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1. NUMBER SYSTEMS 1
 1.1 Introduction 1
1.2 Irrational Numbers 5
1.3 Real Numbers and their Decimal Expansions 8
1.4 Representing Real Numbers on the Number Line 15
1.5 Operations on Real Numbers 18
1.6 Laws of Exponents for Real Numbers 24
1.7 Summary 27


2. POLYNOMIALS 28
2.1 Introduction 28
2.2 Polynomials in One Variable 28
2.3 Zeroes of a Polynomial 32
2.4 Remainder Theorem 35
2.5 Factorisation of Polynomials 40
2.6 Algebraic Identities 44
2.7 Summary 50


3. COORDINATE GEOMETRY 51
3.1 Introduction 51
3.2 Cartesian System 54
3.3 Plotting a Point in the Plane if its Coordinates are given 61
3.4 Summary 65


4. LINEAR EQUATIONS IN TWO VARIABLES 66
4.1 Introduction 66
4.2 Linear Equations 66
4.3 Solution of a Linear Equation 68
4.4 Graph of a Linear Equation in Two Variables 70
4.5 Equations of Lines Parallel to x-axis and y-axis 75
4.6 Summary 77
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5. INTRODUCTION TO EUCLID’S GEOMETRY 78
5.1 Introduction 78
5.2 Euclid’s Definitions, Axioms and Postulates 80
5.3 Equivalent Versions of Euclid’s Fifth Postulate 86
5.4 Summary 88


6. LINES AND ANGLES 89
6.1 Introduction 89
6.2 Basic Terms and Definitions 90
6.3 Intersecting Lines and Non-intersecting Lines 92
6.4 Pairs of Angles 92
6.5 Parallel Lines and a Transversal 98
6.6 Lines Parallel to the same Line 101
6.7 Angle Sum Property of a Triangle 105
6.8 Summary 108


7. TRIANGLES 109
7.1 Introduction 109
7.2 Congruence of Triangles 109
7.3 Criteria for Congruence of Triangles 112
7.4 Some Properties of a Triangle 120
7.5 Some More Criteria for Congruence of Triangles 125
7.6 Inequalities in a Triangle 129
7.7 Summary 134


8. QUADRILATERALS 135
8.1 Introduction 135
8.2 Angle Sum Property of a Quadrilateral 136
8.3 Types of Quadrilaterals 137
8.4 Properties of a Parallelogram 139
8.5 Another Condition for a Quadrilateral to be a Parallelogram 145
8.6 The Mid-point Theorem 148
8.7 Summary 151


9. AREAS OF PARALLELOGRAMS AND TRIANGLES 152
9.1 Introduction 152
9.2 Figures on the same Base and Between the same Parallels 154
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9.3 Parallelograms on the same Base and
between the same Parallels 156
9.4 Triangles on the same Base and between
the same Parallels 160
9.5 Summary 167


10. CIRCLES 168
10.1 Introduction 168
10.2 Circles and its Related Terms : A Review 169
10.3 Angle Subtended by a Chord at a Point 171
10.4 Perpendicular from the Centre to a Chord 173
10.5 Circle through Three Points 174
10.6 Equal Chords and their Distances from the Centre 176
10.7 Angle Subtended by an Arc of a Circle 179
10.8 Cyclic Quadrilaterals 182
10.9 Summary 187


11. CONSTRUCTIONS 187
11.1 Introduction 188
11.2 Basic Constructions 189
11.3 Some Constructions of Triangles 191
11.4 Summary 196


12. HERON’S FORMULA 197
12.1 Introduction 197
12.2 Area of a Triangle – by Heron’s Formula 199
12.3 Application of Heron’s Formula in finding
Areas of Quadrilaterals 203
12.4 Summary 207


13. SURFACE AREAS AND VOLUMES 208
13.1 Introduction 208
13.2 Surface Area of a Cuboid and a Cube 208
13.3 Surface Area of a Right Circular Cylinder 214
13.4 Surface Area of a Right Circular Cone 217
13.5 Surface Area of a Sphere 222
13.6 Volume of a Cuboid 226
13.7 Volume of a Cylinder 228
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13.8 Volume of a Right Circular Cone 231
13.9 Volume of a Sphere 234
10.10 Summary 237


14. STATISTICS 238
14.1 Introduction 238
14.2 Collection of Data 239
14.3 Presentation of Data 240
14.4 Ggraphical Representation of Data 247
14.5 Measures of Central Tendency 261
14.6 Summary 270


15. PROBABILITY 271
15.1 Introduction 271
15.2 Probability – an Experimental Approach 272
15.3 Summary 285


APPENDIX – 1 PROOFS IN MATHEMATICS 286
A1.1 Introduction 286
A1.2 Mathematically Acceptable Statements 287
A1.3 Deductive Reasoning 290
A1.4 Theorems, Conjectures and Axioms 293
A1.5 What is a Mathematical Proof? 298
A1.6 Summary 305


APPENDIX – 2 INTRODUCTION TO MATHEMATICAL MODELLING 306
A2.1 Introduction 306
A2.2 Review of Word Problems 307
A2.3 Some Mathematical Models 311
A2.4 The Process of Modelling, its Advantages and Limitations 319
A2.5 Summary 322


ANSWERS/HINTS 325-350