Class 10 · Mathematics · English medium
Class 10 Mathematics companion
An original companion to Mathematics, NCERT Class 10 Mathematics (2026–27 edition). Official textbook ↗ ncert.nic.in
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Chapters
- ENHinglish
Chapter 1: Real Numbers
Primes as building blocks, and proofs that some numbers are not fractions - ENHinglish
Chapter 2: Polynomials
Class 10 Polynomials (rationalised book, no division algorithm). - ENHinglish
Chapter 3: Pair of Linear Equations in Two Variables
Class 10 Maths chapter 3 (rationalised edition): two linear equations in x and y solved together, with coefficients a1, b1, c1 and a2, b2, c2. - ENHinglish
Chapter 4: Quadratic Equations
Build them from situations, solve them, and let the discriminant say what to expect - ENHinglish
Chapter 5: Arithmetic Progressions
Lists that grow by equal steps: any term, and the sum of many terms, in one line - ENHinglish
Chapter 6: Triangles
Class 10 NCERT Mathematics, Chapter 6 (2026-27 edition). - ENHinglish
Chapter 7: Coordinate Geometry
Class 10 Maths chapter 7 (rationalised edition): coordinate geometry. - ENHinglish
Chapter 8: Introduction to Trigonometry
Six ratios of a right triangle, their values at special angles, and the identities that link them - ENHinglish
Chapter 9: Some Applications of Trigonometry (Heights and Distances)
Find heights and distances you cannot reach, from one length and one angle - ENHinglish
Chapter 10: Circles
Class 10 NCERT Mathematics, Chapter 10 Circles (2026-27). - ENHinglish
Chapter 11: Areas Related to Circles
Class 10 Maths chapter 11 (rationalised edition): areas of sectors and segments, and arc length. - ENHinglish
Chapter 12: Surface Areas and Volumes
Split an object into basic solids, then add the surfaces that show and the space inside - ENHinglish
Chapter 13: Statistics
Mean, mode and median when the data come in classes - ENHinglish
Chapter 14: Probability
This Class 10 chapter defines theoretical (classical) probability, P(E) = favourable outcomes ÷ all outcomes, for experiments whose outcomes
Also in Hinglish
- Chapter 1: Real Numbers (Hinglish)
- Chapter 2: Polynomials (Hinglish)
- Chapter 3: Pair of Linear Equations in Two Variables (Hinglish)
- Chapter 4: Quadratic Equations (Hinglish)
- Chapter 5: Arithmetic Progressions (Hinglish)
- Chapter 6: Triangles (Hinglish)
- Chapter 7: Coordinate Geometry (Hinglish)
- Chapter 8: Introduction to Trigonometry (Hinglish)
- Chapter 9: Some Applications of Trigonometry (Hinglish)
- Chapter 10: Circles (Hinglish)
- Chapter 11: Areas Related to Circles (Hinglish)
- Chapter 12: Surface Areas and Volumes (Hinglish)
- Chapter 13: Statistics (Hinglish)
- Chapter 14: Probability (Hinglish)
A
abscissaभुजThe x-coordinate. It tells how far a point is to the right (positive) or left (negative) of the y-axis.Ch 7 · Coordinate Geometryadjacent sideसंलग्न भुजाFor an acute angle of a right triangle, the side other than the hypotenuse that forms the angle.Ch 8 · Introduction to Trigonometryalternate anglesएकांतर कोणTwo angles on opposite sides of a line that cuts two other lines, between them. They are equal when the two lines are parallel.Ch 9 · Some Applications of Trigonometryaltitude of the Sunसूर्य का उन्नतांशThe angle of elevation of the Sun seen from the ground. The higher the Sun, the shorter the shadows.Ch 9 · Some Applications of Trigonometryangle of depressionअवनमन कोणThe angle between the line of sight and the horizontal when the point looked at is below eye level.Ch 9 · Some Applications of Trigonometryangle of elevationउन्नयन कोणThe angle between the line of sight and the horizontal when the point looked at is above eye level.Ch 9 · Some Applications of TrigonometryarcचापA part of a circle between two of its points. An arc of angle θ has length θ 360 × 2 π r.Ch 11 · Areas Related to Circlesarithmetic meanसमांतर माध्यThe number halfway between two numbers a and c, namely a + c 2.Ch 5 · Arithmetic Progressionsarithmetic progressionसमांतर श्रेढ़ीA list where every step from one term to the next adds the same number.Ch 5 · Arithmetic Progressionsassumed meanकल्पित माध्यA convenient value a, usually a middle class mark, from which the class marks are measured to make the arithmetic smaller.Ch 13 · Statisticsat randomयादृच्छयाChosen or thrown with no bias or control, so that every outcome keeps its natural chance.Ch 14 · ProbabilityB
