| *1. | COORDINATE GEOMETRY (4 hours) | - Brief history of coordinate geometry
- The 2-D Cartesian coordinate system
- Distance between two points in the 2-D plane
- Midpoint of the distance between two points in the 2-D plane.
| The student will be able to:- Specify locations and the position of one point relative to another point using coordinates.
- Represent a floor plan on a grid using coordinates.
- Compute the distance between two points using coordinates.
- Determine whether three points lie in a straight line using coordinates.
- Compute the position of the midpoint of a line segment using coordinates.
- Check whether a triangle is right-angled using coordinates.
- Apply computational thinking to model situations on the coordinate plane and verify geometric properties through systematic reasoning.
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| *2. | INTRODUCTION TO POLYNOMIALS (8 hours) | - Algebraic expressions
- Definition of a polynomial. Degree of a polynomial
- Introduction to linear polynomials and applications
- Exploring linear patterns
- Modelling linear growth and linear decay
- Linear relationships
- Visualising linear relationships
- Slope and y-intercept of a line y = ax + b
| The student will be able to:- Understand the meaning of an algebraic expression.
- Define a polynomial.
- Identify the degree, terms and coefficients of terms in a polynomial.
- Model linear growth and decay using linear polynomials.
- Explain and identify patterns in linear relationships.
- Identify the slope and y-intercept of a linear equation in two variables.
- Graph a linear equation in two variables.
- Use computational thinking to identify patterns, construct linear expressions, and systematically represent and analyse linear relationships using equations and graphs.
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| *3. | NUMBER SYSTEMS (8 hours) | - Introduction to rational numbers
- Representation of rational numbers on the number line
- Density of rational numbers and its proof
- Finding rational numbers between any two rational numbers
- Decimal representation of rational numbers
- Introduction to irrational numbers
- Proof of irrationality of √2 and √3
- The square root spiral
| The student will be able to:- Understand the concept of a rational number.
- Represent rational numbers on the number line.
- Understand the properties of rational numbers.
- Explain the concept of density of rational numbers.
- Compute decimal representation of rational numbers.
- Understand the concept of irrational numbers.
- Prove the irrationality.
- Construct the square root spiral.
- Apply computational thinking to represent rational and irrational numbers through algorithms and visual models, generate decimal expansions systematically, and reason about numbers using step-by-step logical procedures.
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| *4. | INTRODUCTION TO EUCLID'S GEOMETRY: AXIOMS AND POSTULATES (4 hours) | - History of geometry
- Constructing a square with a given side as described in the Baudhayana's Sulbasutras
- Discovering Euclid's definitions
- Axioms: Axioms of measurement and rules for geometric objects
| The student will be able to:- Describe how geometry grew from the practical needs ancient civilisations.
- Describe contributions of India, Egypt and Greece to the development of geometric ideas.
- Understand the role of definitions, axioms, and postulates.
- Explain that there are elements of plane geometry (point, line, surface) for which we have an intuitive sense.
- State the 5 postulates of Euclidean geometry.
- Define parallelism of straight lines.
- Explain the construction of a square as given in the Sulbasutras.
- Justify simple constructions using the axioms.
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| *5. | LINES AND ANGLES (6 hours) | - Rays and angles
- Measures of angles
- Intersecting lines and angles
- Pairs of angles
- Theorems and examples on intersecting lines
- Theorems and examples on parallel lines
| The student will be able to:- Explain the notion of an angle and a ray.
- State that a straight angle equals 180° and a right angle is 90°.
- Classify angles as acute, right, obtuse, or reflex.
- Define parallelism and state the linear pair theorem.
- Follow proof by contradiction in geometry.
- Prove that vertically opposite angles are equal.
- Identify corresponding, alternate, and interior angles.
- Explain transitivity of parallelism.
- Explain why a triangle must have at least two acute angles.
- Apply computational thinking to analyse geometric ideas through axioms and postulates as rules.
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| *6. | SEQUENCES AND PROGRESSIONS (10 hours) | - Introduction to sequences; Explicit or recursive rules
- Arithmetic Progressions (AP): nth term, visualising an AP
- Sum of the first n natural numbers
- Geometric Progressions (GP): nth term, visualising a GP
- Applications of GP in fractals
- Tower of Hanoi puzzle
| The student will be able to:- Identify patterns and predict the next few terms in a sequence.
- Determine recursive and explicit rules for sequences.
- Identify and work with Arithmetic Progressions (AP) and Geometric Progressions (GP).
- Visualise sequences graphically.
