CBSE Class 10 Mathematics Syllabus 2026-27 — Standard & Basic, 14 Chapters, Two Board Exams

What's New in 2026-27?

• Two Board Exams policy: Students can appear for a mandatory February exam and an optional May improvement exam. The higher score counts.
• Standard (041) and Basic (241) continue: Students choose between Maths Standard (for science/commerce stream in Class 11) and Maths Basic (for arts/humanities). The syllabus is the same; question difficulty varies.
• Note — AP moved to Class 9: Arithmetic Progression has been shifted to Class 9 under the new NCF-SE 2023 framework. However, for Class 10 students in 2026-27 (who studied Class 9 under the old syllabus), AP remains part of the Class 10 curriculum for this transitional year.
• Competency-based questions: Greater emphasis on real-world applications, case studies, and multi-step reasoning problems.

Syllabus Overview — Marks Distribution

Unit	Topics	Marks
I: Number Systems	Real Numbers	6
II: Algebra	Polynomials, Pair of Linear Equations, Quadratic Equations, AP	20
III: Coordinate Geometry	Coordinate Geometry (distance, section formula, area)	6
IV: Geometry	Triangles, Circles	15
V: Trigonometry	Intro to Trigonometry, Applications of Trigonometry	12
VI: Mensuration	Areas Related to Circles, Surface Areas and Volumes	10
VII: Statistics & Probability	Statistics, Probability	11
Total Theory		80
Internal Assessment	Periodic Tests, Lab Activities, Portfolio	20
Grand Total		100

Chapter-wise Syllabus

Unit I: Number Systems (6 Marks)

Chapter 1: Real Numbers — Fundamental Theorem of Arithmetic (statement and applications). Euclid's Division Lemma. HCF and LCM using prime factorisation. Proving irrationality of √2, √3, √5. Decimal expansions of rational numbers (terminating, non-terminating recurring).

Key tip: The Fundamental Theorem of Arithmetic is foundational. Practise prime factorisation of large numbers and understand how it connects to HCF/LCM calculation. Questions like "prove √2 is irrational" are almost guaranteed.

Unit II: Algebra (20 Marks)

Chapter 2: Polynomials — Zeroes of a polynomial (graphical meaning). Relationship between zeroes and coefficients of quadratic polynomials: sum = -b/a, product = c/a. Division algorithm for polynomials.

Chapter 3: Pair of Linear Equations in Two Variables — Graphical and algebraic methods: substitution, elimination, cross-multiplication. Consistency of system of equations. Word problems (age, speed, work, fraction problems).

Chapter 4: Quadratic Equations — Standard form ax² + bx + c = 0. Solution by factorisation, completing the square, and quadratic formula. Nature of roots using discriminant (D = b² - 4ac). Word problems leading to quadratic equations.

Chapter 5: Arithmetic Progressions — nth term: a_n = a + (n-1)d. Sum of first n terms: S_n = n/2[2a + (n-1)d] = n/2[a + l]. Word problems on savings, distance, logs, and seating patterns.

Unit III: Coordinate Geometry (6 Marks)

Chapter 6: Coordinate Geometry — Distance formula: √[(x₂-x₁)² + (y₂-y₁)²]. Section formula: internal division. Midpoint formula. Area of a triangle using coordinate formula. Collinearity of three points.

Unit IV: Geometry (15 Marks)

Chapter 7: Triangles — Similar triangles (AAA, AA, SSS, SAS criteria). Basic Proportionality Theorem (Thales Theorem) and its converse. Areas of similar triangles. Pythagoras Theorem and its converse. Problems involving similar triangles and Pythagoras theorem.

Chapter 8: Circles — Tangent to a circle at a point. Proof: tangent is perpendicular to radius at point of contact. Number of tangents from an external point (two). Length of tangent from an external point. Problems involving tangent properties.

Unit V: Trigonometry (12 Marks)

Chapter 9: Introduction to Trigonometry — Trigonometric ratios (sin, cos, tan, cosec, sec, cot) for angles 0°, 30°, 45°, 60°, 90°. Trigonometric identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ. Complementary angle identities.

Chapter 10: Some Applications of Trigonometry — Heights and distances. Line of sight, angle of elevation, angle of depression. Word problems involving towers, buildings, hills, kites, and flying objects. Two-observation problems.

