Class 9 · Mathematics · English medium · Part 2
Ganita Manjari Part 2: Class 9 Maths companion
Textbook of Mathematics for Grade 9 (Part II)
An interactive companion to Ganita Manjari (Grade 9 mathematics, Part 2): original explanations, live explorers, worked examples and practice for propositions, data, algorithms, quadrilaterals, linear equations and solids.
An original companion to Ganita Manjari, NCERT Class 9 Mathematics (2026–27 edition). Official textbook ↗ ncert.nic.in
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Chapters
- ENHinglish
Chapter 9: Propositions and their Converses (Propositions and Converses)
A proposition is a sentence that is either true or false. - ENHinglish
Chapter 10: How Quantities Combine: Understanding Data
Class 9 maths (Ganita Manjari Part 2, Chapter 10). - ENHinglish
Chapter 11: The World of Algorithms
Chapter 11 introduces algorithms: finite lists of exact steps that solve every problem of a kind. - ENHinglish
Chapter 12: Quadrilaterals
Parallelograms, midpoints, medians and tilings - ENHinglish
Chapter 13: Two Variables, One Line (Pair of Linear Equations)
The chapter defines linear equations in two variables in standard form , shows that each has infinitely many solutions (ordered pairs) which - ENHinglish
Chapter 14: Math of Space: Surface Area and Volume
Wrapping and filling boxes, tins, cones, pyramids and balls
Also in Hinglish
- Chapter 9: Propositions aur unke Converses (Hinglish)
- Chapter 10: Quantities Kaise Judti Hain: Data Ko Samajhna (Hinglish)
- Chapter 11: Algorithms ki Duniya (Hinglish)
- Chapter 12: Quadrilaterals (Hinglish)
- Chapter 13: Do Variables, Ek Line (Hinglish)
- Chapter 14: Math of Space: Surface Area aur Volume (Hinglish)
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100% stacked bar chartA stacked bar chart whose bars all have the same length, standing for 100%, so each piece shows a share.Ch 10 · How Quantities Combine: Understanding DataA
algorithmकलन-विधिA finite list of exact steps that, followed in order, solves every problem of a given kind.Ch 11 · The World of AlgorithmsB
basic stepमूल चरणAn action an algorithm uses without explaining it, because we can already do it, such as adding two digits.Ch 11 · The World of AlgorithmsC
centroidकेंद्रकThe point where the three medians of a triangle meet, two-thirds of the way along each median from its vertex.Ch 12 · Quadrilateralsclustered bar chartA bar chart that stands related bars side by side in groups (clusters), every bar starting at 0.Ch 10 · How Quantities Combine: Understanding DatacoefficientगुणांकThe number that multiplies a variable, such as 3 in 3x.Ch 13 · Two Variables, One Linecoincident linesसंपाती रेखाएँTwo equations whose graphs are the same line, so every point is shared.Ch 13 · Two Variables, One Lineconcentrationसांद्रताThe fraction or percentage of a mixture that is one particular substance, such as sugar in a drink.Ch 10 · How Quantities Combine: Understanding DataconcurrentसंगामीLines that all pass through one common point.Ch 12 · QuadrilateralsconeशंकुA solid with a circular base joined to one apex; a right circular cone has its apex directly above the centre.Ch 14 · Math of Space: Surface Area and Volumecongruentसर्वांगसमTwo figures are congruent when one can be placed exactly on the other: they have the same shape and the same size.Ch 9 · Propositions and their ConversesconverseविलोमThe proposition you get by swapping the 'if' part and the 'then' part: the converse of 'if X then Y ' is 'if Y then X '.Ch 9 · Propositions and their ConversesconverseविलोमThe statement if B then A made from if A then B. It needs its own proof.Ch 12 · Quadrilateralsconvex quadrilateralउत्तल चतुर्भुजA quadrilateral whose internal angles are all less than 180 °. A non-convex one has a dent, where one angle is more than 180 °.Ch 12 · Quadrilateralscounterexampleप्रत्युदाहरणOne