📖 NCERT Learning Guides

Area of Sector and Segment of a Circle Class 10: Formulas & Examples

A clear Class 10 guide to sectors and segments of a circle — what they mean, the area of a sector formula, the length of an arc, and how to find the area of a segment, with worked examples.

Mean of Grouped Data Class 10: Formula & 3 Methods

A Class 10 guide to the mean of grouped data — the class-mark idea, the formula x̄ = Σfᵢxᵢ/Σfᵢ, and the direct, assumed-mean and step-deviation methods, all shown on one data set that gives the same answer 25.8.

Measures of Central Tendency Class 10: Mean, Median, Mode

A clear Class 10 overview of the three measures of central tendency — mean, median and mode of grouped data — with each formula, the class-mark idea, when to use each measure, and the empirical relationship, with a worked example.

Median of Grouped Data Class 10: Formula & Examples

A Class 10 guide to the median of grouped data — cumulative frequency, how to find the median class, the formula Median = l + ((n/2 − cf)/f) × h, a worked example giving 25.33, and the empirical relationship linking mean, median and mode.

Mode of Grouped Data Class 10: Formula & Examples

A Class 10 guide to the mode of grouped data — what the modal class is, the mode formula with every variable defined, and worked examples giving a mode of 24.17, plus when the mode is the right measure to use.

Number of Tangents from a Point on a Circle Class 10: Theorem 10.2 & Examples

A student-friendly guide for CBSE Class 10 on how many tangents can be drawn from a point to a circle — none from an inside point, one from a point on the circle, and exactly two from an outside point — plus the length of a tangent and Theorem 10.2 (the two tangents from an external point are equal in length), with worked examples.

Surface Area and Volume Formulas Class 10: All Solids (Chapter 12)

The complete Class 10 formula sheet for Chapter 12: curved/total surface area and volume of the cuboid, cube, cylinder, cone, sphere and hemisphere, each with its meaning and a worked example.

Surface Area of a Combination of Solids Class 10: Method & Examples

A clear Class 10 guide to finding the surface area of combined solids — why you add only the exposed surfaces, a reliable step method, and worked examples (cone-on-hemisphere toy, cube with a hemisphere).

Tangent and Secant of a Circle Class 10: Meaning, Difference & Examples

A student-friendly guide to how a line and a circle can meet in CBSE Class 10 — the three cases (non-intersecting line, secant, tangent), what a secant and a tangent are, the difference between them, the point of contact, and simple examples that decide the case from the distance to the centre.

Tangent to a Circle Class 10: Theorem, Proof & Examples (Tangent ⊥ Radius)

A student-friendly guide to the tangent to a circle for CBSE Class 10 — what a tangent and point of contact are, Theorem 10.1 (the tangent at any point is perpendicular to the radius through the point of contact), a clean proof, and worked examples that use the resulting right angle with the Pythagoras theorem.

Theoretical Probability Class 10: Formula, Meaning & Examples

A clear Class 10 guide to theoretical probability — the classical formula P(E) = favourable/total, equally likely outcomes, elementary and complementary events, and why probability lies between 0 and 1, with worked examples.

Volume of a Combination of Solids Class 10: Method & Examples

A clear Class 10 guide to the volume of combined solids — why volumes simply add (and cavities subtract), a reliable method, and worked examples for a toy and a glass with a hemispherical depression.

Basic Proportionality Theorem (Thales Theorem) Class 10: Statement, Proof & Examples

A student-friendly guide to the Basic Proportionality Theorem (Thales Theorem) for CBSE Class 10 — its statement, the area-based proof, the converse, and worked examples showing how to find a missing length and how to check whether a line is parallel to the third side of a triangle.

Criteria for Similarity of Triangles Class 10: AAA, AA, SSS & SAS (With Examples)

A student-friendly guide to the criteria for similarity of triangles in CBSE Class 10 (Chapter 6, Triangles) — what makes two triangles similar, and how the AAA/AA, SSS and SAS shortcuts let you prove similarity from just three facts, with a clean worked example for each rule.

