New Syllabus Additional Mathematics is specially written for students preparing for the
GCE "O" level examinations. The book covers the Ministry of Education, Singapore Syllabus for Secondary Mathematics implemented from 2007.
The distinctive qualities of this book are its simple and direct treatment of each topic and its emphasis throughout
on examples and practices. New concepts and principles are introduced using short, concise explanations which serve to lay the groundwork for advance students. The language used
throughout is simple and theoretical explanations are kept to a minimum.
Four sets of revision (review) exercises are provided for students to recapitulate
what they have learnt.
The more difficult questions are marked with an *.
This book (first published in 1979) has been carefully revised to cover the
complete syllabus for the Singapore-Cambridge G.C.E. 'O'
Level Examination in Additional Mathematics. There is some reorganisation in the sequence of presentation in order to better prepare pupils for learning
more difficult concepts. For example, in calculus, pupils are taught simple differentiation and its application before dealing with the differentiation of
trigonometrical functions. We hope that pupils will find this approach easier to handle.
Special Features
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Problem Solving Tips to enhance thinking skills
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IT activities to encourage computer-based leaning
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Your Attention to remind students of common errors
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Self-assessment to incite active learning and independent thinking
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Awareness of problem-solving strategies is systematically enhanced
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Thinking Time to provide opportunities for creative and individual thinking
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Revision (Review) exercises to recapitulate previously covered mathematic concepts
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Real-life situations to demonstrate the relevance of mathematics to everyday life
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Graded exercises and challenging problems to cater to different learning abilities
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Exploration activities to promote applications in inter-disciplinary and real life situations
Above is an extract from the preface of the New Syllabus Additional Mathematics Series.
There is an optional workbook for this series.
New Syllabus Additional Math Textbook (8th Edition)
1. Simultaneous Equations, Remainder Theorem and Factor Theorem
1.1 Simultaneous Linear Equations in Two Unknowns
1.2 Simultaneous Linear and Non-Linear Equations in Two Unknowns
1.3 Algebraic Expressions and Polynomials
1.4 Identities
1.5 The Remainder Theorem
1.6 The Factor Theorem
1.7 Factorisation of Cubic Expressions
Summary
Review Examples 1
Review Questions 1
2. Quadratic Equations and Functions
2.1 Symmetric Properties of the Roots of a Quadratic Equation
2.2 Nature Roots of a Quadratic Equation
2.3 Maximum and Minimum Values of Quadratic Functions
2.4 Quadratic Inequalities
2.5 Intersection of a Line and a Curve
2.6 Absolute Value and Absolute Valued Functions
Summary
Review Examples 2
Review Questions 2
3. Partial Fractions
3.1 Proper and Improper Algebraic Fractions
3.2 Partial Fractions
Summary
Review Examples 3
Review Questions 3
4. Indices, Surds and Logarithms
4.1 Indices
4.2 Solving Exponential Equations
4.3 Surds
4.4 Logarithms
4.5 Laws of Logarithms
4.6 Common Logarithms and Natural Logarithms
4.7 Change of Base of Logarithms
Summary
Review Examples 4
Review Questions 4
5. Coordinate Geometry - The Straight Line
5.1 Midpoint of Line Segment
5.2 Parallel and Perpendicular Lines
5.3 Equation of a Straight Line
5.4 Area of Plane Figures (Given the Vertices)
5.5 Determination of Functions from Straight Line Graphs
5.6 Straight Line Graphs
Summary
Review Examples 5
Review Questions 5
Revision Exercise 1
6. Trigonometrical Ratios and Equations
6.1 General Angles in Radians and Degrees
6.2 Trigonometric Ratios of a General Angle
6.3 Trigonometrical Ratios of Special Angles: 30o, 45o , 60o , or ð/6, ð/4, ð/3
6.4 Graphs and Properties of sin x, cos x and tan x
6.5 Further Trigonomtrical Graphs
6.6 Absolute Valued Trigonometrical Functions
6.7 Simple Trigonometrical Equations
6.8 Trigonometrical Ratios of Cotangent, Secant and Cosecant
6.9 Fundamental Identities
6.10 More Trigonometrical Equations
6.11 Proving of Identities
Summary
Review Examples 6
Review Questions 6
7. Further Trigonometrical Identities
7.1 Sum and Difference of Two Angles
7.2 Multiple Angles
7.3 Equations of the type A cos è + B sin è = C
7.4 Factor Formulae
7.5 Further Proving of Identities
Summary
Review Examples 7
Review Questions 7
8. Matrix and Its Application
8.1 Revision
8.2 The Inverse Matrix
8.3 Using Matrices to Solve Simultaneous Equations
Summary
Review Examples 8
Review Questions 8
9. The Binomial Theorem
9.1 Binomial Expansions of the Form (x + y)n
9.2 The Binomial Theorem
Summary
Review Examples 9
Review Questions 9
10. Matrix and Its Application
10.1 Simple Examples in Geometric Proof
10.2 The Midpoint and Intercept Theorem
10.3 The Alternate Segment Theorem, Intersecting Chords Theorem and Tangent-Secant Theorem
10.4 More Proofs in Plane Geometry
Summary
Review Examples 10
Review Questions 10
Revision Exercise 2
11. Further Coordinate Geometry
11.1 Equation of a Circle
11.2 Graphs of Equations
Summary
Review Examples 11
Review Questions 11
12. Differentiation
12.1 The Ideas of Limits
12.2 Gradient of a Curve
12.3 Differentiation of y = ax n
12.4 Differentiation of a Composite Function
12.5 Differentiation of Products
12.6 Differentiation of Quotients
12.7 Higher Derivatives
Summary
Review Examples 12
Review Questions 12
13. Differentiation and Its Applications
13.1 Increasing and Decreasing Functions
13.2 Stationary Points: Maximum and Minimum Points (First Derivative Test)
13.3 Distinguishing Maximum and Minimum Points Using dy 2/dx2 (Second Derivative Test)
13.4 Problems on Maximum and Minimum Values
Summary
Review Examples 13
Review Questions 13
14. Further Applications of Differentiation
14.1 Equations of Tangent and Normal to a Curve
14.2 Connected Rates of Change
14.3 Motion with Variable Velocity and Acceleration
Summary
Review Examples 14
Review Questions 14
15. Differentiation of Trigonometrical Functions
15.1 Differentiation of Trigonometrical Functions
15.2 Applications of Differentiation of Trigonometrical Functions
15.3 Further Applications of Differentiation of Trigonometrical Functions
Summary
Review Examples 15
Review Questions 15
Revision Exercise 3
16. Logarithmic and Exponential Functions
16.1 Graphs of Logarithmic Functions
16.2 Differentiation of Logarithmic Functions
16.3 Problems Involving ln x
16.4 Graphs of Exponential Functions
16.5 Differentiation of Exponential Functions
16.6 Problems Involving ln ex
Summary
Review Examples 16
Review Questions 16
17. Integration
17.1 Integration
17.2 Symbol of Integration
17.3 Integration of a Function Involving a Linear Factor
17.4 Integration of Trigonometrical Functions
17.5 Integration of Functions of the Form 1/ ax + b
17.6 Integration of Exponential Functions
17.7 Definite Integral
17.8 Further Examples of Definite Integration
Summary
Review Examples 17
Review Questions 17
18. Applications of Integration
18.1 Area Under a Curve
18.2 Kinematics
Review Examples 18
Review Questions 18
Revision Exercise 4
Answers
Samples
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