Basic Proportionality Theoremआधारभूत समानुपातिकता प्रमेयA line parallel to one side of a triangle divides the other two sides in the same ratio.Ch 6 · TrianglesC
capacityधारिताThe volume of the space inside a container, often given in litres.Ch 12 · Surface Areas and VolumeschordजीवाA line segment joining two points of a circle.Ch 11 · Areas Related to Circlescircleवृत्तAll the points of a plane that are one fixed distance (the radius) from a fixed point (the centre).Ch 10 · CirclescircumscribeपरिगतA polygon circumscribes a circle when every side of the polygon is a tangent to the circle.Ch 10 · Circlesclass markवर्ग चिह्नThe mid-point of a class, (lower limit + upper limit) ÷ 2. It stands for every observation in the class.Ch 13 · Statisticsclass sizeवर्ग मापThe width of a class, upper limit minus lower limit, written h.Ch 13 · StatisticsclinometerA simple instrument for measuring angles of elevation or depression, such as a protractor with a straw and a hanging weight.Ch 9 · Some Applications of TrigonometrycoefficientगुणांकThe number that multiplies a power of the variable in a term, such as -4 in -4x².Ch 2 · Polynomialscoincident linesसंपाती रेखाएँTwo lines that lie exactly on top of each other, so every point is common.Ch 3 · Pair of Linear Equations in Two VariablescollinearसंरेखीLying on one straight line. For three points, the two shorter distances add up to the longest.Ch 7 · Coordinate Geometrycombination of solidsठोसों का संयोजनA solid made by joining two or more basic solids, such as a cone fixed on a hemisphere.Ch 12 · Surface Areas and Volumescommon differenceसार्व अंतरThe fixed number d added at each step of an AP: any term minus the term before it.Ch 5 · Arithmetic Progressionscomplementary eventsपूरक घटनाएँAn event E and the event not E, written E; exactly one of them happens, so P(E) + P(E) = 1.Ch 14 · Probabilitycomposite numberभाज्य संख्याA whole number greater than 1 with a factor other than 1 and itself, such as 9 or 91. The number 1 is neither prime nor composite.Ch 1 · Real Numbersconcentric circlesसंकेंद्रीय वृत्तCircles that have the same centre.Ch 10 · Circlescongruent figuresसर्वांगसम आकृतियाँFigures with the same shape and the same size.Ch 6 · Trianglesconsistent pairसंगतA pair of linear equations that has at least one solution.Ch 3 · Pair of Linear Equations in Two VariablesconverseविलोमThe statement made by swapping what is given and what is concluded in a theorem.Ch 6 · Trianglescoordinate geometryनिर्देशांक ज्यामितिThe study of geometry using coordinates, so that points, lines and shapes can be handled with algebra.Ch 7 · Coordinate Geometrycoprimeसहअभाज्यTwo integers are coprime when their only positive common factor is 1, like 8 and 15.Ch 1 · Real Numberscorresponding partsसंगत भागMatching vertices, sides and angles of two figures under a stated pairing of their vertices.Ch 6 · Trianglescosecant, secant, cotangentThe reciprocals of sine, cosine and tangent: cosec A = 1 sin A, sec A = 1 cos A, cot A = 1 tan A.Ch 8 · Introduction to Trigonometrycosineकोज्याcos A = side adjacent to A ÷ hypotenuse.Ch 8 · Introduction to Trigonometrycubic polynomialत्रिघात बहुपदA polynomial of degree 3, of the form ax³ + bx² + cx + d with a ≠ 0.Ch 2 · Polynomialscumulative frequencyसंचयी बारंबारताThe running total of the frequencies: the frequency of a class added to the frequencies of all the classes before it.Ch 13 · Statisticscurved surface areaवक्र पृष्ठीय क्षेत्रफलThe area of only the curved part of a solid's surface, leaving out its flat faces.Ch 12 · Surface Areas and VolumesD
