New Mathematics Counts (2nd Edition by Tay Choon Hong, Mark Riddington, Martin Grier) builds on the strengths of its well-received first edition. This edition meets requirements of the latest Mathematics syllabuses for the GCE "N" and GCE 'O" level examinations set by the Ministry of Education, Singapore. The first edition was a revised version of the Mathematics Counts for Secondary 1 to 5 **Normal (Academic).
The series consists of five coursebooks designed specially for students following the Normal (Academic) Course Syllabus prescribed by the Ministry of Education. The material has been prepared not only to help students excel in the GCE 'N' level Mathematics examination but also with a view to preparing these students to proceed to sit for the GCE 'O' level examination. Thus, the series is different from most others.
The material is arranged in a sound pedagogical sequence in which abstract reasoning is supported by concrete examples. For instance, in the chapter on Simultaneous Equations, the graphical solutions to the linear simultaneous equations are presented together with the algebraic solutions. In this approach, the graphical solutions provide the concrete pictorial examples and help students understand better the solutions obtained algebraically.
Care is given to introducing concepts one a time to allow students to grasp them with ease. Understanding of concepts is further enhanced by the judicious use of worked examples and graded exercises.
In Books 1 and 2, emphasis is placed on the mastery and application of basic skills so that a sound basis is formed for subsequent studies. The basic skills include estimation and mental calculation, and the handling of data.
Throughout the series, activities are used to guide students to use thinking skill, such as induction and find out for themselves fundamental mathematical theorems and rules. In addition, students are also introduced to the use of computer programs in a number of activities.
Through appropriate worked examples and activities, students are encouraged to use problem solving strategies (heuristics) such as estimating, building a model, tabulation, systematic listing, working backwards, using equations and simplifying the problem. Wherever possible, diagrams are used to make difficult word problems less daunting and more manageable.
Features of the 2nd Edition books in this series:
Enhances Understanding
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Concepts are presented in a simple, clear and logical manner. The use of diagrams, figures and models helps students visualise mathematical concepts and ideas more clearly.
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Sidebar features provide necessary pointers to key concepts in main text.
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Worked examples guide students in understanding and applying the main concept learned.
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End-of-chapter summaries recap key learning outcomes and important mathematical formulae.
Motivates Learning
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Interesting and relevant chapter openers arouse interest in the topics covered.
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Thought-provoking facts and activities enhance learning and make it more enjoyable through the exploration and investigation of mathematical ideas.
Build Exam Confidence
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Ample questions, carefully gradated according to level of difficulty, are provided throughout the textbook to reinforce concepts covered. They also help students identify their areas of weakness and misconception.
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Challenging questions and past-year examination questions have been incorporated to induce higher-order thinking skills and build exam confidence.
Above is an extract from the preface of the New Mathematics Counts Series.
**A five-year secondary education is called the Normal Stream in Singapore, a four-year education is called Express Stream.
Answer keys:
The textbook provides answer keys.
New Mathematics Counts Series consists of:
There are no workbooks or teacher's guides for this series. Teacher's guides are not necessary for this series. The explanations are clear, and notes and hints are included in the margins. A Scheme of Work (for the entire year) is inserted in each textbook. The Scheme of Work includes specific instructional objectives for each chapter by topics. We do not sell the Scheme of Work separately.
