UNIVERSITY OF MALTA
THE MATRICULATION CERTIFICATE EXAMINATION
INTERMEDIATE LEVEL
PURE MATHEMATICS
May 2007
EXAMINERS’ REPORT
MATRICULATION AND SECONDARY EDUCATION CERTIFICATE
EXAMINATIONS BOARD
IM EXAMINERS’ REPORT MAY 2007
IM Pure Mathematics
May 2007 Session
Examiners’ Report
Part 1: Statistical Information
Table 1 shows the distribution of grades obtained by the candidates and the percentage
obtaining each grade.
Table 1: Distribution of grades obtained by candidates
Grade
A
B
C
D
E
F
Abs
Total
Number
30
50
149
61
130
135
15
570
% of Total
5.3
8.8
26.1
10.7
22.8
23.7
2.6
100%
Part 2: Comments regarding performance
Q1: Part a) was poorly attempted. Many candidates quoted the properties of the
logarithmic function incorrectly. In b) quite a few candidates considered the function
m(t ) to be equivalent to the product mt, which is obviously incorrect. Others took the
initial time to be t = 1, rather than t = 0. Part c) was fairly well done, although many
candidates could not find the coordinates of the midpoint of the line AB.
Q2: This was well attempted. In a), most candidates deduced incorrectly that p( x) > 0
for all x. In c), many candidates got as far as a =
2−2 3
, which is correct, but could not
1− 3
continue further.
Q3: Part a) was poorly done. Many candidates found correctly that there are 33 numbers
267
which are multiples of 9, but then incorrectly found the sum S 267 =
{2(1) + 266(9)}.
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Part b) was well attempted.
Q4: Some students were vague about what the domain and range of a function are.
Besides the sketch of g(x-1) was not easily deduced from that of g(x). In b) the partial
fractions were correctly worked out in most cases, but the resulting integration was
generally incorrect.
Q5: In a) part i) was done correctly, but the subsequent parts were poorly attempted.
In b) the expansion of (1 + 3 x)5 was incorrectly done. Many failed to multiply this
expansion by (1 + ax + bx 2 ) before they equated the resulting coefficients.
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IM EXAMINERS’ REPORT MAY 2007
Q6: In a) some students did not manage to obtain the equation in terms of sines. Those
who did, generally found the solution correctly. Part b) was poorly tackled, and many
students found it difficult to draw a diagram for this problem.
Q7: In a), about half the students did not use the product, quotient and chain rules of
differentiation correctly. In b), many candidates applied the chain rule incorrectly.
Q8: Part a) was poorly attempted. Some did not manage to separate the variables in the
differential equation, others did not integrate correctly, whilst others omitted the constant
of integration. In b), many students used degrees rather than radians to find the required
definite integral. Others integrated the function incorrectly. Most candidates were unable
to draw the necessary sketch.
Q9: Part a) was very poorly attempted. Many students could not manipulate the
equations algebraically even before the differentiation step. The students fared better in
b), although some students did not show any working for their answer, or simply tried to
write down a matrix.
Q10: This question was generally well attempted. However some students lost marks
because in part a) they did not use the given equation to find the inverse, whilst in b) they
did not use the method of the matrix inverse to solve the given equations.
Chairperson
Board of Examiners
July 2007
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