CBSE Class 10 Maths 2026-27: chapter by chapter priorities

Unit marks for 2026-27 and the chapters in each

Source: CBSE Class X Mathematics syllabus 2026-27. The same unit marks apply to Mathematics Standard (041) and Basic (241); the two papers differ in question difficulty. Segment areas are limited to central angles of 60°, 90° and 120°, and heights and distances to angles of 30°, 45° and 60° and at most two right triangles.

How the 80 marks are split by question type (Standard paper)

For Mathematics Basic the split is 60, 12 and 8 marks. The 2026-27 sample paper has 38 questions: Section A, 18 MCQs and 2 assertion-reason (1 mark each); B, 5 questions of 2 marks; C, 6 of 3 marks; D, 4 of 5 marks; E, 3 case studies of 4 marks.

Worked example 1: sum of an arithmetic progression

Find the sum of the first 20 terms of the AP 3, 7, 11, 15, ...

1. Identify a and d: the first term a = 3 and the common difference d = 7 - 3 = 4.
2. Use S_n = (n/2)(2a + (n - 1)d) with n = 20.
3. S_20 = 10 × (6 + 19 × 4) = 10 × (6 + 76) = 10 × 82 = 820.
4. Check with the last term: a_20 = 3 + 19 × 4 = 79, and S = (n/2)(first + last) = 10 × (3 + 79) = 820. The two methods agree.

Worked example 2: nature of roots

For what value of k does 2x^2 - 4x + k = 0 have two equal real roots?

1. Equal roots means the discriminant D = b^2 - 4ac is zero.
2. Here a = 2, b = -4, c = k, so D = 16 - 8k.
3. Set 16 - 8k = 0, so k = 2.
4. Check: 2x^2 - 4x + 2 = 2(x - 1)^2, which has the repeated root x = 1.

Worked example 3: heights and distances

From a point 30 m from the foot of a tower, the angle of elevation of its top is 60°. Find the height.

1. Draw the right triangle: the horizontal side is 30 m, the vertical side is the height h, and the angle at the observer is 60°.
2. tan 60° = opposite/adjacent = h/30.
3. tan 60° = sqrt(3), so h = 30 sqrt(3) m.
4. If a decimal is asked for, use sqrt(3) ≈ 1.732: h ≈ 51.96 m. Always draw the figure, because the diagram itself earns credit in long answers.

Worked example 4: probability

A card is drawn at random from cards numbered 1 to 30. Find the probability that the number is prime.

1. List the primes up to 30: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. That is 10 primes.
2. P(prime) = favourable outcomes / total outcomes = 10/30 = 1/3.
3. Common slip: counting 1 as prime. It is not, because it has only one factor.

Common mistakes, chapter by chapter

• Quadratic equations: forgetting to rearrange to ax^2 + bx + c = 0 before reading off a, b and c for the discriminant.
• Linear equations: stating 'no solution' or 'infinitely many' without showing the ratio test a1/a2, b1/b2, c1/c2.
• Triangles: proving similarity without naming the criterion (AA, SSS or SAS) and the corresponding vertices in order.
• Trigonometry: proving an identity by working on both sides at once instead of transforming one side into the other.
• Statistics: using class marks wrongly, or mixing up the lower limit and the cumulative frequency in the median formula.
• Mensuration: adding the area of a hidden face when finding the surface area of a combined solid.

A revision order and how a tutor helps

A sensible order is to secure the short, predictable units first (real numbers, coordinate geometry, statistics and probability), then spend the most time on algebra, trigonometry and geometry, where long answers and case studies carry the marks. Finish with mensuration, then mixed sample papers. CBSE publishes a sample question paper and marking scheme on cbseacademic.nic.in each year; working through it under timed conditions shows how marks are split within each answer.

In one-to-one lessons a tutor works through problems on the shared whiteboard and sees exactly where a method breaks: a sign in the discriminant, a missing step in a proof, or a figure drawn wrongly. Lessons then target that step with a few short questions and a past-paper style question, and the tutor checks that written answers show the steps the marking scheme rewards. Class 10 students now have two board exam opportunities, a compulsory one in February and an optional second exam in May for improving up to three subjects, so a plan can include a second attempt if needed.

Self-check

• Find the 15th term of the AP 5, 8, 11, ... (Answer: 47)
• Find the discriminant of x^2 + 3x - 4 = 0 and the roots. (Answer: D = 25; x = 1 or x = -4)
• Find the distance between (1, 2) and (4, 6). (Answer: 5)
• Prove that sqrt(2) is irrational, writing every step in full.
• A die is thrown once. What is the probability of getting a number greater than 4? (Answer: 1/3)