degreeघातThe highest power of the variable in a polynomial, such as 3 for 2x³ - x + 5.Ch 2 · Polynomialsdensityघनत्वMass per unit volume. Iron has a density of about 7.8 g per cm³.Ch 12 · Surface Areas and Volumesdependent pairआश्रितA pair in which one equation is a multiple of the other, so both draw the same line and there are infinitely many solutions; it is also consistent.Ch 3 · Pair of Linear Equations in Two VariablesdeviationविचलनHow far a class mark is from the assumed mean: di = xi - a. It is negative below a.Ch 13 · Statisticsdiscriminantविविक्तकरThe number D = b² - 4ac. Its sign tells whether the roots are distinct, equal or not real.Ch 4 · Quadratic Equationsdistance formulaदूरी सूत्रHow far apart two points are, worked out from their coordinates: √ (x2 - x1)² + (y2 - y1)².Ch 7 · Coordinate GeometryE
elementary eventप्रारंभिक घटनाAn event made of exactly one outcome of an experiment.Ch 14 · Probabilityelimination methodविलोपन विधिSolving a pair by making one variable's coefficients equal, then adding or subtracting the equations to remove it.Ch 3 · Pair of Linear Equations in Two Variablesequal rootsबराबर मूलTwo roots with the same value, - b 2a; they occur when D = 0.Ch 4 · Quadratic Equationsequally likelyसमप्रायिकHaving the same chance of happening, because nothing in the set-up favours one outcome over another.Ch 14 · Probabilityequiangular trianglesसमानकोणिक त्रिभुजTwo triangles whose angles are equal in pairs.Ch 6 · Trianglesequidistantसमदूरस्थAt equal distances from two or more given points.Ch 7 · Coordinate GeometryeventघटनाA collection of outcomes of an experiment, such as an even number on a die.Ch 14 · Probabilityexperimental probabilityप्रायोगिक प्रायिकताThe fraction of trials in which an event actually happened.Ch 14 · ProbabilityF
face cardA jack, queen or king; a deck of 52 cards has 12 of them.Ch 14 · ProbabilityFactor Theoremगुणनखंड प्रमेयIf p(α) = 0, then x - α is a factor of p(x), and the other way round.Ch 2 · Polynomialsfactor treeगुणनखंड वृक्षA diagram that splits a number into two factors, again and again, until every branch ends in a prime.Ch 1 · Real Numbersfavourable outcomeअनुकूल परिणामAn outcome that makes a given event happen.Ch 14 · Probabilityfinite APपरिमित समांतर श्रेढ़ीAn AP with a last term, so it has a definite number of terms.Ch 5 · Arithmetic ProgressionsfrequencyबारंबारताThe number of times a value occurs, or the number of observations that fall in a class.Ch 13 · StatisticsFundamental Theorem of Arithmeticअंकगणित की आधारभूत प्रमेयEvery composite number is a product of primes, and this product is unique apart from the order of the factors.Ch 1 · Real NumbersG
general termव्यापक पदThe n th term an = a + (n - 1)d, a formula that gives every term of the AP.Ch 5 · Arithmetic ProgressionsH
HCF (highest common factor)महत्तम समापवर्तकThe largest whole number that divides each of the given numbers exactly.Ch 1 · Real Numbershemisphereअर्धगोलाHalf of a sphere, cut through its centre. Its curved surface is 2 π r² and its flat face is π r².Ch 12 · Surface Areas and Volumeshorizontalक्षैतिजThe level line through the observer's eye, parallel to level ground. Angles of elevation and depression are measured from it.Ch 9 · Some Applications of Trigonometryhypotenuseकर्णThe side opposite the right angle in a right triangle; it is the longest side.Ch 8 · Introduction to TrigonometryI
impossible eventअसंभव घटनाAn event with no favourable outcome; its probability is 0.Ch 14 · Probabilityinconsistent pairअसंगतA pair of linear equations that has no solution; its lines are parallel.Ch 3 · Pair of Linear Equations in Two Variablesinfinite APअपरिमित समांतर श्रेढ़ीAn AP that goes on for ever, with no last term.Ch 5 · Arithmetic Progressionsinternal divisionअंतः विभाजनA point P that lies between A and B, with AP: PB = m1: m2, is said to cut AB internally in that ratio.Ch 7 · Coordinate Geometryintersecting linesप्रतिच्छेदी रेखाएँTwo lines that cross at exactly one point.Ch 3 · Pair of Linear Equations in Two Variablesirrational numberअपरिमेय संख्याA real number that no fraction of two integers can equal, such as √ 2 or π.Ch 1 · Real NumbersL
LCM (lowest common multiple)लघुत्तम समापवर्त्यThe smallest positive whole number that is a multiple of each of the given numbers.Ch 1 · Real Numberslength of a tangentस्पर्श रेखा की लंबाईFor a point P outside a circle, the distance from P to the point of contact of a tangent drawn from P.Ch 10 · Circlesline of sightदृष्टि रेखाThe straight line from an observer's eye to the point being looked at.Ch 9 · Some Applications of Trigonometrylinear equation in two variablesदो चरों वाला रैखिक समीकरणAn equation that can be written as ax + by + c = 0, with a, b, c real and a, b not both zero. Its graph is a straight line.Ch 3 · Pair of Linear Equations in Two Variableslinear polynomialरैखिक बहुपदA polynomial of degree 1, of the form ax + b with a ≠ 0.Ch 2 · PolynomialsM
