Class 10 Maths Notes

CBSE marks the paper by unit, not by chapter, so a chapter's weight follows the unit it belongs to. Before you open the textbook, learn this table — it decides which chapters deserve the hours.

• Unit I — Number Systems, 6 marks: Real Numbers only.
• Unit II — Algebra, 20 marks: Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions. This is the biggest unit in the paper.
• Unit III — Coordinate Geometry, 6 marks: the distance formula and the section formula for internal division.
• Unit IV — Geometry, 15 marks: Triangles and Circles. Circles sits here and not in Mensuration, which is a persistent student error.
• Unit V — Trigonometry, 12 marks: Introduction to Trigonometry, Trigonometric Identities, and Some Applications of Trigonometry.
• Unit VI — Mensuration, 10 marks: Areas Related to Circles, Surface Areas and Volumes.
• Unit VII — Statistics and Probability, 11 marks: Statistics and Probability.

These five chapters carry 26 of the 80 marks between them and none of them needs a diagram. They are also the chapters where a wrong definition costs a whole step, because each later step depends on the one before it.

• Real Numbers — the Fundamental Theorem of Arithmetic and the proofs that √2, √3 and √5 are irrational. Euclid's division lemma is gone.
• Polynomials — the zeros of a polynomial and the relationship between the zeros and the coefficients of a quadratic. The division algorithm is gone.
• Pair of Linear Equations in Two Variables — the graphical method, the conditions for consistency and inconsistency, and algebraic solution by substitution and elimination. The cross-multiplication method is gone.
• Quadratic Equations — solutions by factorisation and by the quadratic formula, and the discriminant as the test for the nature of the roots.
• Arithmetic Progressions — the nth term aₙ = a + (n − 1)d and the sum of the first n terms, in both forms, applied to daily-life problems.

These three units are 33 of the 80 marks and they are where the proofs live. Every marking-scheme line in this part of the paper rewards a correct reason step, not just a correct conclusion, so the theorems have to be known as sequences rather than as statements.

• Coordinate Geometry — the distance formula and the section formula for internal division. The area of a triangle from coordinates is gone.
• Triangles — the Basic Proportionality Theorem and its converse, plus the three criteria for similar triangles. The ratio of areas of similar triangles and both Pythagoras proofs are gone.
• Circles — two results only: the tangent at a point is perpendicular to the radius through it, and tangents from an external point are equal in length.
• Introduction to Trigonometry — the six ratios, their values at 30°, 45° and 60°, and which ratios are undefined at 0° and 90°.
• Trigonometric Identities — sin²A + cos²A = 1, proved and applied. Complementary-angle ratios are gone.
• Some Applications of Trigonometry — angle of elevation and angle of depression, at most two right triangles per problem, and angles only from 30°, 45° and 60°.

The last 21 marks are formula recall and short method. Every question in these two units is decided by whether you remember the right expression, so memorising them exactly is the whole strategy.

• Areas Related to Circles — circumference and area of a circle, the area of a sector, and the area of a segment. Segment problems use a 60° or 90° central angle only.
• Surface Areas and Volumes — surface area and volume of cubes, cuboids, spheres, hemispheres, cylinders and cones, and combinations of exactly two of them.
• Statistics — the mean, median and mode of grouped data, with the median found from the cumulative frequency column and the mode by the empirical relation.
• Probability — the classical definition and simple single-event problems on a die, a coin, cards or numbered slips.

This is the single most useful list on this page. Every item below was in the old syllabus and is not in the 2024-25 one. If a question, a tutor, an app or an old answer key refers to any of them, it is working from a pre-rationalisation source.

• The entire Constructions chapter — no tangent construction, no similar-triangle construction, nothing.
• Euclid's division lemma, and the terminating or recurring decimal representation of rational numbers.
• The division algorithm for polynomials, and the cross-multiplication method for a pair of linear equations.
• Situational problems on equations reducible to a quadratic equation.
• The area of a triangle from coordinates, and the perpendicular-from-the-right-angle similarity theorem.
• The ratio of the areas of two similar triangles, and both Pythagoras results.
• Trigonometric ratios of complementary angles — so sin(90° − A) = cos A and its family are not available.
• Segment problems at 120°, the frustum of a cone, solid-to-solid conversion, and combinations of more than two solids.
• The step-deviation method for the mean, the cumulative frequency graph, the bimodal table and two-event probability.

The question types tell you how to revise. An assertion-reason question is a recall job, a 3-mark short answer is a single method, and a 4-mark case study is four small steps on one situation — none of them needs a different method from the chapter notes.

• Section A — 18 MCQs of 1 mark each, plus 2 assertion-reason questions of 1 mark each. 20 marks of definitions, one-line results and quick substitution.
• Section B — 5 very short answer questions of 2 marks each, with internal choice in 2 of them.
• Section C — 6 short answer questions of 3 marks each, with internal choice in 2 of them. This is where a full method earns its marks.
• Section D — 4 long answer questions of 5 marks each, with internal choice in 2 of them. Proofs and multi-step numericals live here.
• Section E — 3 case studies of 4 marks each, sub-parts of 1, 1 and 2 marks.

Twenty of the hundred marks are not on the paper at all, and they are the twenty a student can control most easily. The split is fixed by CBSE and it is worth knowing before the year starts.

• 10 marks — the pen-paper test and multiple assessment, counted as 5 + 5.
• 5 marks — the portfolio, the classwork and sample work you keep.
• 5 marks — the lab practical, from the activities in the prescribed CBSE and NCERT laboratory manuals.
• The activities are fixed by the manuals, not chosen by the teacher, so the ones to have recorded are the listed ones.

If you have less than a month, work in the order of marks per hour of effort rather than chapter order. The sequence below is the one that pays fastest.

• First, the four Algebra chapters. Twenty marks, formula-light, and every question is a named method.
• Second, Surface Areas and Volumes and Areas Related to Circles. Ten marks of pure recall that can be finished in a few days.
• Third, Statistics and Probability. Eleven marks, and the methods are always the same three.
• Fourth, the Trigonometry unit. Twelve marks, but only if the 30/45/60 table is drilled first.
• Fifth, the Triangles and Circles theorems. Fifteen marks, and these need writing practice, not reading.
• Last, Real Numbers and Coordinate Geometry. Six marks each, and the proofs in Real Numbers take time to hold.