Secondary School Mathematics Material (All Level Compilation) Version 20260224

Title Secondary School Elementary Mathematics Materials Compilation Series (20260224A) Author AprilDolphin – Lim Wang Sheng Date 24/02/2026 Secondary Level Topic Page 1 Basic Algebra – Basic Algebraic Manipulation 2 1 Basic Algebra – Formula Manipulation 12 1 Basic Algebra – Simple Inequalities 18 1 Factors and Multiples 25 1 Percentages 31 1 Coordinate Geometry – Basics 39 1 Coordinate Geometry – Straight Lines 44 2 Direct and Inverse Proportion 47 2 Maps and Scales 50 2 Expansion & Factorisation of Algebraic Expression 54 2 Quadratic Equations and Functions 58 2 Simultaneous Equations (Linear) 70 2 Basic Statistics – Ungrouped Data 75 2 Basic Statistics – Grouped Data 81 2 Shapes of Graphs of Functions 89 3 Applications of Quadratic Equations 100 3 Laws of Indices 103 3 Set Language & Venn Diagram 107 3 Trigonometry, Congruency & Similarity of Triangles 117 3 Matrices 124 4 Financial Arithmetic – Money Exchange 130 4 Financial Arithmetic – Simple & Compound Interest 133 4 Financial Arithmetic – Hire Purchase 136 4 Vectors in Two Dimensions 138 This document is to be released into CC0 Public Domain Dedication by Lim Wang Sheng and all the other authors and editors upon creation.

Title Basic Algebra – Algebraic Manipulation Author AprilDolphin – Lim Wang Sheng Date 2/2/2026 Algebra is basically • Representing known or unknown quantities and numbers with letters and symbols • Performing mathematical operations using letters and symbols, together with numbers Without algebra • Textbook would be ridiculously thick and heavy • Certain statistical analysis will be virtually impossible to conduct as the person conducting the analysis will need to make endless amount of mathematical explanation • Certain fields of Mathematics, dependent on algebra, cannot exist as well Tips to students who are new to basic algebra • Please name your unknowns systematically, so that you won’t be confused. • Never use letters that can be easily confused for something else as shown in the below table (Unless the question specified them as part of the question or insist that you must use them): Common Letters to try Avoid Using Reasoning/Explanation 𝑄 (Upper Case Only) Upper case letter 𝑄 can be confused with “𝑂” or Zero (0) 𝑂, 𝑜 (Lower Case and Upper Case) Upper case letter 𝑂 can be confused with zero (0). Lower case letter 𝑜 can be confused with zero (0). 𝐽, 𝑗 (Lower Case and Upper case) Upper case letter 𝐽 can be confused with 𝐿 and 𝐼 Lower case letter 𝑗 can be confused with 𝑖 𝑙 (Lower Case only) Lower case letter 𝑙 can be confused with 𝑖 or one (1) 𝐼, 𝑖 (Lower case and upper case) Upper case letter 𝐼 can be confused with lower case letter 𝑙 Lower case letter 𝑖 is typically reserved for a specific use at higher level Mathematics

𝑒 (Lower Case Only) Lower case 𝑒 is typically reserved for a specific use at higher level Ma