Telangana Board Subject-wise Syllabus – Class 12 Mathematics

The Intermediate Mathematics has two papers, which are taken over two years. The full syllabus is made up of Mathematics IA (First Year) and Mathematics IIA (Second Year). Each paper has 75 marks and a period of 3 hours in the form of an examination. Both articles are also relevant in the entrance examination as well as the board percentage.

✔ Marks Distribution of Mathematics IIA (Class 12).

Component Marks

Theory Exam 75 marks

Internal Assessment 25 marks

Total 100 marks

Minimum to Pass 35 marks overall

✔ Syllabus of Complete Mathematics IIA (Class 12) Chapter by chapter.

✔ Unit 1: Complex Numbers - 8 Marks

Complex numbers build on the real number system, including the imaginary unit of i. This is an interesting unit that comprises:

Key Topics:

Division complex number algebra (addition, multiplication, division)

Conjugate and modulus properties.

The theorem of De Moivre and its applications.

Cube roots of unity

Complex numbers' square root.

Advanced engineering mathematics is based on complex numbers. Learn how to do algebra and geometric interpretations well.

✔ Unit 2: De Moivre - 6 Marks.

Developing the complex numbers, this unit examines some of the most powerful uses:

Important Concepts:

De Moivre's statement and proof.

Finding nth roots of unity

Solving equations by De Moivre.

Trigonometric ratios expansion.

It can be used in the solution of complex equations.

Problems related to nth roots are highly practiced because they are often analyzed.

✔ Unit 3: Expressions of the 2nd Degree - 8 Marks.

This unit goes back to quadratics, analyzed further:

Core Topics:

Choice of the sign of the quadratic expression.

Maximum and minimum values

Repertoire of expressions of quadratic form.

Based on the nature of roots, there are discriminant roots.

Expression equations In expressions with real coefficients, an expression is said to have real coefficients if it is a finite expression of functions with real coefficients.

Root functions of equal susceptibility.

The knowledge of quadratics is essential in calculus in the future.

✔ Unit 4 Theory of equations 6 Marks.

Extend solving of quadratic equations to uncovering more information about polynomials:

Key Areas:

Roots vs Coefficients. There is a correlation between the roots and coefficients of the equation of state . Correlation between roots and coefficients. There is a correlation between the root and the coefficients of the equation of state.

Forming equations out of root words.

Equation transformation.

Descartes' rule of signs

Several mutually determined roots.

This conceptual unit necessitates efficient comprehension and training of diverse transformations.

✔ Unit 5: Permutation and Combinations - 8 Marks.

Master the basics of counting that are necessary in probability:

Important Topics:

Principles of counting: basic.

Factorial notation and properties Factorial notation Factorial properties

Without and with repetitions: permutations.

Combinations and properties Combinations and their properties.

Problem-solving and applications.

This unit is very point-scoring and has definite concepts. Have a myriad of problem types.

✔ Unit 6: Binomial Theorem - 10 Marks

Chapter one of the greatest weightage!

Core Concepts:

Binomial theorem of the positive index of the integral.

Properties of binomial coefficients

General and middle terms

Highest coefficient and term.

Approximations Applications in approximations.

Introduction: Binomial theorem of rational index

Learn rules by heart, and train the search for particular words in expansions.

✔ Unit 7: Part Fractions - 6 Marks.

Divide rational forms into simpler fractions:

Key Topics:

Improper and Proper Rational Fractions.

Partial fractions decomposition techniques.

Linear (non-repeated and repeated) factors.

Quadratic factors

Integration applications.

Learn how to do systematic decompositions: this can be of great assistance in Calculus.

✔ Unit 8: Measures of Dispersion- 8 Marks.

Know the variability and dispersion of data:

Important Concepts:

range, mean deviation, variance.

Calculations of standard deviation.

Coefficient of variation

Properties of variance

Comparison of variability

Grouped and ungrouped data Learn the applications of formulas with a lot of care.

✔ Unit 9: Probability - 8 Marks

Advanced concepts on Class 11 probability:

Core Topics:

Sample spaces and random experiments.

Events (independent, exhaustive, mutually exclusive).

The theorems of addition and multiplication.

Conditional probability

Bayes' theorem

Independent events

Probability needs rational thinking. Application of practice theorems with Various examples.

Random Variables and Probability Distributions.

✔ Unit 10

Statistical distributions: Introduction

Key Areas:

Random variables- discrete and continuous.

Mass and density functions Probability mass and density functions.

Expected value and variance

Binomial distribution

Mean and variance of a binomial distribution.

Learn the underlying principles of a theoretical basis and then solve numerical problems.

Quick Revision of Mathematics IA (First Year).

You should not forget first-year topics - these are in competitive exams:

Functions, Matrices, Vectors, Addition.

Vectors Product, Trigonometric Equations.

Inverse Functions Hyperbolic Functions.

Manifestation of Triangles, Straight Lines, Pair of Straight Lines.

Direction Cosines, Plane Three-Dimensional Coordinates.

✔ Strategic Preparation Tips

✅ Master Theory First- Mathematics is not about solving problems. Master theorems, proofs, and derivations. Theoretical knowledge is tested by a great number of questions.

✅ Establish Formula books - have detailed formula books on a per-chapter basis. Have theorems, significant results, and conventional formulas. Revise daily.

✅ Learn in a systematic manner: Begin with the NCERT/SCERT textbook tests, and then pass the past year board test and lastly, solve JEE/EAMCET level questions.

Give the Maximum Attention to High-Weightage Units: Binomial Theorem (10 marks), Complex Numbers (8 marks), Quadratic Expressions (8 marks,) and Permutations-Combinations (8 marks).

✅ Solve Past papers - 10 years of Board papers show the pattern of questions, salient issues, and level of difficulty that one should expect.

✅Time Management - Within 3 hours, you will have to answer about 13-15 questions in various units. Exercise in time limits paper writing.

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✔ Common Mistakes to Avoid

✅ Formula Errors – Small formula mistakes lead to completely wrong answers. Verify formulas before using.

✅ Poor Presentation – Show all working steps clearly. Partial marks matter significantly.

✅ Neglecting First Year – Don't ignore Mathematics IA topics. They're the foundation for IIA.

✅ Last-Minute Cramming – Mathematics requires consistent daily practice, not intensive last-week study.

✔ Exam Day Success Strategies

✅ Read the Paper Completely First – Scan all questions before starting. Identify easy ones to attempt first.

✅ Attempt Strategically – Start with high-confidence questions to build momentum and secure marks quickly.

✅ Show Complete Working – Write all steps, formulas used, and reasoning clearly. Examiners award step marks generously.

✅ Verify Answers – If time permits, substitute answers back into equations to verify correctness.

✅ Manage Time Strictly – Don't spend excessive time on a single difficult question.

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