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Mathematics, every topic

46 topics on 3 lines. Kindergarten to Year 10.

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Measurement and space
Number and algebra
Statistics and probability
Needs both

Mathematics, every topic: the learning tree

M Measurement and space

Comparing and sorting (2 skills)
Informal units and time (Needs both, 3 skills)
Formal units (Needs both, 5 skills)
Area, volume and angles (Needs both, 4 skills)
Angle relationships and circles (Needs both, 4 skills)
Length, area and volume (Stage 4) (Needs both, 3 skills)
Geometrical figures and parallel lines (3 skills)
Right-angled triangles (Pythagoras) (Needs both, 1 skill)
Pythagoras, trigonometry and similarity (Needs both, 6 skills)
Introduction to networks (Path) (Needs both, 3 skills)
Measurement, area and volume (Stage 5) (Needs both, 9 skills)
Further trigonometry (Path) (Needs both, 8 skills)
Further area and volume (Path) (4 skills)
Congruence, similarity and geometrical proof (Path) (8 skills)
Circle geometry (Path) (2 skills)

N Number and algebra

Early number sense (Start here, 4 skills)
Place value and counting (5 skills)
Addition and subtraction (4 skills)
Multiplication and division (6 skills)
Fractions and decimals (7 skills)
Primes and indices (3 skills)
Integers, ratios and percentages (Needs both, 7 skills)
Fractions, decimals and percentages (Stage 4) (4 skills)
Algebraic techniques and linear equations (Needs both, 12 skills)
Indices, quadratics and simultaneous equations (6 skills)
Financial mathematics (Stage 5) (6 skills)
Algebraic techniques (Stage 5) (7 skills)
Indices and surds (Stage 5) (8 skills)
Equations and inequalities (Stage 5) (12 skills)
Linear relationships (Stage 5) (Needs both, 15 skills)
Variation and rates of change (Path) (5 skills)
Non-linear relationships (Stage 5) (11 skills)
Polynomials (Path) (6 skills)
Logarithms (Path) (5 skills)
Functions and other graphs (Path) (Needs both, 5 skills)

S Statistics and probability

Collecting and organising data (Needs both, 2 skills)
Data displays (Needs both, 2 skills)
Analysing data (Needs both, 2 skills)
Chance (Needs both, 2 skills)
Probability experiments (Needs both, 4 skills)
Data classification and analysis (5 skills)
Comparing data sets (Needs both, 4 skills)
Bivariate data and lines of best fit (Needs both, 3 skills)
Multistage probability and simulation (Needs both, 3 skills)
Statistical inquiry (Path) (2 skills)
Venn diagrams, sets and conditional probability (Path) (4 skills)

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Biology Years 11–12 · Year 12

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Curriculum details for Biology Years 11–12

NSW Biology Stage 6 (2017); representative Year 11 lesson.

Year 12 in the NSW source sequence · Year 12.

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

In Biology 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.

Chemistry Years 11–12 · Year 12

1 lesson in this selection

Learning tree for Chemistry Years 11–12 · Year 12 1 topic in 1 stage

Year 12 · Year 12
1. Equilibrium:
  1 of 1 skills with lesson material
  1. Gas equilibrium: quotient, extent and physical solutionsLesson material: Exceeding

The full Chemistry Years 11–12 sequence, including what each skill builds on, is in your learning account.

EquilibriumChemical reactions

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Gas equilibrium: quotient, extent and physical solutionsStructure

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Curriculum details for Chemistry Years 11–12

NSW Chemistry Stage 6 (2017); representative Year 12 lesson.

Year 12 in the NSW source sequence · Year 12.

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

In Chemistry 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.

English K–10 · Year 12

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Curriculum details for English K–10

NSW school sequence.

Year 12 in the NSW source sequence · Year 12.

The English K–10 collection follows its named source sequence; detailed outcome alignment for New South Wales is not verified.

In English K–10, some source stages span two years and share lessons; choose a topic within the selected year level and revisit its foundation explanations when needed.

HSC English Advanced · Year 12

1 lesson in this selection

Learning tree for HSC English Advanced · Year 12 4 topics in 1 stage

Year 12 · Year 12
1. Texts and human experiences:
  1 of 4 skills with lesson material
  1. Analyses representations of individual and collective human experiencesLesson material: Exceeding · builds on 2 earlier skills
  2. Explores anomalies, paradoxes and inconsistencies in human behaviour in textsbuilds on 1 earlier skill
  3. Evaluates how texts represent human qualities and emotionsbuilds on 1 earlier skill
  4. Responds to unseen texts under timed conditionsbuilds on 2 earlier skills
2. Critical study of texts:
  0 of 2 skills with lesson material
  1. Evaluates a text's construction, coherence and textual integritybuilds on 1 earlier skill
  2. Weighs different critical interpretations of a text against personal judgmentbuilds on 1 earlier skill
3. Sustained essays under exam conditions:
  0 of 4 skills with lesson material
  1. Sustains a thesis across a complete essaybuilds on 3 earlier skills
  2. Adapts prepared knowledge to an unseen essay questionbuilds on 1 earlier skill
  3. Integrates context and audience response into the argumentbuilds on 2 earlier skills
  4. Writes a full essay in 40 minutes under exam conditionsbuilds on 1 earlier skill
4. Discursive and reflective writing:
  0 of 3 skills with lesson material
  1. Writes discursively, exploring an idea through a personal lensbuilds on 1 earlier skill
  2. Responds to visual and written stimulus in crafted writingbuilds on 2 earlier skills
  3. Writes a reflective statement justifying compositional choicesbuilds on 2 earlier skills

The full HSC English Advanced sequence, including what each skill builds on, is in your learning account.

Texts and human experiencesTextual analysis

Choose a lesson to see its structure.

Analyses representations of individual and collective human experiencesStructure

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Curriculum details for HSC English Advanced

NSW senior secondary sequence.

Year 12 in the NSW source sequence · Year 12.

The HSC English Advanced collection follows its named source sequence; detailed outcome alignment for New South Wales is not verified.

In HSC English Advanced, some source stages span two years and share lessons; choose a topic within the selected year level and revisit its foundation explanations when needed.

