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Mathematics T (954)

OVERALL PERFORMANCE

The number o candidates or this subject was 8592. The percentage o candidates who obtained a

ull pass was 67.09%, an increase o 1.14% compared with the previous year.

The achievement o candidates according to grades is as ollows:

Grade A A B+ B B C+ C C D+ D F

Percentage 8.01 7.18 9.61 11.22 11.08 10.74 9.25 3.09 3.45 3.34 23.03

RESPONSES OF CANDIDATES

PAPER 954/1

General comments

Generally, the majority o answers were well written. However, quite a number o answers were not

well thought o and the logical sequence was not there.

Comments on individual questions

Question 1

Almost all candidates were amiliar with the property log ab = log a + log b, but most o themmade mistakes as they thought that log x2 = (log x)2 and log x+ log y= 5 x+ y= 5.

Answers: x= 27, y= 9

Question 2

Most candidates were able to fnd

dudx

and used the chain rule. However, only a ew were able to

simpliyABBBBBu2 1 or dudx

in terms o x correctly, and express u2 1 as a perect square. Since the

solution required clear proo, the steps involved should have been detailed, but many candidates

just concluded with the answer.

Question 3

Some candidates were aware o the condition or a convergent series which was |r|, 1, but theyailed to realise that ex. 0 or all real values o x and thus, they did not answer the frst part

correctly. As or the second part, more than hal o candidates did not provide the exact value as

required by the question.

Answers: {x: x. 0}, x= ln4

3

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Question 4

Most candidates were able to fnd f(x). However, the majority o candidates ailed to observe thatthe next part requires them to use answer rom the frst part. These candidates did not use the

anti-derivative concept to obtain the answer but used integration by parts instead.

Answers: f(x) = 1 + ln x, 2e ln e

Question 5

There were only a ew candidates who were able to use the defnition or A B to establish the

proo or the frst part.

Answer: k=2

3

Question 6

Candidates could fnd the domain and range but could not gave the answer in the correct set orm,

or vice versa. Majority o the candidates were also very weak in giving explanation and reasoning.

Answers: D = [3, 1) (1, 2], R = (1, 2)

Question 7

Most candidates were able to answer the frst part, but ailed to solve the inequalityp(x) < 0 in

the second part. Most candidates just showed that x2 4x + 5 = 0 had complex roots without

realising that it was always positive. Some candidates just ignored the quadratic actor saying that

it had complex roots.

Answers: a= 9, b = 5, {x : 1

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Question 11

Quite a number o candidates were able to fnd the composite unction and stationary points

correctly and to sketch the graph. However, some candidates ailed to give the overall graph and

presented only partial sketch or incomplete graph. For example, the sketch terminated in the second

quadrant and did not proceed to the third quadrant. As or the second part, many candidates ailed

to sketch the graph y= 1h(x)

correctly. As a result, they were not able to give the right answers or

part (c). Some candidates did not give the answers in the set orm.

Answers: (a) (x 1)3 3(x 1) + 2, (0, 4), (2, 0); (c) (i) k : k, 14 , k 0, (ii) k : k=1

4 ,

(iii) k : k. 14

Question 12

All candidates knew that P1 =1

|P|Adj P. However, quite a number o candidates conused with

transpose o a matrix, adjoint and coactors.

Some candidates were weak in transorming the inormation given into a system o linear equations.

The candidates straight away wrote the matrix equation which they inadvertently missed showing

the transormation o worded problems into mathematical equations clearly.

Answers: (a) |P| = 14, Adj P =2 1 5

8 3 1

4 5 31 2,

17

114

514

514

47

27

314

114

3

14

1 2(b) (ii) x = 5 minutes, y = 8minutes, z = 10 minutes

PAPER 954/2

General comments

In general, the quality o answers given was not satisactory. Candidates showed a wide range o

mathematical abilities. Good candidates gave well-planned answers and systematic steps in their

presentations. On the other hand, weaker candidates showed a lack o aptitude and understanding

o the requirements o the questions.

Comments on individual questions

Question 1

This question was well answered by most candidates. However, in the integration by parts, many

candidates made a wrong choice ou anddu

dv

, thus making the integration more difcult to solve.

Another common mistake was cos y dx= sin y.

Answer: sin y = x2 ln x12

x2 + c

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Question 2

Most candidates were able to answer the frst part o the question, but ailed to solve the

second part o the question. They were conused about the maximum and minimum

values and ailed to make use o 13 sin(q + a) + 15. Another common mistake was1

2