UNIVERSITY OF MALTA
THE MATRICULATION CERTIFICATE EXAMINATION
INTERMEDIATE LEVEL
APPLIED MATHEMATICS
May 2009
EXAMINERS’ REPORT
MATRICULATION AND SECONDARY EDUCATION
CERTIFICATE EXAMINATIONS BOARD
IM EXAMINERS’ REPORT MAY 2009
IM Applied Mathematics
May 2009 Session
Examiners’ Report
Part 1: Statistical Information
Table 1: Distribution of Grades awarded in May 2009
GRADE
Number
% of Total
A
9
9.57
B
12
12.77
C
16
17.02
D
11
11.70
E
14
14.89
F
29
30.85
Abs
3
3.19
Total
94
100
Part 2: Comments regarding candidates’ performance
Q1: This question was fairly well attempted. Some showed a lack of understanding of the basic
principles involved. For instance, in finding the resultant, many students simply added the magnitudes
of the forces, ignoring the directions completely. Others whilst taking moments about A, ignored the
direction of the resulting torque which was in the sense DCB.
Q2: Part i) was very well answered by most students. Some candidates did not appreciate the fact that
the lamina was symmetrical, and proceeded to calculate the distance of the centroid from AD, giving
themselves extra work and introducing errors.
In ii), very few managed to obtain the correct angle between the line CD and the downward vertical.
Many answers were given incorrectly as
θ = tan −1 ( y / x).
Q3: This question was very poorly attempted. Most candidates drew a diagram showing the velocities
of the spheres before impact, but did not bother to show the magnitude and direction of the velocities
after impact. This made it very difficult to write down correctly the equations of momentum and the
Law of Restitution. Many errors were made in choosing the correct sign + / − for the velocities. Some
candidates used the principle of conservation of energy.
Q4: Part (i) was straightforward and very well answered by most.
Part (ii) was correctly answered by few candidates. Most candidates deduced that the path of the bomb
had a minimum point with equation
y=
x2
x2
instead of y = −
. Others assumed the bomb
8000
8000
to move in a straight line. Very few managed to find the correct angle at which the bomb hits the
ground. This could have been easily obtained by finding
dy
at the value of x found in part (i).
dx
Q5: Many students got high marks in this question. Part (i) was well done by most candidates. About
three quarters of the students found this question easy. In (ii), a small number of candidates found
difficulty in solving the equation
384 120
+
= 22.
4 +V V
Q6: Most candidates did not draw a proper force diagram showing reactions and internal forces. Many
assumed incorrect directions for the reactions at the hinges.
Q7: A good number of candidates scored full marks in this question. A common mistake was to take
the particle as hanging by a string attached to O.
Q8: Part (i) was a standard question, and was answered correctly by most students. Part (ii) was not
completed by most students.
2
IM EXAMINERS’ REPORT MAY 2009
Q9: Most of the candidates who managed to draw the correct force diagram got full marks in this
question.
Q10: This was a standard question, and was well answered by most candidates. However, few
candidates stated the inequality
µ≥
F
, or that they were assuming limiting equilibrium.
R
Chairperson
Board of Examiners
July 2009
3