- Euclid’s division lemma
- Fundamental Theorem of Arithmetic – statements after reviewing work done earlier and after illustrating and motivating through examples
- Proofs of results – irrationality of √2, √3, √5, decimal expansions of rational numbers in terms of terminating/non-terminating recurring decimals.

- Zeros of a polynomial
- Relationship between zeros and coefficients of quadratic polynomials
- Statement and simple problems on division algorithm for polynomials with real coefficients.

- Pair of linear equations in two variables and their graphical solution
- Geometric representation of different possibilities of solutions/inconsistency.
- Algebraic conditions for number of solutions
- Solution of a pair of linear equations in two variables algebraically – by substitution, by elimination and by cross multiplication method.
- Simple situational problems must be included. Simple problems on equations reducible to linear equations may be included.

- Definitions, examples, counter examples of similar triangles.
- (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
- (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
- (Motivate) If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.
- (Motivate) If the corresponding sides of two triangles are proportional, their corresponding two triangles are similar.
- (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.
- (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
- (Prove) The ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.
- (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
- (Prove) In a triangle, if the square on one side is equal to sum of the squares on the other two sides, the angles opposite to the first side is a right triangle.

- Trigonometric ratios of an acute angle of a right-angled triangle.
- Proof of their existence (well defined)
- Forest and wild life, coal and petroleum conservation
- Motivate the ratios, whichever are defined at 0° and 90°
- Values (with proofs) of the trigonometric ratios of 30°, 45° and 60°.
- Relationships between the ratios.

- Proof and applications of the identity sin2A + cos2A = 1 (Only simple identities to be given).
- Trigonometric ratios of complementary angles

- Mean, median and mode of grouped data (bimodal situation to be avoided).
- Cumulative frequency graph