# New Discovering Additional Mathematics Textbooks A&B

**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:

- Algebra
- Geometry & Trigonometry
- Calculus

Key Features

**Learning Objectives**

Provided at the start of each section to inform students about what they will be learning in the section.**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.**Worked Examples**

Facilitates students' understanding of concepts and shows how ideas and reasoning can be expressed clearly in mathematical language.**Try it Yourself**

Enables students to practise what have been just learnt in Worked Examples.**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.

**Let's Sum Up**

Consolidates important concepts in the chapter**Flashback + Reflect + Extend Your Learning Curve****Core Vocabulary**

Highlights key terms from the chapter**Getting Started**

Provides relevant real-life applications of concepts in the immediate chapter and acts as a trigger that piques students' interest

**Integrated Exercise**

Requires students to synthesise concepts learnt across different chapters.**Spotlight**

Draws attention to important mathematical information.**Coding**

Provides coding opportunities to support development of computational thinking.**Extra Info**

Provides extra information such as scientific, historical and fun facts to pique students' interest.**Answer Key**

Textbook A:

**Quadratic Functions**Graphs, Always Negative or Positive, Models**Equations and Inequalities**

Nature of roots, Simultaneous Equations, Quadratic Inequalities**Surds**

Four Operations and Equations**INTEGRATED EXERCISE****Polynomials and Partial Fractions**

Remainder and Factor Theorems, Cubic Polynomials and Equations, Partial Fractions**Exponential and Logarithmic Functions and Equations****Binomial Expansions****Coordinate Geometry of Lines and Rectilinear Figures**

Midpoint, Parallel and Perpendicular Lines, Area**Coordinate Geometry of Circles**

Equation, Intersection Points**Trigonometric Functions, Graphs and Equations****Trigonometric Identities and Formulae**

Basic Identities, Addition, Double Angle , R Formulae**INTEGRATED EXERCISE**

Answer Key

Textbook B:

**Differentiation**

Rules of Differentiation, Chain Rule, Product Rule, Quotient Rule**Tangents, Normal and Rates of Change****Maxima and Minima**

Higher Order Derivatives, Increasing and Decreasing Functions, Stationary Points and Their Nature, Maxima and Minima Problems**Further Differentiation**

Trigonometric, Exponential, Logarithmic Functions and Applications of Derivatives**INTEGRATED EXERCISE****Indefinite Integrals**

Basic Rules, Applications, Trigonometric Functions**Definite Integrals**

Area by Curve and Line(s) and below x-axis**Kinematics**

Application of Differentiation and Integration**Proofs in Plane Geometry**

Proofs involving: Parallel Lines, Congruent Triangles, Quadrilaterals, Perpendicular Lines, Angle Bisectors, Similar Triangles, Midpoint Theorem, Circles and Tangent-chord Theorem**INTEGRATED EXERCISE**

Complete series contain:

- Textbooks