Real Numbers:Euclid's Division Lemma, the Fundamental Theorem of Arithmetic, revisiting irrational numbers, and decimal expansions of rational numbers.Polynomials:  polynomials, their degrees, types, and geometrical meaning of the zeroes of a polynomial. Students will learn about the relationship between zeroes and coefficients of quadratic polynomials and apply the Division Algorithm for polynomials.Pair of Linear Equations in Two Variables linear equations in two variables, their graphical representation, and different algebraic methods for solving them (substitution, elimination, and cross-multiplicationQuadratic Equationsequations in one variable, their standard form, and methods for finding their roots (factorization, completing the square, and using the quadratic formula). Arithmetic Progressions:concept of arithmetic progressions (AP), the derivation of the nth term and the sum of the first n terms of an AP. riangles:  Pythagoras Theorem and its converse, along with their applications.Coordinate Geometry:  the Cartesian coordinate system the distance between two points, the section formula (for internal division), and the area of a triangle. Introduction to Trigonometry:  trigonometric identities, and trigonometric ratios.Some Applications of Trigonometry:  trigonometric ratios to solve problems involving heights and distances.Circles:  important theorems related to tangents and chords of a circle.Constructions: dividing a line segment in a given ratio, constructing tangents to a circle from a point on it Areas Related to Circles: (circumference) and area of a circle, as well as the areas of sectors and segments of a circle.Surface Areas and Volumes: cubes, cuboids, cones, cylinders, spheres, and hemispheres. Statistics: the mean, median, and mode of grouped data and understand the concept of cumulative frequency distribution and its graphical representation (ogive)Probability: elementary events, sample space, and calculating the probability of an event.