KindiakMath

O-Level Math

Here are my write-ups on the theory of secondary school mathematics and some non-trivial exercises therein.

Most of these write-ups will incline towards intuitive visual proofs (that can only be formalised using higher-level topics in university mathematics) rather than repetitive formula-based exercises. The content in these write-ups ought to sufficiently cover the first principles intuitions in O-Level Mathematics (both elementary and additional) that build up to A-Level Mathematics.

In this blog, the required topics will be arranged mathematically, rather than education level. Also, proofs will focus on intuition rather than rigour; the latter can be explored throughout the rest of the blog or at least made mention of without detail.

Theory

Numbers

  1. Prime Numbers
  2. Negative Numbers
  3. The Number Line
  4. Basic Business Math
  5. Baby Linear Algebra

Geometry

  1. Baby Proving
  2. Pythagoras’ Trophy
  3. Matchmaking Triangles
  4. Circular Magic
  5. The Rules of Shapes
  6. Visualising Vectors

Algebra

  1. Quadratics Revisited
  2. Return of the Square Root
  3. Solving Cubic Equations
  4. Who Cares About Binomials?
  5. About Higher Powers

Measurement

  1. Similar Triangles
  2. Basic Mensuration
  3. Shapes in Three Dimensions
  4. Baby Trigonometry
  5. Applied Trigonometry

Calculus

  1. The Curvy Gradient
  2. The Chain Rule
  3. Differentiating Products
  4. Stationary Points
  5. Baby Integration
  6. Applied Integration
  7. Further Calculus

Statistics

  1. The Flavours of Average
  2. Measures of Spread [TBC]
  3. Basic Probabilistic Events [TBC]
  4. Visualising Probability [TBC]

Exercises

Numbers

  1. Divisibility Tricks
  2. Number Patterns
  3. Baby Quantitative Finance

Geometry

  1. Leftover Angle Properties
  2. The Triangle Inequality
  3. Quadri-literacy
  4. The Construction Toolkit

Algebra

  1. The Shoelace Formula
  2. Quadratic Identities
  3. Algebraic Calculus
  4. The Parabolic Reflector
  5. Return to Circle Geometry
  6. An Absurd Puzzle
  7. The Cubic Formula
  8. Scientific Notation [TBC]
  9. Power Laws [TBC]

Measurement

  1. Proportion [TBC]
  2. The Parallelogram Puzzle [TBC]
  3. Trigonometric Identities
  4. Multiplying Vectors
  5. Surveying Problems [TBC]
  6. Angles of Elevation [TBC]
  7. Solving Trigonometric Equations

Calculus

  1. Several Differentiation Drills
  2. Rates of Change [TBC]
  3. Graphing Techniques [TBC]

Statistics

  1. Baby Data Visualisation [TBC]
  2. The Three-Door Problem [TBC]
  3. Basic Blackjack [TBC]