Mathematics Curriculum

UNIT I: NUMBER SYSTEMS

1. REAL NUMBERS (15 Periods)

• Fundamental Theorem of Arithmetic: Statements after reviewing work done earlier, illustrating, and motivating through examples.
• Proofs of irrationality.

UNIT II: ALGEBRA

1. POLYNOMIALS (8 Periods)

• Zeros of a polynomial.
• Relationship between zeros and coefficients of quadratic polynomials.

2. PAIR OF LINEAR EQUATIONS IN TWO VARIABLES (15 Periods)

• Graphical method of solving a pair of linear equations in two variables.
• Consistency/Inconsistency.
• Algebraic conditions for the number of solutions.
• Algebraic solutions by substitution and elimination methods.
• Simple situational problems.

3. QUADRATIC EQUATIONS (15 Periods)

• Standard form of quadratic equations \( ax^2 + bx + c = 0 \), \( a ≠ 0 \).
• Solutions by factorization and quadratic formula.
• Relationship between the discriminant and the nature of roots.
• Situational problems based on quadratic equations.

4. ARITHMETIC PROGRESSIONS (10 Periods)

• Motivation for studying Arithmetic Progressions (AP).
• Derivation of the nth term and sum of the first n terms of an AP.
• Application in solving daily life problems.

UNIT III: COORDINATE GEOMETRY

1. Coordinate Geometry (15 Periods)

• Review: Concepts of coordinate geometry, graphs of linear equations.
• Distance formula.
• Section formula (internal division).

UNIT IV: GEOMETRY

1. TRIANGLES (15 Periods)

• Definitions, examples, counter-examples of similar triangles.
• Proofs and motivations for theorems related to similarity of triangles.

2. CIRCLES (10 Periods)

• Tangents to a circle and the point of contact.
• Proofs related to tangents.

UNIT V: TRIGONOMETRY

1. INTRODUCTION TO TRIGONOMETRY (10 Periods)

• Trigonometric ratios of an acute angle in a right-angled triangle.
• Trigonometric ratios for 30°, 45°, 60°.
• Relationships between trigonometric ratios.

2. TRIGONOMETRIC IDENTITIES (15 Periods)

• Proof and application of \( \sin^2 A + \cos^2 A = 1 \).
• Simple identities.

3. HEIGHTS AND DISTANCES (10 Periods)

• Simple problems on heights and distances involving angles of elevation and depression (restricted to 30°, 45°, 60°).

UNIT VI: MENSURATION

1. AREAS RELATED TO CIRCLES (12 Periods)

• Areas and perimeters of sectors and segments of circles.

2. SURFACE AREAS AND VOLUMES (12 Periods)

• Surface areas and volumes of combinations of cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.

UNIT VII: STATISTICS AND PROBABILITY

1. STATISTICS (18 Periods)

• Mean, median, and mode of grouped data (excluding bimodal situations).

2. PROBABILITY (10 Periods)

• Classical definition of probability.
• Simple problems related to the probability of events.