Pearson IIT Foundation Series - Mathematics Class 8

Cover
Half Title
Title
Copyright
Brief Contents
Contents
Preface
Chapter Insights
Series Chapter Flow
Chapter 1: Real Numbers and LCM and HCF
	Remember
	Key Ideas
	Real Numbers
		Types of Numbers
			Natural Numbers
			Whole Numbers
			Integers
			Observation
			Properties of Integers
			Successor and Predecessor of a Given Integer
			Fraction
			Rational Numbers
			Decimal Representation of Rational Numbers
			Notation of Repeating Decimal Numbers
			Observations
			Properties of Rational Numbers
			Density Property of Rational Numbers
			Methods of Expressing Recurring Decimals as Fractional Numbers
		Explanation of Properties
			Irrational Numbers
			Real Numbers
		Block Diagram of Number System
			Representation of Numbers on the Number Line
			Representation of Natural Numbers
			Representation of Whole Numbers
			Representation of Integers
			Representation of Rational Numbers
			Representation of Irrational Numbers on a Number Line
			Properties of Different Types of Numbers
			Properties of Even and Odd Numbers
			Prime Numbers
			Composite Numbers
			Observations
			Different Methods of Finding Prime Numbers
			Twin Primes
			Prime Triplet
			Co-Primes
			Observations
		Units Digits of xn (x ε N and n ε N)
		Divisibility
			Tests of Divisibility
			Test of Divisibility by 2
			Test of Divisibility by 3
			Test of Divisibility by 4
			Test of Divisibility by 5
			Test of Divisibility by 6
			Test of Divisibility by 8
			Test of Divisibility by 9
			Test of Divisibility by 11
			Some Additional Results
			Definition
			Observations
			Some Additional Results
			Number of Factors of a Given Number
			Perfect Numbers
			Observation
		Greatest Common Divisor [GCD] (or) Highest Common Factor [HCF]
			Definition
			Observations
		Methods of Finding GCD
			Prime Factorization Method
		Division Method
		GCD of Three Numbers Using Division Method
			Observations
			Some Additional Results
		Least Common Multiple [LCM]
			Definition
		Methods of Finding LCM
			Prime Factorization Method
			LCM of Three Numbers Using Prime Factorization Method
			Division Method of Finding LCM
			Some Additional Results
		Relationship Between LCM and GCD
			Product of Two Numbers = LCM × GCD
		LCM and GCD of Fractions
		Practice Questions
			Test Your Concepts
				Very Short Answer Type Questions
				Short Answer Type Questions
				Essay Type Questions
			Concept Application
				Level 1
				Level 2
				Level 3
		Answer Keys
			Test Your Concepts
				Very Short Answer Type Questions
				Short Answer Type Questions
				Essay Type Questions
			Concept Application
				Level 1
				Level 2
				Level 3
		Hints and Explanation
			Concept Application
				Level 1
				Level 2
				Level 3
Chapter 2: Squares and Square Roots and Cubes and Cube Roots
	Remember
	Key Ideas
	Introduction
		Properties of a Perfect Square Number
			To Find the Square of a Number by the Column Method
			Procedure
			To Find the Square of the Number by the Diagonal Method
			Finding Squares of the Numbers That Follow a Fixed Pattern
			To Find the Square of a Number by Using (a + b)2 or (a − b)2
		Square Roots
		Methods for Finding Square Roots
			Method of Successive Subtraction for Finding the Square Root
			Prime Factorization Method for Finding the Square Root
			Division Method for Finding the Square Root
			Procedure
		Square Root of Rational Numbers (Perfect Squares)
			Properties of Square Roots
		Square Root of a Decimal Number (Perfect Square)
			Procedure
			Finding the Square Root of Numbers Which Are not Perfect Square Numbers (Approximate Square Roots)
			Cube of a Number and Perfect Cube Number
			Cube Roots
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 3: Indices
	Remember
	Key Ideas
	Introduction
		Laws of Indices
		Exponential Equation
			Unique Prime Factorization Theorem
		Radicals
		Exponents and Radicals
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 4: Polynomials, LCM and HCF of Polynomials
	Remember
	Key Ideas
	Introduction
		Types of Polynomials with Respect to Degree
			Types of Polynomials with Respect to Number of Terms
		Addition of Polynomials
		Subtraction of Polynomials
		Multiplication of Two Polynomials
		Factorization
		Division of a Polynomial by a Polynomial
			Factor Method
			Long Division Method
			Horner’s Method of Synthetic Division
		HCF of Given Polynomials
			Method for Finding HCF of the Given Polynomials
		LCM of the Given Polynomials
			Method to Calculate LCM of the Given Polynomials
