NCERT Solutions for Class 10 Mathematics
NCERT Solutions for Class 10 Maths - Best Study Resource with Free PDF Download
Finding clear, step-by-step NCERT Solutions for Class 10 Maths is one of the most common searches among students preparing for their board exams - and for good reason. The Class 10 Maths syllabus covers 14 chapters, ranging from number theory in Real Numbers to probability models, and even a single skipped step in a geometry proof can cost marks in the board exam. These NCERT solutions, available on EduRev, follow the exact method prescribed by CBSE, so students don't inadvertently learn approaches that examiners won't award full marks for. A particularly tricky area for most students is Chapter 6 (Triangles), where many confuse the criteria for similarity with those for congruence - detailed solutions here address that confusion directly. Whether you are tackling Arithmetic Progressions, Coordinate Geometry, or Trigonometry for the first time, EduRev's Class 10 Maths NCERT solutions PDF download gives you worked examples alongside the official textbook questions, making exam preparation structured and reliable.
NCERT Solutions for Class 10 Maths Chapter 1: Real Numbers (Exercise 1.1)
This chapter opens the Class 10 Maths syllabus with Euclid's Division Lemma and the Fundamental Theorem of Arithmetic. A common mistake students make is applying the division algorithm in the wrong order when finding the HCF of large numbers. Exercise 1.1 focuses entirely on the division lemma and its direct applications. The NCERT solutions for Class 10 Maths on EduRev walk through each problem with clear justifications, helping students understand why every composite number has a unique prime factorisation.
NCERT Solutions for Class 10 Maths Chapter 1: Real Numbers (Exercise 1.2)
Exercise 1.2 shifts focus to proving the irrationality of numbers like √2 and √3 using contradiction - a proof technique many Class 10 students encounter formally for the first time here. Students frequently lose marks by assuming without proof that √p is irrational for any prime p. The Class 10 Maths NCERT solutions available on EduRev model the correct logical structure, showing exactly which assumption is made, how the contradiction arises, and how to conclude the proof precisely.
NCERT Solutions for Class 10 Maths Chapter 2: Polynomials (Exercises 2.1 & 2.2)
Chapter 2 covers the geometrical meaning of zeroes of a polynomial and the relationship between zeroes and coefficients. Many students struggle with Exercise 2.2 because they mechanically apply the formulae α + β = -b/a and αβ = c/a without first identifying the correct coefficients from a rearranged equation. The NCERT solutions for Class 10 Maths on EduRev demonstrate how to rewrite a polynomial in standard form before applying these relations, preventing a very common board-exam error.
NCERT Solutions for Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables (Exercises 3.1, 3.2 & 3.3)
This chapter introduces graphical and algebraic methods - substitution and elimination - for solving pairs of linear equations. A recurring mistake in Exercise 3.2 is sign errors during elimination when coefficients require multiplication before subtraction. Exercises 3.1 through 3.3 are covered in the Class 10 Maths NCERT solutions PDF on EduRev with detailed step-by-step working, including how to verify solutions by substituting back into both original equations - a check that many students skip.
NCERT Solutions for Class 10 Maths Chapter 4: Quadratic Equations
Chapter 4 covers factorisation, completing the square, and the quadratic formula, along with the discriminant's role in determining the nature of roots. Students frequently apply the quadratic formula without first ensuring the equation is in the standard form ax² + bx + c = 0, leading to incorrect values of a, b, and c. The NCERT solutions for Class 10 Maths on EduRev address all exercises in this chapter, highlighting when factorisation is faster and when the formula is the only viable route.
NCERT Solutions for Class 10 Maths Chapter 5: Arithmetic Progressions (Exercises 5.1 & 5.2)
Exercises 5.1 and 5.2 establish the definition of an AP, the general term formula (aₙ = a + (n-1)d), and its applications. One of the most common errors is confusing the number of terms n with the last term l when using the nth-term formula. The Class 10 Maths NCERT solutions on EduRev carefully distinguish between these quantities and show how to determine whether a given number is a term of a particular AP - a question type that frequently appears in board exams.
