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Coordinate geometry has always occupied an important and major part of JEE question paper each year. Considering the weightage analysis for JEE mathematics of past few years, coordinate geometry (2-D) has been found to have occupied approximately 20% of JEE mathematics question paper each year. 

Graduate Aptitude Test in Engineering (GATE) is one of the toughest examinations for engineering graduates in India that primarily tests the aptitude of engineering graduates in solving the engineering problems. 

This chapter in itself is a combination of many other chapters. Although rarely direct questions are asked from this chapter, yet it finds endless applications in calculus and algebra, so basically it serves as a “tool” to solve problems of other topics.

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Negative marking and extensive competition in Graduate Aptitude Test in Engineering (GATE) make it one of the toughest examinations in India at graduate level. There is no limit in the number of attempts in GATE. However, a failure attempt means, loss of one year of life and career. 

JEE syllabus covers the following concepts in quadratic equations and expressions:

• Quadratic equations with real coefficients
• Relations between roots and coefficients
• Formation of quadratic equations with given roots
• Symmetric functions of roots.

Have you also ever "dreamt" of being in one of the most premier institutes of India - the IITs? If your answer to the above question is a big "YES", I am glad to meet you here on this blog! I am Harshita Srivastava, a second year undergraduate student at Indian Institute of Technology, Kanpur.

This topic is the very first lesson taught in chemistry. It introduces the students with the most fundamental but most important tools of chemistry – mole concept and stoichiometry. There are other basic concepts and definitions involved which serve as tools for a chemistry student to solve the concerned problem.

This chapter in itself is a combination of many other chapters. Although rarely direct questions are asked from this chapter, yet it finds endless applications in calculus and algebra, so basically it serves as a “tool” to solve problems of other topics.

• Trigonometric functions: This chapter introduces the definition of the 6 T-ratios as the ratio of the sides of a right angled triangle. Further, the relationship between the T-ratios is taught. Then come the 3 fundamental identities:

1. sin²Ɵ + cos²Ɵ = 1
2. 1 + tan²Ɵ = sec²Ɵ
3. 1 + cot²Ɵ = cosec²Ɵ

These are the most important identities of trigonometry and can be derived from Pythagoras theorem easily. A number of questions can be solved by writing 1 - cos²Ɵ instead of sin²Ɵ.

There is a good technique to memorize the sign of the T-ratios.

This table can be memorised with the help of the phrase:

Add                        Sugar                     To                           Coffee

(This can also be added as a concept map / aid to memory)

A useful thing to solve problems is to note that the range of  is (-∞ , -2] U [2 , ∞). This fact often helps.

                The T-ratios of allied angles must be thoroughly covered.

Another important point to note is that trigonometric functions are periodic. The periodicity of the trigonometric functions is an important property and has wide applications in mathematics and engineering physics. Students should be able to make graph of the functions keeping the periodicity in mind.

One final thing that is expected is that students should be able to integrate the above ideas to prove various identities involving trigonometric functions. They should be able to use algebra in trigonometry and trigonometry in algebra and calculus.

• Compound and multiple angles: This chapter begins with the most elementary formulae of sin(A ± B), cos(A ± B) and tan(A ± B) in terms of sin A, cos A, tan A and sin B, cos B, tan B. Another important formula which is sometimes asked is that of tan(A + B + C). Students should memorize the above formulae by heart.

Further introduced are the most important “A, B” formulae and “C, D” formulae

1. 2 sin A cos B = sin (A + B) + sin (A – B)
2. 2 cos A sin B = sin (A + B) - sin (A – B)
3. 2 cos A cos B = cos (A + B) + cos (A – B)
4. 2 sin A sin B = cos (A - B) - cos (A + B) à (note that this formula is a bit different)
5. sin C + sin D = 2 sin ((C + D) / 2) cos ((C + D) / 2)            (please format this correctly to look mathematical – or rather make it as an image or a concept map)
6. sin C - sin D = 2 cos ((C + D) / 2) sin ((C + D) / 2)
7. cos C + cos D = 2 cos ((C + D) / 2) cos ((C + D) / 2)
8. cos C - cos D = 2 sin ((C + D) / 2) sin ((C + D) / 2)
9. T-ratios of 2A in terms of those of A
10. T-ratios of 3A in terms of those of A
11. T-ratios of submultiple angles

Next taught are the most important T-ratios of multiple and submultiple angles:

Rest this entire chapter is all about applying the correct formula at the correct place. Students should practice enough questions so that these formulae get embedded in their minds.

• Trigonometric equations: This is s straightforward and a simple chapter. One of the best chapters in trigonometry. A number of questions are asked in JEE from this chapter and the questions are fairly direct. Students are expected to solve standard forms of trigonometric equations that occur frequently in engineering. Most of this chapter is the “tool” part and is widely used.

To summarise, most students find trigonometry boring because of so many formulae involved in it. But those aiming for good ranks in competitive exams should not miss even a single formula. The paper setters of competitive exams are well aware of what students generally overlook and so they deliberately introduce questions from those concepts.

For trigonometry, a one liner would be – “practice makes a human perfect”

GATE (Graduate Aptitude Test in Engineering) essentially examines the aptitude of engineering graduates/students in understanding simple problems and applying engineering concepts to solve them. Thus, a GATE aspirant has to develop abilities in solving aptitude-based problems.

Engineering has remained as one of the most sought after career options for bright students over the years. The Graduate Aptitude Test in Engineering (GATE) tests the students’ capability in engineering concepts along with managerial skills. It is considered as one of the toughest examinations in our country. The competition level