CBSE Maths — Class 10 Maths Board Complete Chapter Guide

Chapter Overview & Weightage

CBSE Class 10 Maths is a 80-mark paper (Theory) + 20-mark Internal Assessment. The theory paper has two sections — Section A (MCQs + Assertion-Reason) and Sections B through E (short and long answer). Knowing the chapter-wise weightage is half the battle.

CBSE releases a official marking scheme every year. The unit-wise distribution below is from the 2024-25 curriculum. Within each unit, CBSE shifts question weight between chapters slightly — but the unit totals are fixed.

Unit-Wise Weightage (Theory Paper — 80 Marks)

Unit	Topics	Marks
Unit 1	Number Systems	6
Unit 2	Algebra	20
Unit 3	Coordinate Geometry	6
Unit 4	Geometry	15
Unit 5	Trigonometry	12
Unit 6	Mensuration	10
Unit 7	Statistics & Probability	11
Total		80

Chapter-Wise Breakup (Expected)

Chapter	Marks (Approx.)	Difficulty
Real Numbers	6	Easy
Polynomials	4–5	Easy–Medium
Pair of Linear Equations	5–6	Medium
Quadratic Equations	5	Medium
Arithmetic Progressions	5–6	Medium
Triangles	8	Medium–Hard
Coordinate Geometry	6	Easy–Medium
Introduction to Trigonometry	6	Easy
Applications of Trigonometry	6	Medium
Circles	5	Medium
Areas Related to Circles	4	Medium
Surface Areas & Volumes	6	Medium
Statistics	7	Easy–Medium
Probability	4	Easy
Constructions	3	Easy

Key Concepts You Must Know

Prioritised by exam frequency and mark value:

Algebra (20 marks — highest priority)

Quadratic equations: factorisation, completing the square, discriminant ( $b^2 - 4ac$ ) — nature of roots
AP: nth term, sum of n terms — these formulas appear every single year
Polynomial zeroes relationship: $\alpha + \beta = -b/a$ , $\alpha\beta = c/a$
Linear equations: cross-multiplication method, substitution, graphical interpretation

Geometry (15 marks)

Basic Proportionality Theorem (Thales theorem) and its converse — proof asked in board
AA, SSS, SAS similarity criteria — must know which criterion to apply when
Tangent to circle: tangent is perpendicular to radius; two tangents from external point are equal

Trigonometry (12 marks)

All trigonometric identities — particularly $\sin^2\theta + \cos^2\theta = 1$ and derived forms
Height and Distance: angle of elevation, angle of depression — draw the diagram first, always

Statistics & Probability (11 marks)

Mean (direct, assumed mean, step deviation), Median (ogive method), Mode — know when to use which
Classical probability: favourable outcomes / total outcomes

Mensuration (10 marks)

Combinations: cone + hemisphere, cylinder + cone, frustum — these appear as 5-mark questions

Important Formulas

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

When to use: When factorisation is not straightforward, or when the question explicitly asks you to “solve using the quadratic formula.” Discriminant $D = b^2 - 4ac$ : if $D > 0$ , two real distinct roots; $D = 0$ , equal roots; $D < 0$ , no real roots.

a_n = a + (n-1)d \qquad S_n = \frac{n}{2}[2a + (n-1)d] = \frac{n}{2}(a + l)

When to use: $a_n$ for finding any specific term; $S_n$ for sum problems. Use $S_n = \frac{n}{2}(a+l)$ when you know the last term — it saves a step.

\sin^2\theta + \cos^2\theta = 1

1 + \tan^2\theta = \sec^2\theta

1 + \cot^2\theta = \text{cosec}^2\theta

When to use: Any “prove that” trigonometry question will require converting everything to $\sin$ and $\cos$ , then applying one of these. The second and third are derived from the first.

