If you’ve opened five different websites looking for NCERT Class 10 Maths Solutions and gotten five different chapter lists, you’re not imagining things. CBSE rationalized this syllabus back in 2023, and a lot of “solutions” still floating around online are solving exercises that no longer exist in your 2026-27 exam. This guide fixes that — every chapter below reflects the current 14-chapter, 7-unit syllabus, with accurate step-by-step solutions to the kind of questions you’ll actually see on your board paper.
Why the 2026-27 Syllabus Matters More Than You Think
Before jumping into chapter-wise NCERT Class 10 Maths Solutions, it helps to know what’s changed. The current syllabus dropped several topics that older solution PDFs still include:
- Euclid’s Division Lemma — removed from Real Numbers; the chapter now centers on the Fundamental Theorem of Arithmetic
- The full Constructions chapter — no longer part of the board syllabus
- The polynomial division algorithm — removed from Polynomials
- Area of a triangle using coordinates — removed from Coordinate Geometry, which now covers only distance and section formulas
- Cumulative frequency and ogives — removed from Statistics
Practicing a deleted topic doesn’t just waste time — it can make you second-guess concepts you don’t actually need for the exam. So the chapter breakdown below sticks strictly to what’s examinable this year.
CBSE Class 10 Maths: Units, Chapters & Marks at a Glance
The board paper carries 80 marks for the written exam and 20 marks for internal assessment, split across seven units:
Unit | Marks | Chapters Covered |
Number Systems | 6 | Real Numbers |
Algebra | 20 | Polynomials, Pair of Linear Equations, Quadratic Equations, Arithmetic Progressions |
Coordinate Geometry | 6 | Coordinate Geometry |
Geometry | 15 | Triangles, Circles |
Trigonometry | 12 | Introduction to Trigonometry, Applications of Trigonometry |
Mensuration | 10 | Areas Related to Circles, Surface Areas & Volumes |
Statistics & Probability | 11 | Statistics, Probability |
Algebra alone is worth a quarter of your paper — so if you’re short on time, that’s where focused revision pays off fastest.
Chapter-Wise NCERT Class 10 Maths Solutions
Chapter 1: Real Numbers (Number Systems Unit)
This chapter is built around the Fundamental Theorem of Arithmetic: every composite number can be expressed as a product of primes, and this factorization is unique (apart from the order of factors).
Solved Example: Find the HCF and LCM of 36 and 90 using prime factorization.
36 = 2² × 3²
90 = 2 × 3² × 5
HCF = product of smallest powers of common factors = 2¹ × 3² = 18
LCM = product of greatest powers of all factors = 2² × 3² × 5 = 180
Check: HCF × LCM = 18 × 180 = 3240, and 36 × 90 = 3240. ✓ (This verification trick ; HCF × LCM = product of the two numbers ; is worth remembering; it’s a common 1-mark check-your-work question.)
The chapter also asks you to prove numbers like √5 are irrational, typically using proof by contradiction: assume √5 = p/q (in lowest terms), square both sides to get 5q² = p², which forces both p and q to share a common factor of 5 ; contradicting the “lowest terms” assumption.
Chapter 2: Polynomials (Algebra Unit)
For a quadratic polynomial ax² + bx + c, the relationship between zeroes and coefficients is:
Sum of zeroes (α + β) = −b/a
Product of zeroes (αβ) = c/a
Solved Example: Find the zeroes of x² − 5x + 6 and verify the relationship.
x² − 5x + 6 = (x − 2)(x − 3) = 0
So the zeroes are x = 2 and x = 3.
Sum = 2 + 3 = 5 = −(−5)/1 ✓
Product = 2 × 3 = 6 = 6/1 ✓
Chapter 3: Pair of Linear Equations in Two Variables (Algebra Unit)
Solved Example: Solve by the elimination method: 2x + 3y = 11 and 2x − 4y = −24.
