12th Mathematics Chapter Study Material English Medium 2021 By S Rajan M Sc M Phil M Ed Verified Now
This article provides an overview of the 12th Mathematics Study Material (English Medium, 2021) authored by S. Rajan, M.Sc., M.Phil., M.Ed. , a PG Assistant in Mathematics
. This guide is a specialized resource designed to help students master the Class 12 mathematics syllabus through structured practice and clear conceptual breakdowns. Overview of the Study Material
The material is structured into comprehensive volumes, typically totaling over 270 pages of content, including practice exercises and detailed solutions. It is widely used by students seeking to score high marks (Centum) in their board exams. Core Chapters Covered
Based on standard Class 12 curricula (such as Tamil Nadu State Board or CBSE), the material typically includes the following key units and chapters: Applications of Matrices and Determinants
: Coverage of rank, inverse, and solving systems of linear equations. Complex Numbers : Detailed notes on algebraic properties and polar forms. Theory of Equations : Polynomial equations and their roots. Inverse Trigonometric Functions : Mastery of domain, range, and standard properties. Two-Dimensional Analytical Geometry II This article provides an overview of the 12th
: Focus on conics like circles, parabolas, ellipses, and hyperbolas. Applications of Vector Algebra : Scalar and vector products with geometric applications. Differential Calculus & Applications
: Limits, continuity, and applications like maxima and minima. Integral Calculus
: Integration techniques and applications such as area and volume. Ordinary Differential Equations : Solving first-order and higher-order equations. Probability Distributions : Random variables and mathematical expectation. Discrete Mathematics : Mathematical logic and algebraic structures. Key Features of S. Rajan's Guide One-Mark Question Bank
: Dedicated sections for objective questions to ensure speed and accuracy. Important 5-Mark Questions Key Topics: Indefinite integrals
: Focus on high-weightage long-form questions essential for top scores. Step-by-Step Solutions
: Clear, handwritten or typed walkthroughs for complex problems. Exam-Oriented Approach
: Includes scoring tips, theorems, and definitions crucial for final revisions. Study Resources and Accessibility
Students can find versions of this material on educational platforms such as integration by substitution
Chapter 10: Three-Dimensional Geometry
- Topics: Direction ratios/cosines, equations of lines/planes, distance formulas, sphere geometry.
- Key formulas:
- Plane: ax+by+cz+d=0; distance from point (x0,y0,z0): |ax0+by0+cz0+d|/√(a²+b²+c²)
- Example: Intersection of two planes → line; sphere-plane intersection.
- Pitfalls: Incorrect normal vector calculations.
Chapter 4: Determinants
- Key Topics: Expansion, properties, adjoint, inverse via determinant, solving linear equations (Cramer’s rule & matrix method).
- Study Material Feature: A full page of “Property Quick Test” – 30 fill-in-the-blank statements.
- Common Error Box: Mistaking |A| for value vs. matrix; solved with color-coded examples.
12th Mathematics — Chapter Study Digest
Author: S. Rajan, M.Sc., M.Phil., M.Ed. (English Medium, 2021)
2.2 Important Problems
Problem: Find the square root of $-8 - 6i$. Solution: Let $\sqrt-8-6i = a + ib$. Squaring both sides: $-8 - 6i = a^2 - b^2 + 2abi$. Equating real and imaginary parts:
- $a^2 - b^2 = -8$
- $2ab = -6 \Rightarrow ab = -3 \Rightarrow b = \frac-3a$.
Substitute $b$ in (1): $$a^2 - \left(\frac-3a\right)^2 = -8$$ $$a^2 - \frac9a^2 = -8$$ $$a^4 + 8a^2 - 9 = 0$$ Let $a^2 = t$. Then $t^2 + 8t - 9 = 0$. $(t+9)(t-1) = 0 \Rightarrow t = 1$ (since $t=a^2 \geq 0$). So, $a^2 = 1 \Rightarrow a = \pm 1$. If $a=1, b=-3$. If $a=-1, b=3$. Answer: $\pm(1 - 3i)$.
Chapter 4: Continuity and Differentiability
- Topics: Limits, continuity, differentiability, rules (product, quotient, chain), Rolle’s and Mean Value Theorems, higher derivatives.
- Key formulas:
- Definition: f is continuous at a if lim_x→a f(x) = f(a)
- d/dx[f(g(x))] = f'(g(x)) · g'(x)
- Example: Show continuity/differentiability of piecewise functions; apply L’Hôpital’s rule.
- Pitfalls: Assuming continuity implies differentiability.
How to use this digest
- Read Definitions → Study Worked Examples → Memorize Key Formulas → Attempt Practice Problems → Check Common Mistakes.
- Time allocation: 1–2 hours per chapter for first pass, then 30–45 minutes revision weekly.
Chapter 7: Integrals
- Key Topics: Indefinite integrals, integration by substitution, partial fractions, by parts, definite integrals as limit of sum.
- Unique Offering: “Integration Battle Cards” – compare substitution vs. by-parts for similar integrands.
- 2021 Update: Extra practice for properties of definite integrals (e.g., ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx).