NCERT Ganitha Manjari Class 9 Maths Part II textbook, Chapters 9 to 14, Download
Ganita Manjari Grade 9 Part 2 (CBSE): Chapter-wise Guide, Topics and Keywords
A quick, mobile-friendly map of the NCERT Class 9 Mathematics Part II textbook: what each of Chapters 9 to 14 teaches, what to revise, and chapter-wise PDFs you can download.
Ganita Manjari Grade 9 Part 2 is the new NCERT Class 9 Mathematics textbook for CBSE students. Part II continues Part I and moves learners from middle-school arithmetic into reasoning and proof, data, algorithms, geometry, algebra and solid shapes across Chapters 9 to 14. The title joins Ganita (mathematics) and Manjari (a bouquet of flowers): each chapter is one petal.
Each chapter has Think and Reflect prompts, practice sets after every section and end-of-chapter exercises. Problems and sections marked with an asterisk (*) are enrichment and are not assessed in examinations.
Chapter 9: Propositions and their Converses
Number theory and geometry | Textbook pages 1 to 7
Chapter 9, Propositions and their Converses, is the first chapter of Ganita Manjari Class 9 Part 2 and your introduction to mathematical proof. You learn to write if-then statements, frame the converse of a statement, and decide whether each is true or false. A single counterexample in maths is enough to disprove a claim, as Euler did against Fermat's primes. Worked examples cover perfect squares and their factors, multiples of 3 and 6, and the converse of the Baudhayana-Pythagoras theorem, with practice in Exercise Set 9.1.
What to revise
- Proposition, converse, counterexample
- Perfect squares and the number of factors
- Baudhayana-Pythagoras theorem and its converse
- Fermat's claim about primes and Euler's counterexample
Chapter 10: How Quantities Combine: Understanding Data
Statistics and data | Textbook pages 8 to 36
Chapter 10, How Quantities Combine: Understanding Data, extends the average into the weighted average (weighted mean). You see why a plain average of averages can fail, and how the weighted mean formula handles groups of different sizes, mixtures and concentration, marks with custom weights, and rating systems. The second half of data interpretation for Class 9 compares the stacked bar chart with the 100% stacked bar chart: one keeps totals visible, the other shows proportions, much like a pie chart. Historical notes cover Brahmagupta and Sridharacharya, and the chapter ends with projects on rating schemes and family budgets.
What to revise
- Average of averages and when it works (equal group sizes)
- Weighted mean formula for mixtures and custom weights
- Simple average vs weighted average
- Reading stacked and 100% stacked bar charts, and what each cannot show
Chapter 11: The World of Algorithms
Computational thinking | Textbook pages 37 to 50
Chapter 11, The World of Algorithms, answers "what is an algorithm?" as a clear step-by-step procedure. It begins with the algorithm for addition, then builds a gcd algorithm (the greatest common divisor, also called HCF) using a list of divisors. It progresses to Euclid's subtraction method and the faster Euclid's division algorithm, the same idea as the Aryabhata division method. A short history of Al-Khwarizmi explains where the word comes from, and the chapter is a gentle start to computational thinking in Class 9.
What to revise
- Addition algorithm with carry
- Lists and divisors of a number
- gcd(375, 825) = 75 by each method
- Euclid's algorithm with "m mod n"
- Origin of the word "algorithm" (Al-Khwarizmi)
Chapter 12: Quadrilaterals
Geometry | Textbook pages 51 to 84
Chapter 12, Quadrilaterals, defines a quadrilateral precisely and separates convex and non-convex quadrilaterals. You study the properties of a parallelogram, prove the converses of the parallelogram theorems, and use the equal-and-parallel-sides test. Next come the Midpoint Theorem and its converse, the Centroid Theorem (medians meet in a 2:1 ratio) and the Varignon parallelogram. The chapter closes with tiling the plane using any quadrilateral.
What to revise
- Theorems 1 to 5 on parallelograms and their converses
- Midpoint Theorem and its converse (Theorems 6 and 7)
- Centroid Theorem (Theorem 8) and Varignon parallelogram (Theorem 9)
- Tiling the plane; aperiodic "hat" tile (enrichment)
Chapter 13: Two Variables, One Line
Algebra and graphs | Textbook pages 85 to 122
Chapter 13, Two Variables, One Line, covers linear equations in two variables for Class 9: the standard form ax + by + c = 0, solutions as ordered pairs and their graphs. You then learn the slope of a line and the slope-intercept form y = mx + d. A pair of linear equations is solved by the substitution method, the elimination method and the graphical method. The ratios a1/a2, b1/b2 and c1/c2 tell you whether a pair has a unique solution, no solution or infinitely many solutions (parallel and coincident lines), with plenty of word problems.
What to revise
- Standard form, solutions and graph of a line
- Slope = rise / run; slope-intercept form
- Substitution and elimination methods
- Consistent, parallel and coincident lines
Chapter 14: Math of Space: Surface Area and Volume
Mensuration | Textbook pages 123 to 148
Chapter 14, Math of Space: Surface Area and Volume, is the mensuration chapter of Class 9 Part 2. It builds the cuboid and cube formulas, the curved surface area of a cylinder, the volume of a cone with its slant height, the volume of a pyramid, and the surface area of a sphere (4πr²) and hemisphere, following Archimedes. Hands-on activities and guesstimate problems show how to reason with assumptions. The table below is a quick set of mensuration formulas for Class 9.
| Solid | Surface area | Volume |
|---|---|---|
| Cuboid | 2(lw + wh + lh) | lwh |
| Cylinder | CSA 2πrh; TSA 2πr(h + r) | πr²h |
| Cone | CSA πrl; TSA πr(l + r) | ⅓πr²h |
| Sphere | 4πr² | ⁴⁄₃πr³ |
| Hemisphere | CSA 2πr²; TSA 3πr² | ⅔πr³ |
Download chapter-wise PDFs
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Prelims and Contents
Foreword, About the Book, notes for teachers and students
Download Prelims PDFForeword, contents, notesChapter 10
How Quantities Combine: Understanding Data
Download Chapter 10 PDFNCERT Ganita Manjari, Part IIChapter 14
Math of Space: Surface Area and Volume
Download Chapter 14 PDFNCERT Ganita Manjari, Part IIStudy tips for Class 9 Maths Part 2
- Attempt each Think and Reflect prompt before reading on; they preview the next idea.
- For every theorem in Chapter 12, write its converse and decide if it is true.
- In Chapter 13, check answers by substituting them into both equations.
- Learn the Chapter 14 table and always state units (cm², cm³).
Frequently asked questions
How many chapters are in Ganita Manjari Grade 9 Part 2?
Six, numbered 9 to 14: Propositions and their Converses, How Quantities Combine, The World of Algorithms, Quadrilaterals, Two Variables One Line, and Math of Space.
Are starred (*) questions asked in exams?
No. The textbook marks them as enrichment, not for assessment or examinations.
Which chapter has the most formulas?
Chapter 14, Math of Space, with surface area and volume formulas for six kinds of solids.
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