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Mathematics, every topic

46 topics on 3 lines. Kindergarten to Year 10.

Next up

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 11

1 lesson in this selection

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

Preliminary · Year 11
1. Cell membranes and transport:
  1 of 1 skills with lesson material
  1. Osmosis: water movement and cell responsesLesson material: Starting

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

Cell membranes and transportCells

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Osmosis: water movement and cell responsesStructure

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Curriculum details for Biology Years 11–12

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

Preliminary in the NSW source sequence · Year 11.

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 11

0 lessons in this selection

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No lessons are published for Year 11 in Chemistry Years 11–12 yet.

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Curriculum details for Chemistry Years 11–12

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

Preliminary in the NSW source sequence · Year 11.

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 11

0 lessons in this selection

No lessons match this selection

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Curriculum details for English K–10

NSW school sequence.

Preliminary in the NSW source sequence · Year 11.

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 11

0 lessons in this selection

Learning tree for HSC English Advanced · Year 11 4 topics in 1 stage

Preliminary · Year 11
1. Foundations of analysis:
  0 of 6 skills with lesson material
  1. Annotates unseen texts for technique, tone and meaning
  2. Analyses narrative voice, characterisation and structure in prosebuilds on 1 earlier skill
  3. Analyses imagery, form and sound devices in poetrybuilds on 1 earlier skill
  4. Analyses dramatic and film techniques, including staging and camera workbuilds on 1 earlier skill
  5. Analyses rhetorical devices in speeches and essaysbuilds on 1 earlier skill
  6. Links technique to effect and effect to meaning in analysisbuilds on 2 earlier skills
2. Context and perspective:
  0 of 2 skills with lesson material
  1. Explains how a composer's context shapes meaning and valuesbuilds on 1 earlier skill
  2. Analyses how texts represent perspectives and position audiencesbuilds on 1 earlier skill
3. Building analytical arguments:
  0 of 5 skills with lesson material
  1. Writes a conceptual thesis that answers the question directlybuilds on 1 earlier skill
  2. Frames body paragraphs with conceptual topic sentencesbuilds on 1 earlier skill
  3. Writes introductions and conclusions that frame the argumentbuilds on 1 earlier skill
  4. Selects and embeds textual evidence with analysisbuilds on 2 earlier skills
  5. Writes in a precise analytical registerbuilds on 1 earlier skill
4. Creative craft:
  0 of 6 skills with lesson material
  1. Builds imagery through concrete, sensory detailbuilds on 1 earlier skill
  2. Reveals character through action and dialogue rather than statementbuilds on 1 earlier skill
  3. Punctuates and paces dialogue effectivelybuilds on 1 earlier skill
  4. Shapes narrative structure, openings and endings deliberatelybuilds on 1 earlier skill
  5. Develops a distinctive narrative voice and point of viewbuilds on 1 earlier skill
  6. Crafts a complete short imaginative piecebuilds on 2 earlier skills

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

No lessons match this selection

No lessons are published for Year 11 in HSC English Advanced yet.

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Curriculum details for HSC English Advanced

NSW senior secondary sequence.

Preliminary in the NSW source sequence · Year 11.

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 11

35 lessons in this selection

Learning tree for Mathematics Advanced — Years 11–12 · Year 11 65 skills · 13 topics

