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
If you would like to contribute notes or other learning material, please submit them using the button below.
Related QuestionsVIEW ALL [1]
In the class, weight of students is measured for the class records. Calculate mean weight of the class students using direct method
| Weight in kg | 15 − 25 | 25 − 35 | 35 − 45 | 45 − 55 | 55 − 65 | 65 − 75 |
| No. of students | 4 | 11 | 19 | 14 | 0 | 2 |
Advertisement Remove all ads
