Pearson IIT Foundation Series - Mathematics Class 9

Cover
Copyright
Brief Contents
Contents
Preface
Chapter Insights
Series Chapter Flow
Chaper 1 Number System
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Natural Numbers
		Whole Numbers
		Integers
		Rational Numbers
		Irrational Numbers
		Real Numbers
	NUMBER LINE
		Properties of Real Numbers
		Laws of Indices for Real Numbers
		Exponential Equation
	RADICALS
	SURDS
		Types of Surds
		Laws of Radicals
		Order of a Surd
		Comparison of Monomial Surds
		Addition and Subtraction of Surds
		Multiplication and Division of Surds
		Rationalizing Factor (RF)
		Rationalization of Mixed Surds
		Conjugate of the Surd of the Form a + b
		Comparison of Compound Surds
		Rationalizing the Numerator
		Square root of a Quadratic Surd
		Square Root of a Trinomial Quadratic Surd
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 2 Logarithms
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Definition
	SYSTEM OF LOGARITHMS
		Properties
		Variation of logax with x
		Sign of logax for Different Values of x and a
	ANTILOG
		To Find the Antilog
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 3 Polynomials and Square Roots of Algebraic Expressions
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Constant
		Variable
		Algebraic Expression
		Terms
		Coefficient of a Term
	POLYNOMIAL
		Degree of a Polynomial in One Variable
		Addition of Polynomials
		Subtraction of Polynomials
		Multiplication of Two Polynomials
		Division of a Polynomial by a Monomial
		Division of a Polynomial by a Polynomial
		Factorization
		HCF of Given Polynomials
		LCM of the Given Polynomials
		Relation between the HCF, the LCM and the Productof Polynomials
		Concept of Square Roots
		Rational Integral Function of x
		Homogeneous Expression
		Symmetric Expressions
		Cyclic Expressions
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 4 Linear Equations and Inequations
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Algebraic Expressions
		Open Sentences
	EQUATION
		Linear Equation
		Simple Equation
		Solving an Equation in One Variable
	SIMULTANEOUS LINEAR EQUATIONS
		Solving Two Simultaneous Equations
		Nature of Solutions
		Word Problems and Application of Simultaneous Equations
	LINEAR INEQUATIONS
		Introduction
		Definition
	INEQUATION
		Continued Inequation
		Linear Inequation
		Solving Linear Inequation in One Variable
		Solving Linear Inequations in Two Variables
		System of Inequations
	ABSOLUTE VALUE
		Properties of Modulus
		Interval Notation
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 5 Quadratic Expressions and Equations
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	QUADRATIC EXPRESSION
		Zeroes of a Quadratic Expression
	QUADRATIC EQUATION
		Solutions or Roots of a Quadratic Equation
		Finding the Solutions or Roots of a Quadratic Equation
		Relation Between the Roots and the Coefficientsof a Quadratic Equation
		Nature of the Roots of a Quadratic Equation
		Signs of the Roots of a Quadratic Equation
		Constructing the Quadratic Equation when its Roots are Given
		Equations which can be Reduced to Quadratic Form
		Reciprocal Equation
		Constructing a New Quadratic Equation by Changingthe Roots of a Given Quadratic Equation
		Maximum or Minimum Value of a Quadratic Expression
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 6 Sets and Relations
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	SET
		Elements of a Set
		Representation of Sets
		Some Simple Definitions of Sets
		Operations on Sets
		Dual of an Identity
		Venn Diagrams
		Some Formulae on the Cardinality of Sets
		Ordered Pair
	CARTESIAN PRODUCT OF SETS
		Some Results on Cartesian Product
	RELATION
		Definition
		Domain and Range of a Relation
		Representation of Relations
		Inverse of a Relation
		Types of Relations
		Properties of Relations
	FUNCTION
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 7 Matrices
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Order of a Matrix
		Types of Matrices
		Comparable Matrices
		Equality of Two Matrices
	ADDITION OF MATRICES
		Properties of Matrix Addition
	MATRIX SUBTRACTION
	TRANSPOSE OF A MATRIX
		Symmetric Matrix
		Skew-symmetric Matrix
	MULTIPLICATION OF MATRICES
		Multiplication of a Matrix by Scalar
		Multiplication of Two Matrices
		Properties of Matrix Multiplication
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 8 Significant Figures
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Addition and Subtraction
		Multiplication and Division
	ABSOLUTE ERROR AND RELATIVE ERROR
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 9 Statistics
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	DATA
		Types of Data
		Some Basic Definitions
		Tabulation or Presentation of Data
		Class Interval
		Class Boundaries
	STATISTICAL GRAPHS
		Bar Graph
		Histograms
		Frequency Polygon
		Frequency Curve
		Cumulative Frequency Curves
	MEASURES OF CENTRAL TENDENCIES FOR UNGROUPED DATA
		Arithmetic Mean or Mean (AM)
		Mode
	MEASURE OF CENTRAL TENDENCIES FOR GROUPED DATA
		Mean of Grouped Data
		Median of Grouped Data
		Mode of Grouped Data
	RANGE
	QUARTILES
		First Quartile or Lower Quartile
		Third Quartile or Upper Quartile
		Semi-inter Quartile Range or Quartile Deviation (QD)
		Estimation of Median and Quartiles from Ogive
	MEAN DEVIATION (MD)
		Mean Deviation (MD) for Ungrouped or Raw Data
		Mean Deviation for Discrete Data
		Mean Deviation for Grouped Data
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 10 Probability
