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1.Number System
- Numbers and its Classification, Rational Number and its Representation on the Number Line
- Decimal Representation of Rational Number and Conversion of Decimal Number into Rational Number
- Representation of Decimal Number on Number Line, Finding Irrational Numbers Between Given Two Numbers
- Representing Irrational Number on the Number Line
- Rationalisation
- Introduction to Exponents, Laws of Exponents, BODMAS Rule
- Integral Exponents of Real Numbers
- Integral Exponents of Real Numbers and Solving Equation for x
- Rational Exponents of Real Numbers
- Examples Based on Rational Exponents of Real Numbers
- Chapter Notes – Number System
- NCERT Solutions – Number System Exercise 1.1 – 1.6
- R D Sharma Solutions Number System
- Revision Notes – Number System
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2.Polynomials
- Introduction to Polynomials and Some Basics Questions
- Value of Polynomial, Zeroes of Polynomial and Relationship between Zeroes and Coefficient of Linear Equation
- Division of Polynomials and Division Algorithm and Remainder Theorem
- Factorising by Spliting Method
- Factorisation By Different Methods and Factor Theorem
- Factorisation of Polynomial by Using Algebric Identities
- Chapter Notes – Polynomials
- NCERT Solutions – Polynomials Exercise 2.1 – 2.5
- R S Aggarwal Solutions Polynomials
- Revision Notes Polynomials
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3.Coordinate Geometry
- Representation of Position on Number Line, Finding the location by Using the Axis
- Quadrant, Coordinates of Point on Axis, Distance from Axis
- Finding the Area of Triangle and Rectangle and Mirror Image of Point On Axis
- Chapter Notes – Coordinate Geometry
- NCERT Solutions – Coordinate Geometry Exercise 3.1 – 3.3
- R D Sharma Solutions Coordinate Geometry
- R S Aggarwal Solutions Coordinate Geometry
- Revision Notes Coordinate Geometry
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4.Linear Equations
- Introduction of Linear Equation in Two Variables and Graphical Representation
- Example to find the value of Constant and Graph of Linear Equation in Two Variables
- Equations of lines Parallel to the x-axis and y-axis
- Chapter Notes – Linear Equations
- NCERT Solutions – Linear Equations Exercise 4.1 – 4.4
- R D Sharma Solutions Linear Equations
- R S Aggarwal Solutions Linear Equations
- Revision Notes Linear Equations
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5.Euclid's Geometry
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6.Lines and Angles
- Introduction to Lines and Angles, Types of Angle and Axioms
- Vertically opposite Angles and Angle bisector
- Angle made by a transversal with two Lines and Parallel Lines
- Lines Parallel to same Line; Exterior angle of a triangle; Angle Sum property of a Triangle
- Angle Sum Property of Triangle Including Interior and Exterior Angles
- Chapter Notes – Lines and Angles
- NCERT Solutions – Lines and Angles Exercise 6.1 – 6.3
- R D Sharma Solutions Lines and Angles
- R S Aggarwal Solutions Lines and Angles
- Revision Notes Lines and Angles
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7.Triangles
- Introduction, Types of Triangle, Altitude & Median of Triangle, Congruences, SAS criterion of Congruence
- Questions Based on SAS Criterion
- ASA Criterion of Congruence and Its based Questions
- Questions Based on AAS and SSS Criterion
- RHS Criterion of Congruence and Its based Questions, Questions Based on Multiple Criterion
- Inequalities of Triangle
- Inequalities of Triangle cont., Distance Between a line and The Point, Miscellaneous Questions
- Chapter Notes – Triangles
- NCERT Solutions – Triangles Exercise 7.1 – 7.5
- R D Sharma Solutions Triangles
- Revision Notes Triangles
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8.Quadrilaterals
- Congruence of Triangles- SAS Congruence Criteria, ASA Congruence Criteria, SSS Congruence Criteria, RHS Congruence Criteria; Types of Quadrilateral- Parallelogram, Rectangle, Rhombus, Square, Trapezium, Kite
- Theorem 1; Properties of parallelogram- Theorem 2, Theorem 3;
- Theorem 4; Theorem 5;
- Conditions for a Quadrilateral to be a parallelogram- Theorem 6
- Theorem 8
- Theorem 9
- Theorem 9(Mid-point Theorem);
- Theorem 10
- Chapter Notes – Quadrilaterals
- NCERT Solutions – Quadrilaterals Exercise 8.1 8.2
- R D Sharma Solutions Quadrilaterals
- R S Aggarwal Solutions Quadrilaterals
- Revision Notes Quadrilaterals
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9.Area of Parallelogram
- Parallelograms on the Same Base and between the Same Parallels; A Diagonal of a parallelogram divides it into two triangles of Equal Area
- Questions based on parallelogram and Triangle are on same base & parallel lines and Area of Triangle
- Triangles on the same Base and between the same Parallels
- Miscellaneous Questions Based on Triangles on the same Base and between the same Parallels
- Sums Based on Median of a Triangle
- Two Triangles on the same Base and equal Area lie b/w the same parallel
- Summary of All Concepts and Miscellaneous Questions
- Chapter Notes – Area of Parallelogram
- NCERT Solutions – Area of Parallelogram Exercise 9.1 – 9.4
- R D Sharma Solutions Area of Parallelogram
- Revision Notes Area of Parallelogram
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10.Constructions
- Construction of Perpendicular Bisector of a Line Segment, Different Angles and Angle bisector
