Topics
Set Language
Real Numbers
- Concept of Rational Numbers
- Denseness Property of Rational Numbers
- Concept of Irrational Numbers
- Representation of Irrational Numbers on the Number Line
- Decimal Representation of Rational Numbers
- Period of Decimal
- Conversion of Terminating Decimals into Rational Numbers
- Conversion of Non-terminating and Recurring Decimals into Rational Numbers
- Decimal Representation to Identify Irrational Numbers
- Concept of Real Numbers
- Representing Real Numbers on the Number Line
- Radical Notation
- Fractional Index
- Concept of Surds
- Order of a Surd
- Laws of Radicals
- Four Basic Operations on Surds
- Rationalisation of Surds
- Scientific Notation
- Converting Scientific Notation to Decimal Form
- Arithmetic of Numbers in Scientific Notation
Algebra
- Algebraic Expressions
- Concept of Polynomials
- Polynomials in One Variable
- Standard Form of a Polynomial
- Degree of Polynomial
- Types of Polynomials
- Arithmetic of Polynomials
- Addition of Polynomials
- Subtraction of Polynomials
- Multiplication of Two Polynomials
- Value of a Polynomial
- Roots of a Polynomial Equation
- Remainder Theorem
- Factor Theorem
- Concept of Identity
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b)
- Expansion of (x + a)(x + b)
- Expansion of (a + b + c)2
- Expansion of (x + a)(x + b)(x + c)
- Expansion of (a + b)3
- Expansion of (a - b)3
- Factorisation Using Identities
- Factorisation Using Identity a2 + 2ab + b2 = (a + b)2
- Factorisation Using Identity a2 - 2ab + b2 = (a - b)2
- Factorisation Using Identity a2 - b2 = (a + b)(a - b)
- Factorisation using Identity a2 + b2 + c2 + 2ab + 2bc + 2ac = (a + b + c)2
- Factorisation using Identity a3 + b3 = (a + b)(a2 - ab + b2)
- Factorisation using Identity a3 - b3 = (a - b)(a2 + ab + b2)
- Factorisation using Identity a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
- Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.
- Division Algorithm for Polynomials
- Synthetic Division
- Highest Common Factor
- General Form of Linear Equation in Two Variables
- Graph of a Linear Equation in Two Variables
- Simultaneous Linear Equations
- Comparing the Ratios of Coefficients of a Linear Equation
- Methods of Solving Simultaneous Linear Equations by Graphical Method
- Methods of Solving Simultaneous Linear Equations by Substitution
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
- Consistency and Inconsistency of Linear Equations in Two Variables
- Zeroes of a Polynomial
Geometry
- Concept of Angle - Arms, Vertex, Interior and Exterior Region
- Types of Angles- Acute, Obtuse, Right, Straight, Reflex, Complete and Zero Angle.
- Concept for Angle Sum Property
- Related Angles
- Complementary Angles
- Supplementary Angles
- Adjacent Angles
- Concept of Linear Pair
- Concept of Vertically Opposite Angles
- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Criteria for Congruence of Triangles
- SSS Congruence Criterion
- SAS Congruence Criterion
- ASA Congruence Criterion
- RHS Congruence Criterion
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Types of Quadrilaterals
- Properties of a Square
- Properties of Rectangle
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of Trapezium
- Properties of Isosceles Trapezium
- Properties of Kite
- Theorem: In a Parallelogram, Opposite Sides Are Equal.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Angle Subtended by Chord at the Centre
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem: Parallelograms on the Same Base and Between the Same Parallels.
- Corollary: Triangles on the same base and between the same parallels are equal in area.
- Corollary: A rectangle and a parallelogram on the same base and between the same parallels are equal in area.
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Congruence of Circles
- Circles Passing Through One, Two, Three Points
- Perpendicular from the Centre to a Chord
- Theorem: The Perpendicular from the Centre of a Circle to a Chord Bisects the Chord.
- Converse: The Line Joining the Centre of the Circle and the Midpoint of a Chord is Perpendicular to the Chord.
- Theorem: Equal chords of a circle subtend equal angles at the centre.
- Converse: If the angles subtended by two chords at the centre of a circle are equal, then the chords are equal.
- Theorem: Equal chords of a circle are equidistant from the centre.
- Converse: The chords of a circle which are equidistant from the centre are equal.
- Angle Subtended by an Arc of a Circle
- Angle at the Centre and the Circumference
- Theorem: The angle subtended by an arc of the circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- Theorem: Angles in the Same Segment of a Circle Are Equal.
- Cyclic Quadrilateral
- Theorem: Opposite angles of a cyclic quadrilateral are supplementary.
- Converse: If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.
- Exterior Angle of a Cyclic Quadrilateral
- Theorem: If One Side of a Cyclic Quadrilateral is Produced Then the Exterior Angle is Equal to the Interior Opposite Angle.
- Construction of the Centroid of a Triangle.
- Construction of Orthocentre of a Triangle
- Construction of the Circumcentre of a Triangle
- Construction of the Incircle of a Triangle.
Coordinate Geometry
- Concept for Mapping the Space Around Approximately Through Visual Estimation.
- Plotting a Point in the Plane If Its Coordinates Are Given.
- Cartesian System
- Co-ordinates of Points and Distance
- The Mid-point of a Line Segment (Mid-point Formula)
- Points of Trisection of a Line Segment (Mid-point Formula)
- Section Formula
- The Coordinates of the Centroid
Trigonometry
Mensuration
Statistics
- Concept of Data Handling
- Collecting Data
- Organisation of Data
- Frequency Distribution Table
- Arithmetic Mean - Raw Data
- Mean of Grouped Data
- Mean of Ungrouped Data
- Method of Finding Mean for Grouped Data: Direct Method
- Method of Finding Mean for Grouped Data: Deviation Or Assumed Mean Method
- Method of Finding Mean for Grouped Data: the Step Deviation Method
- A Special Property of the Arithmetic Mean
- Concept of Median
- Median of Grouped Data
- Median of Ungrouped Data
- Concept of Mode
- Mode of Grouped Data
- Mode of Ungrouped Data
- Empirical Relationship Between the Three Measures of Central Tendency
Probability
description
- Surds of the same order
- Simplest form of a surd
- Pure and Mixed Surds
- Simple and Compound Surds
- Binomial Surd
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