Distance Formula Class 10 Maths (Chapter 7): Formula, Steps & Examples

A student-friendly guide to the distance formula for CBSE Class 10 (Chapter 7): the formula √[(x₂−x₁)²+(y₂−y₁)²] with each part explained, why it comes from the Pythagoras theorem, the distance of a point from the origin, distances along an axis, and worked examples including a collinearity check.

nth Term of an AP: Formula, Examples & How to Find It (Class 10)

A student-friendly guide to the nth term of an arithmetic progression for CBSE Class 10 — the formula aₙ = a + (n − 1)d, what each symbol means, and how to find any term, work out which term a value is, build an AP from two given terms, and test whether a number belongs to an AP.

Section Formula Class 10 Maths (Chapter 7): Formula, Midpoint & Examples

A student-friendly guide to the section formula for CBSE Class 10 (Chapter 7): the formula for the point dividing a line segment in the ratio m₁:m₂, with every symbol explained, the midpoint formula as its special case, how to find an unknown ratio (the k:1 method), and worked examples including points of trisection.

Similar Figures Class 10: Meaning, Conditions & Examples (Triangles)

A student-friendly introduction to Chapter 6 (Triangles) for CBSE Class 10 — what similar figures are, how similar differs from congruent, the two conditions for two polygons to be similar, scale factor, and worked examples showing why both conditions are needed.

Sum of n Terms of an AP: Formula, Examples & How to Find It (Class 10)

A student-friendly guide to the sum of the first n terms of an arithmetic progression for CBSE Class 10 — the two formulas Sₙ = n/2[2a + (n − 1)d] and Sₙ = n/2(a + l), what each symbol means, when to use which, and how to find a sum, work out how many terms give a target sum, and recover a term from Sₙ.

Trigonometric Identities (Class 10): 3 Formulas & Proofs

A student-friendly Class 10 guide to the three trigonometric identities — sin²A + cos²A = 1, 1 + tan²A = sec²A, and 1 + cot²A = cosec²A — with their proofs, the conditions on each, and a reliable method for proving exam identities.

Trigonometric Ratios (Class 10): sin, cos, tan Explained

A student-friendly Class 10 guide to the six trigonometric ratios — sin, cos, tan, cosec, sec and cot — defined on a right triangle, with SOH-CAH-TOA, the reciprocal links, and worked examples that find every ratio from just one.

What Is an Arithmetic Progression? Introduction for Class 10 (AP)

A student-friendly introduction to arithmetic progressions for CBSE Class 10 — what an AP is, the first term (a) and common difference (d), the general form, finite vs infinite APs, and how to check whether a list of numbers is an AP.

What Is Coordinate Geometry? Introduction for Class 10 (Chapter 7)

A student-friendly introduction to coordinate geometry for CBSE Class 10 — the coordinate plane, the x- and y-axes, the origin, abscissa and ordinate, the four quadrants and their signs, points on the axes, and how to plot a point (x, y).

Nature of Roots of a Quadratic Equation (Class 10)

A student-friendly Class 10 guide to the nature of roots of a quadratic equation — how the discriminant b² − 4ac tells you, without solving, whether the roots are real and distinct, equal, or not real, with clear worked examples.

Quadratic Equation Word Problems (Class 10) — Step-by-Step Method

A Class 10 guide to solving quadratic equation word problems — a 3-phase form–solve–check method with worked number, area and age examples, and the crucial skill of rejecting roots that don't fit the situation.

Solving Quadratic Equations by Factorisation (Class 10)

A student-friendly Class 10 guide to solving quadratic equations by factorisation — what a root means, how to split the middle term, how to use the zero-product rule, and how to handle repeated roots, with fully worked examples.

How to Form a Quadratic Equation from a Word Problem (Class 10)

A student-friendly Class 10 guide to representing real situations as quadratic equations — a 4-step translation method with worked examples on area, products of numbers and cost problems, ending in standard form ax² + bx + c = 0.

Standard Form of a Quadratic Equation (Class 10) — Definition & Examples

A student-friendly Class 10 guide to what a quadratic equation is and its standard form ax² + bx + c = 0 — with worked examples on identifying a, b, c and checking whether a given equation is really quadratic.

