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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 1B

Chapter 9       Ratio, Rate And Speed 

        9.1          Ratios Involving Rational Numbers

                              A. Meaning of Ratio

                              B. Simplification of Ratios

                              C. Ratios of Three Quantities

                             D. Problems Involving Ratios

        9.2         Average Rate

        9.3         Speed

                              A. Uniform Speed and Average Speed

                              B. Conversion of Units

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Chapter 10 Percentage

        10.1       Meaning Of Percentage

                               A. Introduction

                              B. Expressing One Quantity as a Percentage of Another

        10.2       Reverse Percentages

        10.3       Percentage Increase And Decrease

                               A. Percentage Increase

                              B. Percentage Decrease

        10.4       Discount And GST

                              A. Discount

                               B. GST

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Chapter 11    Number Patterns

        11.1       Number Patterns And Sequences

        11.2       General Term Of A Sequence

                              A. General Term

                              B. Applications of Number Patterns

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Chapter 12    Coordinates And Linear Graphs

        12.1       Cartesian Coordinate System

        12.2       Linear Graphs

        12.3       Gradients Of Linear Graphs

                               A. Positive Gradients

                              B. Negative Gradients

                              C. Special Cases

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Chapter 13    Simple Inequalities

        13.1       Solving Simple Inequalities

                              A. Idea of Inequality

                              B. Solving Inequality

        13.2       Applications Of Simple Inequalities

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Chapter 14    Perimeters And Areas Of Plane Figures

        14.1       Mensuration Of Square, Rectangle, Triangle And Circle

        14.2       Area Of A Parallelogram

        14.3       Area Of A Trapezium

        14.4       Perimeters And Areas Of Composite Plane Figures

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Chapter 15 Volumes And Surface Areas Of Solids

        15.1       Volumes And Total Surface Areas Of A Cube And A Cuboid

                               A. Models of Cube, Cuboid, Prism and Cylinder

                              B. Cube

                              C. Cuboid

        15.2       Volume And Total Surface Area Of A Prism

                               A. Prism

                              B. Volume of Prism

                              C. Surface Area of Prism 

        15.3       Volume And Surface Area Of A Cylinder

         15.4       Volumes And Surface Areas Of Composite Solids

                               A. Conversion between Different Units

                               B. Composite Solids

        In A Nutshell

        Extend Your Learning Curve

        16.1       Collection Of Data

                              A. Taking Measurements in Experiments

                              B. Observing Outcomes of Events

                              C. Conducting Surveys

                              D. Reading Statistical Publications

        16.2       Organisation Of Data

         16.3       Bar Graphs, Pictograms And Line Graphs

                                A. Bar Graphs

                               B. Pictograms

                                C. Line Graphs

        16.4       Pie Charts

        16.5       Histograms

        In A Nutshell

        Extend Your Learning Curve

        Write In Your Journal

Problem-Solving Processes and Heuristics

Answers