particular case that makes the 'if' part of a proposition true and its 'then' part false. One counterexample is enough to show the proposition is false.Ch 9 · Propositions and their Conversescross-sectionअनुप्रस्थ काटThe flat shape made by one thin, straight slice through a solid.Ch 14 · Math of Space: Surface Area and VolumecubeघनA cuboid whose length, width and height are equal.Ch 14 · Math of Space: Surface Area and VolumecuboidघनाभA box-shaped solid with six rectangular faces meeting at right angles.Ch 14 · Math of Space: Surface Area and Volumecurved surface areaवक्र पृष्ठीय क्षेत्रफलThe area of only the curved part of a cylinder, cone or sphere.Ch 14 · Math of Space: Surface Area and VolumeD
data structureडेटा संरचनाA way of organising the values an algorithm works with, such as a sorted list.Ch 11 · The World of Algorithmsdiagonalविकर्णA segment joining two vertices of a polygon that are not ends of the same side.Ch 12 · QuadrilateralsdivisorभाजकA whole number that divides a given number with remainder 0.Ch 11 · The World of AlgorithmsE
efficiencyदक्षताHow much work an algorithm needs, judged by how its number of basic steps grows with the size of the input.Ch 11 · The World of Algorithmselimination methodविलोपन विधिSolving a pair by matching the coefficients of one variable and adding or subtracting so that it cancels.Ch 13 · Two Variables, One Lineexecuteनिष्पादित करनाTo carry out the steps of an algorithm one by one for a particular input.Ch 11 · The World of AlgorithmsF
factor pairTwo whole numbers whose product is a given number, such as 4 and 9 for 36. A pair may use one number twice, as in 6 × 6.Ch 9 · Propositions and their ConversesG
graph of an equationआलेखThe set of all points whose coordinates satisfy the equation; for a linear equation it is a straight line.Ch 13 · Two Variables, One Linegreatest common divisorमहत्तम समापवर्तकThe largest whole number that divides each of two given numbers exactly.Ch 11 · The World of AlgorithmsguesstimateअनुमानA reasoned estimate made with a simple model and stated assumptions when exact data are missing.Ch 14 · Math of Space: Surface Area and VolumeH
hemisphereअर्धगोलाHalf of a sphere cut by a plane through its centre.Ch 14 · Math of Space: Surface Area and VolumeI
if and only ifयदि और केवल यदि' X if and only if Y ', written X Leftrightarrow Y, says that a proposition and its converse are both true.Ch 9 · Propositions and their Conversesimplies' X implies Y ', written X ⇒ Y, means the same as 'if X then Y ': whenever X is true, Y is true too.Ch 9 · Propositions and their Conversesintersecting linesप्रतिच्छेदी रेखाएँLines that meet at exactly one point.Ch 13 · Two Variables, One LineL
linear equation in two variablesदो चरों वाला रैखिक समीकरणAn equation that can be written as ax + by + c = 0, with a and b not both zero.Ch 13 · Two Variables, One LinelistसूचीAn ordered row of values in square brackets, such as [1, 3, 9]; new values are appended at the end.Ch 11 · The World of AlgorithmsM
meanमाध्यThe sum of a set of values divided by the number of values; also called the average.Ch 10 · How Quantities Combine: Understanding Datamedianमाध्यिकाA segment joining a vertex of a triangle to the midpoint of the opposite side.Ch 12 · Quadrilateralsmodशेषफलm bmod n is what is left over after taking as many whole lots of n out of m as possible.Ch 11 · The World of AlgorithmsN
non-planar 4-gonA four-sided figure whose four corners do not all lie in one plane, like a card folded along a diagonal.Ch 12 · QuadrilateralsO
ordered pairक्रमित युग्मTwo numbers written as (x, y), where the order matters: (4, 3) and (3, 4) are different.Ch 13 · Two Variables, One LineP
