O level Maths notes 16122015

GCE ‘N’ AND ‘O’ LEVEL ELEMENTARY MATHEMATICS NOTES Written By: Lai Zhi Yin Mobile: 9232 2940|Email: me@bishantuition.com|Website: bishantuition.com

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 1 Revision Check    Notes to All Students This book is written according to the syllabus of GCE O Level Elementary Mathematics (Subject code: 4016 and 4048) for Year 2016 taken from SEAB website. The purpose in writing this book is to help students break down Mathematics into simpler parts and to achieve a better understanding of the individual concepts. By studying this book solely, you are not guaranteed to get A1 in the O levels. Intensive practise is advised. Notes written in red emphasises the common mistakes committed by students in the exams. Do make sure that you understand everything that is written. Students are advised to write their units clearly in all workings and final answer. Failure to do so can lead to a loss of marks. Students are also advised to write their workings and statements clearly. Writing the statements alone does not earn you marks but by showing clear statements and workings, it reflects your understanding towards the question. In the event that you did not get the final answer correct, it will be easier for the examiner to allocate marks through the workings. Even though some of the examples used are adapted from ‘N’ level ten year series, students taking ‘O’ levels are still advised to read through them thoroughly and make sure that every concept is understood clearly as similar questions may appear in the O levels paper. Being complacent will lead to nothing but failure. If possible, cover the examples with a paper and attempt it first before looking at the answers. Students are recommended to contact me at 9232 2940 as soon as possible should they spot any errors during the process of revisions. Good luck to all of you taking the O and N levels  Lai Zhi Yin

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 2 Revision Check    NUMBER AND ALGEBRA N1. Numbers and Four Operations N1.1 Basic Definitions of Mathematical Terms N1.2 Number Line N1.3 Basic Mathematical Symbols N1.4 Expressing Recurring Decimals as Fraction N1.5 Basic Calculator Skills (CASIO fx-96SG PLUS) N1.6 Approximation and Estimation N1.7 Finding Highest Common Factor (HCF) and Lowest Common Factor (LCM) N1.8 Determining Square Root of Number by Prime Factorisation N1.9 Determining Cube Root of Number by Prime Factorisation N1.10 Word Problems Involving HCF and LCM N1.11 Standard Form N1.12 Law of Indices N2. Ratio and Proportion N2.1 Word Problems Involving Ratio and Proportion N2.3 Maps Scales (Distance and Area) N2.4 Direct Proportion N2.5 Inverse Proportion N3. Percentage N3.1 Conversion between Percentage, Decimal and Fraction N3.2 Expressing One Quantity as a Percentage of Another N3.3 Comparing Two Quantities by Percentage N3.4 Calculating % Profit or Loss N3.5 Increasing or Decreasing a Quantity by a Given Percentage N4. Rate and Speed N4.1 Conversion of Units N4.2 Word Problems Involving Speed N4.3 Word Problems Involving Rate N5. Algebraic Expressions and Formulae N5.1 Evaluation of Algebraic Expressions and Formulae N5.2 Changing the Subject of the Formula N5.3 Addition and Subtraction of Algebraic Expressions N5.4 Multiplication and Division of Algebraic Expressions N5.5 Word Problems involving Algebraic Expressions N5.6 Basic Quadratic Formulas N5.7 Expansion of the Product of Quadratic Expressions

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 3 Revision Check    N5.8 Completing the Square not involving an Equation N5.9 Factorisation of Linear Algebraic and Quadratic Expression N5.10 Number Patterns N6. Functions and Graphs N6.1 Graphs of Common Equations N6.2 Sketching of Curve (Quadratic Equation – Factorisation) N6.3 Sketching of Curve (Completing the Square Method) N6.4 Plotting of Curve on Graph Paper N7. Equations and Inequalities N7.1 Solving Linear Equations in One Unknown N7.2 Simultaneous Equation N7.3 Solving Quadratic Equation N7.4 Solving Fractional Equations that can be reduced to Quadratic Equation N7.5 Solving Quadratic Equations Related Problems N7.6 Solving Linear Inequalities N8. Set Language and Notation (Not Tested in N Levels) N8.1 Definitions of Set Language and Notation N8.2 Venn Diagram N8.3 Word Problems Involving Set Language and Notation N9. Matrices (Not Tested in N Level) N9.1 Order of Matrices N9.2 Addition and Subtraction of Matrices N9.3 Multiplication of Matrices N9.4 Problems Involving Matrices N10. Problems in Real World Context N10.1 Simple Interest N10.2 Compound Interest N10.3 Money Exchange N10.4 Hire Purchase N10.5 Taxation N10.6 Utilities Bills N10.7 Kinematics (Not Tested in N Levels)

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 4 Revision Check    GEOMETRY AND MEASUREMENT G1. Angles, Triangles and Polygons G1.1 Common Characteristics of Angles, Triangles and Polygons G1.2 Properties of Triangles and Quadrilaterals G1.3 Polygons G1.4. Construction of Perpendicular Bisector G1.5 Construction of Angle Bisector G2. Congruency and Similarity G2.1 Enlargement and Reduction of Plane Figure by Scale Factor G2.2 Determining if Two Triangles are Congruent G2.3 Determining if Two Triangles are Similar G2.4 Questions on Congruency and Similarity G2.5 Ratio of Area and Volumes of Similar Plane Figures G3. Properties of Circles G3.1 Symmetrical Properties of Circles G3.2 Symmetrical Properties of Circles G3.3 Angle Properties of Circles G3.4 Problems Involving Properties of Circle G4. Pythagoras’ Theorem and Trigonometry G4.1 Pythagoras Theorem G4.2 TOA CAH SOH G4.3 Trigonometric Ratios G4.4 Sine Rule and Cosine Rule G4.5 Flow Chart to Determine Formula to be used G4.6 Bearings G5. Mensuration G5.1 Formulas of Common Figures and Solids G5.2 Questions on Mensuration G5.3 Basic Conversion between Length, Area and Volume G5.4 Arc Length and Sector Area G5.5 Radian Measure of Angle G6. Coordinate Geometry G6.1 General Equation G6.2 Gradient (m) of a Linear Graph G6.3 Length of Line Segment G6.4 Questions on Coordinate Geometry G7. Vectors in Two Dimensions

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 5 Revision Check    G7.1 Converting Coordinates into Column Vector G7.2 Addition of Vectors G7.3 Parallel Vectors G7.4 Collinear Vectors G7.5 Determining the Ratios of the Area of the Triangles in Vectors G7.6 Question on Vectors G8. Problems in Real World Context (To be Updated in 2017) G8.1 Solving and Interpretation

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 6 Revision Check    STATISTICS AND PROBABILITY S1. Data Analysis S1.1 Tables S1.2 Pie Chart S1.3 Pictogram S1.4 Bar Graph S1.5 Histogram S1.6 Line Graph S1.7 Mean, Mode and Median S1.8 Dot Diagram S1.9 Stem and Leaf Diagram S1.10 Box and Whiskers S1.12 Cumulative Frequency Curve S1.13 Calculations for Grouped Data S2. Probability S2.1 Introduction to Probability S2.2

Elementary Mathematics Notes Written by: Lai Zhi Yin (2016)| Mobile: 9232 2940| Website: bishantuition.com 7 Revision Check    N1. Numbers and Four Operations N1.1 Basic Definitions of Mathematical Terms ☺ Prime number: Number that can on