Cork Institute of Technology
Higher Certificate in Engineering in Maintenance Technology – Award
(NFQ – Level 6)
Summer 2007
Mathematics
(Time: 3 Hours)
Answer FIVE questions.
Attempt Question 1 and FOUR others.
Examiners: Mr. M. Walsh
Mr. J. Connolly
Dr. P. Delassus
Q1. (a) Find dx
dy for 15
32
+
+
x
x (4 marks)
(b) Evaluate dx
x
∫+
4
2
2
2
)1( (4 marks)
(c)
−=
513
402
132
A
−=
435
215
034
B Find A·B (3 marks)
(d) Solve i
i
43
832
+
+ (3 marks)
(e) jiu
ρ
ρ
ρ
43 += jiv
ρ
ρ
ρ
−= 6
Find vu
ρ
ρ
23 − in terms of i
ρ
and j
ρ
. (3 marks)
(f) A footballer scores a penalty 4 times out of 5. In a match he takes 3 penalties.
What is the probability that he misses all 3? (3 marks)
