A) Number System, Arithmetic, and Trigonometry

  • Number Systems: Roman Numerals, Whole numbers, Natural numbers, Integers, Rational and Irrational numbers, Real numbers, Properties and representation on a number line.
  • Arithmetic Operations: LCM, HCF of natural numbers, Squares and square roots, Cubes and cube roots, Laws of exponents.
  • Ratio and Proportion: Ratio and proportions, Direct and indirect proportion, Unitary method, Comparing quantities.
  • Percentage and Fractions: Percentage, Decimals, Fractions, Profit and loss, Discount.
  • Time and Work: Concepts of time, work, and efficiency.
  • Trigonometry: Introduction to trigonometry, Applications to find heights and distances.

B) Algebra, Statistics, and Probability

  • Algebraic Concepts: Algebraic expressions and identities, Factorization, Linear equations in one and two variables, Graphs of linear equations, Polynomials, Quadratic equations.
  • Sequences and Series: Arithmetic Progression (AP).
  • Data Handling and Statistics: Data collection and representation, Average, Pie diagrams, Bar diagrams, Histograms, Frequency polygons.
  • Measures of Central Tendency: Mean, Median, Mode.
  • Probability: Theoretical approach to probability.

C) Geometry, Coordinate Geometry, and Mensuration

  • Fundamental Geometry: Euclid’s Geometry, Lines and angles, Symmetry, Triangles and their properties, Types of triangles and centers (centroid, incenter, circumcenter, orthocenter), Perimeter and area.
  • Congruence and Similarity: Congruence and similarity of triangles, Regular polygons, Quadrilaterals.
  • Circles: Properties, Area related to circles.
  • Coordinate Geometry: Basics of coordinate geometry.
  • Mensuration: Heron’s formula, Pythagorean theorem, Visualizing solid shapes, Area of polygons.
  • Surface Area and Volume: Surface area and volume of cubes, cuboids, cylinders, cones, spheres, and combinations of these solids.