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Year 12 Advanced

43 skills on 4 lines. Start here: Transform sine, cosine and tangent graphs.

Next up

  • Algebra and functions
  • Calculus
  • Probability and data
  • Sequences and finance
  • Needs both

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Mathematics Advanced — Years 11–12 · Year 12

23 lessons in this selection

Learning tree for Mathematics Advanced — Years 11–12 · Year 12 43 skills · 12 topics · builds on 30 skills from earlier years

  1. Stage 6 · Year 12

    1. Further graph transformations and modelling:
      5 of 5 skills with lesson material
    2. Differentiation yr12:
      2 of 5 skills with lesson material
    3. Differential calculus:
      2 of 2 skills with lesson material
    4. Integration:
      3 of 5 skills with lesson material
    5. Integral calculus:
      7 of 9 skills with lesson material
    6. Applications of calculus:
      0 of 3 skills with lesson material
    7. Probability distributions:
      0 of 2 skills with lesson material
    8. Data distributions yr12:
      0 of 3 skills with lesson material
    9. Random variables:
      0 of 3 skills with lesson material
    10. Sequences and series:
      2 of 2 skills with lesson material
    11. Financial maths:
      2 of 3 skills with lesson material
    12. Financial mathematics:
      0 of 1 skills with lesson material

Each skill of Mathematics Advanced — Years 11–12 · Year 12, and what it builds on, is drawn in the network above.

Sequence: NSW syllabus, as used on the learning platform for Mathematics Advanced — Years 11–12; detailed outcome alignment for NSW is not verified.

Further graph transformations and modellingAlgebra and functions

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Transform sine, cosine and tangent graphsStructure
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Solve transformed trigonometric equationsStructure
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Model periodic phenomenaStructure
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Choose and evaluate transformed function modelsStructure
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Logarithmic scales and multiplicative comparisonsStructure
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Differentiation yr12Calculus

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Differentiate exponentials and logarithmsStructure
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Differentiate trigonometric functionsStructure
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Differential calculusCalculus

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Differentiate mixed elementary functionsStructure
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Tangents and normals to elementary curvesStructure
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IntegrationCalculus

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Primitives and the family of antiderivativesStructure
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Numerical integration and trapezoidal approximationStructure
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The Fundamental Theorem and definite integralsStructure
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Integral calculusCalculus

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Primitives of powers of linear functionsStructure
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Find a primitive from an initial conditionStructure
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Definite integrals as signed accumulationStructure
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Recognise reverse-chain integralsStructure
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Integrate exponential functionsStructure
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Reciprocal integrals and logarithmsStructure
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Integrate trigonometric functionsStructure
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Sequences and seriesSequences and finance

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Sequences, partial sums and sigma notationStructure
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Limiting geometric sumsStructure
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Financial mathsSequences and finance

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Arithmetic sequences and their sumsStructure
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Geometric sequences and finite sumsStructure
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Curriculum details for Mathematics Advanced — Years 11–12

NSW Mathematics Advanced (2024); Year 11 from 2026, Year 12 first HSC 2027; retained revision labelled separately.

Year 12 in the NSW source sequence · Year 12.

The Mathematics Advanced — Years 11–12 collection follows its named source sequence; detailed outcome alignment for New South Wales is not verified.

In Mathematics Advanced — Years 11–12, some source stages span two years and share lessons; choose a topic within the selected year level and revisit its foundation explanations when needed.

Focused preparation routes13 routes

Each route teaches one skill, with original, untimed questions. None is a complete NAPLAN programme, a placement test or a promised advantage.

How much is written so far

Every skill with a written lesson, stage by stage.

Skills with a written lesson, by school stageMathematics K–10: 236 of 236 skills have a lesson. Kindergarten: 6 of 6; Years 1–2: 14 of 14; Years 3–4: 13 of 13; Years 5–6: 15 of 15; Years 7–8: 46 of 46; Years 9–10: 142 of 142. English K–10: 335 of 363 skills have a lesson. Kindergarten: 57 of 57; Years 1–2: 52 of 52; Years 3–4: 71 of 71; Years 5–6: 71 of 71; Years 7–8: 57 of 57; Years 9–10: 27 of 55.Mathematics K–10236 of 236 skills have a lessonKindergarten6 of 6Years 1–214 of 14Years 3–413 of 13Years 5–615 of 15Years 7–846 of 46Years 9–10142 of 142English K–10335 of 363 skills have a lessonKindergarten57 of 57Years 1–252 of 52Years 3–471 of 71Years 5–671 of 71Years 7–857 of 57Years 9–1027 of 55Has a lessonNot written yetSource: the platform’s skill trees andlesson filesSkills with a written lesson, by school stageMathematics K–10: 236 of 236 skills have a lesson. Kindergarten: 6 of 6; Years 1–2: 14 of 14; Years 3–4: 13 of 13; Years 5–6: 15 of 15; Years 7–8: 46 of 46; Years 9–10: 142 of 142. English K–10: 335 of 363 skills have a lesson. Kindergarten: 57 of 57; Years 1–2: 52 of 52; Years 3–4: 71 of 71; Years 5–6: 71 of 71; Years 7–8: 57 of 57; Years 9–10: 27 of 55.Mathematics K–10236 of 236 skills have a lessonKindergarten6 of 6Years 1–214 of 14Years 3–413 of 13Years 5–615 of 15Years 7–846 of 46Years 9–10142 of 142English K–10335 of 363 skills have a lessonKindergarten57 of 57Years 1–252 of 52Years 3–471 of 71Years 5–671 of 71Years 7–857 of 57Years 9–1027 of 55Has a lessonNot written yetSource: the platform’s skill trees and lesson files

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