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 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.
Theory
Functions
- Formalising Graphs and Functions [TBC]
- The Four Conic Sections [TBC]
- Baby Functional Analysis [TBC]
- Equations and Inequalities [TBC]
- Sequences and Series [TBC]
- Recursive Algorithms [TBC]
Differential Calculus
- The Gradient Function [TBC]
- Implicit Differentiation [TBC]
- Polynomial Approximations [TBC]
- Baby Numerical Analysis [TBC]
- Baby Multivariable Differentiation [TBC]
Integral Calculus
- Riemann Summation [TBC]
- Reverse Differentiation Plus [TBC]
- Integral Geometry [TBC]
- Refining Riemann Summation [TBC]
- Even More Applied Calculus [TBC]
- Baby Mathematical Modeling [TBC]
Linear Algebra
- Vector Nomenclature [TBC]
- Three-Dimensional Coordinate Geometry [TBC]
- Multiplying Vectors in Multiple Flavors [TBC]
- What is a Matrix? [TBC]
- A Sample of Linear Algebra [TBC]
- Eigenstuff Recursions [TBC]
Complex Numbers
- Baby Complex Analysis [TBC]
- Revisiting the Exponential [TBC]
- A Polar Perspective [TBC]
Probability
- Baby Combinatorics [TBC]
- Probability Vocabulary [TBC]
- Discrete Random Variables [TBC]
- Continuous Random Variables [TBC]
- Frequented Distributions [TBC]
Statistics
- The Bell Curve [TBC]
- Hypothesis Testing [TBC]
- Correlation and Linear Regression [TBC]
- Non-Parametric Tests [TBC]
Past Year Papers
KindiakMath 