Which chapters are most important for Class 10 Maths?

Go by CBSE's 2026-27 unit marks: Algebra 20 (polynomials, linear equations, quadratic equations, AP), Geometry 15 (triangles, circles), Trigonometry 12, Statistics and Probability 11, Mensuration 10, Number Systems 6 and Coordinate Geometry 6. Algebra and Trigonometry together are 32 of the 80 marks.

How do I score full marks in Class 10 Maths?

Three habits: (1) solve every NCERT example and exercise, since board questions closely follow them; (2) show every step, because CBSE's marking schemes award marks for steps; (3) solve past papers and sample papers under timed conditions.

Is NCERT enough for Class 10 Maths?

For most students, yes. Finish all NCERT examples and exercises first, then use NCERT Exemplar and CBSE's sample papers for extra practice. Reference books are optional.

How many hours should I practise Maths daily?

About 1.5–2 hours a day works for most students: a short time on new concepts and the rest on problem solving. In the last month before the Board exam, solve a full paper every two days.

Class 10 Maths Important Questions 2027

CBSE Class 10 Maths is 80 marks of theory and 20 of internal assessment. Algebra (20 marks) and Trigonometry (12) are 40% of the paper. Below are important questions from every chapter, all within the CBSE 2026-27 syllabus; topics CBSE has dropped are listed at the end.

Unit-Wise Marks (CBSE 2026-27)

Unit	Chapters	Marks
Number Systems	Real Numbers	6
Algebra	Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions	20
Coordinate Geometry	Coordinate Geometry	6
Geometry	Triangles, Circles	15
Trigonometry	Introduction to Trigonometry, Trigonometric Identities, Heights and Distances	12
Mensuration	Areas Related to Circles, Surface Areas and Volumes	10
Statistics and Probability	Statistics, Probability	11

Real Numbers and Polynomials

Question	Type
Find the HCF and LCM of 306 and 657 by prime factorisation and verify that HCF × LCM = product of the numbers.	Short answer
Prove that √2 is irrational.	Short answer
Prove that 3 + 2√5 is irrational.	Short answer
Find a quadratic polynomial whose zeroes are 3 and −2, and verify the relation between zeroes and coefficients.	Short answer
If α and β are the zeroes of x² − 5x + 6, find α² + β² and 1/α + 1/β.	Short answer
Find the zeroes of 6x² − 7x − 3 and verify the relation between zeroes and coefficients.	Short answer

Linear and Quadratic Equations

Question	Type
Solve 2x + 3y = 11 and 2x − 4y = −24 by substitution and by elimination.	Short answer
The sum of two numbers is 15 and the sum of their reciprocals is 3/10. Find the numbers.	Long answer
A train travels 360 km at a uniform speed. Had the speed been 5 km/h more, it would have taken 1 hour less. Find its speed.	Long answer
Solve 2x² − 7x + 3 = 0 using the quadratic formula.	Short answer
Find the nature of the roots of 3x² − 4√3x + 4 = 0.	Very short
The product of two consecutive positive integers is 306. Find the integers.	Short answer
For what value of k does kx² + 6x + 1 = 0 have equal roots?	Very short

Arithmetic Progressions

Question	Type
Find the 20th term of the AP 3, 8, 13, 18, …	Very short
Which term of the AP 3, 15, 27, 39, … is 132 more than its 54th term?	Short answer
Find the sum of the first 25 terms of the AP 7, 10.5, 14, …	Short answer
The sum of the first n terms of an AP is 3n² + 5n. Find the AP and its 25th term.	Short answer
How many terms of the AP 24, 21, 18, … must be taken so that their sum is 78?	Short answer

Practise Maths chapter-wise

Super Tutor has chapter-wise Class 10 Maths practice quizzes, revision notes and an AI doubt solver. Free trial, no card needed.

Start free

Trigonometry

Question	Type
Prove that (sin A − cos A + 1)/(sin A + cos A − 1) = 1/(sec A − tan A).	Long answer
Prove that (1 + tan²A)/(1 + cot²A) = tan²A.	Short answer
If tan(A + B) = √3 and tan(A − B) = 1/√3, with 0° < A + B ≤ 90° and A > B, find A and B.	Short answer
From the top of a 7 m building, the angle of elevation of the top of a tower is 60° and the angle of depression of its foot is 45°. Find the height of the tower.	Long answer
A 1.5 m tall boy stands some distance from a 30 m building. As he walks towards it, the angle of elevation of the top from his eyes rises from 30° to 60°. How far did he walk?	Short answer

Coordinate Geometry

Question	Type
Find the distance between (2, 3) and (4, 1), and the midpoint of the segment joining them.	Short answer
Find the ratio in which the line 3x + y − 9 = 0 divides the segment joining (1, 3) and (2, 7).	Short answer
Using the distance formula, show that (1, −1), (5, 2) and (9, 5) are collinear.	Short answer
Find the point on the x-axis that is equidistant from (2, −5) and (−2, 9).	Short answer

Triangles and Circles

Question	Type
State and prove the Basic Proportionality Theorem.	Long answer
In ΔABC, DE ∥ BC. If AD = 2 cm, DB = 3 cm and AE = 3 cm, find EC.	Very short
Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.	Long answer
Prove that the lengths of tangents drawn from an external point to a circle are equal.	Short answer
A tangent from a point 13 cm from the centre of a circle of radius 5 cm touches the circle. Find the length of the tangent.	Very short

Mensuration

Question	Type
A solid is a cone standing on a hemisphere, both of radius 1 cm; the cone's height is 2 cm. Find the volume of the solid.	Short answer
A toy is a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height is 15.5 cm. Find its total surface area.	Long answer
Four equal circles, each touching two others, are drawn inside a square of side 14 cm. Find the area of the region of the square outside the circles.	Short answer
Find the area of the minor segment of a circle of radius 10 cm cut off by a chord that subtends a right angle at the centre.	Short answer

Statistics and Probability

Use this distribution for the first three questions: class 0–10: frequency 7; 10–20: 8; 20–30: 12; 30–40: 13; 40–50: 10.

Question	Type
Find the mean using the assumed mean method. (Answer: 27.2)	Long answer
Find the median. (Answer: about 28.33)	Short answer
Find the mode. (Answer: 32.5)	Short answer
Two dice are thrown together. Find the probability of (a) the same number on both, (b) a sum of 8, (c) a doublet of even numbers.	Short answer
A bag has 3 red and 5 black balls. Find the probability of drawing (a) a red ball, (b) a ball that is not red, (c) a ball that is neither red nor black.	Short answer

Must-Know Proofs

Proof	Why it matters
Basic Proportionality Theorem	CBSE's syllabus asks you to prove it; a likely long-answer question
Tangent is perpendicular to the radius	One of the two circle theorems you must be able to prove
Tangents from an external point are equal	The other circle theorem in the syllabus
√2, √3, √5 are irrational	Short proofs by contradiction
sin²A + cos²A = 1	The base for proving other identities

Not in the CBSE 2026-27 Board Exam

Older question banks still include these, but CBSE no longer assesses them: Euclid's division lemma, the area of a triangle from coordinates, the areas-of-similar-triangles and Pythagoras theorem proofs, constructions, trigonometric ratios of complementary angles, the frustum of a cone, converting one solid into another (melting and recasting), and ogives. State boards may still include some of these.

Unit marks and topic coverage follow CBSE's Class 10 Mathematics (Standard) syllabus for 2026-27. Solve every NCERT exercise before practising these.

CBSE Class 10 Maths Important Questions 2027 — Chapter-Wise