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JEE Main Mathematics Preparation Tips: Important Topics and Strategies
Last updated on February 20th, 2021
Mathematics is probably a lifesaver for a large number of aspirants of JEE Main. This is so because JEE Main Mathematics Preparation is comparatively easier than the other two sections. And due to a foundation based on Sets, Relations and Functions, the learning does not require to start everything from scratch. The first step that comes under the JEE Main Mathematics Preparation Tips is to be updated with the syllabus of JEE Main Mathematics 2021. Being well informed with the syllabus will definitely help you work upon the most important topics.
Latest Updates:
 JEE Main 2021 is scheduled to be conducted in 4 sessions.
 The first session will be conducted from 23rd to 26th February 2021. Read More
 NTA has introduced some changes in the JEE Main 2021 Exam pattern. Check New Exam Pattern here
Mathematics is yet considered to be hard because of the fear created out of it. To overcome your fear, you are advised to start preparing Mathematics pretty well in advance.
 Candidates are advised to practice a sufficient number of IIT JEE previous year question papers.
 When you will start solving previous years papers regularly, you will be able to know:

 the type of questions
 the patterns that might be present in the upcoming examination
 be able to figure out your weaknesses and strengths
In the article below, some suggestions can be useful on how to prepare Maths for JEE Main 2021. Let us start with some very basic JEE Main Mathematics Preparation Tips.
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JEE Main Mathematics Preparation Tips: Basic Rules to Follow
 Revision is Important:
 Students are required to organise their study time and revision time.
 This is because revision ensures that you are on track with the topics which are not under purview but must be worked on.
 Take regular breaks and practice JEE Main previous years’ question papers.
 Revise the topics every alternate day or at least twice a week.
 Topicwise Mocks:
 Attempting mock tests and practice papers can actually tell what level of preparation is needed.
 Solving the question papers enables the candidates to know difficulty levels and their own preparation against it so they can work on their weak areas.
 With online mocks, a deep analysis is easily available online, to understand accuracy, strong topics, timeconsuming topics and weak topics.
 Speedy Calculations:
 With better practice, students will build speed in core topics.
 This speed must be maintained during the examination as well.
 Since there is no sectional timing, ensure that you solve enough questions from each section within 1 and a half hour (90 minutes) such that the score reaches the expected cutoff.
 Accurate Answers:
 If you follow the speed rule in the first 90 minutes, follow the accuracy rule in the next 90 minutes.
 Instead of solving maximum questions, try solving what you can, but with accurate answers.
 This will help build your score and might help you score 90+ in JEE Main Maths.
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JEE Main Mathematics Preparation Tips: Key Pointers
 Firstly, the trend of questions from previous year question papers can be analysed. Questions come from almost every chapter in the exam.
 Secondly, attempt the official JEE Main Mock Test. It will help you overcome the nervousness of exam halls.
 Also, you can learn a formula only through practice. It is very crucial to know all the Mathematics Important Formulas to score better.
 Solve online mock tests on a table and chair. It gives an exam hall viewpoint and helps with time management.
 The graphical approach helps a lot in solving Mathematics questions. Try using that.
 Hit and trial method works in some questions where reverse calculations might be timeconsuming. Use it with care.
 While solving questions, make sure you do not make the most common errors. Marks in JEE Main 2021 will be only for the right answer.
 Strengthen your grip on function theory because it is the foundation for almost each and every topic of class 11th and 12th.
 If solving questions on a rough sheet, use as many sheets as required. Do not scribble over and over on the same sheet.
 Spend around 5 to 10 minutes, in the beginning, searching for easy questions from all the 25 questions. 40% to 50% of JEE Main Mathematics questions are easy and scorable. Around 20% to 30% are moderate and almost 10% to 20% difficult.
 Instead of getting entangled in tough questions, you must try to solve easy questions. Approximately, 20 questions can be solved in 60 minutes that way. Every single mark counts. Don’t waste time.
 Focus on the topics you have a good grip over. Pay attention to them. Memorise formulas and concepts of all the major topics.
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JEE Main Mathematics Preparation Tips: Crucial Topics
 Calculus: Calculus is one of the largest topics of mathematics. It is divided into two major studies – Differential and Integral calculus. Key topics to study in differential calculus are – limits and continuity, application of derivatives, differentiation. Key topics from integral calculus are – Indefinite integral, definite integral, the area under curves.
 Coordinate Geometry: Comparatively easy and scorable, coordinate geometry is the study of shapes and curves on a graph. Major topics to be covered under coordinate geometry are – straight lines, hyperbola, parabola, ellipse, circle.
 Trigonometry: Trigonometry has been considered one of the most important topics since class 10th. Students must have a command over the basics of trigonometry. JEE Main and other exams have questions from trigonometric ratios and trigonometric functions. These are scorable and are moderately tough.
