NCERT Solutions for Class 10 Maths: The Complete Chapter by Chapter Guide (2026)

Difficulty: Moderate. Focus on Euclid's Division Algorithm and the Fundamental Theorem of Arithmetic. You must know how to find HCF using Euclid's method and prove that numbers like $\sqrt{2}$ and $\sqrt{3}$ are irrational. The proof questions are common in board exams. Practice expressing numbers as products of prime factors to find HCF and LCM. Common mistake: confusing HCF and LCM in word problems.

Difficulty: Easy to Moderate. Key concepts include zeroes of a polynomial, the relationship between zeroes and coefficients, and division algorithm. For a quadratic polynomial $ax^2 + bx + c$, remember that the sum of zeroes equals $-b/a$ and the product equals $c/a$. Most students find this chapter straightforward once they understand the relationship formulas.

Difficulty: Moderate. You need to master three methods: graphical, elimination, and substitution. Also learn cross multiplication for faster solving. The word problems in this chapter are extremely important for the board exam. Practice converting real life situations into pairs of equations. Focus on Exercise 3.5 and 3.6 thoroughly.

Difficulty: Moderate to Hard. Learn all three solving methods: factorisation, completing the square, and the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Understanding the discriminant $D = b^2 - 4ac$ is crucial. The nature of roots question appears almost every year. Word problems from this chapter carry 5 marks and are frequently asked.

Difficulty: Moderate. Master the nth term formula $a_n = a + (n-1)d$ and the sum formula $S_n = \frac{n}{2}[2a + (n-1)d]$. Questions often combine both formulas. The word problems here are scoring if you practice them. Common mistake: forgetting that the common difference $d$ can be negative.

Difficulty: Hard. This chapter carries high weightage and includes important theorems like the Basic Proportionality Theorem (Thales) and the Pythagorean Theorem. Proof questions from this chapter are guaranteed in the exam. Practice all the similarity criteria: AAA, AA, SSS, SAS. Exercise 6.3 and 6.4 are most important.

Difficulty: Moderate. Learn the distance formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$, section formula, and area of a triangle using coordinates. This chapter is highly scoring because the questions are formula based. If you know the formulas and practice substitution, you can score full marks here.

Difficulty: Hard. The most feared chapter for many students. Focus on the basic ratios (sin, cos, tan) and their values at standard angles (0, 30, 45, 60, 90 degrees). The three identities $\sin^2\theta + \cos^2\theta = 1$, $1 + \tan^2\theta = \sec^2\theta$, and $1 + \cot^2\theta = \csc^2\theta$ are essential. Proof questions are common.

Difficulty: Moderate. This chapter applies trigonometry to heights and distances problems. Learn to identify angle of elevation and angle of depression in word problems. Draw clear diagrams for every question. The key is setting up the right triangle from the given information. Practice at least 15 to 20 problems from this chapter.

Difficulty: Moderate. Focus on tangent properties and the two key theorems: a tangent is perpendicular to the radius at the point of contact, and tangent lengths from an external point are equal. Proof questions from this chapter appear regularly. Exercise 10.2 is the most important.

Difficulty: Easy to Moderate. Learn the formulas for area and circumference of a circle, area of a sector ($\frac{\theta}{360} \times \pi r^2$), and area of a segment. The questions are formula based and scoring. Common mistake: using diameter instead of radius in formulas.

Difficulty: Moderate. This chapter involves combined solids (like a cone on top of a cylinder). Learn the formulas for all shapes: cylinder, cone, sphere, hemisphere. The key skill is identifying which formula to use for combined shapes. Conversion questions (like melting and recasting) are frequently asked.

Difficulty: Easy. Learn the three methods for finding mean (direct, assumed mean, step deviation), median formula for grouped data, and mode formula. This is one of the easiest chapters to score full marks in. The formulas are straightforward and the calculations are routine. Do not skip this chapter.

Difficulty: Easy. Probability is pure logic. Learn the formula $P(E) = \frac{\text{number of favourable outcomes}}{\text{total outcomes}}$ and understand complementary events where $P(E) + P(\bar{E}) = 1$. Questions involve coins, dice, cards, and real life scenarios. Practice listing all possible outcomes systematically.

Start with Real Numbers and Polynomials in week 1 since they build the foundation for everything else. Cover Linear Equations and Quadratic Equations in weeks 2 and 3. Finish Arithmetic Progressions in week 4. These chapters are algebraic and interconnected, so doing them together makes sense. Aim to complete all exercises in each chapter before moving on.

Triangles will take the longest, so give it a full week. Coordinate Geometry is formula based and can be done in 4 to 5 days. Trigonometry (chapters 8 and 9) needs about 10 days combined since many students find it challenging. Circles is relatively short. By the end of month 2, you should have 10 chapters done.

Areas Related to Circles, Surface Areas and Volumes, Statistics, and Probability can be completed in 2 weeks since they are formula based and scoring. Use the remaining 2 weeks for full revision, sample papers, and previous year papers. Solve at least 5 complete sample papers in exam conditions during this period.