CBSE Class 10 Mathematics (Standard) Important Topics 2027
Every topic ranked by how often and how recently it was asked in 5 board + 2 official sample papers (2022–2026). Blue = board paper, green = sample paper.
Top 10 most important topics
| # | Topic | Chapter | Asked in | Importance |
|---|---|---|---|---|
| 1 | Trigonometric identities (sin2 + cos2 = 1 family) and proving identities | Introduction to Trigonometry | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★★ |
| 2 | Similarity criteria (AA, SSS, SAS) based problems | Triangles | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 3 | Angle/length problems using tangent properties | Circles | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 4 | Heights and distances - two angles / two positions | Some Applications of Trigonometry | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 5 | nth term of an AP | Arithmetic Progressions | Board 2022Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 6 | Single solid surface area / volume (cube, cuboid, cone, cylinder, sphere, hemisphere) | Surface Areas and Volumes | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 7 | Sum of first n terms of an AP | Arithmetic Progressions | Board 2022Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 8 | Area of sector and length of arc | Areas Related to Circles | Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 9 | Empirical relationship / mixed central tendency problems | Statistics | Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 10 | Classical probability - numbered tickets/balls/miscellaneous | Probability | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
Chapter-wise important topics
Real Numbers · Number Systems
| HCF and LCM using prime factorisation asked 6× | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Proving irrationality (root 2, root 3, root 5 type) asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★★☆☆☆ |
| HCF-LCM relationship and word problems asked 5× | Board 2023Board 2024Sample 2025Sample 2026 | ★★☆☆☆ |
| Fundamental Theorem of Arithmetic / prime factorisation asked 5× | Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
Polynomials · Algebra
| Relationship between zeros and coefficients (quadratic) asked 8× | Board 2023Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
| Zeros of a polynomial from graph asked 5× | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| Forming a quadratic polynomial from given zeros asked 3× | Board 2023Sample 2025 | ★☆☆☆☆ |
Pair of Linear Equations in Two Variables · Algebra
| Graphical solution of a pair of linear equations asked 6× | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Word problems on pair of linear equations asked 5× | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★★☆☆☆ |
| Consistency / number of solutions from coefficients asked 4× | Board 2023Board 2026Sample 2025Sample 2026 | ★☆☆☆☆ |
| Solving by substitution method asked 1× | Board 2025 | ★☆☆☆☆ |
| Solving by elimination method asked 1× | Board 2024 | ★☆☆☆☆ |
Quadratic Equations · Algebra
| Word problems on quadratic equations asked 10× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Nature of roots / discriminant asked 6× | Board 2022Board 2023Board 2024Sample 2025Sample 2026 | ★★☆☆☆ |
| Checking whether an equation is quadratic / standard form asked 3× | Board 2023Board 2024Sample 2026 | ★☆☆☆☆ |
| Solving by factorisation asked 2× | Board 2022Board 2024 | ★☆☆☆☆ |
| Solving by quadratic formula asked 1× | Board 2024 | ★☆☆☆☆ |
Arithmetic Progressions · Algebra
| nth term of an AP asked 12× | Board 2022Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Sum of first n terms of an AP asked 13× | Board 2022Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Identifying AP / common difference asked 5× | Board 2023Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Word problems on AP asked 2× | Board 2022Board 2023 | ★☆☆☆☆ |
Triangles · Geometry
| Similarity criteria (AA, SSS, SAS) based problems asked 13× | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Applied problems on similar triangles asked 5× | Board 2024Board 2025Board 2026Sample 2025 | ★★☆☆☆ |
| Proof of BPT (theorem proof question) asked 4× | Board 2023Board 2024Board 2026Sample 2026 | ★☆☆☆☆ |
| Basic Proportionality Theorem (Thales) and its converse asked 3× | Board 2023Board 2026Sample 2025 | ★☆☆☆☆ |
Coordinate Geometry · Coordinate Geometry
| Distance formula asked 8× | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★★★☆☆ |
| Section formula (internal division) asked 6× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Points on axes / collinearity via distance-section asked 5× | Board 2023Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Midpoint formula asked 6× | Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
Introduction to Trigonometry · Trigonometry
| Trigonometric identities (sin2 + cos2 = 1 family) and proving identities asked 16× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★★ |
| Values of trig ratios at 0, 30, 45, 60, 90 degrees asked 6× | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★★☆☆☆ |
| Evaluating expressions using standard values asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★★☆☆☆ |
| Trigonometric ratios from a right triangle asked 3× | Board 2023Board 2026Sample 2025 | ★☆☆☆☆ |
Some Applications of Trigonometry · Trigonometry
| Heights and distances - two angles / two positions asked 15× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Heights and distances - single elevation/depression asked 5× | Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
| Heights and distances - two objects (tower + building etc.) asked 2× | Board 2022Board 2023 | ★☆☆☆☆ |
Circles · Geometry
| Angle/length problems using tangent properties asked 17× | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Circle inscribed in triangle/quadrilateral problems asked 9× | Board 2023Board 2024Board 2025Sample 2026 | ★★☆☆☆ |
| Tangent perpendicular to radius at point of contact asked 5× | Board 2024Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| Lengths of tangents from an external point are equal (and proof) asked 2× | Board 2026Sample 2025 | ★☆☆☆☆ |
Areas Related to Circles · Mensuration
| Area of sector and length of arc asked 11× | Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Area of segment (60/90/120 degrees) asked 6× | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
Surface Areas and Volumes · Mensuration
| Single solid surface area / volume (cube, cuboid, cone, cylinder, sphere, hemisphere) asked 12× | Board 2023Board 2024Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| Volume of combination of solids asked 7× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Surface area of combination of solids asked 5× | Board 2022Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| Word problems on combined solids asked 1× | Board 2024 | ★☆☆☆☆ |
Statistics · Statistics & Probability
| Empirical relationship / mixed central tendency problems asked 10× | Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Median of grouped data asked 7× | Board 2022Board 2023Board 2024Sample 2025 | ★★☆☆☆ |
| Mean of grouped data (direct / assumed mean / step deviation) asked 4× | Board 2022Board 2023Board 2024Sample 2025 | ★☆☆☆☆ |
| Mode of grouped data asked 4× | Board 2022Board 2023Board 2024 | ★☆☆☆☆ |
Probability · Statistics & Probability
| Classical probability - numbered tickets/balls/miscellaneous asked 12× | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| Classical probability - dice and coins asked 6× | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| Classical probability - playing cards asked 3× | Board 2024Board 2025Sample 2025 | ★☆☆☆☆ |
Importance = how often a topic was asked × how recent, with extra weight for the latest official sample paper.