Download SUP Y1 SemII Foundat.. - UR-CST

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KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE DE KIGALI
Avenue de l'Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2012/2013
FACULTY OF APPLIED SCIENCES
SEMESTER II: SUPPLEMENTARY
PT213: FOUNDATIONMATHEMATICS
Year 1
MAXIMUM MARKS: 60
DATE: /12 /2012
TIME: 2 HOURS
Instructions:
1. This paper contains two sections.
2. Section A is compulsory and carry 30 marks.
3. Section B contains three questions of which you have to choose
any two of them. It carries 30 marks.
4. Start every new question from a fresh page.
5. Do not write anything on the question paper.
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KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
FACULTY OF SCIENCE
Department: COMPUTER SCIENCE
Course Code and Title: PT213: FOUNDATION MATHEMATICS
Department: Applied Mathematics
Year: 2013 Sem II : SUPPLEMENTARY EXAMINATION
Academic Year: 2012/13
SECTION A
QUSTION 1
a)Solve the following simultaneous equations
5 x  4 y  2
3 y  5x  4
using matrix method (5 Marks)
'
b) Find y and y
''
1
2
1
2
for x  y  3 (5 Marks)
c) Find the equation of the plane through A(3,2,1) with normal in the direction
1 
 
n  1 
 2
 
(5 Marks)

d) Find the integral x log xdx
(5 Marks)
e) Find the parametric equation of the line through A(-2,5,1) in the direction of the
vector
1 
 
a    1
2 
 
dny
f) Find dx n
(5 Marks)
for the
function
y x
(5 Marks)
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SECTION B
QUESTION 2
Let P divide the vector AB in the ratio m:n. Prove that
rp 
1
(nrA  mrB ) , n  0, m  n  0
mn
(15 arks)
QUESTION 3
dy
a) For the following trigonometric functions find dx . y=tan x, y=csc x, and
y=sec x.
(10 marks)
b)
 sin
2
xdx
(5 Marks)
QUESTION 4
a) Find whether the following equations intersect, and if so find the
coordinates of points of intersection.
X=1+t , y=2-t, z=-1-2t
X=1+2u, y=-6u, z=1
(10 Marks)
a) Calculate the cosine of the angle between the following vectors:
  2
1 
 
 
a   3  and b   2 
1 
 2
 
 
(5 Marks)