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Home
Class 9
Number Systems
Class 9 NCERT (CBSE and ICSE)
Number Systems
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Master this topic as part of
Grade 9
Class 9
1.
Number Systems
1.1.
Rational and Irrational Numbers
1.1.1.
Understand the Concept
1.1.2.
Equivalent Rational Numbers
1.1.3.
Represent Rational Numbers on the Number Line
1.1.4.
Find Rational Numbers Between Given Rational Numbers
1.1.5.
Without Actual Division Identify Terminating Decimals
1.1.6.
Relate Rational Numbers and Decimals
1.1.6.1.
Express Rational Numbers as Terminating and Recurring Decimals
1.1.6.2.
Express Terminating Decimals as Fractions
1.1.6.3.
Express Recurring Decimals as Fractions
1.1.7.
Represent Irrational Numbers on the Number Line
1.1.8.
Find Irrational Numbers Between Given Rational Numbers
1.1.9.
Identify Rational and Irrational Numbers
1.2.
Real Numbers
1.2.1.
Addition and Subtraction of Real Numbers
1.2.2.
Multiplication and Division of Real Numbers
1.2.3.
Real Numbers: Mixed Operations (Simplification)
1.2.3.1.
Simplify and Find Values of Expressions using Rationalization
1.2.3.2.
Simplify Expressions Using the Laws of Radicals
2.
Polynomials
2.1.
Identify Polynomial Expressions
2.2.
Identify the Degree of a Polynomial
2.3.
Identify Coefficients in a Polynomial
2.4.
Evaluate Polynomials
2.5.
Zeros of a Polynomial
2.6.
Square of Binomials
2.7.
Remainder Theorem
2.8.
Factor Theorem
2.9.
Factorization of Polynomials
2.9.1.
Factorization by Taking out the Common Factor
2.9.2.
Factorization by Grouping
2.9.3.
Factoring the Difference of Two Squares
2.9.4.
Factorization of Quadratic Polynomials
2.9.5.
Factorization Using the Identity for Square of a Trinomial
2.9.6.
Factorization of Sum or Difference of Cubes
2.9.7.
Factorization of Degree 3 Polynomials
2.10.
Polynomials in Equations
2.11.
Evaluate Polynomials Using Algebraic Identities
3.
Coordinate Geometry
3.1.
Understand the Terms Related to Coordinate Geometry
3.2.
Identify the Coordinates of a Point on the Cartesian Plane
3.3.
Identify the Coordinates of the Points on the X-axis, Y-axis, and the Origin
3.4.
Identify the Quadrant of a Point
3.5.
Draw the Graphs of Linear Equations
3.6.
Higher Order Thinking Skills (HOTS) Related to the Cartesian Plane
4.
Linear Equations in Two Variables
4.1.
Verify a Solution to a Linear Equation in Two Variables
4.2.
Find the Unknown Variable When the Equation of the Line and Several Conditions are Given
4.3.
Draw Graph of Linear Equations and Find the Unknown Variable
4.4.
Draw Graph of Some Special Type of Linear Equations
4.5.
Word Problems
5.
Introduction to Euclid's Geometry
5.1.
Understanding Points, Line Segments, Rays, Lines, and Planes
5.2.
Euclid's Axioms and Postulates
5.3.
Parallel, Concurrent and Intersecting Lines
6.
Lines and Angles
6.1.
Understand the Concept of Angles and Terms Related to Angles
6.2.
Interior and Exterior Points of an Angle
6.3.
Categorize Angles on the Basis of Their Measures
6.4.
Angles Around a Point
6.5.
Complementary and Supplementary Pairs of Angles
6.6.
Adjacent Angles, Vertically Opposite Angles, and Linear Pair of Angles
6.7.
Parallel Lines, Transversal, and Angles Formed
7.
Triangles
7.1.
Classification of Triangles on the Basis of its Sides and Angles
7.2.
Theorems and Problems Related to Side and Angle Measures of Triangles
7.3.
Congruence of Triangles
7.3.1.
Congruence: Understand the Meaning
7.3.2.
Criteria for Congruence of Triangles
7.3.3.
Problems Related to Congruence of Triangles
7.4.
Inequalities in a Triangle
8.
Quadrilaterals
8.1.
Understand the Concept of Quadrilaterals and Related Terms
8.2.
Theorems and Problems Related to the Angles of a Quadrilateral
8.3.
Theorems and Problems Related to Parallelograms
8.4.
Intercept Theorem and Midpoint Theorem
8.4.1.
Intercept Theorem (Thales Theorem, or Basic Proportionality Theorem) and Related Problems
8.4.2.
Midpoint Theorem and Related Problems
9.
Areas of Parallelograms and Triangles
9.1.
Area of a Triangle
9.2.
Area of a Parallelogram
10.
Circles
10.1.
Terms Related to Circles
10.2.
Theorems and Problems Related to Chord Properties of Circles
10.3.
Theorems and Problems Related to Angles Subtended by Arcs/Chords
10.4.
Theorems and Problems Related to Cyclic Quadrilaterals
10.5.
Problems Related to Circumcircles and In-circles
11.
Constructions
11.1.
Bisector of a Line Segment
11.2.
Construction of Angles
11.3.
Construction of Triangles
12.
Heron's Formula
12.1.
Area of a Triangle Using Heron's Formula
13.
Surface Areas and Volumes
13.1.
Volume and Surface Area of Cuboids and Cubes
13.2.
Volume and Surface Area of Cylinders
13.3.
Volume and Surface Area of Circular Cones
13.4.
Volume and Surface Area of Spheres, Hemispheres and Spherical Shells
13.5.
Mixed Problems on Volume and Surface Area
14.
Statistics
14.1.
Frequency Distribution of an Ungrouped Data
14.2.
Cumulative Frequency Table of an Ungrouped Data
14.3.
Bar Graph
14.3.1.
Drawing Bar Graphs
14.3.2.
Interpreting Bar Graphs
14.4.
Histogram
14.4.1.
Histogram When the Frequency Distribution is Exclusive
14.4.2.
Histogram When the Frequency Distribution is Inclusive
14.4.3.
Histogram When the Class Intervals are of Unequal Size
14.5.
Frequency Polygons
14.5.1.
Frequency Polygons when the Frequency Distribution is Exclusive
14.5.2.
Frequency Polygons when the Frequency Distribution is Inclusive
14.6.
Histograms and Frequency Polygons on a Single Graph
14.7.
Mean, Median, and Mode
14.7.1.
Mean
14.7.1.1.
Arithmetic Mean of Numerical Data
14.7.1.2.
Word Problems on Mean
14.7.2.
Median
14.7.2.1.
Median of Numerical Data
14.7.2.2.
Median of Discrete Series
14.7.3.
Mode
14.7.3.1.
Mode of Ungrouped Data
14.7.3.2.
Empirical Formula for Calculating Mode
15.
Probability
15.1.
Calculate Probability for Events in Random Experiments
16.
Miscellaneous Topics
16.1.
Measuring Areas of Quadrilaterals
16.1.1.
Area of a Quadrilateral
16.1.2.
Area of a Parallelogram
16.1.3.
Area of a Rhombus
16.1.4.
Area of a Trapezium
16.1.5.
Area of a Quadrilateral Using Heron's Formula
16.1.6.
Application of Results on Area of Polygonal Regions
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