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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. 

Chapter 5      Mathematics In Practical Situations                                                                                1

        5.1         Profit And Loss                                                                                                                2

        5.2         Simple Interest And Compound Interest                                                                         7

                             A. Simple Interest                                                                                                     7

                             B. Compound Interest                                                                                              8

        5.3         Hire-Purchase                                                                                                                16

        5.4         Utility Bills                                                                                                                       19

        5.5         Money Exchange                                                                                                           24

        5.6         Taxation                                                                                                                          28

                             A. Individual Income Tax                                                                                        28

                             B. Property Tax                                                                                                       30

        In A Nutshell                                                                                                                                  33

        Extend Your Learning Curve                                                                                                       36

        Write In Your Journal                                                                                                                   36

Chapter 6      Graphs In Practical Situations                                                                                        37

        6.1         Tables, Charts And Graphs                                                                                            38

        6.2         Distance-time Graphs And Speed-time Graphs                                                            43

                             A. Distance-time Graph                                                                                          43

                             B. Speed-time Graph 48

        In A Nutshell                                                                                                                                  64

        Extend Your Learning Curve                                                                                                       68

        Write In Your Journal                                                                                                                   68

Revision Topic 1 

        Numbers, Ratio, Rate And Proportion                                                                                         69

Revision Topic 2

        Percentage, Speed And Practical Mathematics                                                                         76

Revision Topic 3

        Algebraic Manipulation And Formulae                                                                                         85

Revision Topic 4

        Functions And Graphs                                                                                                                 92

Revision Topic 5

        Equations And Inequalities                                                                                                          105

Revision Topic 6

        Set Language And Matrices                                                                                                       111  

Revision Topic     7

        Angles, Polygons, Congruence And Similarity                                                                           119

Revision Topic 8

        Properties Of Circles                                                                                                                  127

Revision Topic 9

        Pythagoras’ Theorem And Trigonometry                                                                                   134

Revision Topic 10

        Mensuration                                                                                                                                 142

Revision Topic 11

        Coordinate Geometry And Vectors In Two Dimensions                                                            150

Revision Topic 12                                                                                                                              

        Statistics And Probability                                                                                                            159

Problem-Solving Processes and Heuristics                                                                                       171