- Construction of Different types of Triangle
- Chapter Notes – Constructions
- NCERT Solutions – Constructions Exercise
- R D Sharma Solutions Constructions
- R S Aggarwal Solutions Constructions
- Revision Notes Constructions
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11.Circles
- Introduction, Important Terms related to circle, Theorem-1, 2, 3 and 4
- Problems Solving
- Problems Based on Parallel Chords, Common Chord of Circles
- Problems Based on Concentric Circles, Triangle in Circle
- Equal Chords and Their Distance, Theorem-5, 6, 7, 8
- Circle Through Points, Theorem-9, Arc of a Circle, Theorem-10
- Chapter Notes – Circles
- NCERT Solutions – Circles Exercise
- R D Sharma Solutions Circles
- R S Aggarwal Solutions Circles
- Revision Notes Circles
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12.Heron's Formula
- Introduction of Heron’s Formula; Area of Different Triangles
- Area of Triangles Using Heron’s Formula (Type-1 level-1 and 2)
- Area of Quadrilaterals Using Heron’s Formula (Type-2 level-1)
- Area of Quadrilaterals Using Heron’s Formula (Type-2 level-2)
- Chapter Notes – Heron’s Formula
- NCERT Solutions – Heron’s Formula Exercise 12.1 12.2
- R D Sharma Solutions Heron’s Formula
- Revision Notes Heron’s Formula
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13.Surface Area and Volume
- Introduction, Surface Area of Cube, Cuboid, Cylinder, Hollow cylinder, Cone, Sphere
- Type-1: Surface Area and Volume of Cube and Cuboid
- Level-2, Question based on Cube and Cuboid, Level-1 Questions based on Cylinder
- Level-2 Questions based on Cylinder, Type-3 Surface Area and Volume of Right Circular Cone (Level-1)
- Level-2 Questions based on Right Circular Cone, Level-1& 2 Questions Based on Sphere & Hemisphere
- Type-5 Short Answer Types Questions,
- Chapter Notes – Surface Area and Volume of a Cuboid and Cube
- Chapter Notes – Surface Area and Volume of A Right Circular Cylinder
- Chapter Notes – Surface Area ad Volume of A Right Circular Cone
- Chapter Notes – Surface Area ad Volume of A Sphere
- NCERT Solutions – Surface Area and Volume Exercise 13.1 – 13.9
- R D Sharma Solutions Surface Areas And Volumes of A cuboid and A cube
- R D Sharma Solutions Surface Areas And Volumes of A Right Circular Cylinder
- R D Sharma Solutions Surface Areas And Volumes of A Right Circular Cone
- R D Sharma Solutions Surface Areas And Volumes of A Sphere
- Revision Notes Surface Areas And Volumes
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14.Statistics
- Data; Presentation of Data; Understanding Basic terms;
- Questions;
- Bar Graph, Histogram, Frequency Polygon;
- Histogram for Grouped Frequency Distribution (Class interval in Inclusive form), Frequency Polygon, Measures of Central Tendency,
- Examples Based on Mean of Ungrouped Data
- Direct Method of Finding Mean of Ungrouped Data, Median of Cont. Freq. Distribution (Grouped Data)
- Mean; Mean for an ungrouped freq. Dist. Table
- Chapter Notes – Statistics – Tabular Representation of Statistical Data
- Chapter Notes – Statistics – Graphical Representation of Statistical Data
- Chapter Notes – Statistics – Measures of Central Tendency
- NCERT Solutions – Statistics Exercise 14.1 – 14.4
- R D Sharma Solutions Tabular Representation of Statistical Data
- R D Sharma Solutions Graphical Representation of Statistical Data
- R S Aggarwal Solutions Statistics
- Revision Notes Statistics
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15.Probability
- Activities; Understanding term Probability; Experiments;
- Event; Probability; Empirical Probability- Tossing a coin;
- Rolling a dice; Miscellaneous Example;
- Chapter Notes – Probability
- NCERT Solutions – Probability Exercise 15.1
- R D Sharma Solutions Probability
- R S Aggarwal Solutions Probability
- Revision Notes Probability
Chapter Notes – Linear Equations
(1) An equation of the form ax+by+c=0, where a, b, c are real numbers such that a and b not both zero is called a linear equation in two variables.
For Example: 2x+3y+5=0, where a=2, b=3 which are not zero. So this is linear equation in two variables.
(2) A linear equation in two variables has infinitely many solutions.
For Example: we have 4x−y−3=0, there is many solution
If we take x=1 , y=1 then LHS=4×1−1−3=0=RHS
If we take x=2 , y=5 then LHS=4×2−5−3=0=RHS
(3) The graph of a linear equation in two variables is a straight line.
For Example:
x+y=4
We have x+y=4⇒y=4−x
When x=0, we have: y=4−0=4
When x=2, we have: y=4−2=2
When x=4, we have: y=4−4=0
Thus, we have the following table:
Plotting the points (0, 4) (2, 2) and (4, 0) on the graph paper and drawing a line joining them.
(4) The equations of x and y-axes are y=0 and x=0 respectively.
For Example:
x+3=0 equation is for x-axes because in this equation y=0.
7y−3=0 equation is for y-axes because in this equation x=0.
(5) The graph of the equation x=a is a straight line parallel to y-axis.
For Example:
The equation for such a line x=−92 is given below:
(6) The graph of the equation y=a is a straight line parallel to x-axis.
For Example: For a line that is parallel to the x-axis, the equation for such a line y=2 is given below:
(7) Every point on the graph of a linear equation in two variables is a solution of the equation. Conversely, every solution of linear equation in two variables represents a point on the graph of the equation.
For Example: In linear equation f(x)=x+2y−1=0 , (3,−1) also lies on this line.