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New Discovering Additional Mathematics Textbooks A&B

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New Discovering Additional Mathematics is a set of textbooks written with learner-centric approach that builds upon the knowledge and skills learnt in elementary mathematics. It is based on the latest O-Level and N(A)-Level Additional Mathematics Syllabus implemented from 2020 by Ministry of Education of Singapore.

Illustrative examples and diagrams help students understand and apply the mathematical concepts that have been learnt. The examples are also carefully selected to promote discussions on relevant Big Ideas in mathematics and modelling of essential problem-solving strategies.

The contents of the syllabus are organised under three strands:

  1. Algebra
  2. Geometry & Trigonometry
  3. Calculus

Key Features

  1. Learning Objectives
    Provided at the start of each section to inform students about what they will be learning in the section.

  2. Connecting Ideas
    Emphasise the links between different mathematical concepts and the Big Ideas of mathematics, mathematics and other disciplines as well as between mathematics and the real world.

  3. Worked Examples
    Facilitates students' understanding of concepts and shows how ideas and reasoning can be expressed clearly in mathematical language.

  4. Try it Yourself
    Enables students to practise what have been just learnt in Worked Examples.

  5. Practice Exercise
    • Basic Mastery : Simple and direct application of a particular concept or skills
    • Intermediate: Application of a few concepts and/or combination of skills
    • Advanced: Higher-order thinking and the application of several concepts or skills, covered within the chapter or across different topics.

  6. Let's Sum Up
    Consolidates important concepts in the chapter

  7. Flashback + Reflect + Extend Your Learning Curve

  8. Core Vocabulary
    Highlights key terms from the chapter

  9. Getting Started
    Provides relevant real-life applications of concepts in the immediate chapter and acts as a trigger that piques students' interest
  10. Integrated Exercise
    Requires students to synthesise concepts learnt across different chapters.

  11. Spotlight
    Draws attention to important mathematical information.

  12. Coding
    Provides coding opportunities to support development of computational thinking.

  13. Extra Info
    Provides extra information such as scientific, historical and fun facts to pique students' interest.

  14. Answer Key

Textbook A:

  1. Quadratic Functions
    Graphs, Always Negative or Positive, Models

  2. Equations and Inequalities
    Nature of roots, Simultaneous Equations, Quadratic Inequalities

  3. Surds
    Four Operations and Equations


  4. Polynomials and Partial Fractions
    Remainder and Factor Theorems, Cubic Polynomials and Equations, Partial Fractions

  5. Exponential and Logarithmic Functions and Equations

  6. Binomial Expansions

  7. Coordinate Geometry of Lines and Rectilinear Figures
    Midpoint, Parallel and Perpendicular Lines, Area

  8. Coordinate Geometry of Circles
    Equation, Intersection Points

  9. Trigonometric Functions, Graphs and Equations

  10. Trigonometric Identities and Formulae
    Basic Identities, Addition, Double Angle , R Formulae


    Answer Key

Textbook B:

  1. Differentiation
    Rules of Differentiation, Chain Rule, Product Rule, Quotient Rule

  2. Tangents, Normal and Rates of Change

  3. Maxima and Minima
    Higher Order Derivatives, Increasing and Decreasing Functions, Stationary Points and Their Nature, Maxima and Minima Problems

  4. Further Differentiation
    Trigonometric, Exponential, Logarithmic Functions and Applications of Derivatives


  5. Indefinite Integrals
    Basic Rules, Applications, Trigonometric Functions

  6. Definite Integrals
    Area by Curve and Line(s) and below x-axis

  7. Kinematics
    Application of Differentiation and Integration

  8. Proofs in Plane Geometry
    Proofs involving: Parallel Lines, Congruent Triangles, Quadrilaterals, Perpendicular Lines, Angle Bisectors, Similar Triangles, Midpoint Theorem, Circles and Tangent-chord Theorem


Complete series contain:

  1. Textbooks