KindiakMath

A-Level Math

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

Most of these write-ups will incline towards intuitive visual proofs (that can 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 A-Level Mathematics and even its Further variant, coupled with a tinge of mathematical rigour comparable to that in university mathematics.

In this blog, the required topics will be arranged mathematically, rather than according to 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.

As a yearly tradition as well, I will write solutions to the various H2 Math papers, starting from 2025. (Actually, I have done up solutions for the past few semesters here; 2025 is the first year I’m doing them on KindiakMath.) Due to copyright reasons I will not be able to reproduce the questions. However, based on the solutions, or your own copy of the ten-year series, you could reverse-engineer or reference the relevant questions that these solutions answer.

Since relocating to Adelaide, I will also write solutions to the various Stage 2 Maths Methods and Stage 2 Specialist Maths papers according to the SACE syllabus, with 2025 being the first paper.

Theory

Functions

  1. Formalising Functions
  2. The Science of Art
  3. Transformation Rebellion
  4. Answers and Estimates
  5. Algebra on Mild Steroids
  6. Recursive Algorithms
  7. Mathematical Dominoes

Calculus

  1. Advanced Differentiation
  2. Mathematical Modelling
  3. Polynomial Approximations
  4. Baby Numerical Analysis
  5. Riemann Summation
  6. Reverse Differentiation Plus
  7. Applied Calculus
  8. Baby Differential Equations
  9. Partial Differential Equations

Linearity

  1. Three-Dimensional Geometry [TBC]
  2. Two Kinds of Vector Products [TBC]
  3. A Sample of Linear Algebra [TBC]
  4. Eigenstuff Recursions [TBC]
  5. Baby Complex Analysis [TBC]
  6. Revisiting the Exponential [TBC]
  7. A Polar Perspective [TBC]

Probability

  1. Baby Combinatorics [TBC]
  2. Probability Vocabulary [TBC]
  3. Discrete Random Variables [TBC]
  4. Continuous Random Variables [TBC]
  5. Frequented Distributions [TBC]
  6. The Bell Curve [TBC]
  7. Hypothesis Testing [TBC]
  8. Baby Regression Analysis [TBC]
  9. Non-Parametric Tests [TBC]

GCE Advanced Level (Singapore)

  1. H2 Math 2022 Suggested Answers: Paper 1 and Paper 2
  2. H2 Math 2023 Suggested Answers: Paper 1 and Paper 2
  3. H2 Math 2024 Suggested Answers: Paper 1 and Paper 2
  4. H2 Math 2025 Suggested Answers: Paper 1 and Paper 2

SACE Stage 2 (South Australia)

  1. SACE Stage 2 Maths Methods 2023 Suggested Answers
  2. SACE Stage 2 Maths Methods 2024 Suggested Answers
  3. SACE Stage 2 Maths Methods 2025 Suggested Answers
  4. SACE Stage 2 Specialist Maths 2023 Suggested Answers
  5. SACE Stage 2 Specialist Maths 2024 Suggested Answers
  6. SACE Stage 2 Specialist Maths 2025 Suggested Answers