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 ObjectivesProvided at the start of each section to inform students about what they will be learning in the section. Connecting IdeasEmphasise 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 ExamplesFacilitates students' understanding of concepts and shows how ideas and reasoning can be expressed clearly in mathematical language. Try it YourselfEnables 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 UpConsolidates important concepts in the chapter Flashback Reflect Extend Your Learning Curve Core VocabularyHighlights key terms from the chapter Getting StartedProvides relevant real-life applications of concepts in the immediate chapter and acts as a trigger that piques students' interest Integrated ExerciseRequires students to synthesise concepts learnt across different chapters. SpotlightDraws attention to important mathematical information. CodingProvides coding opportunities to support development of computational thinking. Extra InfoProvides extra information such as scientific, historical and fun facts to pique students' interest. Answer Key Textbook A: Quadratic FunctionsGraphs, Always Negative or Positive, Models Equations and InequalitiesNature of roots, Simultaneous Equations, Quadratic Inequalities SurdsFour Operations and EquationsINTEGRATED EXERCISE Polynomials and Partial FractionsRemainder and Factor Theorems, Cubic Polynomials and Equations, Partial Fractions Exponential and Logarithmic Functions and Equations Binomial Expansions Coordinate Geometry of Lines and Rectilinear FiguresMidpoint, Parallel and Perpendicular Lines, Area Coordinate Geometry of CirclesEquation, Intersection Points Trigonometric Functions, Graphs and Equations Trigonometric Identities and FormulaeBasic Identities, Addition, Double Angle , R FormulaeINTEGRATED EXERCISEAnswer Key Textbook B: DifferentiationRules of Differentiation, Chain Rule, Product Rule, Quotient Rule Tangents, Normal and Rates of Change Maxima and MinimaHigher Order Derivatives, Increasing and Decreasing Functions, Stationary Points and Their Nature, Maxima and Minima Problems Further DifferentiationTrigonometric, Exponential, Logarithmic Functions and Applications of DerivativesINTEGRATED EXERCISE Indefinite IntegralsBasic Rules, Applications, Trigonometric Functions Definite IntegralsArea by Curve and Line(s) and below x-axis KinematicsApplication of Differentiation and Integration Proofs in Plane GeometryProofs involving: Parallel Lines, Congruent Triangles, Quadrilaterals, Perpendicular Lines, Angle Bisectors, Similar Triangles, Midpoint Theorem, Circles and Tangent-chord TheoremINTEGRATED EXERCISE Complete series contain: Textbooks
