Tricks, Short cuts for JEE Maths
Dec 11, 2018
JEE MATHEMATICS – A Complete Guide (Tricks, Short cuts for JEE Maths)
“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality”
If you have decided to be an engineer and ace the technologically advancing world, then cracking JEE is the first step towards achieving your goal. Every year, lakhs of students struggle to get admitted to the premier technological institutes of India. Only 10% of the total test takers get the chance to achieve their dreams as the competitiveness of the exams are strenuous and demanding. A proper learning strategy and effort will definitely yield positive results. Joint Entrance Examination (JEE) MAIN will be conducted by the NTA from 2019 onwards. This Examination was being conducted by the Central Board of Secondary Education (CBSE) till 2018. 
JEE main is applicable to NITs, IIITs and CFTIs participating though Central Seat Allocation Board subject to the condition that the candidate should have secured at least 75% marks in the 12th class examination, or be in the top 20 percentile in the 12th class examination conducted by the respective Boards.
Mathematics being one the three subjects of the national-level exam, you need to get familiar with the JEE Main Mathematics paper pattern and syllabus. Getting to know this will enable you to structure your preparation accordingly. Also, the exam will be held in computer-based mode twice every year; please note drawing test of Paper II though will continue to be held in pen-paper-based mode. With, however, all these changes, there is no revision made to the syllabus of JEE Main 2019 Mathematics subject.
Out of the three subjects, Mathematics is the easily scoring subject and as well as a demanding subject as it tests your basic mathematical ability to comprehend the given mathematical data and use logical and analytical methods to bring out the accurate answers. Students who are even weak in mathematics have a good chance of doing well if they take consistent effort towards mastering the fundamentals and applying it in the problems.JEE tests your accuracy and speed than your way of solving. For this any students should be equipped with In-depth knowledge of all the basics topics taught in school right from standard 6 to standard 12.In this article, you can get the complete guide to all your queries regarding IITJEE Mathematics 2019.
Complete syllabus of JEE MAIN Mathematics : Tricks, Short cuts for JEE Maths
When you begin your preparation, it is essential to understand the various topics covered under mathematics paper.After going through the chapters, noting down the important topics in every chapter is essential to schedule the study plan for all the chapters.
Tricks, Short cuts for JEE Maths
Chapter-1: Sets, Relations and Functions
Weight-age: 4%
Important topics : Sets, Union, Intersection, and Complement of Sets and their Algebraic Properties, Power Set, Relation, Types of Relations, Equivalence Relations and Functions
Chapter-2: Complex Numbers and Quadratic Equation
Weight-age: 5-6%
Important topics: Representation, Algebra, Square Root of a Complex Number, Triangle Inequality, Quadratic Equations in Real and Complex Number System, Relation between Roots and Coefficients, Formation of Quadratic Equations with given roots.
Chapter-3: Matrices and Determinants
Weight-age: 6-7%
Important topics: Algebra of Matrices & its types, Determinants, Adjoin and Evaluation of Square Matrix are important topics from this unit.
Chapter-4: Permutations and Combinations
Weight-age: 3-4%
Important topics: Fundamental Principle, Permutation and Combination are important topics.
Chapter-5: Mathematical Induction
Weight-age : 1-2%
Important topics: Principle of Mathematical Induction & it’s simple applications
Chapter-6: Binomial Theorem and Its Simple Applications
Weight-age: 3-4%
Important topics: Binomial Theorem for a Positive Integral Index, Properties of Binomial Coefficients and its applications.
Chapter-7: Sequences and Series
Weight-age: 6-7%.
Important topics: Arithmetic and Geometric Progressions, Relation between A.M. and G.M, Sum Up to “n” Terms of Special Series.
Chapter-8: Limit, Continuity and Differentiation
Weight-age: 7-8%
Important topics: Real-Valued Functions, Algebra of Functions, Polynomials, Rational, Trigonometric, Logarithmic and Exponential Functions, Inverse Functions, Graphs of Simple Functions, Limits, Continuity, Differentiation, Derivatives of order up to two, Rolle’s and Lagrange’s Mean Value Theorems.
Chapter-9: Integral Calculus
Weight-age: 10-12%
Important topics: Integral as an Anti-Derivative, Fundamental Integrals, Integration, Fundamental Theorem of Calculus, Properties of Definite Integrals, Evaluation of Definite Integrals.
Chapter-10: Differential Equations
Weight-age: 6-7%
Important topics: Ordinary Differential Equations, Formation & Solution of Differential Equations.
Chapter-11: Co-Ordinate Geometry
Weight-age: 10-12%
Important topics: Cartesian System, Straight Lines, Equations of Internal and External Bisectors of Angles between two lines, Coordinates of Centroid, Orthocenter, and Circumcenter of a Triangle, Circles, Conic Sections, Equations of Conic Sections (Parabola, Ellipse, and Hyperbola).
It is a highly scoring unit as it includes the application of the direct formulas. It requires an understanding of the Geometrical Shapes like Circle, Parabola, Triangle, Hyperbola etc. Majority of questions asked from this topic are of the Straight Line and Circle.
