Form Three Mathematics Paper 2 121/2 Term 1 Instructions: Questions
Form Three Mathematics Paper 2 121/2 Term 1 Instructions: Questions
Form Three Mathematics Paper 2 121/2 Term 1 Instructions: Questions
121/2
TERM 1
INSTRUCTIONS
1. This paper consists of two sections. Answer all the questions in section 1 and any 5 questions
in section 2.
2. KNEC mathematical tables and non-programmable calculators may be used when necessary
Section 1 1 2
Section 2 17 18 19 20 21 22 23 24 total
2
SECTION 1
2 3 (3mk)
3.Find the greatest number which divides 181 and 236 and leaves a remainder of 5 in each case
(2mk)
4.A rectangle measures 20cm by 15cm.If each dimension is increased by 2.5cm, by what
percentage is
5.The angle of elevation of the top of a tree from a point P on horizontal ground is 30º. From
another point Q 8 metres from the base of the tree, the angle of elevation of the top of the tree is
48º.
7.A piece of wire 40cm is bent to form a right-angled triangle whose hypotenuse is 17cm long.
Find the lengths of the other two sides of the triangle (4mk)
4
9. Solve the quadratic equation by completing of squares giving your answer to 3sf
4√5+3√2 (4mk)
2√2–√5
a) (1mk)
b) (1mk)
12. A tourist from Kenya left for Ethiopia. He exchanged sh 9898 into Ethiopian Birr at the rate
of 1 Eth.Birr=ksh7.95. He spent ¾ of the money he got and converted the balance back to
Kenyan money at the rate of 1Eth.Birr=ksh7.98 Calculate what he finally got to 2dp (3mk)
9t²–25a² (3mk)
6t²+19at+15a²
14. Three types of tea costing sh203,sh146 and sh197 per kg are blended in the ratio of 2:5:k.
Find the value of k,if the blend when sold at sh221 per kg gives 30% profit (3mk)
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15. A two digit number is such that 4 times the units digit exceeds the tens digit by1. If the digits
are reversed, the number formed is decreased by 45. Find the number. (3mk)
b)calculate the length of a straight ditch dug from the largest angle meeting the opposite side at
right angles. (1mk)
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SECTION 2
17. A bookseller bought a number of cartons of books at a cost of ksh 57600 from Kagumo
bookstore. Had he bought the same books from Kerugoya bookstore, it would have cost him ksh
480 less per carton. This would have enabled him to buy 4 extra cartons of books for the same
amount of money. By taking x to be the number of cartons of books he actually bought;
a) write an expression in x
ii)for the cost of each carton had he bought from Kerugoya bookstore (1mk)
c)the bookseller later sold all the books he had bought each carton at ksh 720 more than he had
paid for it. Determine the percentage profit he made (2mk)
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18. A cylindrical metal bar of diameter 14cm and length 2m is melted and moulded into
spherical balls. In the process, 5% by volume of metal is lost and what remains makes balls of
radius 3.5cm.
b)find to the nearest whole number the number of balls made (3mk)
i)2x²–5x+3=0 (1mk)
ii)2x²=3x+2 (3mk)
20. a)Plot triangle ABC with coordinates A(1, 1), B(3, 1) and C(1,3 ) (1mk)
b)Plot A′B′C′ the image of ABC under an enlargement scale factor 2 centre A and write down
it’s coordinates (2mk)
c)Plot A′′B′′C′′ the image of A′B′C′ under a reflection in the line x+y=0 and write down it’s
coordinates (3mk)
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d)A′′B′′C′′ is then reflected in the line y=0 to give A′′′B′′′C′′′. Give the coordinates of A′′′B′′′C′′′
(2mk)
21Three businessladies Wanjiku, Muthoni and Njoki decided to buy a lorry. The .marked price
of the lorry was 2.8million shillings. The dealer agreed that the ladies could pay a deposit of 60%
of the marked price and the rest to be paid within a year.The ladies raised the deposit in the ratio
of 3:2:5 respectively. At the end of the year the lorry had realized 2.08million shillings which the
three shared in the ratio of their contribution. However, they were required to contribute for the
balance of the lorry from these earnings again in the ratio of their original contributions.
b)how much did each contribute to pay for the deposit? (3mk)
c)how much did Njoki receive at the end of the year? (1mk)
d)calculate the total amount Muthoni and Njoki contributed to pay for the balance. (3mk)
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e)how much money did Wanjiku remain with after paying her share of the balance? (2mk)
22.a)Make a table and draw the graph of y= sinx–cosx for x in the range 0, with y values to 2dp
and x intervals of 30 (6mk)
i) x=75 (1mk)
23.The figure below is a segment of a circle centre O radius r units.CM is the perpendicular
bisector of AB . B
C
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a)calculate the radius of the circle centre O from which the segment was cut (3mk)
b)calculate the angle that chord AB subtends at the centre of the circle (2mk)
c)hence calculate
24.A rectangular sheet of metal which measures 120cm by 0.8m is 1.5mm thick and is made of
material whose density is 2.2 g/cm³. From each of the four corners of the rectangle, a square of
side 10cm is cut off and the remaining part folded to form an open cuboid.
13
a)calculate
i) the capacity of the cuboid in cm³ to the nearest whole number (3mk)
ii)the mass of the empty cuboid in kg to the nearest whole number (3mk)
b)the cuboid is filled with a liquid whose density is 0.75g/cm³. Calculate the mass in kg of the
cuboid when full of the liquid (2mk)