Grade 9 Foundation
May 13, 2025 2025-07-29 15:56Grade 9 Foundation
Course Description
The Grade 9 Foundation Course is meticulously designed to provide students with a profound understanding of advanced concepts across Mathematics, Physics, Chemistry, and Biology. The curriculum not only reinforces fundamental principles but also transitions learners to a higher level of abstract thinking and application. Emphasis is placed on developing mathematical dexterity, scientific curiosity, and analytical rigor, empowering students to navigate complex problems with confidence. This interdisciplinary program bridges foundational theories with real-world applications, preparing students for academic excellence and competitive examinations alike.
Learning Objective
The course aims to sharpen students’ mathematical reasoning with in-depth modules on sets, polynomials, quadratic equations, coordinate geometry, and trigonometric applications. It builds strong problem-solving skills through advanced algebra, statistics, and probability. Chemistry modules delve into the structure of matter, thermodynamics, chemical kinetics, and introductory organic chemistry, encouraging conceptual clarity and practical insight. In Biology, learners explore cellular structures, genetics, diversity of life, and the intricate functioning of human organ systems. Physics sessions develop an understanding of motion, gravitation, circular motion, work and energy, electrostatics, and sound waves, integrating mathematical tools like calculus and vectors to solve physical problems. Overall, the course fosters analytical thinking, precision, and scientific inquiry, laying the groundwork for higher studies in science and mathematics.
What Will I Learn?
Students will explore complex number systems, dive deep into polynomials and quadratic equations, and master advanced algebraic techniques including matrices and determinants. They will analyze geometric concepts through 3D geometry and straight lines and apply trigonometry to real-world height and distance problems. The curriculum sharpens problem-solving through permutations, combinations, and probability, alongside robust training in statistics and data interpretation. In Chemistry, learners will grasp the atomic structure, chemical kinetics, thermodynamic processes, and the fundamentals of organic chemistry, enriching their understanding with lab-relevant concepts like electrolysis and colligative properties. Biology expands their knowledge of cell biology, molecular genetics, human physiology, microbial utility, and health sciences. Physics introduces calculus applications in motion, gravitational forces, work-energy principles, sound and wave mechanics, and electrostatics. By the end of the course, students will be proficient in critical thinking, scientific analysis, and mathematical modeling, fully prepared for future academic challenges and entrance examinations.
Additional Info
Practice
Regular exercises and interactive activities to reinforce key concepts in each subject.
Doubt-Solving
Dedicated sessions to address and clarify any questions or difficulties students encounter.
Reports
Detailed reports on experiments and projects to track progress and understanding.
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Mathematics
Chemistry
Biology
Physics
Set & Relations
Introduction of Sets, Cardinal Number
Representation of Sets
Types of Sets
Subset, Superset and Power Set
Operation on Sets
Venn Diagram
Application of Sets, Cardinality Formula -I
Application of Sets, Cardinality Formula -II
Ordered Pairs, Cartesian Products of Sets
Relation, Domain, Co-domain and Range
Polynomials
Introduction to Polynomials, Degree of Polynomial, Classification of Polynomial
Value of a Polynomial, Zeros of a Polynomial
Graphical Meaning of Zeros
Remainder Theorem
Factor Theorem
Application of Factor Theorem in Factorisation of Polynomials
Factorisation of Polynomials by Long Division Method
Factorisation by Splitting the Middle Term
HCF & LCM of Polynomials
Relation Between the HCF, the LCM and the Product of Polynomials
Algebraic Identities I
Algebraic Identities II
Algebraic Identities III
Quadratic Equations
Introduction to Quadratic Equation
Roots of a Quadratic Equation
Geometrical Meaning of Zeroes of Quadratic Equations
Solution of a Quadratic Equation by Factorization (By Splitting the Middle Term)
Solution of a Quadratic Equation by Completing the Square Method
Solution of a Quadratic Equation by the Quadratic Formula or the Sridharacharya’s Method
Nature of Roots of a Quadratic Equation
Matrix & Determinants
Introduction to Matrices, Order of Matrix, General Representation of Matrix
