Journal

Special right triangles and their place in geometry
From the angles of a roof in suburban Sydney to the eaves of a beach house along the Mornington Peninsula, geometry hides in plain sight. Special right…
The Pythagorean Theorem: Proofs and Practical Applications
The Pythagorean theorem is one of those rare mathematical ideas that every Australian student meets before finishing secondary school. Whether you sit the HSC…
Understanding arithmetic sequences and series
Arithmetic sequences are one of the simplest patterns in mathematics, yet they appear constantly inside the Australian Curriculum and in everyday life. Each…
What Is a Geometric Sequence? Formulas and Examples
A geometric sequence is a list of numbers in which each term is found by multiplying the previous term by the same constant value. This constant is called the…
Solving Exponential Equations Using Logarithms
For many secondary students across Sydney, Melbourne, and Brisbane, the leap from linear and quadratic equations into the world of exponents feels like moving…
Logarithmic functions: properties and equation-solving strategies
Logarithmic functions appear throughout senior secondary mathematics in Australia, from the Mathematical Methods courses in Year 11 and Year 12 to the…
Exponential Functions: Growth and Decay in Real Models
The exponential family of functions describes anything that multiplies by a fixed factor over equal intervals of time. Whether a quantity doubles, halves, or…
Inverse functions: how to find them and check your answer
Inverse functions come up across the Australian senior secondary curriculum right through to first-year university calculus, yet many students find the topic…
Composite Functions: Evaluate, Simplify, and Check Your Work
Functions become especially useful when one rule feeds its output into another. This process is called composition, and it appears in algebra, modelling,…
Understanding functions: domain and range basics
Functions are one of the main ideas connecting algebra, graphs, statistics, and everyday problem-solving. They describe a relationship in which each allowed…