Angle of Elevation and Angle of Depression (Class 10)

A student-friendly Class 10 guide to the angle of elevation and the angle of depression — what the line of sight is, how the two angles differ, why they are equal for the same two points, with simple worked examples.

Consistent and Inconsistent Pair of Linear Equations (Class 10)

A clear Class 10 guide to consistent, inconsistent and dependent pairs of linear equations — what each term means, and how to use the ratios a1/a2, b1/b2 and c1/c2 to identify the case without drawing a graph.

Elimination Method to Solve a Pair of Linear Equations (Class 10)

A student-friendly Class 10 guide to the elimination method — how to solve a pair of linear equations by making the coefficients of one variable equal and then adding or subtracting, with a 4-step method and worked examples.

Graphical Method of Solving a Pair of Linear Equations (Class 10)

A step-by-step Class 10 guide to the graphical method of solving a pair of linear equations in two variables — how to plot both lines, read the solution from the intersection point, and recognise intersecting, parallel and coincident lines.

Heights and Distances (Class 10): How to Solve Trigonometry Problems

A student-friendly Class 10 guide to heights and distances — a simple 4-step method to find an unknown height or distance using trigonometric ratios, with worked examples on towers, chimneys and observer height.

Substitution Method to Solve a Pair of Linear Equations (Class 10)

A student-friendly Class 10 guide to the substitution method — how to solve a pair of linear equations in two variables by expressing one variable in terms of the other, with 3-step method and worked examples.

Linear Equations in Two Variables (Class 10): What a Pair of Linear Equations Means

A student-friendly introduction to Chapter 3 of CBSE Class 10 Maths — what a linear equation in two variables is, why real situations need a pair of them, the general form, and what it means to solve the pair.

Linear Equations Word Problems (Class 10): How to Form a Pair of Linear Equations

A step-by-step Class 10 guide to turning word problems into a pair of linear equations in two variables — the 4-step method, a phrase-to-maths translation table, and worked examples of the most common problem types.

How to Form a Quadratic Polynomial from the Sum and Product of Its Zeroes (Class 10)

A student-friendly Class 10 guide to forming a quadratic polynomial from the sum and product of its zeroes — using x² − (sum)x + product — including how to build one straight from the zeroes and how to clear fractions.

Relationship Between Zeroes and Coefficients of a Polynomial (Class 10)

A student-friendly Class 10 guide to the relationship between the zeroes and coefficients of a polynomial — for a quadratic, sum of zeroes = −b/a and product = c/a, plus the cubic extension, with worked verification examples.

Geometrical Meaning of the Zeroes of a Polynomial (Class 10)

A student-friendly Class 10 guide to the geometrical meaning of the zeroes of a polynomial — how zeroes are the x-coordinates where the graph meets the x-axis, for linear, quadratic and higher polynomials.

How to Find the Number of Zeroes of a Polynomial from a Graph (Class 10)

A quick, exam-focused Class 10 guide to finding the number of zeroes of a polynomial from a graph by counting how many times the curve meets the x-axis, with worked examples for the NCERT Exercise 2.1 question type.

Types of Polynomials Class 10: Degree, Linear, Quadratic & Cubic

A clear Class 10 guide to what a polynomial is, how to find its degree, and the three types you must know — linear, quadratic and cubic — with easy examples.

Zeroes of a Polynomial Class 10: Meaning, Value of p(x) & How to Find

A clear Class 10 guide to the value of a polynomial p(k), what a zero of a polynomial means, how to check for one, and how to find the zero of a linear polynomial.

Fundamental Theorem of Arithmetic Class 10: Prime Factorisation, HCF & LCM Made Easy

A friendly, exam-focused NCERT companion for the Fundamental Theorem of Arithmetic (Class 10, Real Numbers). Master unique prime factorisation and HCF & LCM become far easier - a concept used across the whole chapter.

Irrational Numbers Class 10: Meaning, Proofs & Exam Guide (Real Numbers 1.3)

A student-friendly, exam-facing guide to irrational numbers (Real Numbers, Section 1.3): what makes a number irrational, the 'p divides a²' idea, and how the proof by contradiction for √2 and √3 actually works.

