CONTENT
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1. Real Numbers
1.1 Introduction
1.2 Euclid’s Division Lemma
1.3 The Fundamental Theorem of Arithmetic
1.4 Revisiting Irrational Numbers
1.5 Revisiting Rational Numbers and Their Decimal Expansions
1.6 Summary
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2. Polynomials
2.1 Introduction
2.2 Geometrical Meaning of The Zeroes of a polynomial
2.3 Relationship between Zeroes and Coefficients of a polynomial
2.4 Division Algorithm for Polynomials
2.5 Summary
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3. Pair of Linear Equations in Two Variables
3.1 Introduction
3.2 Pair of Linear Equations in Two Variables
3.3 Graphical Method of Solution of a Pair of Linear Equations
3.4 Algebraic Methods of Solving a Pair of Linear Equations
3.4.1 Substitution Method
3.4.2 Elimination Method
3.4.3 Cross-Multiplication Method
3.5 Equations Reducible to a Pair of Linear Equations in Two Variables
3.6 Summary
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4. Quadratic Equations
4.1 Introduction
4.2 Quadratic Equations
4.3 Solution of a Quadratic Equation by Factorisation
4.5 Nature or Roots
4.6 Summary
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5. Arithmetic Progressions
5.1 Introduction
5.2 Arithmetic Progressions
5.3 nth Term of an AP
5.4 Sum of First n Terms of an AP
5.5 Summary
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6. Triangles
6.1 Introduction
6.2 Similar Figures
6.3 Similarity of Triangles
6.4 Criteria for Similarity Triangles
6.5 Areas of Similar Triangles
6.6 Pythagoras Theorem
6.7 Summary
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7. Coordinate Geometry
7.1 Introduction
7.2 Distance Formula
7.3 Section Formula
7.4 Area of a Triangle
7.5 Summary
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8. Introduction to Trigonometry
8.1 Introduction
8.2 Trigonometric
8.3 Trigonometric Rations of Some Specific Angles
8.4 Trigonometric Rations of Complementary Angles
8.5 Trigonometric Identities
8.6 Summary
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9.Some Applications of Trigonometry
9.1 Introduction
9.2 Heights and Distances
9.3 Summary
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10. Circles
10.1 Introduction
10.2 Tangent to a Circle
10.3 Number of Tangents from a Point on a Circle
10.4 Summary
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11. Constructions
11.1 Introduction
11.2 Division of a Line Segment
11.3 Construction of Tangents to a Circle
11.4 Summary
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12. Areas Related to Circles
12.1 Introduction
12.2 Perimeter and Area of a Circle – A Review
12.3 Areas of Sector and Segment of a Circle
12.4 Areas of Combinations of Plane Figures
12.5 Summary
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13. Surface Areas and Volumes
13.1 Introduction
13.2 Surface Area of a Combination of Solids
13.3 Volume of a Combination of Solids
13.4 Conversion of Solid from One Shape to Another
13.5 Frustum of a Cone
13.6 Summary
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14. Statistics
14.1 Introduction
14.2 Mean of Grouped Data
14.3 Mode of Grouped Data
14.4 Median of Grouped Data
14.5 Graphical Representation of Cumulative Frequency Distribution
14.6 Summary
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15. Probability
15.1 Introduction
15.2 Probability -A Theoretical Approach
15.3 Summary
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Appendix A1: Proofs in Mathematics
Al.1 Introduction
A1.2 Mathematical Statements Revisited
A1.3 Deductive Reasoning
A1.4 Conjectures, Theorems, Proofs and Mathematical Reasoning
A1.5 Negation of a Statement
A1.6 Converse of a Statement
A1.7 Proof by Contradiction
A1.8 Summary
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Appendix A2: Mathematical Modelling
A2.1 Introduction
A2.2 Stages in Mathematical Modelling
A2.3 Some Illustrations
A2.4 Why is Mathematical Modelling Important?
A2.5 Summary
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