Subtracting the equations: (3y − (−4y)) = 11 − (−24)
7y = 35
y = 5
Substituting back: 2x + 3(5) = 11 → 2x = −4 → x = −2
Solution: x = −2, y = 5
Consistency of the pair (whether it has a unique solution, no solution, or infinitely many) depends on comparing a₁/a₂, b₁/b₂, and c₁/c₂ ; a favorite CBSE assertion-reason question.
Chapter 4: Quadratic Equations (Algebra Unit)
Solved Example (Factorization): Solve x² − 7x + 12 = 0.
x² − 7x + 12 = (x − 3)(x − 4) = 0
x = 3 or x = 4
Solved Example (Quadratic Formula): Solve 2x² − 4x − 3 = 0 using the formula:
x = [−b ± √(b² − 4ac)] / 2a
Here a = 2, b = −4, c = −3
x = [4 ± √(16 + 24)] / 4 = [4 ± √40] / 4 = [4 ± 2√10] / 4 = [2 ± √10] / 2
The discriminant (b² − 4ac) is where most exam marks hide: if it’s positive, you get two real roots; if zero, equal roots; if negative, no real roots at all. Boards love asking you to find the value of k for which an equation has equal roots ; set the discriminant to zero and solve.
Chapter 5: Arithmetic Progressions (Algebra Unit)
nth term: aₙ = a + (n − 1)d
Sum of n terms: Sₙ = n/2 × [2a + (n − 1)d]
Solved Example: Find the 10th term and the sum of the first 10 terms of the AP: 3, 7, 11, 15, …
Here a = 3, d = 4
a₁₀ = 3 + (10 − 1)(4) = 3 + 36 = 39
S₁₀ = 10/2 × [2(3) + 9(4)] = 5 × [6 + 36] = 5 × 42 = 210
Chapter 6: Triangles (Geometry Unit)
The Basic Proportionality Theorem (Thales’ Theorem) states: if a line is drawn parallel to one side of a triangle, intersecting the other two sides at distinct points, it divides those two sides in the same ratio.
Solved Example: In triangle ABC, DE is parallel to BC, with AD = 4 cm, DB = 6 cm, and AE = 3 cm. Find EC.
By BPT: AD/DB = AE/EC
4/6 = 3/EC
EC = (3 × 6)/4 = 4.5 cm
Similarity criteria (AA, SSS, SAS) are the other high-yield concept here ; expect at least one proof-based question worth 3–5 marks.
Chapter 7: Coordinate Geometry (Coordinate Geometry Unit)
This chapter now covers only two exercises: the distance formula and the section formula.
Distance formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
Solved Example: Find the distance between A(2, 3) and B(6, 6).
d = √[(6 − 2)² + (6 − 3)²] = √[16 + 9] = √25 = 5 units
Section formula (a point P dividing AB in the ratio m:n):
P(x, y) = [(mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)]
Chapter 8: Introduction to Trigonometry (Trigonometry Unit)
The core identity you’ll use constantly: sin²θ + cos²θ = 1
Solved Example: If sin θ = 3/5, find cos θ and tan θ (0° < θ < 90°).
Using sin²θ + cos²θ = 1:
cos²θ = 1 − 9/25 = 16/25
cos θ = 4/5
tan θ = sin θ / cos θ = (3/5) / (4/5) = 3/4
Memorize the standard trigonometric ratio table (0°, 30°, 45°, 60°, 90°) cold ; it’s assumed knowledge for nearly every question in this unit.
Chapter 9: Some Applications of Trigonometry (Trigonometry Unit)
Solved Example: The angle of elevation of the top of a tower from a point 30 m away from its base is 30°. Find the height of the tower.
tan 30° = height / 30
1/√3 = height / 30
height = 30/√3 = 10√3 m ≈ 17.32 m
Draw the diagram first, every time ; labeling the angle of elevation correctly is where most marks are lost, not the trigonometry itself.
Chapter 10: Circles (Geometry Unit)
Key theorem: the tangent to a circle is perpendicular to the radius at the point of contact. Also: tangents drawn from an external point to a circle are equal in length.
Solved Example: Find the length of the tangent from a point 13 cm from the center of a circle of radius 5 cm.
