General:

Performance of those candidates who thoroughly studied the subject was extra-ordinarily good. Some candidates scored quite high marks, more than 80 or even more than 90. However, a large number of them failed to obtain pass marks. The students were quite deficient in interpreting their results, wherever they were required. It was observed that, due to computational error, some candidates obtained impossible results, such as value of the co-efficient of correlation outside the range of -1 and 1, however, they did not bother to check their calculations.

Question-wise comments are given below:

Q.1

(a)

The question was quite simple, but a large number of candidates were unable to solve it. Those students who could not solve such an easy question cannot be expected to perform any better unless they bring about significant improvement in their mathematical skills.

(b)

The students were required to solve the question by the laws of logarithms and majority of them performed well. However, few candidates solved the question without using this procedures whereas some used the logarithm after simplifying the numerator and denominator. Such students could not secure any mark. Other common mistakes were as follows:

(i)

Logarithms of values less than 1.0 were not determined correctly.

(ii)

The logarithm was found correctly but the answer was ended there i.e., anti logarithm was not determined.

Q.2

(a)

This question was quite easy and majority of the students got full marks. Those who could not perform well were the ones who were unable to form the correct simultaneous equations.

(b)

The steps to solve the question and the common mistakes are given below:

(i)

The amount of income tax was not deducted for arriving at the net amount of lottery.

(ii)

Using the sum of geometric series, students were to find the total amount in rupees required to be paid as donations. Here some candidates used arithmetic series instead of geometric series. Others computed nth term of geometric series instead of its sum. Still others took 30 days instead of 31 days for March and a few did not convert paisas into rupees.

(iii)

Lastly the students were required to give their opinion whether the amount was sufficient to pay the required donation. Some students left this part unanswered.

Q.3

(a)

It was good to see that students applied various ways to come to the conclusion and most of them were able to apply it correctly thus proving their understanding of the concept.

(b)

Almost all the students attempted this question correctly although a few got confused and applied the formula of present value of periodic payments.

(c)

Only a very small number of students were able to understand the question. Majority was confused in determining the present values of the payments. The following mistakes were commonly made :

(i)

The present value for investment of Rs.800,000 at the end of year 1 was taken as 800,000 instead of Rs.720,721.

(ii)

Present value of Rs.500,000 received at the end of year 2 to 7 was computed as if those were received at the end of year 1 to 7.

(iii)

Students were unaware of the concepts of Net Present Value.

Q.4

(a)

In this part, the candidates encountered the following difficulties:

(i)

They were unable to establish the correct total cost function.

(ii)

They did not determine the average cost function. Instead they took the first derivative of the total cost function.

(iii)

Some of those who took the first derivative of the average cost function, could not find the critical point as they were unable to solve the equation.  +  = 0

(iv)

Some of those who determined the correct critical point, did not apply the second derivative test to confirm it.

(b)

It was a simple question and majority of the candidates were able to secure full marks.

Q.5

(a)

The question was simple and given to test the basic knowledge of students about matrices and most of the students attempted it correctly.

(b)

Most of the candidates correctly drew the three lines but only a few of them were able to identify the common area. Some of the candidates extended the lines into the second and fourth quadrants where the values of ‘x’ and ‘y’ respectively are negative and thus violated the conditions x ≥ 0 and y ≥ 0.

(c)

Although it was a very simple question on the application and concept of simplex tableau, only a small percentage of candidates were able to perform well. It was evident that the students had resorted to selective study and had not studied the topic at all.

Q.6

(a)

Majority of the candidates successfully computed the median. However, some of them did not know that for mean deviation one should take the absolute deviations of individual values from the median and then multiply each deviation with its corresponding frequency. Some students calculated mean deviation from arithmetic mean instead of median and lost all marks.

(b)

Majority of the candidates who calculated mean deviation correctly, were able to calculate the co-efficient also.

Q.7

Both parts of this question were simple and straightforward. Majority of the candidates did mention that the scatter diagram depicts a negative or inverse relationship between the two variables but rarely indicated that this relationship is linear. Surprisingly some candidates did not know the basic fact that the value of the correlation co-efficient cannot be outside the range of -1 and 1.

Q.8

It was again a simple and straightforward question which is asked very frequently in the examinations . A large number of candidates were successful in establishing the least square regression line.

Q.9

Majority of the candidates was able to solve this question. Most of those who failed to solve it used incorrect  formula for finding z values.

They used the formula z =  instead of z =

Q.10

This question consisted of three parts.

(a)

The candidates were required to find the number of ways in which a team can be selected under certain conditions. Inspite of explicit statement in the question that the candidates have to determine the number of ways, some candidates computed the probability of selecting the team.

(b)

The most common mistake was that the students could not find the correct value of ‘p’ i.e., the probability of having a blood pressure greater than 136. Instead, they took ‘p’ as the probability of having a blood pressure less than 136.

(c)

The most common mistake was that students computed the probability that EXACTLY two cars will have flat tyres instead of computing the probability that ATLEAST two cars will have flat tyres.

Q.11

Since the sample size was small and only sample standard deviation was given, t – distribution should have been used. However, many students used z-distribution. Also, candidates were weak in interpreting the results and very few could explain that precision can be increased by increasing the sample size.