Chapter-12: 3-D Geometry
Weight-age: 5-6%
Important topics: Co-Ordinates of a Point in Space, Section Formula, Direction Ratios and Direction Cosines, The Angle between two Intersecting Lines, Skew Lines & its Equation, Equations of a Line and a Plane in different forms and Coplanar Lines.
Chapter-13: Vector Algebra
Weight-age: 3-4 %
Important topics: Vector and Scalars, Components of a Vector in 2D and 3D Space, Scalar and Vector Products are some must-read topics in this section.
Chapter-14: Statistics and Probability
Weight-age: 4-5%.
Important topics: Measures of Dispersion, Calculation of Standard Deviation, Variance and Mean Deviation, Probability, Bayes’s Theorem, Bernoulli Trials and Binomial Distribution.
Chapter-15: Trigonometry
Weight-age: 6-7%.
Important topics: Trigonometrical Identities, Equations, Functions and questions based on Heights & Distances.
Chapter-16: Mathematical Reasoning
Weight-age: 3-4%.
Important topics: Statements, Logical Operations, Understanding of Tautology, Contradiction, Converse, and Contrapositive statements.
Now spend time to look at the number of questions from each chapter from the previous year papers which is consolidated from the year 2006-2018.
The weight-age given to the units have differed over the years drastically. Therefore, it is important to understand that the given data is just to get an idea of the number of questions asked. Students can utilize the above data to schedule their preparation such that they don’t lose out on easily scoring units.
More than just seeing the numerical data, it is highly advisable for a candidate to solve all the previous year question papers during mocks to get an idea of the varying degrees of questions asked from the chapters and also to understand the level of difficulties of questions.
20 Key Shortcut Tricks for IIT JEE Mathematics ;Tricks, Short cuts for JEE Maths
In IITJEE getting a correct answer matters less compared to the time you took to solve it. Minimum the amount of time taken per question maximum is the chance you get to solve more number of questions. Therefore, it is important to learn as many possible short-cut tricks to improve your speed and accuracy of solving a problem.
- Learn essential Vedic mathematical tricks to get to the answer fast
- Improve your mental mathematical ability
- L-Hospital Rules should be used to solve Limits Problem
- To solve Partial Differentiation, you should use Chain Rule
- Make Algebra your weapon. Create the ability to picturize functions as graphs and learn to apply vertical and horizontal origin shifts carefully.
- To solve the Permutation-Combination and Probability problems, use basics of Bayes’ Theorem, Derangement and various ways of Distribution. You must be aware of cases, where objects are identical and not
- Integral Calculus can be scoring if you use tricks and some basic varieties of integral functions. You can save a lot of time by using properties and applying them wisely.
- Solving the Co-ordinate Geometry questions would be fun if you understand the various forms of Conic Section and can convert the tougher ones to these basic forms. Co-ordinate Geometry questions can be solved easily using Complex Numbers.
- To score well in Trigonometry, learn all the important formulas and properties along with their graphs and substitution in this section.
- Be well-aware of the result of the Algebraic Calculation and Properties of Conics for the Co-Ordinate Geometry Questions.
- More importance should give to some topics like Algebra, Coordinate Geometry and 3-D Geometry & Vector.
- You should focus more on the Calculus, Limit & Continuity, Sequence and Series which have more weight-age in the syllabus.
- Do not forget to review chapters like Mathematical Determinants, as these are relatively easy and can help you to score easily.
- Squares of Integers from 1 to 30
- Pythagorean Triplets
- Values of Cube Roots of Unity
- Non-Standard Trigonometric values
- Standard Integration Formulae
- Solution of Triangles
- Solve as many sample papers and mocks as possible to grasp the real-time exam feel.
Revision Game plan for IIT JEE Mathematics 2019
S. No
|
MUST complete Topics
|
Secondary Topics
|
Brush up Topics
|
1
|
Algebra
|
Limit & Continuity
|
Permutations and Combinations
|
2
|
Integration
|
Matrix & Determinants
|
Quadratic Equation
|
3
|
Calculus (Differential & Integral)
|
Analytical Geometry
|
Vector
|
4
|
Complex Numbers
|
Applications of Derivatives
|
Mathematical Reasoning
|
5
|
Probability & Statistics
|
Differentiations
|
3-D Geometry
|
6
|
Vector Algebra
|
Sequence and Series
|
Sets, Relations and Functions
|
7
|
Co-Ordinate Geometry
|
_
|
Mathematical Induction
|
8
|
Trigonometry
|
_
|
Binomial Theorem and Its Simple Applications
|
OVER-ALL NCERT CLASS 11 AND 12 WEIGHT-AGE:
The revision strategy will enable you to enhance your already learned topics and master yourself in your weak areas too. Always try to grasp the harder concepts well and practice as many problems as possible. Remember that success in JEE Main is hard earned and you are just a step away from reaching there and making it yours.
With all the above mentioned strategies employed, you can assure yourself that you can be one of the successful in getting admitted to a premier institution.
With all the formulas and derivatives, May the force be with you!!
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