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Grade 9
Geometry
Triangles
Grade 9
1.
Number System
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.
Cube of Binomials and Cubic Polynomials
2.8.
Remainder Theorem
2.9.
Factor Theorem
2.10.
Factorization of Polynomials
2.10.1.
Factorization by Taking out the Common Factor
2.10.2.
Factorization by Grouping
2.10.3.
Factoring the Difference of Two Squares
2.10.4.
Factorization of Quadratic Polynomials
2.10.5.
Factorization Using the Identity for Square of a Trinomial
2.10.6.
Factorization of Sum or Difference of Cubes
2.10.7.
Factorization of Degree 3 Polynomials
2.11.
Inverse of a Polynomial
2.12.
Polynomials in Equations
2.13.
Evaluate Polynomials Using Algebraic Identities
3.
Geometry
3.1.
Introduction to Euclid's Geometry
3.1.1.
Axioms, Theorems and Corollaries
3.1.2.
Understand the Concept and Properties of a Point, Line Segment, Ray, Line, and Plane
3.1.3.
Euclid's Axioms and Postulates
3.1.4.
Parallel, Concurrent and Intersecting Lines
3.2.
Angles and Lines
3.2.1.
Understand the Concept of Angles and Terms Related to Angles
3.2.2.
Interior and Exterior Points of an Angle
3.2.3.
Categorize Angles on the Basis of Their Measures
3.2.4.
Angles Around a Point
3.2.5.
Complementary and Supplementary Pairs of Angles
3.2.6.
Adjacent Angles, Vertically Opposite Angles, and Linear Pair of Angles
3.2.7.
Parallel Lines, Transversal, and Angles Formed
3.3.
Triangles
3.3.1.
Classification of Triangles on the Basis of its Sides and Angles
3.3.2.
Theorems and Problems Related to Side and Angle Measures of Triangles
3.3.3.
Congruence of Triangles
3.3.3.1.
Congruence: Understand the Meaning
3.3.3.2.
Criteria for Congruence of Triangles
3.3.3.3.
Problems Related to Congruence of Triangles
3.3.4.
Inequalities in a Triangle
3.4.
Quadrilaterals and Parallelograms
3.4.1.
Understand the Concept of Quadrilaterals and Related Terms
3.4.2.
Theorems and Problems Related to the Angles of a Quadrilateral
3.4.3.
Theorems and Problems Related to Parallelograms
3.4.4.
Intercept Theorem and Midpoint Theorem
3.4.4.1.
Intercept Theorem (Thales Theorem, or Basic Proportionality Theorem) and Related Problems
3.4.4.2.
Midpoint Theorem and Related Problems
3.5.
Circles
3.5.1.
Terms Related to Circles
3.5.2.
Theorems and Problems Related to Chord Properties of Circles
3.5.3.
Theorems and Problems Related to Congruent Circles
3.5.4.
Theorems and Problems Related to Angles Subtended by Arcs/Chords
3.5.5.
Theorems and Problems Related to Cyclic Quadrilaterals
3.5.6.
Problems Related to Circumcircles and In-circles
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.
Identify the Mirror Image of a Point
4.6.
Identify the Distance of a Point from the Coordinate Axis
4.7.
Draw the Graphs of Linear Equations
4.8.
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 Slope and Intercepts of a Linear Equation
5.3.
Find the Unknown Variable When the Equation of the Line and Several Conditions are Given
5.4.
Draw Graph of Linear Equations and Find the Unknown Variable
5.5.
Draw Graph of Some Special Type of Linear Equations
6.
Mensuration
6.1.
Measurement of Areas
6.1.1.
Measuring Areas of Triangles
6.1.1.1.
Area of a Triangle Using Base and Altitude
6.1.1.2.
Area of a Triangle Using Heron's Formula
6.1.2.
Measuring Areas of Quadrilaterals
6.1.2.1.
Area of a Quadrilateral
6.1.2.2.
Area of a Parallelogram
6.1.2.3.
Area of a Rhombus
6.1.2.4.
Area of a Trapezium
6.1.2.5.
Area of a Quadrilateral Using Heron's Formula
6.1.2.6.
Application of Results on Area of Polygonal Regions
6.2.
Volume and Surface Area
6.2.1.
Volume and Surface Area of Cuboids and Cubes
6.2.2.
Volume and Surface Area of Cylinders
6.2.3.
Volume and Surface Area of Circular Cones
6.2.4.
Volume and Surface Area of Spheres, Hemispheres and Spherical Shells
6.2.5.
Mixed Problems on Volume and Surface Area
7.
Statistics and Probability
7.1.
Statistics
7.1.1.
Frequency Distribution of an Ungrouped Data
7.1.2.
Cumulative Frequency Table of an Ungrouped Data
7.1.3.
Bar Graph
7.1.3.1.
Drawing Bar Graphs
7.1.3.2.
Interpreting Bar Graphs
7.1.4.
Histogram{There are minor defects in the questions which need to be rectified}
7.1.4.1.
Histogram When the Frequency Distribution is Exclusive
7.1.4.2.
Histogram When the Frequency Distribution is Inclusive
7.1.4.3.
Histogram When the Class Intervals are of Unequal Size
7.1.5.
Frequency Polygons
7.1.5.1.
Frequency Polygons when the Frequency Distribution is Exclusive
7.1.5.2.
Frequency Polygons when the Frequency Distribution is Inclusive
7.1.6.
Histograms and Frequency Polygons on a Single Graph
7.1.7.
Mean, Median, and Mode
7.1.7.1.
Mean
7.1.7.1.1.
Arithmetic Mean of Numerical Data
7.1.7.1.2.
Word Problems on Mean
7.1.7.1.3.
Mean for Ungrouped Frequency Distributions
7.1.7.1.3.1.
Direct Method for Finding Mean
7.1.7.1.3.2.
Assumed-Mean Method
7.1.7.1.3.3.
Step-Deviation Method for Finding Mean
7.1.7.2.
Median
7.1.7.2.1.
Median of Numerical Data
7.1.7.2.2.
Median of Discrete Series
7.1.7.3.
Mode
7.1.7.3.1.
Mode of Ungrouped Data
7.1.7.3.2.
Empirical Formula for Calculating Mode
7.2.
Probability
7.2.1.
Calculate Probability for Events in Random Experiments
Grade 9 Pakistan School Math
Triangles
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