April 18, 2017 | Author: Catalyst Educare | Category: N/A
CPT – Mathematics Shortcuts, Tips and Tricks CPT consists of two papers. Each is of 2 hours duration and has 100 questions. Thus a student gets 120 minutes for solving 100 questions, i.e. 1.2 minutes per question. This sounds really difficult and challenging. However a student at Catalyst is trained to believe that this is achievable and is trained in the techniques to handle 100 questions in 120 minutes. The trick to perform well in an exam like CPT lies in conquering the correct approach, which Catalyst teaches you. Given below are some of the tricks which can help you save your valuable time during the exam and answer the questions correctly.
Example 1 The roots of the cubic equation x3 + 7 x 2 − 21x − 27 = 0 are given by (a) (-1,-3,-9)
(b) (-1, 3, -9)
(c) (1, -3, -9)
(d) (1, 3,9)
An average student will take about 4 minutes to solve this question. A student at Catalyst is taught the following approach: Substitute one of the values in place of x in the given equation. Among all the given values 1 will be the easiest to substitute. Substituting 1 in place of x, we get the left hand side as (1 + 7 – 21 – 27) which is ≠ 0 (right hand side). Hence 1 is not a root of the given equation. Thus we can eliminate the options (c) and (d) which contain 1. Answer will be one among the options (a) & (b). Thus, we have immediately eliminated 2 out of 4 options without spending much time. Now (a) & (b) both have -1 & -9. So, we substitute 3 in place of x and get the left hand side as 33 + 7 *32 − 21*3 − 27 = 0 (right hand side). Hence 3 is a root of the equation. Thus the correct option is (b).
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Thus, the question which normally takes 4 minutes to be solved has been solved in less than a minute. This gain of 3 minutes can be instrumental you are giving an exam like CPT.
Example 2 1 1 1 Find the sum of the series 1 + + 2 + ....... + ( n−1) 3 3 3 (a)
1 3
(b)
2 3
(c)
3 2
(d) None of these
1 This is a geometric series of n terms with first term as 1 and common ratio . Students 3 1 n 1 − 3n − r 1 ( ) use the following formula to arrive at the answer: a = 1. = ...... and so 1 (1 − r ) 1 − 3 on.
However, Catalyst advises its students to look at the options before proceeding to solve it. It does not require anything more than common sense to realize that the answer should contain an n (since it is sum to n terms). None of options (a), (b) and (c) contains n. Hence the correct option is (d). Thus the time taken to solve the question is equal to the time taken to read it. This illustrates the importance of looking at the options before solving the questions because many a times the question can be solved simply by playing with the options.
Example 3 Find the roots of the equation x 2 − 24 x + 135 = 0 (a) 9,6
(b) 9,15
(c) 3,15
(d) None of these
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As soon as a student sees this sum, he starts factorizing 135 and makes several combinations of the factors of 135 to find which of them gives (-24) as the sum. This takes several minutes. A student at Catalyst is taught to solve this question in the following manner: Here the co-efficient of x 2 is 1. Thus the sum of the roots will be equal to 24 and the product of the roots will be equal to 135. [Remember the basic formula for a quadratic equation: x2 – (sum of the roots)*x + (product of the roots) = 0 ] For option (a) Sum of the given values = 9 + 6 = 15 ⇒ Incorrect option. Hence eliminated. For option (b) Sum of the given values = 9 + 15 = 24; Product of the values = 9*15 = 135 Hence (b) is the correct option. This method takes less than 30 seconds to arrive at the correct option.
Example 4 In how many years will a sum of money double itself at 5% rate of interest, compounded annually? (a) 15 years 1 month (c) 16 years 7 months
(b) 14 years 2 months (d) 16 years 3 months
A student will solve this question using the formula: n r A = P 1 + 100
5 ⇒ 2 P = P 1 + 100 ⇒ 2 = (1.05 )
n
n
After this the student will have to find out log value of 2 and 1.05, and then solve the question.
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A student at Catalyst is at advantage for such a question because we teach him to solve the question as follows: 72 years r approximately. Hence a sum of money will double itself at 5% compound interest in 72 = 14.4 years approximately. From this we see that the correct option is (b). 5
Rule of 72: A sum of money will double itself at r% compound interest in
Note: This rule gives an approximate value. Thus if the options are very close like (a) 14 years 3 months (c) 16 years 7 months
(b) 14 years 2 months (d) 16 years 3 months
then we cannot use this rule of 72. However, it can still be used to eliminate options (c) & (d) and we can make a safe guess.
CPT is an MCQ (Multiple Choice Questions) Examination. In an MCQ Exam, each question is followed by some options and the student is required to mark the correct option. Thus it is very different from the exams you have been giving till now where the student has to answer the question completely by showing all the steps involved. Hence, the approach to CPT should also be different from the exams you are used to give since your childhood. For any exam, having the full subject knowledge without knowing the correct approach is only half the preparation. Catalyst prepares you not only by teaching you the subject but also by inculcating in you the proper approach towards the exam. The above examples are given to give you an overview of the kind of teaching takes place in our classrooms. We stress on smart work along with hard work. This is the recipe for success in an exam like CPT. ALL THE BEST!!
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