			Relation among the HCF, the LCM, and the Product of the Polynomials
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 5: Formulae
	Remember
	Key Ideas
	Introduction
		Subject of a Formula
			Change of Subject
			Evaluation of the Subject of a Formula
			Characteristics of Subject in a Formula
		Worked-Out Examples
		Framing of Formula
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 6: Ratio, proportion and Variation
	Remember
	Key Ideas
	Introduction
		Ratio
			Terms of a Ratio
			Properties of a Ratio
			Simplest Form of a Ratio
			Comparison of Ratios
			Alternate Method
			Types of Ratios
			Examples Based on Basic Concepts of Ratios
		Proportion
			Continued Proportion
			Mean Proportional of a and c
		Types of Variation
			Direct Variation
			Inverse Variation
			Joint Variation
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 7: Percentages
	Remember
	Key Ideas
	Introduction
		Percentage
			Expressing x% as a Fraction
			Expressing the Fraction a/b as a Decimal and as a Percentage
			Problems Based on Basic Concepts
			Percentage—a Relative Value
			Comparison of Percentages
		Cost of Living Index
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 8: Profit and Loss, Discount and Partnership
	Remember
	Key Ideas
	Introduction
		Cost Price (C.P.)
		Selling Price (S.P.)
		Profit
		Loss
		Overheads
		Discount
			Successive Discounts
		Partnership
			Types of Partnership
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 9: Simple Interest and Compound Interest
	Remember
	Key Ideas
	Introduction
		Principal or Sum
		Amount
		Rate of Interest
		Simple Interest
			Formula for the Computation of Simple Interest
			Worked Out Examples
		Compound Interest
		Growth and Depreciation
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 10: Time and Work, Pipes and Cisterns
	Remember
	Key Ideas
	Introduction
		Sharing of the Money Earned
		Pipes and Cisterns
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 11: Time and Distance
	Remember
	Key Ideas
	Introduction
		Speed
		Average Speed
			Alternate Method
		Relative Speed
		Trains
		Boats and Streams
		Races
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 12: Linear Equations and Inequations
	Remember
	Key Ideas
	Introduction
		Numbers and Symbols
			Numerical expressions
			Algebraic Expressions
			Mathematical Sentence
			Mathematical Statement
		Identities, Absolute Inequalities, and Contradictions
			Open sentences
		Equation
			Linear Equation
			Simple Equation
			Properties of Equality
			Solving an Equation in One Variable
		Simultaneous Linear Equations
		Solving Two Simultaneous Equations
			Elimination by Cancellation
			Elimination by Substitution
			Adding Two Equations and Subtracting One Equation from the Other
			Graphical Method
		Plotting the Points
		Nature of Solutions
		Word  Problems and Application of Simultaneous Equations
		Signs of Inequalities
			Notation
			Definition
		Inequation
			Continued Inequation
			Linear Inequation
			Linear Inequation in One Variable
			Linear Inequations in Two Variables
		System of Inequations
			Absolute Value
			Properties of Modulus
			Interval Notation
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 13: Sets
	Remember
	Key Ideas
	Introduction
		Set
			Elements of a Set
			Some Sets of Numbers and their Notations
			Cardinal Number of a Set
			Representation of Sets
		Some Simple Definitions of Sets
			Empty Set or Null Set
			Singleton Set
			Equivalent Sets
			Equal Sets
			Disjoint Sets
			Subset and Superset
			Proper Subset
			Power Set
			Universal Set
			Complement of a Set
		Operations on Sets
			Union of Sets
			Intersection of Sets
			Difference of Sets
			Symmetric Difference of Sets
		Some Results
		Dual of an Identity
		Venn Diagrams
			Some Formulae on the Cardinality of Sets
		Ordered Pair
			Properties of Ordered Pairs
			Cartesian Product of Two Sets
			Some Important Points on Cartesian Product of Sets
			Representation of A × B Using Arrow Diagram
			Representation of A × B Using a Tree Diagram
			Graphical Representation of A × B
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 14: Statistics
	Remember
	Key Ideas
	Introduction
		Data
			Types of Data
			Some Basic Definitions
			Tabulation or Presentation of Data
			Individual Series
			Discrete Series
			Continuous Series
		Class Interval
		Class Boundaries
			Class Size
			Class Mark or Mid-Value
			Statistical Graphs
			Bar Graph
		Histograms
			Important Observations
		Arithmetic Mean or Mean (A.M.)