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

Stage 6 · Year 12

Further graph transformations and modelling
1. Transform sine, cosine and tangent graphsBuilds on: Base sine, cosine and tangent graphs (Year 11); Combine transformations and reconstruct a rule (Year 11)
2. Logarithmic scales and multiplicative comparisonsBuilds on: Derive and apply logarithm laws (Year 11); Change of base and logarithmic equations (Year 11)
3. Solve transformed trigonometric equationsBuilds on: Transform sine, cosine and tangent graphs; Trigonometric equations on restricted domains (Year 11)
4. Model periodic phenomenaBuilds on: Transform sine, cosine and tangent graphs; Solve transformed trigonometric equations
5. Choose and evaluate transformed function modelsBuilds on: Combine transformations and reconstruct a rule (Year 11); Model periodic phenomena
Differentiation yr12
1. Differentiate exponentials and logarithmsBuilds on: Differentiate composite functions (Year 11); Euler’s number and exponential gradients (Year 11); Derive and apply logarithm laws (Year 11)
2. Differentiate trigonometric functionsBuilds on: Differentiate products (Year 11); Differentiate quotients (Year 11); Differentiate composite functions (Year 11); Prove and apply trigonometric identities (Year 11)
3. Second derivative, concavity and inflectionNot written yetBuilds on: Differentiate mixed elementary functions; Continuity and differentiability
4. Stationary points and complete curve sketchesNot written yetBuilds on: Second derivative, concavity and inflection; Cubic stationary points and monotonic intervals (Year 11)
5. Model and solve optimisation problemsNot written yetBuilds on: Stationary points and complete curve sketches; Quadratic models in context (Year 11)
Differential calculus
1. Differentiate mixed elementary functionsBuilds on: Differentiate exponentials and logarithms; Differentiate trigonometric functions; Choose and combine differentiation rules (Year 11)
2. Tangents and normals to elementary curvesBuilds on: Differentiate mixed elementary functions; Tangent and normal equations (Year 11)
Integration
1. Primitives and the family of antiderivativesBuilds on: Power rule and linearity (Year 11)
2. Numerical integration and trapezoidal approximationBuilds on: Definite integrals as signed accumulation
3. The Fundamental Theorem and definite integralsBuilds on: Definite integrals as signed accumulation; Find a primitive from an initial condition
4. Areas bounded by a curve and the x-axisNot written yetBuilds on: The Fundamental Theorem and definite integrals; Integrate exponential functions; Reciprocal integrals and logarithms; Integrate trigonometric functions
5. Rates and accumulated change in contextNot written yetBuilds on: Find a primitive from an initial condition; Differentiate mixed elementary functions; Integrate exponential functions; Integrate trigonometric functions
Integral calculus
1. Definite integrals as signed accumulationBuilds on: Average change, secants and instantaneous change (Year 11); Piecewise functions and continuity (Year 11)
2. Primitives of powers of linear functionsBuilds on: Primitives and the family of antiderivatives; Differentiate composite functions (Year 11)
3. Find a primitive from an initial conditionBuilds on: Primitives and the family of antiderivatives; Primitives of powers of linear functions
4. Recognise reverse-chain integralsBuilds on: Primitives of powers of linear functions; The Fundamental Theorem and definite integrals; Differentiate composite functions (Year 11)
5. Integral properties, symmetry and digital verificationNot written yetBuilds on: The Fundamental Theorem and definite integrals; Even and odd functions (Year 11)
6. Integrate exponential functionsBuilds on: Recognise reverse-chain integrals; Differentiate exponentials and logarithms
7. Reciprocal integrals and logarithmsBuilds on: Recognise reverse-chain integrals; Differentiate exponentials and logarithms
8. Integrate trigonometric functionsBuilds on: Recognise reverse-chain integrals; Differentiate trigonometric functions
9. Areas relative to the y-axis and inverse curvesNot written yetBuilds on: Areas bounded by a curve and the x-axis; Logarithmic graphs and inverse reflection (Year 11)
Applications of calculus
1. Continuity and differentiabilityNot written yetBuilds on: Differentiate quadratics from first principles (Year 11); Piecewise functions and continuity (Year 11); Absolute value, piecewise rules and equations (Year 11)
2. Exponential growth and decay modelsNot written yetBuilds on: Differentiate exponentials and logarithms; Change of base and logarithmic equations (Year 11)
3. Displacement, velocity and accelerationNot written yetBuilds on: Derivatives as rates and one-dimensional velocity (Year 11); Rates and accumulated change in context
Probability distributions
1. Discrete probability distributionsNot written yetBuilds on: Random variables and data types (Year 11); Frequency tables and cumulative data (Year 11)
2. Expectation, variance and discrete decisionsNot written yetBuilds on: Discrete probability distributions; Expand, factorise and simplify expressions (Year 11)
Data distributions yr12
1. Continuous density and interval probabilityNot written yetBuilds on: The Fundamental Theorem and definite integrals; Random variables and data types (Year 11)
2. Normal models and the empirical ruleNot written yetBuilds on: Continuous density and interval probability; Second derivative, concavity and inflection
3. Standardisation and normal probabilitiesNot written yetBuilds on: Normal models and the empirical rule; Cumulative distributions and quantiles
Random variables
1. Cumulative distributions and quantilesNot written yetBuilds on: Continuous density and interval probability; Continuity and differentiability
2. Continuous expectation and varianceNot written yetBuilds on: Continuous density and interval probability; Integral properties, symmetry and digital verification
3. Recover normal model parameters from probabilitiesNot written yetBuilds on: Standardisation and normal probabilities; Straight-line equations and graphs (Year 11)
Sequences and series
1. Sequences, partial sums and sigma notationBuilds on: Functions, relations and function notation (Year 11); Index laws, zero, negative and fractional powers (Year 11)
2. Limiting geometric sumsBuilds on: Geometric sequences and finite sums
Financial maths
1. Arithmetic sequences and their sumsBuilds on: Sequences, partial sums and sigma notation; Linear models, simultaneous equations and break-even (Year 11)
2. Geometric sequences and finite sumsBuilds on: Sequences, partial sums and sigma notation; Exponential graphs and end behaviour (Year 11); Change of base and logarithmic equations (Year 11)
3. Annuities, contributions and withdrawalsNot written yetBuilds on: Geometric sequences and finite sums; Reducing balance loans and repayment schedules
Financial mathematics
1. Reducing balance loans and repayment schedulesNot written yetBuilds on: Geometric sequences and finite sums; Change of base and logarithmic equations (Year 11)

Each arrow points from a skill to one that builds on it
From an earlier year — optional
Not written yet

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

Choose a lesson to see its structure.

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.

Mathematics Extension 1 — Years 11–12 · Year 12

1 lesson in this selection

Learning tree for Mathematics Extension 1 — Years 11–12 · Year 12 35 skills · 6 topics

