*These expert opinions were contributed by Mr Mohan, a HashLearn Tutor who is currently studying Electrical Engineering at IIT Madras.*

Mathematics is primarily based on logical deduction, and it has been described as “an essential tool for physics”, and physics has already been described as “a rich source of inspiration and insight in mathematics”. Here are a few notable steps in the process of learning Maths

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**A DEEP UNDERSTANDING OF THE MATHEMATICAL CONCEPTS AND MATHEMATICAL EQUATIONS IS IMPORTANT**

For example, 𝑦2=4𝑎𝑥 is the equation of a parabola with its vertex at the origin.Here are a few deductions from the equation:

*It is symmetric about the x-axis.**The length of latus rectum is 4a. (Two parabolas have the same shape if their latus rectums are equal)*

**DON’T TRY TO MEMORIZE ALL FORMULAE **

Filter out the unnecessary formulae. Being able to derive them is what that matters. Get the necessary formulas into your brain as you apply them to related questions. Please do know the limitations of the formula, eg. AM-GM inequality is applicable only for positive reals.

JEE problems are neither formula based nor too lengthy; they are usually based on some fundamental concepts or some simple tricks.

**Related**: How to remember what you study

**PROBLEMS SOLVING CAN BE BROKEN DOWN INTO TWO TYPES**

a. Learning Oriented

b. Exam Oriented

**LEARNING ORIENTED**

Illustrations are the ones that help you a lot.

**Step1: **Try those questions

**Step2: **Go through the solution

**Step3: **Compare it with your answer or your approach.

**Step4: **Analyse thoroughly.

**POST ANALYSIS IS WHAT THAT MATTERS A LOT.** This helps you solving new problems as this

consolidates your experience in your brain

**EXAM ORIENTED**

- Speed and Time management are essential here. It comes with practice and high concentration
- Ballparking can be employed if it is an objective type exam (Please keep in mind the penalty for a wrong answer). You should wisely use the options given

For example, the options are sometimes useful in solving indefinite integrals by helping us know what to substitute as a new variable and get a straightforward solvable integral.

Also, you can sometimes get the required answer for the generalised problem from the limiting case.

eg.*, tangent for a secant, circle for an ellipse and point for a circle.*

**T**HERE ARE SOME STANDARD WAYS TO SOLVE SOME **QUESTIONS. TRY TO FIGURE IT OUT**

For example, if you take the *trigonometric equations* chapter

1) **Range method**

2) **Graphical method**

3) **Direct simplification**

4) **Usage of identities **

are some of the standard methods to solve the problems.

In Range method, we compare the ranges of LHS and RHS of the equation.And in the graphical method, we draw the graphs of LHS and RHS and find the intersecting points.

**WHILE SOLVING PROBLEMS**

- Step 1: Understand the question and catch the keywords in the question.
- Step 2: This is the crucial step. Analyzing the given quantities and constraints we have to find the unknown numbers.
- Step 3: Experiences that we get from solving previous questions and known relations help us to start off the solution.
- Step 4: If you think that you are going the wrong route, pause for a moment and reanalyse the question.

**MATERIAL FOR PREPARATION**

- For JEE mains RD Sharma class 11th and 12th are good enough. Also, go through the illustrations in objective RD Sharma
- Mathematics for IIT JEE by R.D.SHARMA.(Theory and examples are excellent)
- Integral calculus for JEE mains and advanced by Amit M Agarwal.(Exercises are also useful in this book)
- Algebra for JEE Mains and Advanced by SK Goyal.
- Course in mathematics for IIT JEE – TMH publications.
- Mathematics for the JEE Mains and Advanced by Manan Khurma (Illustrations and theory are just sufficient)
- Previous year questions.
- https://mathinsight.org/ – This is an excellent website to learn the basics of undergraduate maths like curl, divergence, etc.
- Try to write the summary and essential concepts including most used formulae, good problems in short notes. This helps during revision.(Do not waste much time in writing it too neatly.)

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