8/8/2019 Supplementary Exam Bct 10

1/4

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

2/4

Question one

(a) Solve the triangle DEF and find its area given that EF= 35mm, DE = 25 mm and

8/8/2019 Supplementary Exam Bct 10

3/4

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

8/8/2019 Supplementary Exam Bct 10

4/4

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