To command on mathematics in IIT JEE examination, Algebra is one of the key to get through. This portion of mathematics covers various topics, such as, Set Theory, Quadratic Equations, Logarithms, Permutations, Matrices and Determinants and Probability. In order to attain success in this field it involves the understanding of the topic versus marks ratio. There are direct questions being asked on Determinants and Matrices. Permutations and Combinations as well as Probability are most important sections. In IIT JEE Main exam mostly questions are fetched on Complex numbers, Probability and progressions & series.
There are many portions in Algebra section and it has a weightage which is most often equal to the weightage of Calculus and together they cover around 65 percent of entire Maths. So let’s find out the important topics of Algebra for JEE Main:
1: Complex Numbers and Quadratic Equations
Algebra of complex numbers, modulus and argument (or amplitude) of a complex number, square root of a complex number, triangle inequality, Quadratic equations in real and complex number system and their solutions, Relation between roots and coefficients etc.
2: Matrices and Determinants
Types and algebra of matrices, properties of determinants order two and three, area of triangles using determinants. Adjoint and inverse of a square matrix, Test of consistency and solution of simultaneous linear equations in two or three variables.
3: Permutations and Combinations
Fundamental principle of counting, permutation as an arrangement and combination as selection
4: Mathematical Induction and Reasoning
Statements, logical operations. ‘and’, ‘or’, ‘implies’, ‘implied by’, ‘if and only if’. Understanding of tautology, contradiction, converse and contrapositive.
5: Binomial Theorem
Binomial theorem for a positive integral index, general term and middle term, properties of Binomial coefficients and simple applications.
6: Sequences and Series
Arithmetic and Geometric progressions, Relation between A.M. and G.M. Sum up to n terms of special series: Sn, Sn2, Sn3. Arithmetico – Geometric progression.
7: Statistics and Probability
Measures of Dispersion
Calculation of mean, median, mode of grouped and ungrouped data. Calculation of standard deviation, variance and mean deviation for grouped and ungrouped data.
Probability of an event, addition and multiplication theorems of probability, Baye’s theorem, probability distribution of a random variable, Bernoulli trials and Binomial distribution.
The above topics are bifurcated into different subtopics which must be emphasised on. A few points to study and cover Algebra are:
- Priority wise: Progressions & Series, Permutations & Combinations, Binomial, probability, Complex numbers, Matrices & determinants (these are arranged in the order of ease and weightage combined)
- Algebra requires huge practice with the blend of understanding the concepts. Start any topic with NCERT and solve ALL the questions even if you find them extremely easy.
- Once you are done with that move on to R D Sharma objective and then finally any one of Cengage Algebra G Tejwani or Sk Goyal Arihant publication can be considered the reference book.
- Always go through solved examples first and then start solving the unsolved questions
- At the end of any chapter, go for previous year questions on that chapter and this time focus on speed and accuracy.
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All the best!!