Square Matrix, Principal Diagonal, Trace of a Matrix, Equality of Matrices
Addition, Subtraction and Scalar Product
Determinants of 2x2 Matrix
Minor and Cofactor
Determinants of 3x3 Matrix
Application of Determinant: Area of Triangles
Application of Determinant: Collinearity of Points
Introduction to 3D Geometry
Introduction to Coordinate Geometry
Coordinate Axes and Coordinate Planes in Three Dimensional Space
Coordinates of a Point in Space
Distance Between Two Points
Application of Distance Formula
Straight Lines
Recalling Distance Formula, Section Formula
Straight Lines, Slope or Gradient of a Line
Some Results on the Slope of a Line
Equations of Some Standard Lines
Different Forms of Equations of Oblique Lines: Point Slope Form, Two Point Form
Slope Intercept Form, X-Y Intercept Form
Trigonometry and Its Applications
Introduction to Trigonometry
Trigonometric Ratios: Problem Solving
Trigonometric Ratios of Some Specific Angles
Trigonometric Identities
Angle of Elevation, Angle of Depression
Application of Trigonometry
Problems on Height and Distance
Complex Number
The Real Number System, Imaginary Numbers
Introduction to Complex Numbers and Its Notation
Cartesian Representation of a Complex Number, Equality of Complex Numbers
Addition of Complex Numbers, Conjugate of Complex Numbers and Its Properties
Properties of Addition of Complex Numbers
Difference of Two Complex Numbers, Multiplication of Two Complex Numbers
Properties of Multiplication of Complex Numbers
Division of Complex Numbers
Power of i, Modulus of a Complex Number
Properties of Modulus of a Complex Number
Sequence and Series
Sequence & Series
Arithmetic Progression
Sum of 'n' Terms of an A.P., Arithmetic Mean (A.M.)
rth Term of Finite A.P. from the End
Properties of A.P.
Geometric Progression
Sum of 'n' Terms of a G.P.
rth Term of Finite G.P. from the End
Properties of G.P., Selection of Terms in G.P.
Harmonic Progression, General Term of an H.P., Relation Between A.M., G.M., and H.M.
Arithmetic-Geometric Progression
Some Special Series
Important Formulas for Means
Triangles
Introduction and Revision of Triangles, Congruence of Shapes and Figures, Congruence of Triangles, Criteria for Congruence of Triangles
Some Properties of a Triangle, Some More Criteria for Congruence of Triangles, Inequalities in a Triangle
Triangle Inequality Proof
Angle Sum Property of a Triangle, Exterior Angle of a Triangle Theorem
Triangle and Its Properties (Trigonometry)
Sine Formula, Cosine Formula
Quadrilaterals
Introduction and Revision of Quadrilaterals, Angle Sum Property of a Quadrilateral, Types of Quadrilaterals
Complex or Self-Intersecting Quadrilaterals
Properties of a Quadrilaterals - I
Properties of a Quadrilaterals - II
Another Condition for a Quadrilateral to Be a Parallelogram, The Mid-point Theorem - I
The Mid-point Theorem - II
Equal-Intercept Theorem
Angle Sum Property of a Triangle, Diagonals of a Parallelogram and Its Relationship to the Area
Parallelograms and Triangles Between the Same Parallels
Triangles on the Same or Equal Bases and Having Equal Areas
Permutation & Combination
Introduction to P & C
Factorial Notation
Addition Theorem
Multiplication Theorem
Introduction to Permutation and Application of Permutation Formula
Number of Permutations Under Certain Conditions, Formation of Groups, Permutation of Alike Objects -I
Combination, Total Number of Combinations
Distribution of Alike Objects
Summation of Numbers (3 Different Ways)
Probability
Basic Terms, Types of Events, Algebra of Events, Probability of Equally Likely Outcomes
Axiomatic Approach to Probability
Probability of the Event A or B, Probability of Event Not A
Probability Involving Permutation and Combination Concept - I
Statistics
Introduction, Collection of Data, Presentation of Data, Graphical Representation of Data (Bar Graph, Double Bar Graph, Histogram)
Graphical Representation of Data (Frequency Curve and Cumulative Frequency Curves)
Measures of Central Tendency (Arithmetic Mean or Mean (AM)), Mean of Ungrouped Frequency
Mean of Ungrouped Frequency Distribution by Assumed Mean Method
Some Important Results About AM, Median
Mode, Empirical Relationship Among Mean, Median and Mode
Central Tendency of Grouped Data (Mean) by Various Method - 1
Central Tendency of Grouped Data (Mean) by Various Method - 2
Central Tendency of Grouped Data (Mean) by Various Method - 3
Cumulative Frequency, Median of Grouped Data
Mode of Grouped Data
Mean Deviation
Mean Deviation for Ungrouped, Discrete Data and Grouped Data - I
Mean Deviation for Ungrouped, Discrete Data and Grouped Data - II
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