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

Algebra

  1. Visualising Vectors
  2. Quadratic Functions Again
  3. Return of the Square Root
  4. Solving Cubic Equations
  5. Who Cares About Binomials?
  6. About Higher Powers

Measurement

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

Calculus

  1. Vroom, Vroom! [TBC]
  2. Baby Differentiation [TBC]
  3. Turning Points [TBC]
  4. Baby Integration [TBC]
  5. Applied Calculus [TBC]

Statistics

  1. Central Tendency [TBC]
  2. Measures of Spread [TBC]
  3. Basic Probabilistic Events [TBC]
  4. Visualising Probability [TBC]

Exercises

Numbers

  1. Divisibility Tricks [TBC]
  2. Number Patterns [TBC]

Geometry

  1. Leftover Angle Properties [TBC]
  2. Surveying Problems [TBC]
  3. The Triangle Inequality [TBC]
  4. The Construction Toolkit [TBC]
  5. Quadri-literacy [TBC]

Algebra

  1. Coordinate Geometry Bookkeeping [TBC]
  2. Quadratic Identities and Factorisation [TBC]
  3. Return to Circle Geometry [TBC]
  4. The Cubic Formula [TBC]
  5. Scientific Notation [TBC]

Measurement

  1. Proportionality [TBC]
  2. The Parallelogram Puzzle [TBC]
  3. Trigonometric Identities
  4. Angles of Elevation [TBC]
  5. Solving Trigonometric Equations [TBC]

Calculus

  1. Several Differentiation Formulas [TBC]
  2. The Volume of a Sphere [TBC]

Statistics

  1. The Three-Door Problem [TBC]
  2. Basic Blackjack [TBC]