New Mathematics Counts 2 (2nd Edition)
1. Algebraic Expressions and Factorisation
1.1 Expansion of Linear Algebraic Expression
1.1.1 Expansion of a (b + c)
1.1.2 Expansion of (a + b) (c + d)
1.1.3 Expansion of (a + b) 2 and (a – b) 2
1.1.4 Expansion of (a +b) (a - b)
1.2 Factorisation of Algebraic Expressions
1.2.1 Factorisation by Taking Out the Common Factor
1.2.2 Factorisation by Grouping
1.2.3 Factorisation by Using the Cross Method
1.2.4 Factorisation by Using the Special Results of a2 + 2ab + b2 and
a 2 – 2ab + b2
1.2.5 Factorisation by Using the Special Result of a2 – b2
Summary
Enrichment Maths (Mental Squares)
10 Minutes Concept Check
Revision Paper 1
2. Algebraic Fractions, Equations and Inequalities
2.1 Algebraic Fractions
2.1.1 Simplification of Algebraic Fractions
2.1.2 Multiplication and Division of Simple Algebraic Fractions
2.2 Solving Simple Equations
2.2.1 Solving Equations Involving Addition or Subtraction
2.2.2 Solving Equations Involving Multiplication and Division
2.2.3 Solving Equations Involving More Than One Operation
2.3 Solving Equations Involving Algebraic Fractions
2.4 Applications of Equations
2.4.1 Problems Involving Simple Equations
2.4.2 Problems Involving Simple Algebraic Fractions
2.5 Inequalities and Their Applications
2.5.1 Inequalities
2.5.2 Application of Inequalities
Summary
Enrichment Maths (Identifying Patterns)
10 Minutes Concept Check
Revision Paper 2
3. Cartesian Coordinates and Linear Graphs
3.1 Cartesian Coordinate System
3.2 Linear Functions and Graphs
3.2.1 Linear Functions
3.2.2 Graphs of Linear Equations
3.2.3 horizontal and Vertical Linear Relationships
3.3 Gradients of Straight Line Graphs
3.3.1 Positive and Negative Gradients
3.3.2 Gradients of Horizontal and Vertical Lines
Summary
Enrichment Maths (Descartes and the Fly)
10 Minutes Concept Check
Revision Paper 3
4. Proportions and Map Scales
4.1 Direct Proportion
4.1.1 Real- Life Problems Involving Direct Proportion
4.1.2 Tabular, Algebraic and Graphical Approach in Direct Proportion
4.2 Inverse Proportion
4.2.1 Real- Life Problems Involving Inverse Proportion
4.2.2 Tabular, Algebraic and Graphical Approach in Inverse Proportion
4.3 Problems Involving Map Scales
Summary
Enrichment Maths (A full Tank)
10 Minutes Concept Check
Revision Paper 4
Review Paper 1
Review Paper 2
5. Simultaneous Linear Equations
5.1 Introduction
5.2 Algebraic Method of Solving Simultaneous Linear Equations
5.2.1 Substitution Method
5.2.2 Elimination Method
5.3 Graphical Method of Solving Simultaneous Linear Equations
5.4 No Solution and Infinitely Many Solutions
5.5 Problem Solving Using Simultaneous Linear Equations
Summary
Enrichment Maths (A Business Graph)
10 Minutes Concept Check
Revision Paper 5
6. Triangles, Polygons and Congruence
6.1 Simple Geometric Constructions
6.1.1 Angle Bisectors
6.1.2 Perpendicular Bisectors
6.2 Triangles and Their Properties
6.2.1 Types of Triangles
6.2.2 Sum of the Angles of a Triangle
6.2.3 Exterior Angle of a Triangle
6.3 Constructing Triangles
6.4 Quadrilaterals and Their Properties
6.4.1 Sum of the Angles of a Quadrilateral
6.4.2 Properties of Special Quadrilaterals
6.5 Constructing Quadrilaterals
6.6 Polygons and Their Properties
6.6.1 Types of Polygons
6.6.2 Sum of the Interior Angles of a Polygon
6.6.3 Sum of the Exterior Angle of a Polygon
6.7 Congruence
6.7.1 Congruent Figures
6.7.2 Congruent Polygons
Summary
Enrichment Maths (Fun with Tangrams)
10 Minutes Concept Check
Revision Paper 6
7. Mensuration
7.1 Pyramids
7.1.1 Introduction
7.1.2 Total Surface Area of Pyramids
7.1.3 Volume of Pyramids
7.2 Cones
7.2.1 Introduction
7.2.2 Total Surface Area of Cones
7.2.3 Volume of Cones
7.3 Spheres
7.3.1 Introduction
7.3.2 Total Surface Area of Spheres
7.3.3 Volume of Spheres
Summary
Enrichment Maths (Tetrahedrons and Octahedrons)
10 Minutes Concept Check
Revision Paper 7
8. Statistics and Simple Probability
8.1 Statistical Representations
8.1.1 Dot Diagrams
8.1.2 Stem- and- Leaf Diagrams
8.2 Statistical Averages
8.2.1 Introduction
8.2.2 Mean of Ungrouped Data
8.2.3 Median of Ungrouped Data
8.2.4 Mode of Ungrouped Data
8.2.5 Use and Purpose of Mean, Median and Mode
8.2.6 Mean of Grouped Data
8.3 Probability
8.3.1 Introduction
8.3.2 Favourable outcomes and Simple Space
8.3.3 Simple Probability
Summary
Enrichment Maths (Spinning Averages)
10 Minutes Concept Check
Revision Paper 8
Review Paper 3
Review Paper 4
Answers
Samples
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