cos
2
θ
without using mathematical tables.
48.
Three quantities are such that s varies jointly with p and the square root of t. Given that s = 600 when p = 10 and t = 25, find a).An equation connecting s, p and t. b).The value of s when p=15 and t= 9.
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