 Algebra: This is the vastest topic of Mathematics. Questions from algebra could vary from easy to very hard. It depends on your ability to decipher how long a question can take. Major topics to be covered under algebra are – sets, relations and functions, matrices and determinants, permutations and combinations, complex numbers, probability, differential equations, quadratic equations and expressions, progressions and series, binomial theorem.
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How to Study Maths for JEE Main 2021 at home?
It is a proven fact that when you are at your home, books are the best source of knowledge to study properly. But it is also very important to note that due to the changed exam mode into the computerbased environment, JEE Main 2021 will not be exactly a pen and paperbased exam. Students also require to learn various tricks over how to increase productivity while attempting the full examination of 3 hours. Given below are some JEE Main Mathematics Preparation Tips to Study from Home.
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Question Paper PDFs for JEE Main Mathematics Preparation (by Allen Kota)
To begin with the JEE Main Mathematics Preparation Tips at home, it is often suggested that computers and smartphones are contributors to distractions. To end this struggle for students, download these question paper PDFs of JEE Main 2019 Mathematics section prepared by Allen Kota. If possible, it is also suggested to print these papers and solve them offline in a traditional pen and paper mode. Do remember to first use “Papers & Answers” as this pushes you to attempt the questions on your own, rather than copying the whole solution. Given below are links for JEE Main Mathematics PDF question papers:
Date  Shift  Papers & Answers  Paper & Solutions 
9 January  1  Click Here  Click Here 
2  Click Here  Click Here  
10 January  1  Click Here  Click Here 
2  Click Here  Click Here  
11 January  1  Click Here  Click Here 
2  Click Here  Click Here  
12 January  1  Click Here  Click Here 
2  Click Here  Click Here 
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Free Online Mock Tests Provided by NTA for JEE Main Mathematics Preparation
Another part of JEE Main Mathematics Preparation Tips at home is free online mocks. The online mock tests provided by NTA (National Testing Agency) are a simulation of the actual exam which will help students understand how to attempt the examination in a computerbased environment. The only disadvantage here is that these are full mock tests and not subjectwise mock tests. Although, students can utilise this portal if they have completed the syllabus for JEE Main Mathematics and want to do revision.
 To access the mock tests head over to this website – https://nta.ac.in/quiz.
 After this, just select the examination and paper from 2020, 2019, or 2018 sessions.
 Once selected, start your mock test.
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NTA ContentBased Lectures (by IITPAL) for JEE Main Mathematics Preparation
National Testing Agency has provided video lectures recorded by a few reputed IIT Professors under the nemesis of IITPAL on Youtube. These lectures are divided into subtopics for each chapter to focus only on main topics. There are more than 200 videos of approximately 50 to 60minute runtime for each video. This is probably one of the most useful JEE Main Mathematics Preparation Tips. To access these videos
 To begin with, head over to the official website of NTA – www.nta.ac.in
 Next, click on the ‘Students’ tab.
 Then, under the ‘Test Practice’ section, select ‘Content Based Lectures’.
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JEE Main Mathematics Preparation Tips: ELearning Platforms
There are various elearning platforms which are the best source for preparation of almost each and every competitive examination. In the past few years, the use of smartphones and online courses have increased multiple folds due to decreased cost of the internet in India. A lot of EdTech companies started growing and now provide video lectures, mock tests, study material and a lot more stuff which helps students improve their preparation levels. Given below are some Elearning portals which can help students boost their JEE Main Mathematics Preparation.

Unacademy
 This is the largest learning platform in India with a continuously growing user base.
 Students can watch completely free lectures on various subjects and topics directly streamed by the toppers of various examinations.
 Also, students can interact with the educators or teachers through the comment section given below the video.

EduRev
 This application is a learning application which provides subjectwise notes and video lectures.
 It also houses a large number of Mock Tests and topicwise tests for students to work on their weak topics.
 Students will also find a large database of questions from previous years provided within the application.

Khan Academy
 This application provides video lectures according to the curriculum of CBSE and for IIT JEE too.
 Video lectures of Khan Academy are very well explained to understand the topics of JEE Main Mathematics thoroughly.
 With each video lecture, students are also asked questions on the topic for which they earn points and badges as rewards.

Vedantu
 This application houses all the major resources required for a student.
 From Solutions of questions from books of major writers to All India Mock Tests and live video lectures, students will find all the necessary resources, completely free!
 The speciality of this application is their inhouse WAVE technology which lets students (or users) interact with a question putup on the screen by the educator.
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JEE Main Mathematics Preparation Tips: Weightage Analysis
Given below is the chapterwise weightage of JEE Main Mathematics which will help you understand what topics should be given more time. It is nonetheless a universal fact that about 3040% of the syllabus is part of the Calculus which is divided into Limits and Derivatives, Differentiation, Integration, Applications of Calculus, Differential Equations and much more. Students who can complete Calculus build huge confidence to cover other chapters as well.
