Additional Additional Mathematics Additional Mathematics

• Nature/Scope: • Assume the knowledge of O-Level Math content and includes more in-depth some topics. • Major topics includes : . – Functions, polynomials, logarithm . Geometry & - geometry proofs, trigonometric ratios and identities, . - Differentiation & Integration, . Math Processes - develop reasoning, problem-solving skills, proofs and making connections among mathematical concepts. Additional Mathematics Syllabus

• New Syllabus 4049 (O-Level) / 4051 (N-Level) • First Exam in 2021 (O-Level) and (N-Level) • Topics based on o Algebra (Chapters 1 – 8) o Geometry and Trigonometry (Chapters 9 – 13) o Calculus (Chapters 14 – 20)

• https://www.seab.gov.sg/docs/default-source/national- examinations/syllabus/nlevel/2020syllabus/4044_y20_sy.pdf • https://www.seab.gov.sg/docs/default-source/national- examinations/syllabus/olevel/2020syllabus/4047_y20_sy.pdf Scheme of Assessment – 4049 (O-Level) Scheme of Assessment – 4051 (N-Level) Elementary Math 4048 (O-level) Math Syllabus A 4045 (N-level) Additional Mathematics

Aptitude : • For 3NA Add Math: Achieve a good pass in NA Math and must be doing O-Level Math • Must enjoy practicing Math problems especially algebra;

Advantages : • More options in the next level of education • Trains up your level of perseverance and independence Additional Mathematics

Prospects : • In Junior College ( L1R5 ) : • H1 Math builds on O-level Math; • H2 Math assume some of A Math content, H3 is an extension of H2. • In Polytechnics : • Only need 1 Math subject (E Math or A Math in EMR3); • PFP (MA ≤3), DPP ( MA ≤ 4) • EMB3 ≤19 for 4NA to 5NA. • Career prospects : Computer Science & Engineering courses in Polytechnics and University (Aerospace, civil, bioengineering, mechanical, computer science) Requirement for Junior College

• Can be considered as a subject for L1R5 Junior College

Without A Math With A Math

H1 mathematics H2 mathematics

Saint Andrew JC

National JC Subject Requirement for University

(NUS)

(NTU) Requirement for Polytechnic

• Needs only 1 Math subject to go Polytechnic (Elementary or Additional Mathematics) Requirement for Polytechnic

• Needs only 1 Math subject to go Polytechnic (mainly Elementary Mathematics) Example 1 – Simultaneous Equation

• In Sec 2 • Solving simultaneous linear equations • E.g: 2x + y = 9 2x – 3y = 29

• In Sec 3 Add Math • Solve simultaneous linear and non-linear equations. • E.g: 2x + y = 1 y2 + (2x+3)2 = 10 Use substitution method! Example 1 – Simultaneous Equation

E.g: y2 + (2x+3)2 = 10 ---- (1) 2x + y = 1 2x = 1 – y ---- (2)

Sub (2) into (1): y2 + (1 – y +3)2 = 10 y2 + (4 – y)2 = 10 Quadratic y2 + 16 – 8y + y2 = 10 Equation! 2y2 – 8y + 6 = 0 Example 1 – Simultaneous Equation

y2 – 4y + 3 = 0 (y – 1) (y – 3) = 0 Cross / Box method! y = 1 or y = 3

Sub y = 1 into (2): Sub y = 3 into (2): 2x = 1 – 1 2x = 1 – 3 x = 0 x = - 1

Therefore, x = 0, y = 1 or x = -1, y = 3. Example 2 – Indices • In lower sec Math, • you learnt to simplify • a2 x a3 • b7 ÷ b4 • In Sec 3 Add Math, • you will learn 8 laws of indices ( 5 laws would also be covered in Sec 3E Math ) am x an = am+n am ÷ an = am-n am x bm = (a x b)m am ÷ bm = (a ÷ b)m (am)n = amn am/n = (am) 1/n a0 = 1 a -m = 1÷am Example 2 – Indices Other Add Math Algebra Content

• That’s not all you learn in Add Math algebra.

• You still have o Polynomials (+, -, x, ÷) o Remainder Theorem o Solving cubic equations o Partial fractions o Exponential & Logarithms functions (O Level only) o (O level only)… Example 3 – Linear Graph and Gradient

• In Sec 1 & 2 Math, • you have learnt to find gradient between 2 points (with/without formula).

• In Sec 3 E Math, you will learn to find • length between 2 points • gradient of 2 parallel lines • equation of a straight line (y = mx + c) Example 3 – Linear Graph and Gradient

• In Sec 3 A Math Geometry, you will learn to find • midpoint between 2 points • area of triangles and quadrilaterals (using coordinates of vertices of triangle / quadrilaterals) • Relationship between gradient of perpendicular lines m1m2 = -1 • equation of perpendicular line using y - y1 = m(x – x1) or y = mx + c

(Note: Manipulating these terms mainly involves algebra) Other O-Level Add Math Geometry Content

• Linear Laws* (how to convert non-linear graph to straight line) o Examples : y2 = 2x + 3, xy2 = 2x + 5y, o y = px2 + x + q, y = kbx

• Circles o (x – a)2 + (y – b)2 = r2

• Plane geometry (proofs) (CLT*) Trigonometry Content (E Math)

• In Sec 3 E Math, you will learn Trigonometry o Trigonometric ratios of acute angles o Trigonometric ratios of obtuse angles o Area of a triangle o Sine Rule o Cosine Rule o Bearing o Angles of elevation & depression o Simple 3D problems Example 4 – Trigonometry Other Add Math Trigonometry Content

• In Sec 3 A Math, you will learn Trigonometry o Trigonometric ratios of any angles o Graphs of Sine, Cosine & Tangent Functions o Prove trigonometric identities o Solve trigonometric equations o Addition formulae o Double angle formulae o R-formulae etc Add Math Calculus Content

• In Sec 4 AM, you will learn Calculus o Differentiation o Integration o Kinematics (Only for “O” level syllabus) Example 6 – Calculus Importance of Additional Mathematics

Additional Mathematics trains you to become a stronger critical thinker and improves your confidence in dealing with numbers and logic. I cannot stress the importance of having strong arithmetic and logic skills in our society.

Practice and prefect the algebra during the holidays for a good start with A Math in 2021 