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Class 9
Constructions
Class 9
1.
Number Systems
1.1.
Rational and Irrational Numbers
1.1.1.
Understand the Concept
1.1.2.
Find Rational Numbers Between Given Rational Numbers
1.1.3.
Without Actual Division Identify Terminating Decimals
1.1.4.
Relate Rational Numbers and Decimals
1.1.4.1.
Express Rational Numbers as Terminating and Recurring Decimals
1.1.4.2.
Express Terminating Decimals as Fractions
1.1.4.3.
Express Recurring Decimals as Fractions
1.1.5.
Represent Irrational Numbers on the Number Line
1.1.6.
Find Irrational Numbers Between Given Rational Numbers
1.1.7.
Identify Rational and Irrational Numbers
2.
Real Numbers
2.1.
Operations on Real Numbers
2.1.1.
Addition and Subtraction of Real Numbers
2.1.2.
Multiplication and Division of Real Numbers
2.2.
Rationalization of Real Numbers
2.3.
Exponents of Real Numbers
3.
Polynomials
3.1.
Identify Polynomial Expressions
3.2.
Identify the Degree of a Polynomial
3.3.
Identify Coefficients in a Polynomial
3.4.
Evaluate Polynomials
3.5.
Zeros of a Polynomial
3.6.
Square of Binomials
3.7.
Remainder Theorem
3.8.
Factor Theorem
3.9.
Factorization of Polynomials
3.9.1.
Factorization by Taking out the Common Factor
3.9.2.
Factorization by Grouping
3.9.3.
Factoring the Difference of Two Squares
3.9.4.
Factorization of Quadratic Polynomials
3.9.5.
Factorization Using the Identity for Square of a Trinomial
3.9.6.
Factorization of Sum or Difference of Cubes
3.9.7.
Factorization of Degree 3 Polynomials
3.10.
Polynomials in Equations
3.11.
Evaluate Polynomials Using Algebraic Identities
4.
Coordinate Geometry
4.1.
Understand the Terms Related to Coordinate Geometry
4.2.
Identify the Coordinates of a Point on the Cartesian Plane
4.3.
Identify the Coordinates of the Points on the X-axis, Y-axis, and the Origin
4.4.
Identify the Quadrant of a Point
4.5.
Draw the Graphs of Linear Equations
4.6.
Higher Order Thinking Skills (HOTS) Related to the Cartesian Plane
5.
Linear Equations in Two Variables
5.1.
Verify a Solution to a Linear Equation in Two Variables
5.2.
Find the Unknown Variable When the Equation of the Line and Several Conditions are Given
5.3.
Draw Graph of Linear Equations and Find the Unknown Variable
5.4.
Draw Graph of Some Special Type of Linear Equations
5.5.
Word Problems
6.
Introduction to Euclid's Geometry
6.1.
Understanding Points, Line Segments, Rays, Lines, and Planes
6.2.
Euclid's Axioms and Postulates
6.3.
Parallel, Concurrent and Intersecting Lines
7.
Lines and Angles
7.1.
Understanding Basic Terms
7.2.
Angles Around a Point
7.3.
Complementary and Supplementary Pairs of Angles
7.4.
Adjacent Angles, Vertically Opposite Angles, and Linear Pair of Angles
7.5.
Parallel Lines, Transversal, and Angles Formed
8.
Triangles
8.1.
Classification of Triangles on the Basis of its Sides and Angles
8.2.
Theorems and Problems Related to Side and Angle Measures of Triangles
8.3.
Congruence of Triangles
8.3.1.
Congruence: Understand the Meaning
8.3.2.
Criteria for Congruence of Triangles
8.3.3.
Problems Related to Congruence of Triangles
8.4.
Inequalities in a Triangle
9.
Quadrilaterals
9.1.
Understand the Concept of Quadrilaterals and Related Terms
9.2.
Theorems and Problems Related to the Angles of a Quadrilateral
9.3.
Theorems and Problems Related to Parallelograms
9.4.
Intercept Theorem and Midpoint Theorem
9.4.1.
Intercept Theorem (Thales Theorem, or Basic Proportionality Theorem) and Related Problems
9.4.2.
Midpoint Theorem and Related Problems
10.
Areas of Parallelograms and Triangles
10.1.
Area of a Triangle
10.2.
Area of a Parallelogram
11.
Circles
11.1.
Terms Related to Circles
11.2.
Theorems and Problems Related to Chord Properties of Circles
11.3.
Theorems and Problems Related to Angles Subtended by Arcs/Chords
11.4.
Theorems and Problems Related to Cyclic Quadrilaterals
11.5.
Problems Related to Circumcircles and In-circles
12.
Constructions
12.1.
Bisector of a Line Segment
12.2.
Construction of Angles
12.3.
Construction of Triangles
13.
Heron's Formula
13.1.
Area of a Triangle Using Heron's Formula
13.2.
Applications of Heron's Formula
14.
Surface Areas and Volumes
14.1.
Volume and Surface Area of Cuboids and Cubes
14.2.
Volume and Surface Area of Cylinders
14.3.
Volume and Surface Area of Circular Cones
14.4.
Volume and Surface Area of Spheres, Hemispheres and Spherical Shells
14.5.
Mixed Problems on Volume and Surface Area
15.
Statistics
15.1.
Frequency Distribution of an Ungrouped Data
15.2.
Cumulative Frequency Table of an Ungrouped Data
15.3.
Bar Graph
15.3.1.
Drawing Bar Graphs
15.3.2.
Interpreting Bar Graphs
15.4.
Histogram
15.4.1.
Histogram When the Frequency Distribution is Exclusive
15.4.2.
Histogram When the Frequency Distribution is Inclusive
15.4.3.
Histogram When the Class Intervals are of Unequal Size
15.5.
Frequency Polygons
15.5.1.
Frequency Polygons when the Frequency Distribution is Exclusive
15.5.2.
Frequency Polygons when the Frequency Distribution is Inclusive
15.6.
Histograms and Frequency Polygons on a Single Graph
15.7.
Mean, Median, and Mode
15.7.1.
Mean
15.7.1.1.
Arithmetic Mean of Numerical Data
15.7.1.2.
Word Problems on Mean
15.7.2.
Median
15.7.2.1.
Median of Numerical Data
15.7.2.2.
Median of Discrete Series
15.7.3.
Mode
15.7.3.1.
Mode of Ungrouped Data
15.7.3.2.
Empirical Formula for Calculating Mode
16.
Probability
16.1.
Calculate Probability for Events in Random Experiments
Class 9 NCERT (CBSE and ICSE)
Constructions
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Grade 9
Pakistan