Post on 09-Apr-2018
8/8/2019 Supplementary Exam Bct 10
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MATHEMATICS
TIME: 3 HOURS
JANUARY 2010
BCT 010
NYANDARUA INSITUTE OF SCIENCE AND
TECHNOLOGY
SUPPLEMENTARY EXAM
DIPLOMA IN BUILDING AND CONSTRUCTION
INSTRUCTIONS
You should have the following for this examination
Answer booklet
Mathematical table
Scientific calculator
This paper consists ofeightquestions
Answer anyfive questions
All questions carry equal marks
Maximum marks for each part of a question are as shown
This paper consists of four printed pages
Alphonce Kimutai Kirui2011 NiST
8/8/2019 Supplementary Exam Bct 10
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Question one
(a) Solve the triangle DEF and find its area given that EF= 35mm, DE = 25 mm and
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Question Four
(a) Given that A= i+3j-7k and B= 5i-2j+4kdetermine;
i. A B
ii. A B
iii. The angle between the two vectors 10mks
(b) i. Find the Angle between the vectors u= 2i+4jand v= 5i-2j
ii. Find the area of the triangle whose sides are the vectors
A=4i+7j-3k
B= 9i-2j+5k 10mks
Question five
(a) i. Solve the equation
(x-2yi) +(y+3xi) = 2+3i
ii. Determine the modulus and argument of the complex number z=2+3i and express z
in polar form. 10mks
(b) Prove that
xx
x
x
tansecsin1
sin1=
+
5mks
Question six
(a) A car starts from rest and its speed is measured every second for 6s:
Time t(s) 0 1 2 3 4 5 6
Speed v(m/s) 0 2.
5
5.
5
8.7
5
12.
5
17.
5
24.0
Determine the distance traveled in 6 seconds (i.e. the area under the v/t graph) by
i. The Trapezoidal Rule 4mks
ii. The Mid-Ordinate Rule 4mks
iii. Simpsons Rule 4mks
(b) The areas of seven cross-sections of a water reservoir at intervals of 10m are
210,250,320,350,290,230, 170 m2;
Calculate the capacity of the reservoir in litres 8mks
BEST OF LUCK 3
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Question seven
(a) Given thatz1= 3+2i, z2= -3+5i and213
111
zzz
+= determine:
i. z3 in the form a+bi
ii. Represent z1,z2 and z3 on an Argand diagram 10mks
(b) The 1st , 12th and the last term of an arithmetic progression are 4, 31.5, and 376.5
respectively. Determine
i. The number of terms in the series
ii. The sum of all the terms in the series
iii. The 80th term 10mks
(c) Solve 5cos2t+3sint-3=0 for values of t from 0 to 360 5mks
Question eight
(a) A box contains 100 copper plugs, 27 of which are oversize and 16 undersize. A plug is
taken from the box, tested and replaced. A second plug is then similarly treated.
Determine the probability that
i. Both plugs are acceptable
ii. The first is oversize and the second undersize
iii. One is oversize and the other undersize 10mks
(b) A block of copper having a mass of 50 kg is drawn out to make 500m of wire of
uniform cross-section. Given that the density of copper is 8.91g/cm3, calculate
i. The volume of copper
ii. The cross-sectional are of the wire and
iii. The diameter of the cross section of the wire 10mks
BEST OF LUCK 4