Unit VI: Mensuration (10 Marks)

Chapter 11: Areas Related to Circles — Area of a sector: (θ/360) × πr². Area of a segment. Length of an arc: (θ/360) × 2πr. Combination problems (area of shaded regions involving circles, squares, triangles, rectangles).

Chapter 12: Surface Areas and Volumes — Combination of solids (frustum of a cone, hemisphere on cylinder, cone on cylinder). Conversion between solids (melting and recasting). Surface area and volume of frustum of a cone.

Unit VII: Statistics & Probability (11 Marks)

Chapter 13: Statistics — Mean (direct, assumed mean, step deviation methods) of grouped data. Median of grouped data (formula). Mode of grouped data (formula). Ogive (cumulative frequency graph). Finding median from ogive.

Chapter 14: Probability — Classical/theoretical probability. Complementary events: P(A) + P(A') = 1. Problems on coins, dice, cards, balls in a bag. Impossible and sure events. Range of probability: 0 ≤ P(A) ≤ 1.

New Two Board Exams Policy (2026-27 Onwards)

Starting from the 2026-27 session, CBSE Class 10 students will have the option to appear for two board examinations instead of one. This is a significant policy change under NEP 2020.

• First Board Exam (February-March 2027): This is MANDATORY for all students. It covers the full syllabus and follows the standard 80+20 marks pattern (80 marks theory + 20 marks internal assessment).
• Second Board Exam (May 2027): This is OPTIONAL and available as an improvement opportunity. Students who are unsatisfied with their first exam performance can re-appear to improve their scores.
• Best Score Counts: If a student appears for both exams, the higher score of the two will be considered for the final result and certificate.
• No Penalty for Not Appearing: There is no negative consequence for choosing not to appear for the second exam. It is purely an improvement opportunity.
• Same Syllabus: Both exams cover the same syllabus — there is no reduction or change in scope for the second exam.

This policy aims to reduce exam anxiety and give students a fair chance to demonstrate their best performance. It is especially beneficial for students who face health issues, personal difficulties, or exam-day nervousness during the first attempt.

Standard vs Basic — Which to Choose?

Aspect	Standard (041)	Basic (241)
Difficulty	Higher — includes HOTS and proof-based questions	Standard — focuses on direct application
Eligibility for Class 11	Science, Commerce, Humanities — all streams	Humanities and Commerce only (Maths not allowed without Standard)
Question Types	More multi-step problems, theorem proofs	More direct formula application, fewer proofs
Recommended for	Students aiming for Science stream, Engineering, CA	Students planning Arts, Humanities, Commerce without Maths

Exam Pattern 2026-27

Question Type	Number of Questions	Marks per Question	Total Marks
MCQ (Section A)	20	1	20
Short Answer I (Section B)	5	2	10
Short Answer II (Section C)	6	3	18
Long Answer (Section D)	4	5	20
Case-based (Section E)	3	4	12
Total			80

Preparation Tips

1. Focus on Algebra (20 marks): This is the highest-weighted unit. Master quadratic equations (formula, discriminant, word problems) and pair of linear equations (all three methods). These chapters together can secure 20 marks.
2. Memorise trigonometric values and identities: Create a table of sin, cos, tan for 0°, 30°, 45°, 60°, 90° and revise it every day. The three identities must be at your fingertips.
3. Practise Heights and Distances with diagrams: Always draw a clear figure first. Label the angle of elevation/depression, the height, and the distance. Then set up the trigonometric equation.
4. Solve NCERT + Exemplar problems: Complete every NCERT exercise first, then solve the Exemplar for additional practice. Board questions are derived from these sources.
5. Master Statistics formulas: Mean (3 methods), Median, and Mode formulas must be memorised. Practise constructing ogives and reading median from the graph.
6. Practise case-based questions: Section E (12 marks) is case-based with real-world scenarios. Solve at least 20 case-based questions from sample papers.
7. Time management: 80 marks in 3 hours. Attempt Section A (MCQs) first, then Section E (case-based), then Sections B-D. This ensures easy marks are secured first.

---

Prepared by Bright Tutorials, Nashik (Shop No. 53-57, Business Signature, Hariom Nagar, Nashik Road, Nashik 422101) | brighttutorials.in | This syllabus guide is based on the official CBSE curriculum for 2026-27. Students should refer to the latest CBSE circulars for any updates. For personal study use only.