Class X Mathematics

Unit I: Number Systems (06 marks)

  1. Real Numbers
    • Fundamental Theorem of Arithmetic, proofs of irrationality (e.g., √2, √3, √5), and decimal expansions.

Unit II: Algebra (20 marks)

  1. Polynomials
    • Zeros of polynomials, relationship between zeros and coefficients, division algorithm (geometrical meaning).
  2. Pair of Linear Equations in Two Variables
    • Graphical and algebraic methods (substitution, elimination, cross-multiplication), consistency/inconsistency.
  3. Quadratic Equations
    • Standard form, solutions by factorization, nature of roots (discriminant), word problems.
  4. Arithmetic Progressions
    • nth term, sum of first n terms, applications in daily life problems.

Unit III: Coordinate Geometry (06 marks)

  1. Coordinate Geometry
    • Distance formula, section formula (internal division), area of triangle (using coordinates).

Unit IV: Geometry (15 marks)

  1. Triangles
    • Similarity criteria (AAA, SSS, SAS), basic proportionality theorem (Thales), Pythagoras theorem, areas of similar triangles.
  2. Circles
    • Tangent properties, number of tangents from an external point, theorems on tangents.

Unit V: Trigonometry (12 marks)

  1. Introduction to Trigonometry
    • Trigonometric ratios (sin, cos, tan, etc.), values for standard angles (0°, 30°, 45°, 60°, 90°), identities.
  2. Some Applications of Trigonometry
    • Heights and distances (one/two pole problems), angle of elevation/depression.

Unit VI: Mensuration (10 marks)

  1. Areas Related to Circles
    • Area of sector, segment, combination problems.
  2. Surface Areas and Volumes
    • Surface area and volume of combinations of solids (cube, cuboid, cylinder, cone, sphere, hemisphere).

Unit VII: Statistics and Probability (11 marks)

  1. Statistics
    • Mean, median, mode of grouped data, cumulative frequency graph (ogive).
  2. Probability
    • Classical definition, simple problems on single events.