Stage 6 · Year 11

Working with functions
1. Index laws, zero, negative and fractional powersA starting point: builds on no earlier skill
2. Expand, factorise and simplify expressionsBuilds on: Index laws, zero, negative and fractional powers
3. Functions, relations and function notationBuilds on: Index laws, zero, negative and fractional powers
4. Algebraic fractions and valid cancellationBuilds on: Expand, factorise and simplify expressions
5. Surds, exact arithmetic and conjugatesBuilds on: Expand, factorise and simplify expressions
6. Straight-line equations and graphsBuilds on: Functions, relations and function notation
7. Choose a method to solve quadratic equationsBuilds on: Expand, factorise and simplify expressions; Surds, exact arithmetic and conjugates
8. Domain, range, intercepts and interval notationBuilds on: Functions, relations and function notation; Algebraic fractions and valid cancellation
9. Parallel and perpendicular linesBuilds on: Straight-line equations and graphs
10. Linear inequalities and feasible valuesBuilds on: Straight-line equations and graphs
11. Discriminant, root type and parameter conditionsBuilds on: Choose a method to solve quadratic equations
12. Quadratic graph features and completing the squareBuilds on: Choose a method to solve quadratic equations; Domain, range, intercepts and interval notation
13. Reciprocal functions and asymptotic behaviourBuilds on: Domain, range, intercepts and interval notation
14. Linear models, simultaneous equations and break-evenNot written yetBuilds on: Straight-line equations and graphs; Parallel and perpendicular lines
15. Circles and semicircle relationsNot written yetBuilds on: Domain, range, intercepts and interval notation; Choose a method to solve quadratic equations
16. Even and odd functionsNot written yetBuilds on: Domain, range, intercepts and interval notation
17. Composition of functionsNot written yetBuilds on: Functions, relations and function notation; Domain, range, intercepts and interval notation
18. Reconstruct quadratic functions and compare coefficientsBuilds on: Quadratic graph features and completing the square
19. Intersections involving quadratic functionsBuilds on: Quadratic graph features and completing the square; Straight-line equations and graphs
20. Quadratic inequalities and sign intervalsBuilds on: Quadratic graph features and completing the square; Linear inequalities and feasible values
21. Cubic graphs from powers and factorsBuilds on: Quadratic graph features and completing the square; Expand, factorise and simplify expressions
22. Direct and inverse variationNot written yetBuilds on: Reciprocal functions and asymptotic behaviour; Index laws, zero, negative and fractional powers
23. Piecewise functions and continuityNot written yetBuilds on: Domain, range, intercepts and interval notation; Even and odd functions
24. Quadratic models in contextNot written yetBuilds on: Quadratic graph features and completing the square; Intersections involving quadratic functions
25. Absolute value, piecewise rules and equationsNot written yetBuilds on: Piecewise functions and continuity; Straight-line equations and graphs
Exponentials logarithms
1. Exponential graphs and end behaviourNot written yetBuilds on: Domain, range, intercepts and interval notation; Index laws, zero, negative and fractional powers
2. Logarithms as inverse exponent questionsNot written yetBuilds on: Exponential graphs and end behaviour
Exponential and logarithmic functions
1. Euler’s number and exponential gradientsNot written yetBuilds on: Exponential graphs and end behaviour; The derivative as a gradient function
2. Derive and apply logarithm lawsNot written yetBuilds on: Logarithms as inverse exponent questions; Index laws, zero, negative and fractional powers
3. Logarithmic graphs and inverse reflectionNot written yetBuilds on: Logarithms as inverse exponent questions; Domain, range, intercepts and interval notation
4. Change of base and logarithmic equationsNot written yetBuilds on: Derive and apply logarithm laws
Graph transformations
1. Translate graphs and relationsNot written yetBuilds on: Domain, range, intercepts and interval notation; Quadratic graph features and completing the square; Reciprocal functions and asymptotic behaviour; Logarithmic graphs and inverse reflection
2. Reflect and dilate graphsNot written yetBuilds on: Translate graphs and relations
3. Translated circles and completing two squaresNot written yetBuilds on: Circles and semicircle relations; Translate graphs and relations; Choose a method to solve quadratic equations
4. Combine transformations and reconstruct a ruleNot written yetBuilds on: Translate graphs and relations; Reflect and dilate graphs; Piecewise functions and continuity; Absolute value, piecewise rules and equations
Trigonometry
1. Exact acute ratios and right-triangle modellingBuilds on: Surds, exact arithmetic and conjugates; Straight-line equations and graphs
2. Angles of any magnitude and unit-circle ratiosBuilds on: Exact acute ratios and right-triangle modelling
3. Sine rule, cosine rule and triangle areaBuilds on: Angles of any magnitude and unit-circle ratios; Choose a method to solve quadratic equations
4. Radians and exact angle conversionBuilds on: Angles of any magnitude and unit-circle ratios
5. Base sine, cosine and tangent graphsBuilds on: Radians and exact angle conversion; Even and odd functions
6. Trigonometric equations on restricted domainsBuilds on: Base sine, cosine and tangent graphs; Prove and apply trigonometric identities; Choose a method to solve quadratic equations
Trigonometry and measure of angles
1. The sine-rule ambiguous caseBuilds on: Sine rule, cosine rule and triangle area
2. Arc lengths, sectors and segmentsBuilds on: Radians and exact angle conversion; Sine rule, cosine rule and triangle area
Trigonometric identities and equations
1. Secant, cosecant and cotangentBuilds on: Radians and exact angle conversion
2. Complementary-angle identitiesBuilds on: Secant, cosecant and cotangent
3. Prove and apply trigonometric identitiesBuilds on: Secant, cosecant and cotangent; Algebraic fractions and valid cancellation
Intro differentiation
1. Average change, secants and instantaneous changeNot written yetBuilds on: Straight-line equations and graphs; Functions, relations and function notation
2. Differentiate quadratics from first principlesNot written yetBuilds on: The derivative as a gradient function; Expand, factorise and simplify expressions; Algebraic fractions and valid cancellation
3. Power rule and linearityNot written yetBuilds on: Differentiate quadratics from first principles; Index laws, zero, negative and fractional powers
4. Tangent and normal equationsNot written yetBuilds on: Power rule and linearity; Parallel and perpendicular lines; Angles of any magnitude and unit-circle ratios
Introduction to differentiation
1. The derivative as a gradient functionNot written yetBuilds on: Average change, secants and instantaneous change
2. Differentiate productsNot written yetBuilds on: Power rule and linearity
3. Differentiate quotientsNot written yetBuilds on: Power rule and linearity; Algebraic fractions and valid cancellation
4. Read and sketch derivative graphsNot written yetBuilds on: Power rule and linearity; The derivative as a gradient function
5. Cubic stationary points and monotonic intervalsNot written yetBuilds on: Power rule and linearity; Cubic graphs from powers and factors; Quadratic inequalities and sign intervals
6. Choose and combine differentiation rulesNot written yetBuilds on: Differentiate products; Differentiate quotients; Differentiate composite functions
7. Derivatives as rates and one-dimensional velocityNot written yetBuilds on: Power rule and linearity; Read and sketch derivative graphs
Differentiation yr12
1. Differentiate composite functionsNot written yetBuilds on: Power rule and linearity; Composition of functions
Probability and data
1. Sets, notation and Venn diagramsA starting point: builds on no earlier skill
2. Random variables and data typesBuilds on: Sample spaces, events and probability rules
3. Test independence and solve event problemsBuilds on: Conditional probability and restricted sample spaces
4. Histograms, polygons, mode and medianBuilds on: Frequency tables and cumulative data
Probability distributions
1. Sample spaces, events and probability rulesBuilds on: Sets, notation and Venn diagrams
2. Conditional probability and restricted sample spacesBuilds on: Sample spaces, events and probability rules
Data distributions yr12
1. Frequency tables and cumulative dataBuilds on: Random variables and data types