- Analyse fractals using GP and solve the Tower of Hanoi puzzle.
- Use computational thinking to identify patterns and model sequences.
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| *7. | TRIANGLES: CONGRUENCE THEOREMS (12 hours) | - Practical applications and rigidity of triangles
- Conditions of congruence (SAS, SSS, ASA, RHS, AAS) and proofs
- Isosceles triangle properties
- Propositions and their converses
- Diagram accuracy and SSA case
| The student will be able to:- Explain triangle rigidity and its use in structures.
- Describe congruence and identify corresponding parts.
- Use and apply the various congruence axioms/conditions.
- Prove properties of isosceles triangles.
- Understand propositions, converses, and counter-examples.
- Explain why SSA is not generally valid for congruence.
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| *8. | MENSURATION: AREA AND PERIMETER (10 hours) | - Perimeter of shapes and circles (Introduction to π)
- Length of an arc
- Areas: rectangles, parallelograms, triangles, circles
- Heron's formula and Brahmagupta's formula
- Squaring a rectangle
| The student will be able to:- Define perimeter and the constant ratio of π.
- Compute circumference and arc length.
- Apply Heron's formula for triangular areas.
- Derive and use formulas for circle and sector areas.
- Apply Brahmagupta's formula for cyclic quadrilaterals.
- Use computational thinking to break down complex shapes and calculate properties step-by-step.
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| **9. | EXPLORING ALGEBRAIC IDENTITIES (12 hours) | - Visualising identities with geometric models
- Factorisation of expressions and quadratics
- Algebra tiles usage
- Simplifying rational expressions
| The student will be able to:- Visualise algebraic identities using geometric models.
- Determine factors using identities.
- Interpret factorisation through algebra tiles.
- Simplify rational expressions.
- Apply decomposition strategies and step-by-step procedures to factor and simplify.
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| **10. | 4-GONS (QUADRILATERALS) (12 hours) | - Properties and theorems of parallelograms
- Midpoint theorem and its applications
- Central symmetry in parallelograms
| The student will be able to:- Define 4-gons and prove parallelogram characteristics.
- Prove the midpoint theorem and its converse.
- Work with triangle medians and concurrency.
- Understand reflection, rotation, and tiling of 4-gons.
- Discover geometric patterns through drawing and paper manipulation.
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| **11. | CIRCLES (12 hours) | - Definitions (chord, diameter, radius, etc.)
- Chords subtending angles; Perpendicular bisectors
- Subtended angles by an arc; Cyclicity of points
| The student will be able to:- Explain basic circle terms and unique circles through 3 points.
- Construct circumcircles and find circumcentres.
- Understand theorems relating to chords, distances from centre, and angles in segments.
- Determine when points are concyclic and properties of cyclic quadrilaterals.
- Identify cultural circle motifs (Dharmachakra, etc.) and historical uses (wheels).
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| **12. | LINEAR EQUATIONS IN TWO VARIABLES (14 hours) | - Practical examples and solutions
- Graphical representation and slope-intercept form
- Solving pairs of equations (Graphical, Substitution, Elimination)
- Consistency and inconsistency
| The student will be able to:- Graph and solve pairs of linear equations.
- Determine the nature of solutions (consistent vs inconsistent).
- Model daily-life phenomena using equations, tables, and graphs.
- Use systematic step-by-step procedures to represent and interpret relationships.
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| **13. | MENSURATION: SURFACE AREA AND VOLUME (6 hours) | - Surface areas and volumes of spheres, hemispheres, and cones
- Recognition of cuboids, cubes, cylinders, and pyramids
| The student will be able to:- Compute surface areas and volumes for various 3D shapes.
- Understand relationships between shapes (e.g., cube as a special case of cuboid).
- Recognize 3D shapes in real-life contexts.
- Analyze patterns by varying dimensions systematically.
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| **14. | STATISTICS (8 hours) | - Graphical representation of data
- Measures of central tendency (Mean, Median, Mode)
| The student will be able to:- Collect, organize, and interpret data for investigations.
- Apply weighted averages in different settings.
- Interpret stacked bar graphs and 100% stacked bar graphs.
- Use computational strategies to interpret statistical data for decision-making.
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| **15. | INTRODUCTION TO PROBABILITY (8 hours) | - Concept of randomness and probability scale
- Empirical vs Theoretical probability
- Tree diagrams and tables
| The student will be able to:- Understand randomness and use the probability scale (0 to 1).
- Estimate empirical probability from experiments.
- Define theoretical probability and compute event outcomes.
- Use simulations and pattern recognition to model random experiments.
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