High School Mathematics: Chapter-wise 80/20

1) Number Systems

• Irrational ↔ rational tests; decimal expansions (terminating/non-terminating repeating).
• Laws of exponents with rational indices; √a, a^(m/n).

2) Polynomials

• Identities: (a±b)², a³±b³; factor by grouping.
• Division algorithm; remainder/factor theorem quick checks.

3) Coordinate Geometry

• Distance + midpoint; area of triangle by coordinates (base formula).
• Plotting linear equations; intercept read-offs.

4) Linear Equations in Two Variables

• Slope/intercept from ax+by+c=0; solution by substitution/elimination (easy numbers).
• Word problems → convert to two linear equations.

5) Introduction to Euclid’s Geometry

• Axiom vs postulate vs theorem; parallel postulate idea; common examples.

6) Lines & Angles

• Linear pair, vertically opposite, alt./corr./int. angles with transversals.
• Triangle exterior angle = sum of two interior opposite angles.

7) Triangles

• Congruence: SSS, SAS, ASA, RHS—state → reason → conclude.
• Triangle inequalities; medians/angle bisector basics.

8) Quadrilaterals

• Parallelogram properties; mid-point theorem; conditions for parallelogram.
• Special quads (rectangle/rhombus/square): what’s same, what’s new.

9) Areas of Parallelograms & Triangles

• Same base & same parallels → equal area; area transformations.

10) Circles

• Perpendicular bisector from center; equal chords ↔ equal distances; angle subtended facts.
• Tangent basics (radius ⟂ tangent at contact).

11) Constructions

• Segment/angle bisector; triangle with given sides/angles. Steps + clean labels.

12) Heron’s Formula

• A=s(s−a)(s−b)(s−c)A=\sqrt{s(s-a)(s-b)(s-c)}A=s(s−a)(s−b)(s−c)​, quick s-table; mix with perimeter questions.

13) Surface Areas & Volumes

• TSA/CSA/Volume: cuboid, cube, cylinder, cone, sphere; units sanity.

14) Statistics

• Mean/median/mode (ungrouped + simple tables); bar/hist basics.

15) Probability

• Classical probability = favourable/total; complement rule.