Grade 10 Foundation
March 12, 2025 2025-07-29 15:56Grade 10 Foundation
Course Description
The Grade 10 Foundation Course is a focused academic program designed to prepare students for board exams and competitive tests like JEE, NEET, and NTSE. It offers integrated learning across Mathematics, Physics, Chemistry, Biology, and Logical Reasoning. In Math, students build conceptual clarity in real numbers, polynomials, quadratic equations, progressions, geometry, trigonometry, and statistics. Science covers key themes: light, electricity, and magnetism in Physics; reactions, acids-bases, metals, and carbon compounds in Chemistry; and life processes, reproduction, heredity, and ecosystems in Biology. Logical Reasoning enhances analytical thinking and structured problem-solving. The curriculum ensures a smooth transition from core understanding to advanced application.
Learning Objective
This course aims to strengthen core academic skills and problem-solving abilities in Math and Science. Students will refine algebraic thinking, geometrical reasoning, data interpretation, and trigonometric fluency. Science objectives include understanding mechanisms across physical, chemical, and biological systems and applying concepts through structured logic and practical analysis. The course fosters scientific temper, quantitative reasoning, and a disciplined thought process—key for academic success and entrance exam readiness.
What Will I Learn?
Students will master algebra, coordinate geometry, progressions, trigonometry, and statistics, along with their real-world applications. Physics topics include optics, current, magnetism, and motion. Chemistry covers chemical equations, acids and bases, metal reactivity, bonding, and hydrocarbons. Biology introduces digestion, respiration, reproduction, heredity, and environment. Logical reasoning builds critical thinking and pattern recognition. The course helps students build strong academic foundations, exam confidence, and real-world analytical skills.
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
Physics
Biology
Real Numbers
Introduction
Real Numbers
Euclid’s Division Lemma
Finding H.C.F. by Euclid’s Division Lemma
The Fundamental Theorem of Arithmetic
Irrational Numbers
Some Results on Irrational Numbers
Rational Numbers and their Decimal Expansion
Imaginary Numbers
Complex Numbers and their Notation
Operations on Complex Numbers
Polynomials
Introduction to Polynomials
General Equation of Polynomial of nth Degree
Zeroes of a Polynomial
Geometrical meaning of Zeroes of Polynomial (linear, quadratic, cubic)
Relationship Between the Zeroes and Coefficients of a quadratic Polynomial
Relationship between zeroes and coefficient of a cubic polynomial
Factor theorem
Remainder theorem
HCF and LCM of Polynomials
Pair of Linear Equations in Two Variables
Introduction
Simultaneous Linear Equations in Two Variables
Solution of the System of Equations
Representing Pair of Linear Equations in Two Variables Graphically
Graphical Method of Solution of a Pair of Linear Equations
Consistent & Inconsistent System of Linear Equations
Substitution Method
Elimination Method
Cross Multiplication Method
Equations Reducible to a Pair of Linear Equations in Two Variables
Applications of Pair of Linear Equations
Linear Inequalities
Quadratic Equations
Introduction
Roots of a Quadratic Equation
Solving A Quadratic Equation by Splitting the Middle Term
Solving A Quadratic Equation by Completing the Square Method
Solving A Quadratic Equation by Finding the Roots by Using the Quadratic Formula
Nature of Roots
Sum and Product of the Roots
To Construct a Quadratic Equation whose Roots are Given
Word Problems on Quadratic Equations
Equations Reducible to Quadratic Equations
Quadratic Inequations
Maximum or Minimum Value of a Quadratic Expression
Arithmetic Progressions
Introduction
Arithmetic Progressions
nth term of an Arithmetic progression
Sum of n Terms of an AP - I
Sum of n Terms of an AP - II
Selection of terms in an AP
Arithmetic Mean (AM)
Geometric Progression
nth term of a GP
Sum of n terms of a GP
Geometric Mean (GM)
Harmonic Progression (HP)
nth term of a HP
Harmonic Mean (HM)
Relation between AM, HM and GM
Triangles
Introduction
Similarity of Polygons
Basic Proportionality Theorem
Converse of BPT
Criterion for Similarity of Triangles – I
Criterion for Similarity of Triangles - II
Areas of Two Similar Triangles
Pythagoras Theorem
Vertical Angle Bisector Theorem
Concurrency - Geometric Centres of a Triangle
Coordinate Geometry
Introduction
The Coordinate Plane and Sign Convention
Distance Formula
Section formula
Midpoint Formula
Trisection of a Line Segment
Centroid of triangle
Median and altitude of Triangle
Area of triangle
Area of Quadrilateral
Slope of A Line
Slopes of Parallel and Perpendicular Lines
Trigonometry
Introduction to Trigonometry
History of Trigonometry
System of Measurement of Angles
Trigonometric Ratios
Pythagoras Theorem
Trigonometric Ratio
Trigonometric Ratios of Complementary Angles
Trigonometric Identities
Applications of Trigonometry
Application of Trigonometry
Angle of Elevation & Depression
Applications of Trigonometry (Problem Solving) - I
Applications of Trigonometry (Problem Solving) - II
Circles
Introduction to Circles
Basic Terminology
Angle Subtended by a Chord Related Theorems
Angles Subtended by an Arc & Related Theorems and Cyclic Quadrilateral
Tangent to a Circle
Number of Tangents from a Point on a Circle and Related Theorems
Problem Solving
Common Tangents to Circles
Locus and its Equation
Areas Related to Circles
Introduction
Basic Terminology
Circumference and Area of Circular Ring
Area of Sector
Area of Segment
Areas of Combinations of Plane Figures
Problem Solving
Surface Areas and Volumes
Introduction to Surface Area and Volume
Surface Area & Volume of Cuboid & Cube
Surface Area & Volume of a Cylinder and Hollow Cylinder
Surface Area & Volume of a Right Circular Cone
Surface Area & Volume of Sphere and Spherical shell
Surface Area & Volume of hemisphere and Hemispherical shell
Combination of Solids
Recasting of Solids
Pipe flow and Frustum of cone
Problem Solving
Statistics
Introduction
Mean of ungrouped data
Mean of Grouped Data
Median of ungrouped data
Median of Grouped Data
Mode of ungrouped data
Mode of grouped data
Empirical relationship
Ogive Curve
Probability
Introduction of Probability
Sample Space and Event
Measurement of Probability
Probability of an Event E
Probability of Non-occurrence of an Event E
Classification of a Pack (or Deck) of Cards
Important cases
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