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Observations
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
	HINTS AND EXPLANATION
		CONCEPT APLICATION
Chapter 11 Banking and Computing
	BANKING (PART I)
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Remittance of Funds
		Safe Deposit Lockers
		Public Utility Services
	DEPOSIT ACCOUNTS
		Savings Bank Account
	TYPES OF CHEQUES
		Bearer Cheque
		Crossed Cheque
		Bouncing of Cheques
		Parties Dealing with a Cheque
		Current Account
		Term Deposit Accounts
	LOANS
		Demand Loans
		Term Loans
		Overdrafts (ODs)
	COMPOUND INTEREST
	HIRE PURCHASE AND INSTALMENT SCHEME
		Hire Purchase Scheme
		Instalment Scheme
Chapter 11 Banking and Computing
	COMPUTING (PART II)
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	ARCHITECTURE OF A COMPUTER
		Input Device
		Central Processing Unit (CPU)
		Output Device
		Block Diagram of a Computer
		Hardware
		Software
		Algorithm
		Flowchart
	OPERATORS
		Shift Operators
		Logical Operators
		Relational Operators
		Arithmetical Operators
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 12 Geometry
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	LINE
		Line Segment
		Ray
	ANGLE
		Types of Angles
	PARALEL LINES
		Properties of Parallel Lines
		Transversal
		Intercepts
	TRIANGLES
		Types of Triangles
		Important Properties of Triangles
		Congruence of Triangles
	QUADRILATERALS
		Different Types of Quadrilaterals
	GEOMETRICAL RESULTS ON AREAS
	SOME THEOREMS ON TRIANGLES
		Mid-point Theorem
		Basic Proportionality Theorem
		Similarity
		Pythagorean Theorem
	POLYGONS
		Convex Polygon and Concave Polygon
		Some Important Results on Polygons
	CONSTRUCTION OF TRIANGLES
	CONSTRUCTION OF QUADRILATERALS
	CIRCLES
		Arc of a Circle
		Semi-circle
		Segment of a Circle
		Congruence of Circles
		Arcs–Chords
		Constructions Related to Circles
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 13 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 Rhombus
		Area of a Square
	POLYGON
		Area of a Polygon
		Area of an Equilateral Triangle
		Area of an Isosceles Triangle
		Area of Right Triangle
	CIRCLES
		Circumference of a Circle
		Area of a Ring
		Sector of a Circle
	SOLIDS
		Volume of a Solid
		Cubes and Cuboids
		Right Circular Cylinder
		Pyramid
		Circular Cone
		Torus (Solid Ring)
		Sphere
		Polyhedrons
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 14 Coordinate Geometry
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	COORDINATES OF A POINT
		Convention of Signs
	POINTS ON THE PLANE
		Point on X-axis and Y-axis
		Distance Between Two Points
	STRAIGHT LINES
		Inclination of a Line
		Slope or Gradient of a Line
		Intercepts of a Straight Line
		Equation of a Line in General Form
		Equations of Some Standard Lines
		Oblique Line
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 15 Locus
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	EQUATION OF A LOCUS
		Steps to Find the Equation of a Locus
	Concurrency—Geometric Centres of a Triangle
		Geometric Centres of a Triangle
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	Hints and Explanation
		Concept Application
Chapter 16 Trigonometry
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	ANGLE
		Systems of Measurement of Angle
	TRIGONOMETRIC RATIOS
		Pythagorean Triplets
		Trigonometric Identities
		Trigonometric Ratios of Compound Angles
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 17 Percentages, Profit and Loss, Discount and Partnership
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	PERCENTAGE
		Expressing x% as a Fraction
		Expressing a Fraction a/b as a Decimal and as a Percentage
		Percentage: A Relative Value
		Comparison of Percentages
	PROFIT AND LOSS
		Cost Price (CP)
		Selling Price (SP)
		Profit
		Loss
		Overheads
		Partnership
		Types of Partnership
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 18 Sales Tax and Cost of Living Index
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Sales Tax
		Value-Added Tax (VAT)
		Cost of Living Index
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
		ANSWER KEYS
			TEST YOUR CONCEPTS
			CONCEPT APPLICATION
		HINTS AND EXPLANATION
			CONCEPT APPLICATION
Chapter 19 Simple Interest and Compound Interest
	REMEMBER
	KEY IDEAS
	INTEREST
		Simple Interest
		Compound Interest
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
	HINTS AND EXPLANATION
		CONCEPT APLICATION
Chapter 20 Ratio, Proportion and Variation
	REMEMBER
	KEY IDEAS
	RATIO
		Terms of a Ratio
		Properties of a Ratio
		Types of Ratios
	PROPORTION
		Properties of Proportion
		Continued Proportion
	TYPES OF VARIATION
		Direct Variation
		Indirect Variation
		Joint Variation
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION
Chapter 21 Shares and Dividends
	REMEMBER
	KEY IDEAS
	INTRODUCTION
		Nominal Value of a Share (NV)
		Market Value of a Share (MV)
		Dividend
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
		ANSWER KEYS
			TEST YOUR CONCEPTS
			CONCEPT APLICATION
Chapter 22 Time and 'Work
	REMEMBER
	KEY IDEaS
	INTRODUCTION
		Sharing of the Money Earned
	PIPES AND CISTERNS
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APLICATION
	HINTS AND EXPLANATION
		CONCEPT APLICATION
Chapter 23 Time and Distance
	REMEMBER
	KEY IDEAS
	INTRODUCTION
	SPEED
		Average Speed
		Relative Speed
	PRACTICE QUESTIONS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	ANSWER KEYS
		TEST YOUR CONCEPTS
		CONCEPT APPLICATION
	HINTS AND EXPLANATION
		CONCEPT APPLICATION