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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 2B

Chapter 7      Pythagoras’ Theorem                                                                                                     1

        7.1         Pythagoras’ Theorem                                                                                                      2

        7.2         Applications Of Pythagoras’ Theorem                                                                            9

        7.3         Determination Of Right-angled Triangles                                                                       16

        In A Nutshell                                                                                                                                  22

        Extend Your Learning Curve                                                                                                       26

        Write In Your Journal                                                                                                                   26

Chapter 8      Mensuration Of Pyramids, Cones and Spheres                                                           27

        8.1         Pyramids                                                                                                                        28

                             A. Introducing Pyramids                                                                                          28

                             B. Nets and Surface Areas of Pyramids                                                                30

                             C. Volumes of Pyramids                                                                                         33

        8.2         Cones                                                                                                                            40

                             A. Introducing Cones                                                                                               40

                             B. Net and Surface Area of a Cone                                                                        41

                             C. Volume of a Cone                                                                                              43

        8.3         Spheres                                                                                                                          50

                             A. Introducing Spheres                                                                                            50

                             B. Surface Area of a Sphere                                                                                  50

                             C. Volume of a Sphere                                                                                           52

        In A Nutshell                                                                                                                                  58

        Extend Your Learning Curve                                                                                                       62

        Write In Your Journal                                                                                                                   62

Chapter 9      Set Language And Notation                                                                                          63

        9.1         Set Notation                                                                                                                    64

                             A. Sets                                                                                                                     64

                             B. Equal Sets                                                                                                           67

                             C. Subsets                                                                                                               68

                             D. Universal Set and Empty Set                                                                             69

        9.2         Venn Diagrams And Complement Of A Set                                                                  73

                             A. Venn Diagrams                                                                                                   73

                             B. Complement of a Set                                                                                         75

        9.3         Union And Intersection Of Sets                                                                                      78

                             A. Union of Sets                                                                                                      78

                             B. Intersection of Sets                                                                                             80

        In A Nutshell                                                                                                                                  87

        Extend Your Learning Curve                                                                                                       91

        Write In Your Journal                                                                                                                   91

Chapter 10    Data Analysis                                                                                                                92

        10.1       Dot Diagrams                                                                                                                 93

        10.2       Stem-and-leaf Diagrams                                                                                                98

        10.3       Measure Of Central Tendency: Mean                                                                          110

                             A. Measures of Central Tendency                                                                         110

                             B. Definition of Mean                                                                                             110

                             C. Mean of Grouped Data                                                                                     112

        10.4       Measure Of Central Tendency: Median                                                                       117

        10.5       Measure Of Central Tendency: Mode                                                                          123

                             A. Definition of Mode                                                                                             123

                             B. Comparison between Mean, Median and Mode                                               125

        In A Nutshell                                                                                                                                  130

        Extend Your Learning Curve                                                                                                      134

        Write In Your Journal                                                                                                                  134

Chapter 11    Probability                                                                                                                      135

        11.1       The Meaning Of Probability                                                                                          136

                             A. Introduction                                                                                                        136

                             B. Terms and Definitions                                                                                       136

        11.2       Sample Space                                                                                                               146

                             A. Sample Space                                                                                                   146

                             B. Basic Properties of Probabilities                                                                        149

        In A Nutshell                                                                                                                                 154

        Extend Your Learning Curve                                                                                                      158

        Write In Your Journal                                                                                                                  158

Problem-solving   Processes And Heuristics                                                                                      159

Answers                                                                                                                                              165