Mathematics , Stage – 5

Stage 5 Mathematics (Years 9–10)

Stage 5 Mathematics extends the foundational skills developed in Stage 4 and prepares students for senior study and practical applications beyond school. It emphasizes deeper problem‑solving, abstract reasoning, and the ability to connect mathematics with real‑world contexts such as science, technology, finance, and everyday decision‑making.

What Students Learn

• Number & Algebra:

  • Indices, surds, and scientific notation.

  • Algebraic techniques including expansion, factorisation, and solving linear and quadratic equations.

  • Simultaneous equations and inequalities.

  • Patterns, sequences, and introduction to functions.

• Measurement & Geometry:

  • Pythagoras’ theorem and trigonometry in two and three dimensions.

  • Properties of circles, polygons, and geometric proofs.

  • Surface area and volume of complex solids.

  • Scale drawings, similarity, and congruence.

• Statistics & Probability:

  • Data collection, analysis, and representation using graphs and technology.

  • Measures of spread (range, interquartile range, standard deviation).

  • Probability concepts including relative frequency, compound events, and two‑way tables.

  • Introduction to probability distributions.

• Financial Mathematics:

  • Simple and compound interest.

  • Depreciation, loans, and investments.

  • Budgeting, taxation, and financial decision‑making.

Learning Outcomes

By the end of Stage 5, students will:

• Apply advanced algebraic and numerical techniques to solve complex problems.

• Use trigonometry and geometry to model and solve spatial problems.

• Analyse and interpret data using statistical tools and probability concepts.

• Make informed financial decisions using mathematical reasoning.