Stage 6 · Year 12

Proof by mathematical induction
1. Mathematical induction for sumsA starting point: builds on no earlier skill
2. Induction for divisibilityNot written yetA starting point: builds on no earlier skill
Inverse trigonometric functions
1. Inverse trig functions and principal branchesNot written yetA starting point: builds on no earlier skill
2. Inverse trig identities and compositionsNot written yetA starting point: builds on no earlier skill
3. Transformed inverse trig graphsNot written yetA starting point: builds on no earlier skill
Introduction to vectors
1. Vector magnitude, direction and coordinatesNot written yetA starting point: builds on no earlier skill
2. Displacement, midpoint and distance in 2D/3DNot written yetA starting point: builds on no earlier skill
3. Vector arithmetic and parallelismNot written yetA starting point: builds on no earlier skill
4. Magnitude and unit vectorsNot written yetA starting point: builds on no earlier skill
5. Scalar product, angles and orthogonalityNot written yetA starting point: builds on no earlier skill
6. Projection and perpendicular componentsNot written yetA starting point: builds on no earlier skill
7. Position, displacement and vector pathsNot written yetA starting point: builds on no earlier skill
8. Constant velocity and cross-current motionNot written yetA starting point: builds on no earlier skill
9. Velocity, acceleration and vector integrationNot written yetA starting point: builds on no earlier skill
10. Projectile modelling and component equationsNot written yetA starting point: builds on no earlier skill
11. Projectile flight features and inverse launch problemsNot written yetA starting point: builds on no earlier skill
Further calculus skills
1. Parametric and inverse-function derivativesNot written yetA starting point: builds on no earlier skill
2. Inverse trig derivatives and combined rulesNot written yetA starting point: builds on no earlier skill
3. Inverse trig integral formsNot written yetA starting point: builds on no earlier skill
4. Integration with a given substitutionNot written yetA starting point: builds on no earlier skill
5. Integrating squares of sine and cosineNot written yetA starting point: builds on no earlier skill
Further applications of calculus
1. Multiplicity, derivative zeroes and curve shapeNot written yetA starting point: builds on no earlier skill
2. Related rates in geometry and contextNot written yetA starting point: builds on no earlier skill
3. Growth and decay towards a fixed levelNot written yetA starting point: builds on no earlier skill
4. Area between curves with changing orderNot written yetA starting point: builds on no earlier skill
5. Solids of revolution about either coordinate axisNot written yetA starting point: builds on no earlier skill
6. Differential equations, slope fields and initial valuesNot written yetA starting point: builds on no earlier skill
7. Separate variables and retain equilibrium solutionsNot written yetA starting point: builds on no earlier skill
8. Logistic growth and contextual differential equationsNot written yetA starting point: builds on no earlier skill
The binomial distribution and sampling distribution of the mean
1. Bernoulli variables, expectation and varianceNot written yetA starting point: builds on no earlier skill
2. Binomial assumptions and exact probabilitiesNot written yetA starting point: builds on no earlier skill
3. Binomial moments, expected frequencies and applicationsNot written yetA starting point: builds on no earlier skill
4. Population, sample and the distribution of sample meansNot written yetA starting point: builds on no earlier skill
5. Central limit theorem and sample-size effectsNot written yetA starting point: builds on no earlier skill
6. Probability bounds for a sample meanNot written yetA starting point: builds on no earlier skill

Each arrow points from a skill to one that builds on it
Not written yet

Sequence: NSW syllabus, as used on the learning platform for Mathematics Extension 1 — Years 11–12; detailed outcome alignment for NSW is not verified.

Proof by mathematical inductionAlgebra and proof

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Mathematical induction for sumsStructure

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Curriculum details for Mathematics Extension 1 — Years 11–12

NSW Mathematics Extension 1 (2024); Years 11–12; Advanced corequisite.

Year 12 in the NSW source sequence · Year 12.

The Mathematics Extension 1 — Years 11–12 collection follows its named source sequence; detailed outcome alignment for New South Wales is not verified.

In Mathematics Extension 1 — 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.

Year 3 numeracy
- Equal groups foundation · Equal groups with 2s, 5s and 10s
Year 3 reading
- Main idea foundation · The whole idea, and the words that support it
Year 5 numeracy
- Fractions foundation · Equivalent fractions, then applying them
- Data displays foundation · Column graphs, line graphs and two-way tables
- Chance and outcomes foundation · Count the outcomes, then compare the chances
Year 5 reading
- Inference and evidence foundation · A careful inference, and what proves it
Year 7 numeracy
- Integers foundation · Order and calculate with numbers below zero
- Fractions of a quantity · Equal groups find a fraction of an amount
Year 7 reading
- Narrative point-of-view foundation · Whose knowledge each narrative voice gives you
Year 9 numeracy
- Linear equations foundation · Equality diagrams for brackets and unknowns on both sides
Year 9 reading
- Argument and evidence foundation · Whether each claim fits its evidence
Year 7 selective entry
- Area reasoning foundation · A Year 6 area route
- Reading comparison foundation · A Year 6 reading route comparing two texts

How much is written so far

Every skill with a written lesson, stage by stage.

Other subject areas

Mathematics & numeracy
English and HSIE
Sciences
School technologies and computing
School languages
Academic Music, Drama and Dance
Academic Visual Arts and media
- Visual Arts — school syllabus
- School photography, film and digital media
PDHPE and Health and Movement Science
- PDHPE K–10
- Health and Movement Science
Study and examination preparation