NCERT Solutions for Class 10 Maths Chapter 5: Arithmetic Progressions (Exercises 5.3 & 5.4)
Exercises 5.3 and 5.4 focus on the sum of the first n terms of an AP using Sₙ = n/2 [2a + (n-1)d]. A typical mistake is using this formula when only the first and last terms are known, missing the simpler form Sₙ = n/2 (a + l). The NCERT solutions for Class 10 Maths PDF on EduRev illustrate both forms and guide students in choosing the more efficient one, which is a real time-saver during the board exam.
NCERT Solutions for Class 10 Maths Chapter 6: Triangles (Exercises 6.1-6.3)
Chapter 6 is one of the most proof-heavy chapters in the Class 10 Maths syllabus, covering the Basic Proportionality Theorem (Thales' theorem) and criteria for similarity of triangles - AA, SSS, and SAS. Many students lose marks by writing similarity statements with vertices in the wrong order, which invalidates the correspondence. The NCERT solutions for Class 10 Maths on EduRev demonstrate how to establish correct vertex correspondence before writing any ratio, a discipline that applies to all similarity-based problems.
NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry (Exercise 7.1)
Exercise 7.1 applies the Distance Formula to find lengths between two points and to verify geometric properties - such as whether three points form a right-angled or equilateral triangle. A frequent error is taking a square root of a negative intermediate value due to sign mistakes while squaring differences. The Class 10 Maths NCERT solutions on EduRev show the correct arithmetic layout for each step, reducing the calculation errors that are surprisingly common even among well-prepared students.
NCERT Solutions for Class 10 Maths Chapter 7: Coordinate Geometry (Exercise 7.2)
Exercise 7.2 introduces the Section Formula for internal division and applies it to find centroids and midpoints. Students often apply the formula for external division when the question asks for internal division, especially when negative ratios appear in word problems. The NCERT solutions for Class 10 Maths PDF download on EduRev clarify how to read the ratio from the problem correctly and model the formula application in a clear, reproducible format suitable for board exam answers.
NCERT Solutions for Class 10 Maths Chapter 8: Introduction to Trigonometry
This chapter defines the six trigonometric ratios for acute angles and establishes key identities such as sin²θ + cos²θ = 1. One area where students consistently lose marks is in trigonometric identity proofs, where they manipulate both sides of the equation simultaneously - which is not a valid proof technique. The Class 10 Maths NCERT solutions on EduRev demonstrate the correct approach of transforming only one side until it matches the other, along with the standard values for 0°, 30°, 45°, 60°, and 90°.
NCERT Solutions for Class 10 Maths Chapter 9: Some Applications of Trigonometry (Exercise 9.1)
Exercise 9.1 applies trigonometric ratios to real-world problems involving angles of elevation and depression - such as finding the height of a tower from a distance on flat ground. A common error is treating the angle of depression as measured from the vertical rather than from the horizontal. The NCERT solutions for Class 10 Maths on EduRev include clearly labelled diagrams for each problem in this exercise, which is essential since the diagram itself is worth marks in the CBSE board exam.
NCERT Solutions for Class 10 Maths Chapter 10: Circles (Exercises 10.1 & 10.2)
Chapter 10 covers the properties of tangents to a circle, including the theorem that the tangent at any point is perpendicular to the radius at that point. Exercise 10.2 involves multi-step proofs where students must use both the Pythagorean theorem and congruence criteria together. The Class 10 Maths NCERT solutions on EduRev structure each proof with clearly numbered reasoning steps, helping students understand what justification is required at each stage of a formal geometric proof.