Since the tangent, radius, and the line joining the external point to the center form a right triangle:
Tangent length = √(d² − r²) = √(13² − 5²) = √(169 − 25) = √144 = 12 cm
Chapter 11: Areas Related to Circles (Mensuration Unit)
Area of a sector = (θ/360°) × πr²
Solved Example: Find the area of a sector with radius 14 cm and a central angle of 90°.
Area = (90/360) × (22/7) × 14² = (1/4) × (22/7) × 196 = 154 cm²
Chapter 12: Surface Areas and Volumes (Mensuration Unit)
This chapter is almost entirely about combinations of solids ; a cone on a cylinder, a hemisphere scooped out of a cube, and similar composite shapes.
Solved Example: A cylinder has a hemisphere of the same radius on top. Radius = 7 cm, cylinder height = 14 cm. Find the total surface area.
Total surface area = curved surface area of cylinder + curved surface area of hemisphere + area of base circle
= 2πrh + 2πr² + πr²
= 2 × (22/7) × 7 × 14 + 2 × (22/7) × 49 + (22/7) × 49
= 616 + 308 + 154 = 1078 cm²
The trap here is adding the flat top of the cylinder; since the hemisphere sits on top, that circular face isn’t exposed and shouldn’t be counted.
Chapter 13: Statistics (Statistics & Probability Unit)
Mean (Direct Method) = Σfᵢxᵢ / Σfᵢ
Solved Example: Find the mean of the following grouped data:
Class | Frequency (f) | Midpoint (x) | fx |
0–10 | 5 | 5 | 25 |
10–20 | 8 | 15 | 120 |
20–30 | 12 | 25 | 300 |
30–40 | 5 | 35 | 175 |
Σf = 30, Σfx = 620
Mean = 620 / 30 = 20.67 (approx.)
Chapter 14: Probability (Statistics & Probability Unit)
Probability of an event = (Number of favorable outcomes) / (Total number of outcomes)
Solved Example: A die is thrown once. What is the probability of getting a number greater than 4?
Favorable outcomes: {5, 6} → 2 outcomes
Total outcomes: {1, 2, 3, 4, 5, 6} → 6 outcomes
P(number > 4) = 2/6 = 1/3
How to Actually Use These Solutions, Not Just Read Them
A solution guide should not only indicate if your answer is correct or incorrect it should also help you to see what you did wrong. When applied correctly, it can teach you how to tackle a tough question, how your thought process went astray and how to prevent repeating that same error. Follow the following simple rules while using NCERT Class 10 Maths Solutions:
- Give the question a real attempt: Do not solve the problem as soon as it gets difficult. Attempt various methods, remember the appropriate formula and work out as far as possible independently.
- Look at the approach: When checking the answer, don’t just look at the answer; look at the approach. Know the reasons for the use of a formula, theorem, or calculation. This is helpful when the exam asks you a version of the question you haven’t memorized.
- Determine why the answer was incorrect: It could be due to a small calculation error, or to a flawed concept. Identify where/why the error occurred rather than just substituting the correct number for the error.
- Return to challenging questions: If you had questions that were challenging and you got confused, mark them. The revisit of these during Class 10 Maths revision allows you to work on real issues instead of revisiting the same thing equally.
- Close the page without the solution: Once you grasp the way they solve the problem, shut the page and do the problem once more. The steps should be repeatable without the need to refer to what you just read.
- Include timed practice: When you feel you know a chapter, complete the exercises within a specific amount of time. Practice the concepts using timers regularly to improve the calculation speed, accuracy, and confidence in the CBSE exam.
Conclusion
Do not memorise the answer; read the NCERT Class 10 Maths Solutions and learn the method. Use more revision time on Algebra, and continue to practise Geometry, Trigonometry, Statistics and Probability to get the skill of being more accurate and confident.
Don’t let errors go uncorrected. Highlight tricky questions, review them a couple of days later, and independently re-do them. A Chapter 10 Maths home tutor can give personalized attention to help an individual overcome the challenges of a particular chapter. Mathematics Home Tutor can also make the students feel more confident to face the Class 10 Maths exam with stronger concepts.
