Final exams are almost round the corner. Students are busy with their last minute revisions and trying to get the most out of their study hours these days.
But you do not need to panic as I am here and have come up with some great insights into each chapter for your Mathematics exam. These key revision points and quick tips will help you prepare intelligently for the exams. Even if you have left out certain chapters for last minute preparations or revisions, these tips will help you get through them better.
Chapter 1 – Sets
1. Concept of Subset, Superset and Power Set
2. Union and Intersection of Sets
a) Students are advised to understand the definitions and apply these definitions while attempting the paper.
b) One 4 marks question is sure from the topic “Practical problem on union and intersection of two and three sets”.
c) If possible draw a Venn Diagram.
d) Practise as many questions as you can.
Chapter 2 – Relations and Functions
1. Cartesian Product of Sets
2. Concept of Relations
3. Real Vaued Functions
a) This chapter has the weightage of 10 marks, one 6 marks question is expected to come from this topic.
b) The frequently asked questions are from these chapters based on “Concept of Relations” and “Quotient of Two Functions”.
c) Remember graphs of all of the functions provided in section “Some functions and their Graphs” in NCERT textbook.
d) To achieve 90% and above in the examination students are supposed to practise from R.D Sharma and other reference books.
e) Practise as many questions as possible.
f) Domain and range hold important part in this chapter, so do as many as questions on this.
g) Even if the complete solution to a particular question is not known, try to write till the known steps.
Chapter 3 – Trigonometric Functions
1. Signs of Trigonometric Functions
2. Trigonometric Functions and Their Graphs
3. Trigonometric Identities
4. Trigonometric Equations
a) Trigonometry is full of formula’s, so learn them all, the easiest way to learn them is write them on a paper and put it on your room’s wall, revise it again and again.
b) Almost all the topics taught in this chapter hold great importance as this chapter forms a base for trigonometry.
c) Things you should know from this chapter are as follows:
1. Relation between trigonometric ratios
2. Table for trigonometric ratios of some standard angles
3. Trigonometric ratios of complementary angles
4. Trigonometric identities and their proofs.
d) Practice as many questions as possible from this chapter.
Chapter 4 – Principle of Mathematical Induction
a) This is student’s favourite topic, most of the students find this chapter interesting.
b) You just need to practise questions from this topic.
c) One question will surely come from this topic.
Chapter 5 – Complex Numbers and Quadratic Equations
1. Modulus and Conjugate of a Complex Number
2. Polar Representation of Complex Numbers
a) Most of the questions are asked from “Polar representation” and “Quadratic Equations with Complex Roots”.
b) You can prepare this chapter in less time, so do not keep it chapter away from your final exam preparation.
c) Practise questions given in the NCERT textbook as well as questions from R.D Sharma.
Chapter 6 – Binomial Theorem
1. General and Middle Term of a Binomial Expansion
a) Questions are mostly asked from the topic “General and Middle Term of a Binomial Expansion”.
b) Practise questions on above topic.
c) Calculation mistakes here are prone to happen, so practise these questions very well before the exam. This chapter is scoring.
Chapter 7 – Permutations and Combinations
1. Concept of Permutations when All Objects are Distinct
2. Concept of Permutations when All Objects are Not Distinct
3. Concept of Combinations
1.Care should be taken in no mess with the question of permutation and combination
2.Permutation question factorial should be taken correctly and solution should be done correctly.
Chapter 8 – Linear Inequalities
1. Solving Linear Inequalities in One Variable
2. Solving a System of Linear Inequalities in Two Variables
1.Solution by graphical method should be done using the concept of away from the origin and towards the origin
2.Solution of the equation any method should be done carefully
Chapter 9 – Sequences and Series
1. Sum of n Terms of an Arithmetic Progression
2. Properties of Arithmetic Progressions and the Concept of Arithmetic Mean
3. nth term and Sum of n Terms of a Geometric Progression
4. Concept of Geometric Mean and Its Relation with Arithmetic Mean
5. Sum of n Terms of Special Series
a) This is the most important chapter from the exam point of view (huge weightage and many concepts).
b) All topics are important; since one is linked to another, so you can’t skip even an exercise.
c) Since this chapter is very vast, the variety of questions can be asked from this topic, so apart from your NCERT textbook, practise from other reference books too.
d) These questions can take much time, so try a variety of questions so that you gain confidence for your final examination.
e) Most probably questions are asked on sum of series. In this “Sum of n Terms of Special Series” is teacher’s favourite area. We suggest you to try different questions on this topic from different reference books.
f) Leave at least 10 minutes for revision of answer sheets.
Chapter 10 – Straight Lines
1. Angle between Two Lines
2. Point-slope and Two-point Form of Straight Lines
3. Slope-Intercept Form of Straight Lines
4. Intercept Form of Straight Lines
5. Normal form of Straight Lines
6. Distance of a Point from a Line and Distance between Two Parallel Lines
a) Figures should be neatly drawn with proper labelling.
b) Make sure you know all the forms of the straight lines and all other formulas given in the chapter.
c) Write all the formulas used in the chapter on a separate sheet and do revise them before the exams.
d) Practise all the examples and problems given in the NCERT textbook.
Chapter 11 – Conic Sections
a) Make sure you know all the formulas used in the chapter.
b) You can write down all the formulas to speed up recollection of the same during the exam.
c) Make neat figures and label it properly.
d) Practise the questions and examples given in the NCERT textbook.
Chapter 12 – Introduction to Three-Dimensional Geometry
1. Distance between Two Points in Three Dimensional Space
2. Section Formula
a) Learn the formulae for finding the distance between two points and section formula. Revise all the formulae before exams as well.
b) Practise as many questions as you can from this chapter.
Chapter 13 – Limits and Derivatives
1. Limit of a Polynomial and a Rational Function
2. Limit of a Trigonometric Function
3. Derivative of a Function
4. Derivative of Trigonometric and Polynomial Functions
a) This chapter requires a lot of practice. You must practise all questions from the NCERT textbook and from other reference books too.
b) You should know which formula will be applied in which question.
c) Learn the formulas given in the NCERT textbook and revise the same before the exam.
d) Product and quotient rule are important in derivatives.
Chapter 14 – Mathematical Reasoning
1. Negation of a Statement
3. Validity of “If-then” and “If and only if” Statements
4. Validation of a Statement by Method of Contradiction and by Giving a Counter Example
a) This is an easy chapter and does not require calculations.
b) Understand the meaning of a statement and the role of connectives and quantifiers.
c) Understand the methods used for checking validity of statements like contrapositive, direct method, etc
Chapter 15 – Statistics
1. Mean Deviation for Continuous Frequency Distribution
2. Variance and Standard Deviation of Continuous Frequency Distribution
3. Coefficient of Variation
a) This chapter involves lots of calculations. It is a time consuming but simple chapter based on simple formulas. So you must not leave this chapter.
b) You should know the technique to find variance or standard deviation for different types of data sets.
c) Do the calculations carefully and recheck your answer at the end.
d) Make proper tables for this chapter.
Chapter 16 – Probability
1. Finding Probability Using Complement of a Known Event
2. Algebra of Events and Mutually Exclusive and Exhaustive Events
3. Probability of an Event
a) This is a very important chapter. Go through all the examples and questions given in the NCERT textbook and also practise questions from reference books.
b) Make sure that your fundamentals are clear in this chapter as it is only based on your understanding of the topics.
c) Understand the difference between “with replacement” and “without replacement”.
d) Take your time to read and understand the questions before answering them.
All the best with your revisions and exams!
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