UP Board Class 10 Maths Syllabus 2026-27

Marks distribution

Total: 100 marks — 70 marks written exam, 30 marks internal assessment (minimum passing: 23 written + 10 internal = 33).

Unit	Topic	Marks
I	Number Systems	5
II	Algebra	18
III	Coordinate Geometry	5
IV	Geometry	10
V	Trigonometry	12
VI	Mensuration	10
VII	Statistics and Probability	10

Topics covered

Unit I — Number Systems (5 marks): Fundamental theorem of arithmetic, proving irrationality of numbers like √2, √3, √5.

Unit II — Algebra (18 marks): Polynomials (zeroes and their geometric meaning, relationship between zeroes and coefficients of quadratic polynomials); pairs of linear equations in two variables (graphical and algebraic methods — substitution and elimination); quadratic equations (standard form, solving via factorization and the quadratic formula, discriminant and nature of roots, real-life applications); arithmetic progressions (nth term, sum of first n terms, applications).

Unit III — Coordinate Geometry (5 marks): Lines in two dimensions, graphs of linear equations, distance formula, section formula (internal division).

Unit IV — Geometry (10 marks): Similar triangles (definitions, the basic proportionality theorem and its converse, similarity criteria — AAA, SAS, SSS); circles (tangent to a circle, properties of tangents from an external point).

Unit V — Trigonometry (12 marks): Trigonometric ratios of acute angles in a right triangle, ratios for 0° and 90°, values at 0°, 30°, 45°, 60°, 90°; trigonometric identities (sin²θ + cos²θ = 1, etc.); heights and distances (angle of elevation/depression, limited to angles of 30°, 45°, 60°, and no more than two right triangles per question).

Unit VI — Mensuration (10 marks): Areas related to circles (sectors and segments); surface areas and volumes of combinations of solids (cube, cuboid, sphere, hemisphere, right circular cylinder/cone — combinations of at most two different solids).

Unit VII — Statistics and Probability (10 marks): Mean, median, and mode of grouped data; theoretical probability, simple problems based on a single event.

Internal assessment (30 marks)

1. First internal assessment (August, 10 marks): project work plus oral questioning. Prescribed project booklet: भारत का परम्परागत गणित ज्ञान (India’s Traditional Mathematical Knowledge).
2. Second internal assessment (December, 10 marks): project work plus practice-notebook record.
3. Third internal assessment (10 marks): combined score from four unit tests held across the year (July, August, November, December).

Each student prepares one project from a list of suggested topics (Pythagoras theorem verification, statistics in population studies, geometry in architecture, trigonometric ratio charts, contributions of Indian mathematicians like Ramanujan, taxation, loan repayment calculations, etc.), plus one mandatory project chosen from the prescribed booklet भारत का परम्परागत गणित ज्ञान (covering India’s mathematical tradition, traditional calculation methods, and major Indian mathematicians).