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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’s 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 3A

Chapter 1      Indices                                                                                                                              1

        1.1         Positive Indices And Laws Of Indices                                                                             2

        1.2         Zero And Negative Integral Indices                                                                                 7

        1.3         Fractional Indices                                                                                                           11

                             A. nth Root of a Positive Number                                                                           11

                             B. Fractional Indices                                                                                                12

        1.4         Standard Form                                                                                                              16

                             A. Representation of Very Small or Very Large Numbers                                     16

                             B. Computation                                                                                                       18

                             C. Rounding and Truncation Errors in a Calculator                                                20

        1.5         Comparing Indices                                                                                                         22

        In A Nutshell                                                                                                                                  24

        Extend Your Learning Curve                                                                                                       28

        Write In Your Journal                                                                                                                   28

Chapter 2      More About Quadratic Equations                                                                                   29

        2.1         Factorisation Method                                                                                                      30

        2.2         Graphical Method                                                                                                           32

        2.3         Completing The Square Method                                                                                    36

        2.4         Quadratic Formula                                                                                                         40

        2.5         Fractional Equations                                                                                                       43

        2.6         Problems Involving Quadratic Equations                                                                       45

        In A Nutshell                                                                                                                                  51

        Extend Your Learning Curve                                                                                                       55

        Write In Your Journal                                                                                                                   55

Chapter 3      Linear Inequalities                                                                                                           56

        3.1         Basic Properties Of Inequalities                                                                                     57

        3.2         Linear Inequalities In One Unknown                                                                             60

        3.3         Simultaneous Linear Inequalities                                                                                    63

        3.4         Applications Of Linear Inequalities                                                                                 66

        In A Nutshell                                                                                                                                  70

        Extend Your Learning Curve                                                                                                       73

        Write In Your Journal                                                                                                                   73

Chapter 4      Conditions Of Congruence And Similarity                                                                     74

        4.1         Congruent Triangles                                                                                                       75

                             A. Side-Side-Side Congruence                                                                               75

                             B. Side-Angle-Side and Angle-Side-Angle Congruence                                         77

                             C. Right Angle-Hypotenuse-Side Congruence                                                       80

        4.2         Similar Triangles                                                                                                             85

                             A. Angle-Angle-Angle Similarity                                                                              85

                             B. Side-Side-Side Similarity                                                                                    88

                             C. Side-Angle-Side Similarity                                                                                  90

        4.3         Ratio Of Areas Of Similar Plane Figures                                                                       96

        4.4         Ratio Of Volumes Of Similar Solids                                                                             101

        In A Nutshell                                                                                                                                 108

        Extend Your Learning Curve                                                                                                      115

        Write In Your Journal                                                                                                                  115

Chapter 5      Functions And Graphs                                                                                                  116

        5.1         Graph Sketching Of Quadratic Functions                                                                    117

                             A. Graph of y = ±(x – h)² + k                                                                                  118

                             B. Graph of y = ±(x – p)(x – q)                                                                              121

        5.2         Graphs Of Power Functions                                                                                         125

                             A. Graph of y = axⁿ for n = 0, 1, 2 and 3                                                                125

                             B. Graph of y = axⁿ for n = –2 and –1                                                                    127

        5.3         Graphs Of Sums Of Power Functions                                                                         131

        5.4         Graphs Of Exponential Functions                                                                                 135

        5.5         Gradients Of Curves                                                                                                     139

        In A Nutshell                                                                                                                                 147

        Extend Your Learning Curve                                                                                                      156

        Write In Your Journal                                                                                                                  156

Chapter 6      Properties Of Circles                                                                                                     157

        6.1         Chords Of A Circle                                                                                                        158

        6.2         Angles In A Circle                                                                                                          168

                             A. Angle at the Centre and Angle at the Circumference                                       168

                             B. Angle in a Semicircle                                                                                         172

                             C. Angles in the Same Segment                                                                           173

        6.3         Angles In The Opposite Segments                                                                               179

        6.4         Tangents To A Circle                                                                                                    184

                             A. Tangent at a Point 184

                             B. Tangents from an External Point 186

        In A Nutshell                                                                                                                                 193

        Extend Your Learning Curve                                                                                                      200

        Write In Your Journal                                                                                                                  200

Problem-Solving Processes and Heuristics                                                                                       201

Answers                                                                                                                                              209