Applications of Trigonometry Class 10: How to Approach the Chapter

A methodology-first guide to Applications of Trigonometry Class 10 Maths - heights and distances, angles of elevation and depression, common mistakes, and your roadmap to full marks.

Areas Related to Circles Class 10: How to Approach the Chapter

A methodology-first guide to Areas Related to Circles Class 10 Maths - sectors and segments, how CBSE tests it, common mistakes, and your roadmap to full marks.

Arithmetic Progressions Class 10: How to Approach and Master the Chapter

A methodology-first guide to Arithmetic Progressions Class 10 Maths - the chapter snapshot, key concepts, how CBSE tests it, common mistakes, and your roadmap to full marks.

Circles Class 10: How to Approach and Master the Chapter

A methodology-first guide to Circles Class 10 Maths - the chapter snapshot, tangent properties and theorems, how CBSE tests it, common mistakes, and your roadmap to full marks.

Coordinate Geometry Class 10: How to Approach and Master the Chapter

A methodology-first guide to Coordinate Geometry Class 10 Maths - the chapter snapshot, key formulas, how CBSE tests it, common mistakes, and your roadmap to full marks.

Pair of Linear Equations Class 10: How to Approach and Master the Chapter

A methodology-first guide to Pair of Linear Equations Class 10 Maths - the chapter snapshot, key concepts, how CBSE tests it, common mistakes, and your roadmap to full marks.

Polynomials Class 10: How to Approach and Master the Chapter

A methodology-first guide to Polynomials Class 10 Maths - the chapter snapshot, key concepts, how CBSE tests it, common mistakes, and your roadmap to full marks.

Probability Class 10: How to Approach and Master the Chapter

A methodology-first guide to Probability Class 10 Maths - theoretical probability, how CBSE tests it, common mistakes, and your roadmap to full marks.

Quadratic Equations Class 10: How to Approach and Master the Chapter

A methodology-first guide to Quadratic Equations Class 10 Maths - the chapter snapshot, key concepts, how CBSE tests it, common mistakes, and your roadmap to full marks.

Real Numbers Class 10: How to Approach and Master the Chapter

A methodology-first guide to Real Numbers Class 10 Maths - the chapter snapshot, key concepts, how CBSE tests it, common mistakes, and your roadmap to full marks.

Statistics Class 10: How to Approach and Master the Chapter

A methodology-first guide to Statistics Class 10 Maths - mean, median and mode of grouped data, how CBSE tests it, common mistakes, and your roadmap to full marks.

Surface Areas and Volumes Class 10: How to Approach the Chapter

A methodology-first guide to Surface Areas and Volumes Class 10 Maths - solids and combinations, how CBSE tests it, common mistakes, and your roadmap to full marks.

Triangles Class 10: How to Approach and Master the Chapter

A methodology-first guide to Triangles Class 10 Maths - the chapter snapshot, similarity and theorems, how CBSE tests it, common mistakes, and your roadmap to full marks.

Trigonometry Class 10: How to Approach and Master the Chapter

A methodology-first guide to Introduction to Trigonometry Class 10 Maths - the chapter snapshot, key concepts, how CBSE tests it, common mistakes, and your roadmap to full marks.

Class 10 Maths All Formulas: Complete Chapter-wise Formula Sheet

Every key CBSE Class 10 Maths formula organised chapter by chapter - your complete, bookmark-worthy revision formula sheet.

Class 10 Maths Chapter List: All 14 Chapters (2027)

All 14 CBSE Class 10 Maths chapters grouped by unit - what each covers, the marks, and a sensible order to study them.

How to Study NCERT Maths Class 10: A Method That Actually Works

A concrete, repeatable method for studying NCERT Class 10 Maths - the per-chapter study cycle, a weekly rhythm, and revision that actually sticks.

NCERT Class 10 Maths Guide: Chapters, Book Structure & Study Plan

Your map to the NCERT Class 10 Maths book - all 14 chapters by unit, how long it takes, how to work through it, and how it maps to the board exam.