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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 4A

Chapter 1      Standard Deviation                                                                                                          1

        1.1         Standard Deviation For Ungrouped Data                                                                        2

                             A. Definition                                                                                                              2

                             B. Formula                                                                                                                3

        1.2         Standard Deviation For Grouped Data                                                                            8

                             A. Definition                                                                                                              8

                             B. Formula                                                                                                                9

                             C. Using a Calculator to Calculate Mean and Standard Deviation                         11

        1.3         Comparison Of Two Data Sets                                                                                      15

        In A Nutshell                                                                                                                                  22

        Extend Your Learning Curve                                                                                                       26

        Write In Your Journal                                                                                                                   26

Chapter 2      Probability  Laws                                                                                                                      27

        2.1         Probabilities Of Simple Combined Events                                                                     28

                             A. Possibility Diagram                                                                                             28

                             B. Tree Diagram                                                                                                      30

        2.2         Mutually Exclusive Events                                                                                             35

        2.3         Independent Events                                                                                                        41

        2.4         Further Probabilities                                                                                                        49

        In A Nutshell                                                                                                                                  56

        Extend Your Learning Curve                                                                                                       59

        Write In Your Journal                                                                                                                   59

Chapter 3      Matrices                                                                                                                         60

        3.1         Definition Of A Matrix                                                                                                     61

        3.2         Addition And Subtraction Of Matrices                                                                          67

                             A. Addition                                                                                                               67

                             B. Subtraction                                                                                                          69

        3.3         Multiplication Of A Matrix By A Scalar                                                                          73

        3.4         Multiplication Of Matrices                                                                                               77

        In A Nutshell                                                                                                                                  87

        Extend Your Learning Curve                                                                                                       90

        Write In Your Journal                                                                                                                   90

Chapter 4      Vectors In Two Dimensions                                                                                           91

        4.1 Introduction To Vectors                                                                                                          92

                             A. Scalars and Vectors                                                                                           92

                             B. Vector Representation and Notations                                                                 93

                             C. Equal Vectors                                                                                                     93

        4.2 Operations On Vectors                                                                                                          98

                             A. Addition                                                                                                               98

                             B. Subtraction                                                                                                        101

                             C. Scalar Multiplication                                                                                          104

        4.3         Position Vectors                                                                                                            112

        4.4         Vectors On The Coordinate Plane                                                                                116

        4.5         Applications Of Vectors In Geometry                                                                           124

        In A Nutshell                                                                                                                                  130

        Extend Your Learning Curve                                                                                                      134

        Write In Your Journal                                                                                                                  134

Problem-Solving Processes and Heuristics                                                                                       135

Answers                                                                                                                                              143