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Number Systems
- Review of representation of natural numbers, integers, rational numbers on the number line.
- Rational numbers as recurring/terminating decimals.
- Operations on real numbers.
- Examples of non-recurring/non-terminating decimals.
- Existence of non-rational numbers (irrational numbers) such as √2, √3, and their representation on the number line.
- Rationalization (with precise meaning) of real numbers.
- Laws of exponents for real numbers.
Study Material
Polynomials
- Definition of polynomial in one variable.
- Coefficients, terms and degree of a polynomial.
- Types of polynomials (zero, linear, quadratic, cubic).
- Monomials, binomials, trinomials.
- Addition, subtraction and multiplication of polynomials.
- Division algorithm for polynomials (restricted to polynomials with linear divisor).
Study Material
Coordinate Geometry
- The Cartesian plane.
- Coordinates of a point.
- Names and signs of the quadrants.
- Plotting points in the plane.
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Linear Equations in Two Variables
- Linear equations in two variables.
- Graph of a linear equation.
- Examples and problems from real life, including age and number problems.
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Introduction to Euclid’s Geometry
- Euclid’s approach to geometry.
- Definitions, axioms, and postulates.
- Equivalent versions of Euclid’s fifth postulate.
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Lines and Angles
- Intersecting and non-intersecting lines.
- Pairs of angles: complementary, supplementary, adjacent, linear pair, vertically opposite angles.
- Properties of angles when two lines intersect or when a transversal crosses two lines.
- Lines parallel to the same line are parallel to each other.
- Angle sum property of a triangle.
Study Material
Triangles
- Congruence of triangles.
- Criteria for congruence: SSS, SAS, ASA, RHS.
- Properties of a triangle—inequalities, angles, and sides.
- Triangle inequality theorem.
- Inequality relations between sides and angles.
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Quadrilaterals
- Angle sum property of quadrilateral.
- Types of quadrilaterals and their properties.
- Mid-point theorem.
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Areas of Parallelograms and Triangles
- Meaning of area.
- Area of a triangle using base and height.
- Area of parallelograms.
- Relationship between the areas of a triangle and parallelogram with the same base and between the same parallels.
Study Material
Circles
- Definitions related to circles: chord, arc, diameter, radius, secant, sector, segment.
- Angle subtended by a chord at a point.
- Perpendicular from the center to the chord.
- Circle through three points.
- Equal chords and their distances from the center.
- Cyclic quadrilaterals.
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Constructions
- Basic constructions using a ruler and compass.
- Construction of bisectors of line segments and angles.
- Construction of triangles using ASA, SSS, SAS criteria.
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Heron’s Formula
- Heron’s formula for finding the area of a triangle.
- Application of Heron’s formula in real-life contexts.
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Surface Areas and Volumes
- Surface areas and volumes of cubes, cuboids, spheres, hemispheres, right circular cylinders/cones.
- Conversion of units.
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Statistics
- Collection and presentation of data (tabular form).
- Graphical representation: bar graphs, histograms (with uniform width), and frequency polygons.
- Measures of central tendency: mean, median, mode (of ungrouped data).
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Probability
- History, scope and meaning of probability.
- Experimental (empirical) probability.
- Simple problems based on single events.
Study Material
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