pair of linear equationsरैखिक समीकरण युग्मTwo linear equations in the same two variables, considered together.Ch 13 · Two Variables, One Lineparallel linesसमांतर रेखाएँLines in a plane that never meet; they have equal slopes.Ch 13 · Two Variables, One Lineparallelogramसमांतर चतुर्भुजA quadrilateral whose opposite sides are parallel.Ch 12 · Quadrilateralsperfect squareपूर्ण वर्गA whole number that equals some whole number multiplied by itself, such as 49 = 7 × 7.Ch 9 · Propositions and their Conversespie chartपाई चार्टA circle divided into slices whose angles are in proportion to the parts of a whole.Ch 10 · How Quantities Combine: Understanding DatapropositionकथनA sentence that is either true or false, but not both. A false sentence such as ' 15 is a multiple of 4 ' is still a proposition.Ch 9 · Propositions and their ConversespyramidपिरामिडA solid with a flat base whose every point is joined to one apex outside the base.Ch 14 · Math of Space: Surface Area and VolumeQ
quadrilateralचतुर्भुजA flat figure made of four segments joining four points, no three on a line, in which the sides meet only at shared corners.Ch 12 · QuadrilateralsR
right circular cylinderलंब वृत्तीय बेलनA solid with two equal parallel circular ends whose axis is perpendicular to them.Ch 14 · Math of Space: Surface Area and VolumeS
self-intersecting 4-gonA four-sided figure in which two sides cross each other; it is not counted as a quadrilateral here.Ch 12 · QuadrilateralsshareA part written as a fraction or percentage of its whole; 180 L out of 500 L is a 36% share.Ch 10 · How Quantities Combine: Understanding Dataslant heightतिर्यक ऊँचाईThe distance from a cone's apex to its rim along the surface: l = √ h² + r².Ch 14 · Math of Space: Surface Area and VolumeslopeढालThe steepness of a line: rise divided by run between any two of its points.Ch 13 · Two Variables, One Lineslope-intercept formढाल-अंतःखंड रूपThe form y = mx + d, which shows the slope m and the y -intercept d directly.Ch 13 · Two Variables, One LinesolutionहलValues of x and y that, used together, make both sides of the equation equal.Ch 13 · Two Variables, One LinesphereगोलाAll points in space at a fixed distance r from a centre.Ch 14 · Math of Space: Surface Area and Volumestacked bar chartA bar chart in which the parts of each whole are joined end to end, so the full bar shows the total.Ch 10 · How Quantities Combine: Understanding Datastandard formमानक रूपThe layout ax + by + c = 0, with every term on one side and 0 on the other.Ch 13 · Two Variables, One Linesubstitution methodप्रतिस्थापन विधिSolving a pair by writing one variable in terms of the other and putting it into the other equation.Ch 13 · Two Variables, One Linesurface areaपृष्ठीय क्षेत्रफलThe total area of the outside of a solid, in square units.Ch 14 · Math of Space: Surface Area and VolumeT
tilingA covering of the plane by copies of one or more shapes, with no gaps and no overlaps.Ch 12 · Quadrilateralstotal surface areaसंपूर्ण पृष्ठीय क्षेत्रफलThe area of every face of a solid, flat and curved, added together.Ch 14 · Math of Space: Surface Area and VolumeV
variableचरA name for a value that an algorithm keeps track of and may change, such as carry or best.Ch 11 · The World of AlgorithmsVarignon parallelogramThe parallelogram formed by joining the midpoints of the sides of a quadrilateral in order.Ch 12 · QuadrilateralsvolumeआयतनThe amount of space a solid occupies or a container holds, in cubic units.Ch 14 · Math of Space: Surface Area and VolumeW
weightभारIn a weighted mean, the number that says how much a value counts: a group's size, an amount mixed, or an importance.Ch 10 · How Quantities Combine: Understanding Dataweighted meanभारित माध्यThe sum of each value times its weight, divided by the sum of the weights.Ch 10 · How Quantities Combine: Understanding DataY
y-intercepty-अंतःखंडThe value d where a line meets the y -axis, at the point (0, d).Ch 13 · Two Variables, One Linencert.ai is an independent learning companion aligned to the NCERT curriculum. It is not affiliated with or endorsed by NCERT.