major sectorदीर्घ त्रिज्यखंडThe larger of the two sectors made by two radii, with angle 360 ° - θ.Ch 11 · Areas Related to Circlesmajor segmentदीर्घ वृत्तखंडThe larger segment cut off by a chord; its area is π r² minus the minor segment.Ch 11 · Areas Related to Circlesmeanमाध्यThe sum of all the observations divided by their number; for data with frequencies, Σ fixi ÷ Σ fi.Ch 13 · Statisticsmeasure of central tendencyकेंद्रीय प्रवृत्ति का मापA single number that represents a whole set of data: the mean, the median or the mode.Ch 13 · Statisticsmedianमाध्यकThe middle value of data arranged in order, so that half the observations lie below it and half above.Ch 13 · Statisticsmedian classमाध्यक वर्गThe first class whose cumulative frequency is greater than n 2; the median lies inside it.Ch 13 · Statisticsmidpointमध्य-बिंदुThe point halfway along a segment; its coordinates are the averages of the endpoints' coordinates.Ch 7 · Coordinate Geometryminor sectorलघु त्रिज्यखंडThe smaller of the two sectors made by two radii; its angle θ is less than 180 °.Ch 11 · Areas Related to Circlesminor segmentलघु वृत्तखंडThe smaller segment cut off by a chord; its area is the sector minus triangle OAB.Ch 11 · Areas Related to Circlesmodal classबहुलक वर्गThe class with the highest frequency in a grouped frequency distribution.Ch 13 · StatisticsmodeबहुलकThe value that occurs most often. For grouped data it is estimated inside the modal class with the mode formula.Ch 13 · StatisticsN
nature of rootsमूलों की प्रकृतिWhether a quadratic equation has two distinct real roots, two equal real roots or no real roots.Ch 4 · Quadratic Equationsnon-intersecting lineअप्रतिच्छेदी रेखाA line that has no point in common with a given circle.Ch 10 · CirclesnormalअभिलंबThe line through the centre of a circle and a point of contact; it is perpendicular to the tangent there.Ch 10 · CirclesO
opposite sideसम्मुख भुजाFor an acute angle of a right triangle, the side that does not touch the angle.Ch 8 · Introduction to TrigonometryordinateकोटिThe y-coordinate. It tells how far a point is above (positive) or below (negative) the x-axis.Ch 7 · Coordinate GeometryP
pair of linear equationsरैखिक समीकरण युग्मTwo linear equations in the same two variables, considered together.Ch 3 · Pair of Linear Equations in Two VariablesparabolaपरवलयThe U-shaped graph of a quadratic polynomial. It opens upward when a > 0 and downward when a < 0.Ch 2 · Polynomialsparallel linesसमांतर रेखाएँLines in a plane that never meet, however far they are drawn.Ch 3 · Pair of Linear Equations in Two Variablesperpendicular bisectorलंब समद्विभाजकThe line through the midpoint of a segment at right angles to it. Its points are equidistant from the two ends.Ch 7 · Coordinate Geometrypoint of contactस्पर्श बिंदुThe single point that a tangent shares with a circle.Ch 10 · Circlespoints of trisectionसमत्रिभाजन बिंदुThe two points that cut a segment into three equal parts, dividing it in 1: 2 and 2: 1.Ch 7 · Coordinate Geometryprime factorisationअभाज्य गुणनखंडनA number written as a product of primes, such as 60 = 2² × 3 × 5.Ch 1 · Real Numbersprime numberअभाज्य संख्याA whole number greater than 1 whose only factors are 1 and itself, such as 2, 7 or 13.Ch 1 · Real Numbersproof by contradictionA proof that assumes the opposite of the claim, reasons correctly to something impossible, and so rejects the assumption.Ch 1 · Real NumbersQ
quadrantचतुर्थांशA sector of angle 90 °, one quarter of a disc.Ch 11 · Areas Related to Circlesquadratic equationद्विघात समीकरणAn equation that can be written as ax² + bx + c = 0, with a, b, c real and a ≠ 0.Ch 4 · Quadratic Equationsquadratic formulaद्विघाती सूत्रx = -b ± √ b² - 4ac 2a, the roots of ax² + bx + c = 0 when b² - 4ac ≥ 0.Ch 4 · Quadratic Equationsquadratic polynomialद्विघात बहुपदA polynomial of degree 2, of the form ax² + bx + c with a ≠ 0.Ch 2 · PolynomialsR
