| Chapter 1: Real Numbers | Fundamental Theorem of Arithmetic, HCF & LCM by prime factorisation, proving irrationality of $\sqrt{2}, \sqrt{3}, \sqrt{5}$ | NCERT Chapter PDF & Notes |
| Chapter 2: Polynomials | Relationship between zeroes and coefficients: $\alpha + \beta = -b/a$, $\alpha\beta = c/a$ | NCERT Chapter PDF & Notes |
| Chapter 3: Linear Equations in Two Variables | Graphical consistency, substitution and elimination methods, word problems | NCERT Chapter PDF & Notes |
| Chapter 4: Quadratic Equations | Factorisation, quadratic formula $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$, nature of roots via discriminant $D = b^2-4ac$ | NCERT Chapter PDF & Notes |
| Chapter 5: Arithmetic Progressions (AP) | $n^{\text{th}}$ term $a_n = a + (n-1)d$, sum of $n$ terms $S_n = \frac{n}{2}[2a + (n-1)d]$ | NCERT Chapter PDF & Notes |
| Chapter 6: Coordinate Geometry | Distance formula $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, Section formula $\left(\frac{m_1x_2+m_2x_1}{m_1+m_2}, \frac{m_1y_2+m_2y_1}{m_1+m_2}\right)$ | NCERT Chapter PDF & Notes |
| Chapter 7: Triangles | Basic Proportionality Theorem (Thales Theorem) & AAA, SAS, SSS similarity criteria | NCERT Chapter PDF & Notes |
| Chapter 8: Circles | Tangent perpendicular to radius at point of contact, equal tangents from an external point | NCERT Chapter PDF & Notes |
| Chapters 10–13: Trigonometric Ratios, Identities & Heights and Distances | $\sin^2\theta + \cos^2\theta = 1$, $1+\tan^2\theta = \sec^2\theta$, $1+\cot^2\theta = \csc^2\theta$, angles of elevation & depression | NCERT Chapter PDF & Notes |
| Chapter 16: Areas of Circle, Sector and Segment | Sector area $\frac{\theta}{360^\circ}\pi r^2$, arc length $\frac{\theta}{360^\circ}2\pi r$, area of segment | NCERT Chapter PDF & Notes |
| Chapter 17: Volume and Surface Area of Solids | Surface area and volume of combinations of cubes, cuboids, spheres, hemispheres, cylinders, and cones | NCERT Chapter PDF & Notes |
| Chapter 18: Mean, Median and Mode of Grouped Data | Direct, assumed mean & step-deviation mean; $\text{Median} = l + \left(\frac{n/2 – cf}{f}\right)h$; $\text{Mode} = l + \left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)h$ | NCERT Chapter PDF & Notes |
| Chapter 19: Probability | Classical probability $P(E) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}}$, $P(E) + P(\bar{E}) = 1$ | NCERT Chapter PDF & Notes |