Topic  Number of Questions 
Sets, Relations and Functions  1 
Complex Numbers and Quadratic Equations  2 
Matrices and Determinants  2 
Permutations and Combinations  1 
Mathematical Induction  1 
Binomial Theorem and its applications  1 
Sequences and Series  2 
Limit, Continuity and Differentiability  1 
Differential Calculus  4 
Integral Calculus  5 
Differential Equations  1 
Coordinate Geometry  2 
Three Dimensional Geometry  3 
Vector Algebra  1 
Statistics and Probability  2 
Trigonometry  2 
Mathematical Reasoning  1 
Check:
Latest JEE Main News
 “Classes for Engineering Courses to Start from 15 September”, Says AICTE Amid COVID19 Surge
 JEE Main 2021 May Session Postponed, Education Minister Confirms; Check Details
 JEE Main April 2021 Postponed Amid Spike In COVID19 Cases, New Dates 15 Days Prior To Exam
 AICTE Says PCM Not Mandatory For Engineering: Boon or Bane?
 Dr Ramesh Pokhriyal Announces JEE Advanced 2021 For 3rd July, 75% Criteria Removed
Recommended Books for JEE Main Mathematics Preparation
Mathematics section requires comprehensive preparation. The following table represents some of the best books for JEE Main along with their author’s name that students can prefer for their Maths Section preparation:
Book  Author 
IIT Mathematics  M.L. Khanna 
Differential Calculus  Das Gupta 
Class XI and XII Mathematics  R.D. Sharma 
Mathematics for JEE Main  Cengage (Publisher) 
Integral Calculus for IITJEE  Amit Agarwal 
Calculus and Analytic Geometry  Thomas and Finney 
Problems in Calculus of One Variable  I. A. Maron 
Higher Algebra  Hall and Knight 
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JEE Main Mathematics Preparation Tips: Few Sample Questions
Question 1.
The locus of the point of intersection of the lines xcost+(1cost)y=asint and xsint(1+cost)y+asint=0 is
1) x2y2=a2 3) y2 = ax
2)x2+y2=a2 4) x2 = ay
Answer
Rearranging the above equations, we get
1cost/sint=ax/y and 1+cost/sint=a+x/y
multiplying the above equations ,we get x2+y2=a2
Question 2.
Lines ax+by+c=0, where 3a+2b+4c=0 & a,b,c all belong to the set of real numbers that are concurrent at the point?
1) (3,2) 3) (3,4)
2) (2,4) 4) (3/4, 1/2)
Answer.
We know that,
3a+2b+4c =0
which equals (3/4)a+(1/2)b+c=0
So, the line passes through (3/4,1/2)
Question 3.
If the area of the triangle formed by the equation 8×26xy+y2=0 and the line 2x+3y=a is 7 then the value of a is?
1) 14 3) 7
2) 28 4) 17
Answer.
Equation of the sides of the given triangle are y=2x, y=4x and 2x+3y=a
So, vertices of the triangle are (a/8,a/4);(a/14,2a/7) and (0,0)
By the determinant method, the area of the triangle formed by these coordinates comes out to be a2/112 which is equal to 7
This gives the value of a as 28.
Question 4.
If the line x=k; k= 1,2,3,…..,n meet the line y=3x+4 at the points Ak(xk,yk), k= 1,2,3…..,n then the ordinate of the centre of the mean position of points Ak, k= 1,2,3,…..,n is
1) n+1/2 3) 3(n+1)/2
2) 3n+11/2 4) None of the above
Answer.
We have yk=3k+4, the ordinate of intersection of x=k and y=3x+4 . So the ordinate of the mean position of the points Ak k= 1,2,3,…..,n is
(1/n){sum of all yk’s} which comes out to be 3n+11/2
Question 5.
If the point (3,4) lies on the locus of the point of intersection of the lines xcost+ysint =a and xsintycost=b, the point (a,b) lies on the line 3x4y=0 then a+b=?
1) 1 3) 7
2) 3 4) 12
Answer.
Squaring and adding the given equations of the lines we get
x2+y2=a2+b2 as the locus of the point of intersection of these lines.
Since (3,4) lies on the locus we get
9+16=a2+b2
Also (a,b) lies on 3x4y=0 so 3a4b=0
Solving the two equations for a and b, we get a+b= 7
Question 6.
Equation of the circle with centre (4,3) touching internally and containing the circle x2+y2=1is
1) x2+y2+8x6y+9=0 3) x2+y28x+6y+9=0
2)x2+y2+8x6y+11=0 4) x2+y28x+6y11=0
Answer.
