Syllabus

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Chapter name

1. Orienting Yourself: The Use of Coordinates

• 1.1 Introduction
• 1.2 Settling In
• 1.3 The 2-d Cartesian Coordinate System
• 1.4 Distance Between Two Points in the 2-D Plane

1. Introduction to Linear Polynomials

• 2.1 Introduction
• 2.2 Linear Polynomials
• 2.3 Exploring linear patterns
• 2.4. Linear growth and linear decay
• 2.5 Linear Relationships
• 2.6 Visualising linear relationships

1. The World of Numbers

• 3.1. The Dawn of Mathematics: The Human Need to Count
• 3.1.1 A History Written in Bone
• 3.1.2 The Indian Context: Trade and Astronomy
• 3.2.2 The Bakh?h?l? Manuscript and Brahmagupta’s Rules
• 3.3 Integers: Expanding the Horizon
• 3.3.1 The Arithmetic of Integers
• 3.4 Filling the Spaces: Fractions and Rational Numbers
• 3.4.1 Representation of Rational Numbers on the Number Line
• 3.4.2 The Density of Rational Number
• 3.5 Irrational Numbers
• 3.5.1 The Proof of Irrationality of
• 3.5.2 Construction of Length
• 3.5.3 The Story of Pi (π) and Madhava’s Infinite Series
• 3.6 Real Numbers: Decimals and Cyclic Patterns
• 3.6.1 Rational Decimals: Terminating and Repeating
• 3.6.2 The Magic of Cyclic Numbers
• 3.6.3 Irrational Decimals: Chaos and Infinity
• 3.7 Conclusion: The Never-Ending Journey

1. Exploring Algebraic Identities

• 4.1 Introduction
• 4.2 Visualising Identities
• 4.3 Factorisation of Algebraic Expressions Using Identities
• 4.4. More Identities
• 4.5 Factorisation Using Algebra Tiles
• 4.6 Factorisation Without Using Algebra Tiles
• 4.7 Finding New Identities
• 4.8 Simplifying Rational Expressions

1. I’m Up and Down, and Round and Round

• 5.1 Definitions
• 5.2 Symmetries of a Circle
• 5.3 How Many Circles?
• 5.4 Chords and the Angles They Subtend
• 5.5 Midpoints and Perpendicular Bisectors of Chords
• 5.6 Distance of Chords from the Centre
• 5.6.1 Which of the two unequal chords is farther from the centre?
• 5.7 Angles Subtended by an Arc
• 5.7.1 Angle subtended by an arc at a point on the circle outside the arc
• 5.8 Concyclicity of Points

1. Measuring Space: Perimeter and Area

• 6.1 Perimeter of a Shape
• 6.2 Perimeter of a Circle —The C/D Ratio
• 6.3 π Is Irrational
• 6.4 Length of an Arc of a Circle
• 6.5 Problems, Puzzles, and Paradoxes on Perimeter
• 6.6 Area of a Rectangle
• 6.7 Area of a Parallelogram
• 6.8 Area of a Triangle
• 6.8.1 Heron’s formula
• 6.9 Squaring a Rectangle
• 6.10 Area of a Circle
• 6.10.1 Area of Sector of a Circle

1. The Mathematics of Maybe: Introduction to Probability

• 7.1 What is Probability?
• 7.1.1 What is Randomness?
• 7.1.2 The Probability Scale
• 7.2 Measuring Probability Objectively
• 7.2.1 Experimental Probability: Performing Observations or Experiments
• 7.2.2 Theoretical Probability
• 7.2.3 Analysing Statistical Data Using Probability
• 7.3 Elements of Probability: Sample Spaces and Events
• 7.3.1 Sample Space
• 7.3.2 Events
• 7.4 Tree diagrams

1. Predicting What Comes Next: Exploring Sequences and Progressions

• 8.1 Introduction to Sequences
• 8.2 Explicit Rule for a Sequence
• 8.3 Recursive Rule for a Sequence
• 8.4 Arithmetic Progressions
• 8.4.1 Visualising an AP
• 8.5 Sum of the First n Natural Numbers
• 8.6 Geometric Progressions
• 8.6.1 Fun with Fractals
• 8.6.2 Visualising a GP

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