UNIVERSITY OF MALTA
THE MATRICULATION CERTIFICATE EXAMINATION
INTERMEDIATE LEVEL
PURE MATHEMATICS
May 2006
EXAMINERS’ REPORT
MATRICULATION AND SECONDARY EDUCATION
CERTIFICATE EXAMINATIONS BOARD
IM EXAMINERS’ REPORT MAY 2006
IM Pure Mathematics
May 2006 Session
Examiners’ Report
Part 1: Statistical Information
Table 1 shows the distribution of grades obtained by the candidates and the
percentage obtaining each grade.
Table1: Distribution of grades in the May 2006 session
Grade
A
B
C
D
E
F
Abs
Total
Number
50
84
121
84
83
124
8
554
9.03
15.16
21.84
15.16
14.98
22.38
1.44
100%
% of Total
Part 2: Comments regarding performance
Q1:
This was generally well answered. In part (b), common errors were
Log
Q2:
a Log a
2x
x
=
or y = .
b Log b
2
y
This question was generally well answered.
Most errors occurred in part (c), where many candidates produced the wrong
sketch of q( x) and found difficulties in deducing the values for which q(x) ≥ 0.
Q3:
Part (a) was mostly well done.
In (b), algebraic mistakes were committed in simplifying the first n terms of
the geometric series. The most common errors were S n = 3 − 1n or Sn = 2n. Very few
candidates attempted to obtain the required inequality.
Q4: In (a), a good number of candidates were unable to define the domain and
range of the given function.
In (b), many candidates did not distinguish between factorising and solving the
quadratic equation. Some candidates failed to indicate where the curve cuts the y-axis,
whilst many others did not find the gradient of the tangent at the required point, but
just assumed it.
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IM EXAMINERS’ REPORT MAY 2006
Q5: In (a), the majority of candidates calculated the number of permutations
correctly, but the number of combinations needed for the second part was not correct,
leading to incorrect probabilities. The probability of the complement of an event was
correctly identified by the majority of candidates although the final result was not
correct.
Part (b) was poorly attempted by many students, even though only the first
three terms of the binomial expansion were required. Besides, the value of x used in
the final part was inappropriate in quite a few cases.
Q6: In (a), many candidates found difficulty in factorising the given quadratic.
Others ignored the fact that the result had to be expressed in radians.
In (b), most candidates failed to show that the suggested triangle was
equilateral. The area of the minor segment was correctly attempted, but the perimeter
of the segment was defined incorrectly.
Q7: About half the candidates found part (a) difficult. The product, quotient and
chain rules of differentiation were applied incorrectly or not applied at all.
Part (b) was attempted by very few candidates. Of these, a good proportion
applied the chain rule incorrectly, thus losing marks in the process.
Q8: Part (a) was not well answered. Some candidates did not separate y from x
correctly, others integrated incorrectly, whilst others forgot the constant of
integration.
In (b), many students who failed to answer this question correctly used
degrees rather than radians in the evaluation of the integral, or simply integrated the
function incorrectly. Almost none of the candidates drew the required sketch
correctly.
Q9: This question was generally well answered. In (a), some candidates did not
rationalise the denominator correctly, whilst others committed trivial mistakes whilst
working out part (b).
Q10: This question was well attempted by most candidates. In part (iii), however,
some candidates failed to use the inverse to solve the given set of simultaneous
equations.
Chairperson
Board of Examiners
July 2006
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