rational numberपरिमेय संख्याA number equal to a fraction p q of two integers with q ≠ 0, such as 3 4 or -5.Ch 1 · Real Numbersreal numberवास्तविक संख्याAny rational or irrational number; together they fill the whole number line.Ch 1 · Real NumbersrootमूलA number that makes the equation true when put in place of x. A quadratic equation has at most two roots.Ch 4 · Quadratic EquationsS
scale factorस्केल गुणकThe common ratio of matching sides of two similar figures.Ch 6 · Trianglessecantछेदक रेखाA line that meets a circle at two points.Ch 10 · Circlessection formulaविभाजन सूत्रThe coordinates of the point dividing AB internally in the ratio m1: m2: x = m1x2 + m2x1 m1 + m2, and similarly for y.Ch 7 · Coordinate Geometrysectorत्रिज्यखंडThe region of a disc between two radii and the arc joining their ends.Ch 11 · Areas Related to Circlessegmentवृत्तखंडThe region of a disc between a chord and one of the arcs it cuts off.Ch 11 · Areas Related to Circlessimilar figuresसमरूप आकृतियाँFigures that have one shape, whatever their sizes: one is an exact enlargement or reduction of the other.Ch 6 · Trianglessimilarity criterionसमरूपता की कसौटीA short set of facts (AA, SSS or SAS) that is enough to prove two triangles similar.Ch 6 · Trianglessineज्याsin A = side opposite A ÷ hypotenuse.Ch 8 · Introduction to Trigonometryslant heightतिर्यक ऊँचाईThe length along a cone's sloping side from the tip to the rim of the base: l = √ r² + h².Ch 12 · Surface Areas and Volumessolution of a pairहलValues of x and y that satisfy both equations of the pair at the same time.Ch 3 · Pair of Linear Equations in Two Variablessplitting the middle termमध्य पद का विभाजनWriting bx as two terms whose coefficients have product ac and sum b, so the expression factorises in pairs.Ch 4 · Quadratic Equationsstandard formमानक रूपA quadratic equation written as ax² + bx + c = 0: every term on the left, in falling powers of x.Ch 4 · Quadratic Equationssubstitution methodप्रतिस्थापन विधिSolving a pair by writing one variable in terms of the other and putting that expression into the other equation.Ch 3 · Pair of Linear Equations in Two Variablessure eventनिश्चित घटनाAn event for which every outcome is favourable; its probability is 1.Ch 14 · ProbabilityT
tangentस्पर्श रेखाA line that meets a circle at exactly one point, its point of contact.Ch 10 · Circlestangent (ratio)स्पर्शज्याtan A = side opposite A ÷ side adjacent to A; also sin A cos A.Ch 8 · Introduction to TrigonometrytermपदOne number in a list; an is the term in position n.Ch 5 · Arithmetic Progressionstheoretical probabilityसैद्धांतिक प्रायिकताFor equally likely outcomes, P(E) = m n: favourable outcomes divided by all possible outcomes.Ch 14 · Probabilitytotal surface areaकुल पृष्ठीय क्षेत्रफलThe area of the whole outer surface of a solid: its curved parts and flat faces together.Ch 12 · Surface Areas and Volumestrigonometric identityत्रिकोणमितीय सर्वसमिकाAn equation in trigonometric ratios that is true for every angle for which both sides are defined.Ch 8 · Introduction to Trigonometrytrigonometric ratioत्रिकोणमितीय अनुपातA ratio of two sides of a right triangle taken for one of its acute angles, such as sin A or cos A.Ch 8 · Introduction to Trigonometrytrigonometric ratioत्रिकोणमितीय अनुपातA ratio of two sides of a right triangle, tied to one of its acute angles, such as tan θ = opposite adjacent.Ch 9 · Some Applications of Trigonometrytrigonometryत्रिकोणमितिThe branch of mathematics that studies how the sides and angles of triangles are related.Ch 8 · Introduction to TrigonometryV
volumeआयतनThe amount of space a solid takes up, measured in cubic units such as cm³.Ch 12 · Surface Areas and VolumesZ
zero of a polynomialबहुपद का शून्यकA real number k with p(k) = 0. On the graph of y = p(x) it is where the curve meets the x -axis.Ch 2 · Polynomialszero of a polynomialशून्यकA value of x at which the polynomial equals 0; the zeroes of ax² + bx + c are the roots of ax² + bx + c = 0.Ch 4 · Quadratic Equationsncert.ai is an independent learning companion aligned to the NCERT curriculum. It is not affiliated with or endorsed by NCERT.