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Discovering Mathematics is a series of textbooks designed for the students in secondary schools. It follows the secondary Mathematics syllabus issued by the Ministry of Education, Singapore, which will be implemented from 2007 onwards. This series of Mathematics books covers the entire syllabus for the Singapore-Cambridge GCE O-Level Mathematics.

The emphasis of this series is on empowering students to learn mathematics effectively and independently. Depending on the topic covered, different approaches are adopted for the presentation of concepts to facilitate easy understanding by students. In some topics, an intuitive or an experimental approach is adopted to enable students to internalize concepts and instill in them an interest to explore the topics further.

Some features of this series include the following:

1. Class activities which allow the student to learn mathematics through discovery. Some of the class activities make use of Geometer�fs Sketchpad (available at www.keypress.com).
2. Worked examples are followed by a similar question (Try It!) so that students can chek if they have understood the concepts presented earlier.
3. Every lesson has an exercise. The questions in the exercise are sequenced as Basic Practice (simple questions involving a direct application of the concepts, Further Practice (more challenging questions on direct application, Maths@Work (questions that apply mathematical concepts to real-life situations, and Brainworks (questions involving higher order thinking or an open-ended approach to problems).
4. Each chapter is followed by a review exercise, an Extend Your Learning Curve activity to encourage students to explore mathematical concepts further or apply mathematics in real-life situations, and some questions requiring sentence or paragraph answers to encourage students to reflect on their learning experiences.
5. The right margins contain remarks on important information, concepts or definitions covered earlier related to the current material to help students recall them, discussion questions, interesting puzzles or facts that are related to mathematics, and some website references.
6. A list of general processes and heuristics for problem-solving is provided after the last chapter in each book, with worked examples using concepts pertinent to the material covered in the book. 

Discovering Mathematics Textbook 2A

Chapter 1      Proportion                                                                                                                       1

        1.1         Map Scale And Calculation Of Area                                                                              2

                             A. Map Scale                                                                                                            2

                             B. Calculation of Area                                                                                              3

        1.2         Direct Proportion                                                                                                              8

        1.3         Inverse Proportion                                                                                                          17

        In A Nutshell                                                                                                                                  27

        Extend Your Learning Curve                                                                                                       30

        Write In Your Journal                                                                                                                   31

Chapter 2      Expansion and factorization Of Algebraic Expressions                                                 32

        2.1         Expansion Of the Products Of Algebraic Expressions                                                  33

                             A. Product of Single Terms                                                                                     33

                             B. Product of Two Expressions                                                                              33

        2.2         Special Products Of Algebraic Expressions                                                                  40

        2.3         Factorisation By Using Special Products Of Algebraic Expressions                             45

        2.4         Factorisation of ax²+ bx + c                                                                                          50

                             A. Algebra Tiles                                                                                                       50

                             B. x²+ bx + c                                                                                                            53

                             C. ax²+ bx + c                                                                                                          56

        In A Nutshell                                                                                                                                  60

        Extend Your Learning Curve                                                                                                       62

        Write In Your Journal                                                                                                                   62

Chapter 3      Simple Algebraic fractions                                                                                             63

        3.1         Simplifying Simple Algebraic Fractions                                                                         64

        3.2         Multiplication And Division Of Algebraic Fractions                                                        67

        3.3         Addition And Subtraction Of Algebraic Fractions                                                          70

        3.4         More About Formulae                                                                                                    74

        3.5         Changing The Subject Of A Formula                                                                             79

        In A Nutshell                                                                                                                                            83

        Extend Your Learning Curve                                                                                                       85

        Write In Your Journal                                                                                                                   85

Chapter 4      Congruence and Similarity                                                                                            86

        4.1         Meaning Of Congruence                                                                                                87

                             A. Congruent Figures                                                                                              87

                             B. Congruence and Transformation                                                                       89

        4.2         Similarity                                                                                                                        101

        4.3         Scale Factors                                                                                                                111

        4.4         Scale Drawings                                                                                                             116

        In A Nutshell                                                                                                                                  122

        Extend Your Learning Curve                                                                                                      126

        Write In Your Journal                                                                                                                  126

Chapter 5      Linear Equations In Two Unknowns                                                                             127

        5.1         Meaning Of Linear Equations In Two Unknowns                                                         128

        5.2         Solving Simultaneous Linear Equations In Two Unknowns By Graphical Method      134

        5.3         Solving Simultaneous Linear Equations In Two Unknowns By Substitution Method   141

        5.4         Solving Simultaneous Linear Equations In Two Unknowns By Elimination Method    144

        5.5         Solving Problems Using Simultaneous Equations                                                        149

        In A Nutshell                                                                                                                                  155

        Extend Your Learning Curve                                                                                                      158

        Write In Your Journal                                                                                                                  158

Chapter 6      Quadratic Functions And Equations                                                                             159

        6.1         Idea Of Functions And Linear Functions                                                                      160

                             A. Idea of Functions                                                                                               160

                             B. Linear Functions                                                                                                163

        6.2         Graphs Of Quadratic Functions                                                                                    172

                             A. Graph of y = ax ²+ bx + c, where a ðn 0                                                           172

                             B. Graph of y = ax ²+ bx + c, where a , 0                                                             177

        6.3 Solving Quadratic Equations By Factorisation                                                                     183

        6.4 Applications Of Quadratic Equations                                                                                   188

        In A Nutshell                                                                                                                                  192

        Extend Your Learning Curve                                                                                                      195

        Write In Your Journal                                                                                                                  196

Problem-solving Processes and Heuristics                                                                                        197

Answers                                                                                                                                             203