\text{Arc length} = \frac{\theta}{360} \times 2\pi r \qquad \text{Area of sector} = \frac{\theta}{360} \times \pi r^2

\text{Area of segment} = \text{Area of sector} - \text{Area of triangle}

When to use: All Chapter 12 questions. The segment formula is the most tested — subtract the triangle area carefully.

\text{Frustum Volume} = \frac{\pi h}{3}(r_1^2 + r_2^2 + r_1 r_2)

\text{Frustum Curved SA} = \pi l (r_1 + r_2), \quad l = \sqrt{h^2 + (r_1 - r_2)^2}

When to use: Frustum is the “hard” question in Chapter 13 — always worth 5 marks. Draw the frustum, label $r_1$ , $r_2$ , $h$ before writing any formula.

\bar{x} = A + \frac{\sum f_i d_i}{\sum f_i}, \qquad d_i = x_i - A

When to use: When class midpoints are large numbers. Pick $A$ = middle class midpoint to keep $d_i$ small.

Solved Previous Year Questions

PYQ 1 — AP (Board 2024, 2 Marks)

Question: The sum of first 20 terms of an AP is 400 and the sum of first 40 terms is 1600. Find the sum of the last 20 terms (terms 21 to 40).

Solution:

S_{20} = 400, \quad S_{40} = 1600

Sum of last 20 terms = $S_{40} - S_{20}$

= 1600 - 400 = \mathbf{1200}

This is a 30-second question if you remember: “sum of terms from $(n+1)$ to $2n$ ” = $S_{2n} - S_n$ . No formula substitution needed. Spotted this shortcut? That’s 2 marks in 30 seconds.

PYQ 2 — Trigonometry Proof (Board 2023, 3 Marks)

Question: Prove that $\dfrac{\sin\theta - 2\sin^3\theta}{2\cos^3\theta - \cos\theta} = \tan\theta$

Solution:

Take LHS and factorise the numerator and denominator:

\text{LHS} = \frac{\sin\theta(1 - 2\sin^2\theta)}{\cos\theta(2\cos^2\theta - 1)}

Now use $\cos^2\theta = 1 - \sin^2\theta$ :

2\cos^2\theta - 1 = 2(1-\sin^2\theta) - 1 = 1 - 2\sin^2\theta

So numerator and denominator both have the factor $(1 - 2\sin^2\theta)$ :

= \frac{\sin\theta \cdot (1-2\sin^2\theta)}{\cos\theta \cdot (1-2\sin^2\theta)} = \frac{\sin\theta}{\cos\theta} = \tan\theta = \text{RHS} \quad \blacksquare

Students often try to expand and simplify from both sides simultaneously in a “prove that” question. CBSE does not award full marks for that approach. Always work from LHS to RHS (or RHS to LHS) in one direction only.

PYQ 3 — Heights and Distances (Board 2024, 4 Marks)

Question: Two poles of equal heights are standing opposite each other on either side of a road 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°. Find the height of the poles and the distances of the point from the poles.

Solution:

Let height of each pole = $h$ , and the point P divides the road such that distance from first pole = $x$ , from second pole = $80 - x$ .

For the 60° pole:

\tan 60° = \frac{h}{x} \Rightarrow \sqrt{3} = \frac{h}{x} \Rightarrow h = x\sqrt{3} \quad \cdots(1)

For the 30° pole:

\tan 30° = \frac{h}{80-x} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{80-x} \Rightarrow h = \frac{80-x}{\sqrt{3}} \quad \cdots(2)

From (1) and (2):

x\sqrt{3} = \frac{80-x}{\sqrt{3}} \Rightarrow 3x = 80 - x \Rightarrow 4x = 80 \Rightarrow x = 20 \text{ m}

Therefore: $h = 20\sqrt{3}$ m, distances are 20 m and 60 m.

Always draw the diagram first in height-and-distance problems. Label all angles and unknowns before writing any equation. Students who skip the diagram almost always set up the wrong ratio.