Let the equation of the required circle be (x+4)2+(y3)2=r2
If the above circle touches the circle x2+y2=1 internally, then the distance between the centres of the circles is equal to the difference of their radii
42+32=r1
Which implies r=6
So the equation of the circle is x2+y2+8x6y11=0
Question 7.
If the normal chord at a point ‘t’ on the parabola y2=4axsubtends a right angle at the vertex, then the value of t is
1)4 3) 3
2)1 4) 2
Answer.
Equation of the normal at ‘t’ to the parabola y2=4ax is y= tx+2at+at3
The joint equation of the lines joining the vertex to the points of the intersection of parabola and the normal is
y2=4ax[y+tx/2at+t3]
4tx2(2t+t3)y2+4xy=0
Since these lines are at right angles so the coefficient of x2+y2=0
So, it comes out to be 2.
Question 8.
The angle between a diagonal of a cube and one of its edges is,
1) cos1(1/3) 3) /3
2) /4 4) /6
Answer.
Let a= a1i, b=a1j ,c=a1k.
Then the vector d= a1(i+j+k) is a diagonal of the cube. The angle between one of the edges a, b or c and the diagonal d is given by,
cos=a.d/ad which comes out to be cos1(1/3).
Question 9.
Volume of the tetrahedron with vertices P(1,2,0) ; Q(2,1,3) ; R(1,0,1) and S (3,2,3) is
1) 1/3 3) 1/4
2) 2/3 4) ¾
Answer.
Volume of the tetrahedron is given by a scalar triple product,
Volume of tetrahedron= ⅙PQ.(PR x PS)
Here PQ, PR and PS are three vectors made from the above provided coordinates.
So, the volume of tetrahedron comes out to be ⅔ after solving the triple product.
Question 10.
If A,B,C and D are four points in space and ABxCD+BCxAD+CAxBD=(area of triangle ABC). Then the value of is
1) 1 3) 3
2) 2 4) 4
Answer.
Let D be the origin of reference and DA=a, DB= b, DC= c
So, ABxCD+BCxAD+CAxBD= (ba) x (c) +(cb) x (a) + (ac) x (b)
= 2axb+bxc+cxa
=2(2 area of ABC)
Hence equals 4
Check
JEE Main Syllabus 2021
The JEE Main Syllabus 2021 for all the three subjects are given below in brief.
 JEE Main Mathematics Syllabus – Sets, relations and functions, complex numbers and quadratic equations, matrices and determinants, permutations and combinations, mathematical signs, binomial theorems, etc.
 JEE Main Physics Syllabus – Kinematics, Laws of Motion, Functions, Gravity, Solids and Liquids, Thermodynamics, Energy and Power, Rotating Motion etc. Check Complete JEE Main Syllabus for Physics
 JEE Main Chemistry Syllabus – Basic concepts of chemistry, chemical bonds and molecular structures, chemical kinetics, chemical thermodynamics, states of substances etc. Check Complete JEE Main Syllabus for Chemistry
Mathematics can be easily scorable if you know the tricks and short methods for harder calculations. Remember that in a board examination marks are given for each step but in competitive exams like JEE Main, each question has 4 marks only. Now that question can take 10 steps or it can take 2 steps. That choice is the smart decision which brings out the toppers.
Keep revising your topics and maintain a small handbook for the basic formulae of trigonometry, calculus and other major sections. Mathematics is a mixture of hard work and smart work. You cannot just rely on one of them to ensure a good score. Work on your weak topics but even more on strong topics to give you an edge on them.
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FAQs
Last updated on October 20th, 2020
Ans.We strongly advise the candidates to commence their preparation as soon as possible. It is preferable to start from class XI or XII alongside board exam preparations. With this, candidates get enough time to study and complete the syllabus along with ample time in their hands for revision which is as important as preparation.
Last updated on October 20th, 2020
Ans. Maths XI & XII recommended books by NCERT are:
 Coordinate Geometry S. L. Loney
 Problems in Calculus of One Variable by I.A. Maron
 Higher Algebra by Hall & Knight
 Trigonometry by S. L. Loney
Last updated on October 20th, 2020
Ans. Yes, it is possible for you to get a good rank in JEE Main with 6 months of preparation. For that, you will have to work hard for the exam to complete the exam syllabus as soon as possible and start revision timely.
Last updated on February 20th, 2021
Ans.As per the current situation, we would suggest that there is no harm in taking a drop to prepare for the JEE Main 2021. It is alright if you couldn’t study properly alongside your Class XII boards and couldn’t sit for the exam with absolute comfort. Start with a fresh mind next year and make it your goal to crack the exam.
Last updated on October 20th, 2020
Ans.The best way to practice for JEE Main 2021 is to solve maximum sample papers and take up as many mock tests as possible. If candidates attempt mock tests on a regular basis, they will get to know how questions should be answered during the real exam.