- NCERT Solutions for Class 10 Maths Chapter 10: Circles (Exercises 10.1 & 10.2)
- NCERT Solutions for Class 10 Maths Chapter 10: Circles (Exercise 10.2)
NCERT Solutions for Class 10 Maths Chapter 11: Areas Related to Circles (Exercise 11.1)
Exercise 11.1 focuses on calculating the area and circumference of circles, sectors, and segments. A very common mistake is using the formula for a sector's area (θ/360 × πr²) with the angle in radians instead of degrees, or confusing the area of a segment with that of a sector. The NCERT solutions for Class 10 Maths PDF on EduRev explicitly identify which formula applies to each sub-part and explain how to subtract the triangular area when computing a minor segment's area.
NCERT Solutions for Class 10 Maths Chapter 12: Surface Areas and Volumes (Exercises 12.1 & 12.2)
This chapter deals with surface areas and volumes of combinations of solids - such as a cone mounted on a cylinder or a hemisphere capped on a cylinder. Students frequently add the curved surface areas of both components without subtracting the shared circular face, leading to an overestimate. The Class 10 Maths NCERT solutions on EduRev detail precisely which faces are exposed and which are internal for each combination, a distinction that is critical for arriving at the correct total surface area.
NCERT Solutions for Class 10 Maths Chapter 13: Statistics (Exercises 13.1, 13.2 & 13.3)
Chapter 13 covers mean, median, and mode for grouped data. A frequent source of error in Exercise 13.1 is using the wrong class mark (midpoint) when setting up the mean calculation, particularly when class intervals are unequal. Exercise 13.3 introduces the ogive method for estimating the median graphically. The NCERT solutions for Class 10 Maths on EduRev work through each statistical method - direct, assumed mean, and step-deviation - showing students when each is most efficient to apply.
NCERT Solutions for Class 10 Maths Chapter 14: Probability (Exercise 14.1)
Exercise 14.1 applies the classical definition of probability to experiments like drawing cards, rolling dice, and selecting coloured balls from bags. A recurring conceptual error is counting favourable outcomes without first listing the complete sample space, which leads to undercounting. The Class 10 Maths NCERT solutions PDF download on EduRev shows how to construct sample spaces systematically for each scenario, making it less likely that outcomes will be missed when the problem involves two or more simultaneous events.
Best NCERT Solutions for Class 10 Maths: How to Use Them Effectively for Board Exam Preparation
The best way to use NCERT solutions for Class 10 Maths is not simply to copy answers, but to attempt each question independently and then compare your method step by step. Chapters like Quadratic Equations and Arithmetic Progressions have multiple valid solution paths, and checking against a worked solution reveals whether your approach was optimal for the three-mark or five-mark format CBSE uses. On EduRev, the solutions are formatted to match the answer-writing style expected in board exams, so students can also use them to calibrate how much working must be shown. Focusing especially on chapters like Triangles and Circles - which together account for a significant portion of the geometry marks - while using these Class 10 Maths NCERT solutions is a practical exam strategy.
Class 10 Maths NCERT Solutions: Chapter-Wise Coverage Across the Full Syllabus
The CBSE Class 10 Maths board paper draws questions directly from the NCERT textbook exercises, making complete chapter-wise coverage non-negotiable. Chapters such as Coordinate Geometry, Trigonometry, and Statistics together account for a substantial share of the total marks, yet students often under-prepare Statistics because it appears late in the syllabus. The NCERT solutions for Class 10 Maths available on EduRev cover every exercise across all 14 chapters - from Real Numbers through Probability - ensuring that no chapter is left unrevised. Using these solutions alongside the textbook questions is the most reliable method to build both conceptual understanding and the answer-presentation skills that CBSE examiners reward.
FAQs on NCERT Solutions for Class 10 Mathematics
| 1. How do I solve quadratic equations using the quadratic formula in Class 10 maths? |  |
| 2. What's the difference between arithmetic and geometric progressions that I need to know for exams? | |
| 3. Why do I keep getting circle theorems wrong in my maths tests? | |
| 4. How do I find the probability of combined events without making calculation errors? | |
| 5. What trigonometric ratios do I actually need to memorise for Class 10 board exams? | |
