CBSE PROBLEM SOLVING ASSESSMENT (PSA)

 CBSE PSA ,2013

ABOUT 

However, the so called ‘syllabus’ for both types of tests remains the same, and roughly comprises of the following:

1. Questions on properties of numbers, divisibility, LCM, HCF, remainder theorem and their applications.
2. Basic arithmetic and its applications like calculating simple and compound interest, ratio and proportion, profit, loss and discount, mixtures and work-time or time-speed based problems, essentially commercial mathematics.
3. Basic algebra and its applications like simple and quadratic equations, series, exponents, polynomials, functions.
4. Geometry and mensuration. Comprising of primarily two dimensional figures, and application of basic theorems.
5. Modern maths: Set theory, Venn diagrams, permutation, combination and probability.

Although the syllabus and breadth of areas remain the same in both types of exams, there is a huge difference in types of questions that are asked and hence the approach to prepare and attempt questions also varies.

The quant in these exams (SNAP, IRMA, etc) is what could be primarily called a Speed and Accuracy Test. The number of questions is large, but most of the questions are either direct formula-based questions or direct application of a basic concept. The premium is on speed. Those who can solve questions quickly rule the roost. Consider few sample questions:

A trader bought two watches for Rs 2,000 each. One he sold at 5 per cent profit and the second at 7 per cent loss. Calculate net profit/loss.

This is a simple question of calculating a percentage (2 per cent) on Rs 2,000, which is 40.

Consider another question. If today a father is four times as old as his son and five years ago he was five times as old as his son, find their present ages. This again is a simple application of algebra, or substituting the given options.

For this type of quantitative aptitude , the following preparation strategy is suggested:

1. Leave no area unprepared, as coverage is more important than depth. Even dreaded topics like probability and permutation and combinations should not be left.
2. Cram and make yourself familiar with all basic formulae (for mensuration, algebra, logarithms and modern maths) and theorems (for geometry) as a starting point. Practise them well to the extent that you become well-versed with their application in basic questions.
3. Each functional area in quant has five to 10 standard sub-areas associated with it and each such sub-area has two to three basic concepts involving standard questions related with it. For example in work-time and time-speed questions, the sub-areas are relative speed, pipes and cisterns, boats, circular motion, clocks and work efficiency. You should familiarise yourself with each sub-area and standard questions. Again, practise well so as to solve any similar question quickly, efficiently and correctly. Remember, this will potentially comprise 80 per cent of quantitative aptitude section. You have to ensure 100 percent accuracy in them.
4. Many questions require nothing but faster calculation; hence it is sine qua non that you have complete mastery over the multiplication tables of first 30 natural numbers and the squares, cubes and square roots of the first 20 numbers. Memorising reciprocals of the first 30 numbers is also helpful in dividing faster. You will find it extremely useful in arithmetic problems like computing compound interest.
5. While attempting questions, divide your attempts into multiple rounds (at least two). In round one, attempt only those questions, of which you are 100 percent sure, and solving them is just a matter of time. The prime test of this ‘doability’ is that you should not have one iota of doubt that you can solve the question. If there are certain questions that you have solved earlier and hence know are doable but time-consuming, put a circle over them and return to them if time permits in the second round. Similarly, questions where nothing strikes your mind in first 10 to 15 seconds are best left. Put a different symbol — say a sign of interrogation — over all such questions and you can return to them in your third round. For questions about which you have no clue in first five seconds, put a cross in front of them and leave. They are a potential round four questions, subject to availability of time.

The big challenge

The syllabus of quantitative aptitude sections of these exams as mentioned earlier is same as for other exams. The difference lies in nature of questions. Here not merely the width but the depth and clarity of basic concepts, along with complete mastery over first principles, is an absolute necessity.

Although the questions derive from basic concepts, application is of a high degree. For example, although in geometry the basic theorems involved are the same (around a dozen), a single question may involve application of multiple theorems or a single theorem will only become applicable when some further construction is done in the question. Mere familiarity with the topic and basic formulae is not going to help you score well here.
Let’s see what extra must be done. Following guidelines will be helpful:

1. You need to identify your ‘areas of strength’. Areas of strength are those areas where your grip over the first principles is very clear, you are psychologically at ease even with the difficult questions and can easily comprehend and solve newer type questions. Typically this will be the area where you were ahead of your friends, either from day one, or were able to grasp fundamentals swiftly. You probably invest maximum time in solving problems in this area, and also enjoy it. Statistically, your accuracy is also highest for such topics. Your mock test scores will also indicate that. Everyone has few of these areas. It could be number system or geometry or algebra. You really need to introspect and cogitate to discover your areas of strength and further groom them to become your ‘milch cows’.
2. The larger trick lies in picking the sitters from other areas, and scoring heavily in areas of strength. Invest more time in solving difficult questions from these areas of strength. If the number is consistently 10 to 15, then you are on the right track. If it is lesser then you need to identify another such area of strength. The logic is simple, and can be explained using an analogy drawn from cricket. Every batsman has few pet shots, using which he scores most of his runs, say a pull, flick and cut. He is only average with other shots, but the mastery over these few shots is such that he rarely leaves an opportunity to score using them. You also need to identify, develop and hone your areas of strength in the same way.
3. People who are really good at quantitative aptitude are those who have got a larger number of areas of strength and keep on adding more to their repertoire. To further bolster your areas of strength, start modifying and altering questions from them after solving them. Better still, try to frame your own questions in areas of strength. The exercise of framing one's own questions is very helpful in further mastery.
4. Now again, while attempting the actual paper or mock tests, the operating logic is simple. The surface-level questions, if any, should be done in round one. Then one should invest time in questions from one’s areas of strength. However there is a caveat: no matter how good you are in one particular sphere, there still could be questions, which you cannot solve, so the criterion of reasonable time investment per question has to be kept in mind. As per this criterion, if you are clueless about a question after investing two minutes even in your area of strength, the chances are that it is beyond you at that point. Leave it; there are other battles to be fought.

In the end, at the cost of sounding clichéd, I may add that mastering quantitative aptitude is not a fixed rigid goal but a process, which can be refined to no end. Applying patience and perseverance can help you in achieving this task.