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Year 12 Standard

63 skills on 5 lines. Start here: Find and interpret the intersection of two lines.

Next up

  • Algebra and functions
  • Financial mathematics
  • Networks
  • Probability and data
  • Trigonometry
  • Needs both

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Mathematics Standard — Years 11–12 · Year 12

63 lessons in this selection

Learning tree for Mathematics Standard — Years 11–12 · Year 12 63 skills · 17 topics · builds on 18 skills from earlier years

  1. Stage 6 · Year 12

    1. Standard 1: Algebraic relationships:
      3 of 3 skills with lesson material
    2. Standard 1: Ratios and rates:
      4 of 4 skills with lesson material
    3. Standard 2: Algebraic relationships:
      6 of 6 skills with lesson material
    4. Standard 2: Ratios and rates:
      5 of 5 skills with lesson material
    5. Standard 1: Investment:
      3 of 3 skills with lesson material
    6. Standard 1: Depreciation and loans:
      4 of 4 skills with lesson material
    7. Standard 2: Investment and loans:
      7 of 7 skills with lesson material
    8. Standard 2: Annuities:
      3 of 3 skills with lesson material
    9. Standard 2: Network flow:
      2 of 2 skills with lesson material
    10. Standard 2: Critical path analysis:
      3 of 3 skills with lesson material
    11. Standard 1: Bivariate data analysis:
      2 of 2 skills with lesson material
    12. Standard 1: Relative frequency and probability:
      3 of 3 skills with lesson material
    13. Standard 2: Bivariate data analysis:
      3 of 3 skills with lesson material
    14. Standard 2: Relative frequency and probability:
      4 of 4 skills with lesson material
    15. Standard 2: The normal distribution:
      3 of 3 skills with lesson material
    16. Standard 1: Right-angled triangles:
      3 of 3 skills with lesson material
    17. Standard 2: Trigonometry:
      5 of 5 skills with lesson material

Each skill of Mathematics Standard — 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 Standard — Years 11–12; detailed outcome alignment for NSW is not verified.

Standard 1: Algebraic relationshipsAlgebra and functions

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Find and interpret the intersection of two linesStructure
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Find revenue, cost and break-even graphicallyStructure
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Compare linear and exponential practical modelsStructure
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Standard 1: Ratios and ratesAlgebra and functions

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Interpret, simplify, compare and divide in a ratioStructure
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Read scaled maps and plans and estimate material costsStructure
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Convert and compare rates and unit pricesStructure
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Read distance-time graphs and compare fuel efficiencyStructure
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Standard 2: Algebraic relationshipsAlgebra and functions

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Solve and interpret simultaneous linear equationsStructure
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Model cost, revenue, profit and break-evenStructure
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Graph and interpret exponential growth and decayStructure
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Construct quadratic graphs and locate their featuresStructure
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Interpret quadratic models in practical contextsStructure
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Recognise, graph and solve reciprocal modelsStructure
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Standard 2: Ratios and ratesAlgebra and functions

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Solve ratio allocations and capture-recapture estimatesStructure
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Construct scaled plans and calculate land and material quantitiesStructure
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Calculate water volume from rainfall over an areaStructure
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Convert rates and interpret travel, prices and fuel efficiencyStructure
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Calculate power, energy consumption and electricity costStructure
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Standard 1: InvestmentFinancial mathematics

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Calculate and rearrange simple-interest modelsStructure
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Calculate compound future value and present valueStructure
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Compare savings, term deposits and property investment modelsStructure
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Standard 1: Depreciation and loansFinancial mathematics

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Compare straight-line and declining-balance depreciationStructure
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Calculate reducing-balance repayments and compare borrowingStructure
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Read credit-card statements and calculate daily compound interestStructure
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Compare credit-card choices against stated financial goalsStructure
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Standard 2: Investment and loansFinancial mathematics

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Calculate and rearrange simple-interest relationshipsStructure
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Calculate compound future and present valuesStructure
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Compare savings and investment growth with spreadsheetsStructure
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Read share information and calculate costs and dividend yieldStructure
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Compare straight-line and declining-balance asset modelsStructure
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Calculate loan balances and compare repayment choicesStructure
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Calculate statement balances, daily interest and credit-card costsStructure
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Standard 2: AnnuitiesFinancial mathematics

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Build contribution and withdrawal annuity tablesStructure
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Use interest-factor tables for annuity future and present valueStructure
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Compare annuity and repayment scenarios using digital toolsStructure
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Standard 2: Network flowNetworks

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Represent directed flow and calculate feasible path capacitiesStructure
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Find maximum flow and evaluate capacity changes and demandStructure
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Standard 2: Critical path analysisNetworks

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Build activity networks with correct dependencies and dummy edgesStructure
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Calculate earliest and latest times, floats and critical pathsStructure
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Build Gantt charts and evaluate scheduling changesStructure
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Standard 1: Bivariate data analysisProbability and data

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Choose variables and distinguish association from causationStructure
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Construct scatterplots and interpret a best-fit modelStructure
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Standard 1: Relative frequency and probabilityProbability and data

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Build sample spaces and calculate simple-event probabilitiesStructure
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Represent and calculate two-stage outcomes with replacementStructure
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Estimate probabilities, expected counts and assess statistical claimsStructure
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Standard 2: Bivariate data analysisProbability and data

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Define bivariate variables and describe scatterplotsStructure
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Calculate and interpret Pearson correlation using technologyStructure
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Fit a least-squares line and assess predictionsStructure
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Standard 2: Relative frequency and probabilityProbability and data

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Build sample spaces and calculate event probabilitiesStructure
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Use arrays and trees for multistage probabilitiesStructure
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Use relative frequency and expected counts in decisionsStructure
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Represent two attributes in Venn diagrams and two-way tablesStructure
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Standard 2: The normal distributionProbability and data

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Recognise normal models and compare values with z-scoresStructure
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Estimate normal probabilities using the empirical ruleStructure
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Compare normal extremeness and make bounded statistical judgementsStructure
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Standard 1: Right-angled trianglesTrigonometry

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Choose and solve right-triangle side and angle problemsStructure
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Read, convert and use compass and true bearingsStructure
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Solve elevation, depression and navigation problemsStructure
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Standard 2: TrigonometryTrigonometry

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Solve right-triangle side and angle problemsStructure
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Use the sine rule with appropriately determined anglesStructure
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Use the cosine rule and included-angle area formulaStructure
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Use bearings and radial surveys to represent landStructure
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Select and combine triangle methods in practical problemsStructure
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Curriculum details for Mathematics Standard — Years 11–12

NSW Mathematics Standard (2024); common Year 11, Standard 1 and Standard 2 Year 12.

Year 12 in the NSW source sequence · Year 12.

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

In Mathematics Standard — 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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