			Arithmetic Mean for Raw Data
			Mean of Discrete Series
			Some Important Results about A.M.
		Median
			Definition
			Some Important Facts About Median
		Mode
			Emperical Relationship among Mean, Median, and Mode
			Observations
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 15: Matrices
	Remember
	Key Ideas
	Introduction
		Order of a Matrix
			Representation of Route Maps as a Matrix
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
		Concept Application
			Level 1
			Level 2
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
		Concept Application
			Level 1
			Level 2
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
Chapter 16: Geometry
	Remember
	Key Ideas
	Introduction
		Plane
		Line
		Line Segment
		Ray
		Coplanar Lines
		Intersecting Lines
		Angle
		Perpendicular Lines
		Complementary Angles
		Supplementary Angles
		Adjacent Angles
			Linear pair
			Vertically Opposite Angles
		Concurrent lines
		Parallel lines
			Properties of Parallel Lines
			Transversal
		Intercepts
		Equal Intercepts
		Proportional Intercepts Property
		Constructions
		Triangle
		Types of Triangles
			Scalene Triangle
			Isosceles Triangle
			Equilateral Triangle
			Acute-Angled Triangle
			Right-Angled Triangle
			Obtuse Angled Triangle
			Isosceles Right-Angled Triangle
		Congruence
		Congruence of Triangles
		Concurrent Lines in Triangles
			Median
		Perpendicular Bisector
		Angle Bisector
		Altitude
		Constructions
		Construction of Triangles
		Construction of a Circumcircle
		Construction of an Incircle
		Construction of Triangles (Special Cases)
		Quadrilaterals
		Different Types of Quadrilaterals
		Circle
		Chord
			Properties of Chords and Related Theorems
			Angles Subtended by Equal Chords at the Centre
		Angles Subtended by an Arc
			Property 1
			Property 2
		Cyclic Quadrilateral
		Introduction
		Line Symmetry
		Point Symmetry
			Illustrations
			Image of a Point with Respect to a Line
			Image of a Line Segment with Respect to a Line
			Image of an Angle about a Line
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
Chapter 17: Mensuration
	Remember
	Key Ideas
	Introduction
		Plane Figures
			Units of Measurement
			Estimating Areas
			Area of a Rectangle
			Area of a Parallelogram
			Area of a Triangle
			Area of a Trapezium
			Area of a Rhombus
			Area of a Square
			Polygon
			Area of a Polygon
			Area of a Regular Polygon
			Area of an Equilateral Triangle
			Area of an Isosceles Triangle
			Area of a Right-angled Triangle
			Isosceles Right Triangle
			Right Triangle with Angles 30º, 60º, and 90º
		Circumference of a Circle
			Area of a Ring
		Sector of a Circle
		Solids
			Volume of a Solid
			Prisms
			Volume of a Prism
		Cubes and Cuboids
			Cuboid
			Cube
			Right Circular Cylinder
		Cone
			Right Circular Cone
		Sphere
			Solid Sphere
			Hemisphere
			Spherical Shell
		Formulae to Memorise
			Sphere
			Hemisphere
			Spherical Shell
			Alternate Method
	Practice Questions
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Answer Keys
		Test Your Concepts
			Very Short Answer Type Questions
			Short Answer Type Questions
			Essay Type Questions
		Concept Application
			Level 1
			Level 2
			Level 3
	Hints and Explanation
		Concept Application
			Level 1
			Level 2
			Level 3
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