Difficulty Distribution

Difficulty	Approx. % of Marks	Chapters
Easy (scoring)	35%	Real Numbers, Intro Trig, Probability, Coordinate Geometry, Polynomials
Medium	45%	AP, Quadratics, Linear Equations, Statistics, Circles, Areas
Hard (differentiator)	20%	Triangles (proofs), SA&V Combinations, Heights & Distances, Constructions

The 80/20 rule works perfectly here: the Easy + Medium chapters cover 80% of marks and require straightforward formula application. Toppers secure these first, then attempt Hard chapters for the remaining 20%.

Expert Strategy

Month 1 — Foundation (if you have time) Cover Algebra units first. Quadratic Equations + AP together give you 10–12 marks and the concepts are interconnected. Then do Trigonometry (Chapter 8 and 9 together — 12 marks, highly predictable patterns).

Month 2 — Geometry Block Triangles, Circles, Coordinate Geometry. Triangles proofs need dedicated practice — CBSE asks the same 4-5 proofs every year in rotation. Learn those proofs cold.

Last 15 Days — PYQ Sprint Solve the last 5 years’ board papers under timed conditions. CBSE repeats question types (not always the exact numbers) with very high frequency. If you’ve solved a Heights & Distances question with two poles from 2022, you’re prepared for the 2025 variant.

Section A (MCQs and Assertion-Reason) is 40 marks and takes 20-25 minutes if you’re well-prepared. This is the highest mark-per-minute section. Practice MCQs from NCERT Exemplar specifically — CBSE picks directly from that book more often than most students realise.

The 5-mark questions are worth your attention. Boards always have 3 five-mark questions. These typically come from: Triangles proof, SA&V combination, and one from Algebra/Statistics. If you’ve practised these chapter types, you can score 15 out of 15 on these alone.

Constructions is free marks. 3 marks, and 100% students who practise the 4-5 standard constructions score full marks. The examiner literally watches you use your compass — there’s no trick involved.

Common Traps

AP Trap — “Which term is the first negative term?” Students find $n$ using $a_n = 0$ and then answer $n+1$ . But $n$ must be a positive integer — if you get $n = 8.5$ , the first negative term is the 9th term, not the 8th (which would be zero or positive).

Quadratic Equations — Missing the word “real and equal.” If the question asks for $k$ such that roots are equal, set $D = 0$ . If roots are real, set $D \geq 0$ . Missing the equality loses a mark in checking — always write “real and equal $\Rightarrow D = 0$ ” explicitly.

Circles — PA = PB confusion. When two tangents PA and PB are drawn from an external point P, students often confuse the length of the tangent with the chord AB. The tangent length is PA (or PB), not the chord. Questions often ask for both — read carefully.

Statistics — Mean vs Median vs Mode. Questions often give grouped data and ask for all three. Mean: use assumed mean method for large midpoints. Median: always use the ogive (cumulative frequency) approach and the formula $M = l + \frac{n/2 - cf}{f} \times h$ . Mode: modal class is the class with highest frequency — not the highest midpoint.

Mensuration units mismatch. A classic 1-mark killer: the radius is given in cm but the question asks for volume in litres, or dimensions are in different units. Always convert to a single unit at the start of the problem before substituting.

The Assertion-Reason questions (Section A, last 5 MCQs) follow a pattern. Both A and R can be true and R correctly explains A (full marks). Both true but R does not explain A (partial). A is true, R is false. A is false, R is true. Practise identifying this difference — it’s a 10-mark section that trips up unprepared students who read only the assertion.

Last-Day Checklist

Carry extra pencil and eraser — construction questions require clean lines
For graph questions, always label both axes and write the scale
In “show that” or “prove that” proofs, write LHS = … = … = RHS — don’t skip steps even if obvious
Leave the 5-mark questions last; attempt all 2-mark questions first to secure easy marks
Re-read your answer for units — especially in SA&V and Coordinate Geometry (distances)