IIT-JEE Super Course in Mathematics - Vol 1 Algebra I

Cover
Contents
Preface
Chapter 1: Prerequisites
	Study Material
		Set of Real Numbers
			Rational Numbers
			Integers
			Irrational Numbers
		Surds
			Equality of surds
			Rationalizing factor
			Roots of surds
		H.C.F (or G.C.D) and L.C.M
			H.C.F
			L.C.M
			Results
		Ratio, Proportion and Variation
			Ratio
			Proportion
			Results
			Variation
		Indices
			Laws of indices
		Logarithms
			Results
			Common logarithms
			Antilogarithms
		Polynomials
			Remainder theorem
		Modulus
		Inequalities
			Results
		Arithmetic Mean, Geometric Mean
		Determinants
		Important Results in Geometry
			Triangles
			Circles
		Locus—Equation of a locus
		Trigonometry Fundamentals
			Definition of an angle
			Units of measurement of an angle
			Definition of radian measure
			Area of a sector
			Definitions of trigonometric functions (or circular functions) of an angle
			Observation 1
			Observation 2
			Observation 3
			Observation 4
		Fundamental Counting Principle
Chapter 2: Quadratic Equations and Expressions
	Study Material
		Roots of the Quadratic Equation
		Symmetric Functions
		Nature of Roots of a Quadratic Equation
		Introduction to Complex Numbers
			Algebra of complex numbers
		Common Roots
		Quadratic Expressions
		Maximum and Minimum Values of a Quadratic Expression
		Polynomial Equation of Degree n
		Summary
		Topic Grip
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		IIT Assignment Exercise
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		Additional Practice Exercise
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Questions
		Solutions
			Answer Keys
			Hints and Explanations
Chapter 3: Trigonometry
	Study Material
		Introduction
		Trigonometry Fundamentals
			Definition of an angle
			Units of measurement of an angle
			Definition of radian measure
		Periodic Property of Circular Functions and Graphs of Circular Functions
			f(x) = sin x and f(x) = cos x
			f(x) = tan x
			f(x) = cosec x
			f(x) = sec x
			f(x) = cotx
		Formulas for Circular Functions of Related Angles
		Circular Functions of Compound Angles
		Product Formulas
		Circular Functions of Multiples of an Angle A
		Inverse Circular Functions
		Trigonometric Equations
			Equations of the form sin x = k — (1)
			Equations of the form cos x = k — (2)
			Equation of the form tan x = k — (3)
			Equations of the form a cos x + b sin x = c — (4)
		Summary
		Topic Grip
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		IIT Assignment Exercise
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Questions
		Additional Practice Exercise
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Questions
		Solutions
			Answer Keys
			Hints and Explanations
Chapter 4: Properties of Triangles
	Study Material
		Introduction
		Law of sines (or sine formulas)
		Law of cosines (or Cosine Formulas)
		Projection Formulas
		Formulas for r, r1, r2 and r3
		Heights and distances
			Angle of elevation and Angle of depression
		Summary
		Topic Grip
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		IIT Assignment Exercise
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		Additional Practice Exercise
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Questions
		Solutions
			Answer Keys
			Hints and Explanations
Chapter 5: Sequences and Series
	Study Material
		Sequences
		Series
		Arithmetic Series (or Series in AP)
		Geometric Series (or Series in GP)
			Infinite geometric series
		Arithmetico-Geometric Series
		Harmonic Series (Series in HP)
		Arithmetic Mean, Geometric Mean and Harmonic Mean
			Arithmetic Mean
			Geometric Mean
			Harmonic Mean
		Procedure to Find the AMs, GMs, HMs Between a and b
			Arithmetic Means
			Geometric Means
			Harmonic Means
		Summation Symbol Σ (sigma)
		Summation of Series
		Partial Fractions
		Summary
		Topic Grip
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		IIT Assignment Exercise
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Question
		Additional Practice Exercise
			Subjective Questions
			Straight Objective Type Questions
			Assertion–Reason Type Questions
			Linked Comprehension Type Questions
			Multiple Correct Objective Type Questions
			Matrix-Match Type Questions
		Solutions
			Answer Keys
			Hints and Explanations