Class 9 Mathematics

Chapters

1. 1Coordinates and Distance in the PlaneLesson: Coordinates and Distance in the Plane · 15 sections · chapter quiz

   A delivery app needs to tell a rider exactly where a house is. A cinema seat is 'row F, seat 12'. Coordinates give every point on a flat surface a precise address.

   • • I can locate and plot points using the 2-D Cartesian coordinate system.
   • • I can identify quadrants, axes and the origin and describe positions precisely.
   • • I can find the distance between two points using the distance formula and explain why it works.
2. 2Linear Polynomials and Linear RelationshipsLesson: Linear Polynomials and Linear Relationships · 15 sections · chapter quiz

   A taxi charges ₹40 plus ₹15 per km. A candle shortens by 2 cm every hour. Both change by the same amount at every step — these are linear relationships, described by linear polynomials.

   • • I can identify polynomials, their degree and linear polynomials ax + b.
   • • I can find the value and zero of a linear polynomial.
   • • I can model linear growth and decay and represent linear relationships by tables and graphs.
3. 3The World of Numbers: Real NumbersLesson: The World of Numbers: Real Numbers · 15 sections · chapter quiz

   People first needed numbers to count sheep; then zero and negatives; then fractions for sharing. But the diagonal of a unit square is a length no fraction can describe exactly. The story of numbers keeps expanding.

   • • I can classify numbers as natural, whole, integers, rational and irrational.
   • • I can show that between any two rationals there is another (density) and represent rationals on the number line.
   • • I can prove that √2 is irrational and relate decimals to rational and irrational numbers.
4. 4Exploring Algebraic Identities and FactorisationLesson: Exploring Algebraic Identities and Factorisation · 15 sections · chapter quiz

   Algebra tiles turn identities into pictures: a big square split into smaller squares and rectangles shows (a + b)² = a² + 2ab + b² at a glance. In Class 9 we extend these ideas to cubes and to factorising.

   • • I can visualise and prove identities such as (a + b)², (a − b)², (a + b)(a − b) and (a + b + c)².
   • • I can use identities for cubes: (a + b)³, (a − b)³ and a³ + b³ + c³ − 3abc.
   • • I can factorise polynomials and simplify rational expressions.
5. 5Circles: Chords, Arcs and AnglesLesson: Circles: Chords, Arcs and Angles · 15 sections · chapter quiz

   A Ferris wheel goes up and down and round and round. Wheels, bangles and the rim of a well are circles — perhaps the most symmetric shape of all — and they hide elegant theorems.

   • • I can use the vocabulary of circles: centre, radius, chord, diameter, arc, segment, sector.
   • • I can prove and use properties of chords: equal chords subtend equal angles, the perpendicular from the centre bisects a chord, equal chords are equidistant from the centre.
   • • I can use the angle subtended by an arc at the centre and on the circle, and recognise concyclic points.
6. 6Measuring Space: Perimeter and AreaLesson: Measuring Space: Perimeter and Area · 15 sections · chapter quiz

   A running track has straight parts and semicircular ends. How long is one lap, and how much grass is inside? Measuring space combines perimeter and area — and circles bring in the remarkable number π.

   • • I can find perimeters of polygons and circles and explain π as the ratio C/D.
   • • I can find arc lengths and areas of rectangles, parallelograms, triangles (including Heron's formula) and circles.
   • • I can reason about perimeter-and-area puzzles and paradoxes.
7. 7Introduction to ProbabilityLesson: Introduction to Probability · 15 sections · chapter quiz

   Weather forecasts say '70% chance of rain'. Cricket captains call a toss. Doctors talk about risks. Probability is the mathematics of maybe — it measures uncertainty with numbers.

   • • I can describe probability as a number from 0 to 1 measuring how likely an event is.
   • • I can list sample spaces and find theoretical probabilities of events.
   • • I can use experiments, simulations and tree diagrams to estimate and compute probabilities.
8. 8Sequences and ProgressionsLesson: Sequences and Progressions · 15 sections · chapter quiz

   Seats in a theatre increase by 2 each row; a bacteria colony doubles every hour. Predicting what comes next requires rules for sequences.

   • • I can describe sequences using explicit and recursive rules.
   • • I can find the nth term of arithmetic and geometric progressions.
   • • I can find the sum of the first n natural numbers and of an AP, and explain the method.
9. 9Propositions and Their ConversesLesson: Propositions and Their Converses · 15 sections · chapter quiz

   'If it is raining, the ground is wet.' Is the reverse — 'if the ground is wet, it is raining' — also true? Not necessarily! Mathematics needs to be careful about which way an implication works.

   • • I can identify propositions in 'if … then …' form with hypothesis and conclusion.
   • • I can write the converse of a proposition and decide whether it is true.
   • • I can use counterexamples and proofs to justify mathematical claims.
10. 10How Quantities Combine: Averages, Mixtures and DataLesson: How Quantities Combine: Averages, Mixtures and Data · 15 sections · chapter quiz

    Section A of 30 students averaged 70 marks and section B of 20 students averaged 80. Is the class average 75? No! Understanding how quantities combine prevents such mistakes.

    • • I can compute weighted averages and explain why an 'average of averages' can mislead.
    • • I can solve mixture problems using weighted averages.
    • • I can find mean, median and mode of data and interpret graphs including histograms and frequency polygons.
11. 11The World of AlgorithmsLesson: The World of Algorithms · 15 sections · chapter quiz

    Every time you search a map for the fastest route or a phone sorts your photos, an algorithm is at work. In fact, you have used algorithms since Class 1 — for adding numbers digit by digit!

    • • I can describe an algorithm as a precise, finite sequence of steps.
    • • I can write and follow algorithms for adding numbers, listing divisors and finding the GCD (including Euclid's algorithm).
    • • I can compare algorithms for efficiency and describe simple data structures such as lists and stacks.
12. 12Quadrilaterals: Parallelograms and TilingsLesson: Quadrilaterals: Parallelograms and Tilings · 15 sections · chapter quiz

    Builders check that a frame is a parallelogram by measuring its diagonals; artists cover walls with any four-sided tile shape. Proofs show why these methods always work.

    • • I can define quadrilaterals precisely and classify them.
    • • I can prove properties of parallelograms and the conditions that make a quadrilateral a parallelogram.
    • • I can prove and apply the mid-point theorem and explain why any quadrilateral tiles the plane.
13. 13Two Variables, One Line: Linear EquationsLesson: Two Variables, One Line: Linear Equations · 15 sections · chapter quiz

    Two pens and three notebooks cost ₹110. One equation, two unknowns — many answers. Add a second fact, and there may be exactly one answer. Lines on a graph show why.

    • • I can write linear equations in two variables in standard form ax + by + c = 0 and find solutions.
    • • I can graph a linear equation and use slope-intercept form y = mx + c.
    • • I can solve a pair of linear equations by substitution, elimination and graphs, and interpret the result.
14. 14Math of Space: Surface Area and VolumeLesson: Math of Space: Surface Area and Volume · 15 sections · chapter quiz

    How much tin is needed for a can, how much water fills a tank, and how much ice cream fits in a cone? Surface area measures covering; volume measures filling.

    • • I can find surface areas and volumes of cuboids, cubes, cylinders, cones and spheres/hemispheres.
    • • I can explain where formulas come from using nets, slicing and comparisons.
    • • I can apply surface area and volume to real objects and pyramids.