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Form 4 Exam Standard Mathematics Paper 2 Questions and Answers
Given that
L
=
m
−
1
m
+
1
, express in terms of m
2
L
+
1
2
L
−
1
(3m 14s)
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1.
The total cost C of assembling radios is partly a constant and partly varies as the number x of radios assembled. The cost of assembling 144 radios is sh 24600 and the cost of assembling 324 radios is sh 29400.Find a).the equation relating C and x. b).the cost assembling 256 radios.
2.
The heights of all Form 3 students in a school were measured to the nearest centimeter and recorded in the table below. a).State the modal class b).Calculate the median height to 4 significant figures.
3.
The major arc of a circle subtends an angle of
240
0
at the centre of the circle. Given that the length of the arc is 88cm, calculate the diameter of the circle.
(
T
a
k
e
π
=
22
7
)
4.
A boat which can sail at a speed of 25km/h in still water sailed upstream from a point P to a point Q and back to point P taking 5 hours for the round trip. The distance from P to Q is 60km.Find the speed of the river current.
5.
a).Expand and simplify
(
1
+
2
x
)
8
up to the term in
x
3
. b).Use the simplified expression in (a) above to evaluate
(
1.02
)
8
to 4 significant figures.
6.
In a certain year the population of a constituency was 480000 people. Out of these 40% were above the age of 15 years. During that year there was a vaccination, but only 180000 people were vaccinated in the constituency. A person was picked at random from the constituency in that year. Find the probability that this person was below 15 years and was vaccinated.
7.
Three points O,A and B lie on a horizontal ground such that A is 40m North of O and B is 60m on a bearing
070
0
from A. At B a vertical tower stands so that the angle of elevation of the top of the tower from O is
20.3
0
.Calculate a).the distance OB b).the height of the tower.
8.
The cost of one kilogram of rice is sh r and the cost of one kilogram of sugar is sh s. Mogaka spent sh 470 in buying 3kg of rice and 5kg of sugar. Wafula spent sh 360 in buying 2kg of rice and 4kg of sugar. a).Write down a equations to represent the above information. b).Find the cost of each item.
9.
The equation of a circle is
x
2
+
y
2
+
10
x
+
14
y
=
-
10
Determine the coordinates of the centre and its radius.
10.
Khaemba borrowed a loan of sh 500000 from a bank and arranged to repay the loan in five equal yearly instalments of sh 100000 each. The bank charges compound interest at 15% per annum and ledger fees at 3% per annum. In order to repay the amount of the loan on time, Khaemba paid each instalment together with interest and ledger fees at the end of every year for five years. Calculate the total
11.
The equation of a curve is
y
=
2
x
3
-
6
x
+
5
a).Determine i).The gradient function of the curve. ii).The coordinates of two stationary points of the curve. b).Identify which is a maxima and which is a minima. c).Sketch the curve
y
=
2
x
3
-
6
x
+
5
. d).Find the equation of the tangent to the curve at the point (2, 9) in the form y =mx +c.
12.
A school water reservoir is supplied with water by two pumps P and Q.The probability that pump P fails is
1
10
and the probability that Q fails is
1
5
. a).Draw a simple tree diagram to illustrate this information. b).Calculate the probability that. i).both pumps are working. ii).both pumps are not working. iii).Only one pump is working. iv).At least one pump is working.
13.
A woman is now five times as old as her son. In five years’ time she will be three times as old as her son. Find their present age.
14.
In a research experiment a new drug for a deadly livestock disease was being tried. A sample of cows which were found to have the disease was used in the experiment In this sample 54 cows were treated with the drug and the remaining 18 cows were not treated. a).Calculate the probability that a cow picked at random from the sample is i).treated with the drug. ii).not treated with the drug. b).The
15.
An arithmetic progression (AP) has the first term as a and common difference as d. a).Write down the first, third and the eleventh terms of the AP in terms of a and d. b).The AP above is such that it is increasing and its first, third and eleventh terms of the AP form the first three terms of a G.P. The sum of the fifth and ninth terms of the AP is 80. i).Find the first term and the common
16.
The acceleration of an object in motion is given by a = 2-6t,where t is time in seconds after the object passes a fixed point O. a).Given that the initial velocity is 8m/s ,express the velocity V in terms of t. b).Determine the time the object is momentarily at rest. c).i).Write down an expression for the displacement S metres from the fixed point O after t seconds. ii).Calculate the displacement
17.
Kalome a senior salesman is a paid no commission on the first sh 30000 worth of goods he sells each month. He receives commission at the rate of
3
1
2
% for the goods sold up to sh 70000 and at the rate of 5% on anything above that. Kalome is also paid a basic salary of sh 4040 and a house allowance of sh 1500 per month. At the end of March his gross income was sh 8665 while at the end of April
18.
The equation of a curve is
y
=
2
x
3
-
6
x
+
3
. a).Find the coordinates of the two turning points of the curve. b).For each point determine whether it is a maximum or a minimum point. c).Sketch the curve. d).Find the equation of the tangent to the curve at the point (2,7).
19.
Given that
L
=
m
-
1
m
+
1
, express in terms of m
2
L
+
1
2
L
-
1
20.
The radius of a cone increases in the ratio 4:3 while its height decreases in the ration 3:4.Determine the percentage increase in the volume of the cone.
21.
Three business partners Kamau, Abedi and Yusuf contributed sh 200000,sh 300000 and sh 500000 respectively and bought a matatu. The three agreed that one quarter of the profits from the matatu at the end of each month would be saved for emergencies. One fifth of the remainder would be used for buying spare parts and repairs. The rest would be shared among the three partners in the ratio of their
22.
The table below shows the rate at which income tax is charged for all taxable incomes. Mr. Karanja earns a basic salary of sh 18440 per month. He is housed by the company and therefore 15% of his monthly salary is added to his basic salary as taxable income. He is entitled to a family relief of sh 485 per month. Calculate how much income tax Mr. Karanja pays per month.
23.
A dining set can be bought by cash or on hire purchase.On cash payment the customer is given a 10% discount on the marked price. The hire purchase terms require the customer to pay
1
3
of the HP price as deposit followed by 8 equal monthly instalments of sh 1350 each.If the HP price is sh 1200 more than the marked price, calculate the cash price of the dining set.
24.
The price of one skirt is sh s and the price of one blouse is sh b. Jemima bought 3 skirts and 4 blouses at a total cost of sh 1150.Amina bought 2 skirts and 5 blouses at a total cost of sh 1000 a).Write down in matrix form two simultaneous equations representing the above information. b).Hence use matrices to solve the simultaneous equations.
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