MATHSPP2QNS
MATHSPP2QNS
MATHSPP2QNS
Instructions to Candidates
(a) Write yoUr name and admission nUmber in the spaces provided above.
(b) Sign and write the date of examination in the spaces provided.
(c) This paper consists of two sections; Section I and Section II.
(d) Answer all qUestions in Section I and only five qUestions from Section II.
(e) Show all the steps in your calculations, giving the answers at each stage in the spaces provided
below each question.
(f) Marks may be given for correct w rking even if he answer is wrong.
(g) Non-programmable silent electronic calcUlators and KNEC mathematical tables may be used, except
where stated otherwise.
(h) This paper consists of 17 printed pages.
(i) Candidates should check the question paper to ascertain that all the pages are printed as indicated
and that no questions are missing.
(j) Candidates should answer the questions in English.
Section II
17 18 19 20 21 22 23 24 Total
2
3. The length of a rectangle is three times its breadth. If the breadth is decreased by 2m and the
length increased by 4m, the area of the rectangle is decreased by a third. Find the area of the
original rectangle. (3 marks)
3
5. A square based pyramid has a height 50cm.The sloping edges make an angle of 75◦ with the
base. Find the volume of the pyramid. (3marks)
Find the equation of the circle in the form ax2 by 2 cx dy e 0 where a, b, c, d and e are
integers. (3 marks)
5
9. Tractor A can plough a peace of land in 4 12 h o u r s while tractor B can do the same
amount of work in 7 12 hours. Both tractors began to plough the piece of land but after 2
hours tractor A broke down and B had to clear the remaining work. The two tractors are
operated by different owners. The whole work was valued at Ksh.13 500 and was shared
proportionally to work done. Calculate the amount of money received by the owner of tractor
B. (4 marks)
10. The gradient of the curve y = 2x2 + c at the point (p, 5) equals 8 .Find the values of p and
c. (3 marks)
11. A theatre is designed so that the next row of seats has d less seats than the row behind. The first
row has a seats while the tenth row has 435 seats. There are 25 rows of seats in all. The entire
theatre contains 9000 seats. Find the values of a and d. (3 marks)
6
3
12. Find the value of a if (2 x 4)dx 25 (4 marks)
a
13. The figure below shows part of the a curve which passes through point A (3,8)
14. Pascal earned an interest of Ksh 2 122 312 after seven years on an investment project which
paid 13% per annum interest compounded semi-annually. Find the amount Pascal invested to
the nearest thousand (3 marks)
dl
15. The rate of growth of a great white shark, ,is inversely proportional to the square root of its
dt
age, t years. When a shark is four years old, its growth rate is 0.14m/year. Determine the
gro wt h rat e of a 25-year old shark. (3 marks)
8
16. The figure below represents the curve of the function y 1 P sin dx for the range
250 x 550
(b) The angle that line EB makes with the plane ABCD. (2 marks)
(c) The angle between plane JEF and plane ABCD. (2 marks)
(d) The angle between plane ADI and plane ABCD. (4 marks)
10
18. The figure below shows triangle PQR and its image P'Q'R' under a transformation matrix T
(a) Determine the matrix of transformation that maps triangle PQR onto triangle P'Q'R'.
(3 marks)
(c) Triangle PQR is mapped onto triangle PQR by a transformation defined by the matrix
2 0
0 2
(i) Draw triangle PQR on the same grid (3 marks)
(ii) Find a single matrix that maps triangle PQR onto triangle PQR (2 marks)
11
19. The figure below shows a semi-circle centre (5, 0) and radius 5 units.
b) Find the percentage error in the area of the semi-circle when mid-ordinate rule is used
as in (a)(ii) above. Take 227 (2 marks)
12
20. Mario has to transport 42 tonnes of potatoes to the market in a day. A lorry and a trailer are
available. The lorry can carry 4 tonnes of potatoes per trip while the trailer carries 6 tonnes
of potatoes per trip. A lorry uses 2 litres of fuel per trip while a trailer uses 4 litres of fuel
per trip. The two vehicles are to use at most 24 litres of fuel. The number of trips made by the
lorry should be less than the number of trips made by the trailer. The lorry should make more
than 4 trips while the trailer makes at most 9 trips
(a) Taking x and y to represent the number of trips made by lorry and trailer respectively, write
the inequalities that represent the above information. (4 marks)
(b) On the grid provided, plot the inequalities in (a) above. (4 marks)
(c) If a lorry makes a profit of Ksh 35 000 per trip and a trailer makes a p r o f i t K sh.28
000 per trip, using a search line or otherwise, determine the maximum profit made by
Mario (2 marks)
13
21. Bag A contains 4 red balls and 5 white balls while bag B contains 6 red balls and 4 white ones.
(a) A bag is picked at random and a ball is picked, find the probability that the ball is white.
(2 marks)
(b) A ball is removed from A and placed in bag B. Two balls are then picked from B at random one
at a time without replacement; find the probability that the two balls are of the same colour.
(4 marks)
(c) Three boys and three girls sit in a row of six seats. Find the probability that:-
(i) Three girls sit together. (2 marks)
22. (a) A point Q is 2610nm to the east of P(0◦, 155◦E). Find the longitude of Q. (3 marks)
(b) The position of three cities are A(15◦N, 20◦W ),B(50◦N, 20◦W ) and R(50◦N, 60◦E). A plane
left city A at 0250hrs and flew to city B where it stopped for 3hours then flew on to city C,
maintaining a speed of 900 knots throughout. Calculate;
(i) the total distance covered by the plane from city A to R via B in nautical miles.( 3 marks)
(ii) the local time(to the nearest minute) at city R when the plane arrived. (4 marks)
15
In that year, Kamau earned a basic salary of Ksh.45,000 per month. He also enjoyed the following
monthly allowances. House allowance Ksh.35 000, Commuter allowance Ksh.10 000, Medical
allowance Ksh 15 000. He has an insurance scheme for which he pays a monthly premium of
Ksh.22 000. He is therefore entitled to a relief of 15% of the premium paid. He contributes 10%
of his basic salary to a pension scheme, which is exempted from taxation. He was entitled to a
personal relief of Ksh.1 280 per month.
Calculate;
(a) Kamau’s monthly taxable income. (2 marks)
(c) The following deductions are also made from Kamau’s salary every
month.
(i) N.H.I.F of Ksh.320
(ii) Cooperative society shares of Ksh.6 000
(iii) Union dues of Ksh.200.
Calculate Kamau’s net monthly salary (3 marks)
16
24. The figure below shows the edges AB = 90 m and AD = 60 m of a trapezoidal field ABCD drawn
to scale. Angle DAB = 45◦.
(a) Complete trapezium ABCD such that angle ABC = 75◦ (3 marks)
(b) Locate by construction and shade a region R within the trapezium which satisfy the conditions
below.