Year 9 student Lucas worked on linear simultaneous equations with a focus on mastering substitution methods.

Year 10 student Zara reviewed trigonometry, covering SOH CAH TOA and applying both sine and cosine rules to solve triangle problems.

Meanwhile, Year 11 student Jake analysed a previous test by simplifying and rationalising surds as well as tackling elementary set theory and simplifying linear expressions with non-numerical coefficients.

There is a serious level of misunderstanding of how induction and negated statements work for the Year 11 student. Gaps in showing working for rationalising surds led to arithmetic errors that were hard to trace.

In Year 9, forgetting to double-check answers or clarify what questions required meant basic mistakes undermined confidence—especially with negative numbers.

A Year 4 student still avoided writing clear working when adding fractions or converting decimals, which made it difficult for her teacher to spot whether she misunderstood steps or just miswrote digits during tests.

A Lucas tutor recently noticed a Year 9 student who, after previously relying on hints for algebraic manipulation, managed to form and solve quadratic equations almost entirely independently.

In Year 11 physics, another student shifted from confusion about nuclear reactions to confidently explaining both fission and fusion in detail, even comparing how energy is released in each process.

Meanwhile, a younger primary student who initially made frequent mistakes when working with arrays to find fractions began grouping and counting dots accurately by the third exercise, needing far fewer reminders and showing she could spot equivalent fractions herself.