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 Advanced — Years 11–12; detailed outcome alignment for NSW is not verified.

Working with functionsAlgebra and functions

Choose a lesson to see its structure.

Index laws, zero, negative and fractional powersStructure

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Expand, factorise and simplify expressionsStructure

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Algebraic fractions and valid cancellationStructure

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Surds, exact arithmetic and conjugatesStructure

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Choose a method to solve quadratic equationsStructure

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Discriminant, root type and parameter conditionsStructure

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Functions, relations and function notationStructure

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Domain, range, intercepts and interval notationStructure

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Straight-line equations and graphsStructure

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Parallel and perpendicular linesStructure

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Linear inequalities and feasible valuesStructure

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Quadratic graph features and completing the squareStructure

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Reconstruct quadratic functions and compare coefficientsStructure

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Intersections involving quadratic functionsStructure

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Quadratic inequalities and sign intervalsStructure

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Cubic graphs from powers and factorsStructure

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Reciprocal functions and asymptotic behaviourStructure

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TrigonometryTrigonometry

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Exact acute ratios and right-triangle modellingStructure

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Angles of any magnitude and unit-circle ratiosStructure

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Sine rule, cosine rule and triangle areaStructure

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Radians and exact angle conversionStructure

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Base sine, cosine and tangent graphsStructure

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Trigonometric equations on restricted domainsStructure

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Trigonometry and measure of anglesTrigonometry

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The sine-rule ambiguous caseStructure

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Arc lengths, sectors and segmentsStructure

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Trigonometric identities and equationsTrigonometry

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Secant, cosecant and cotangentStructure

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Complementary-angle identitiesStructure

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Prove and apply trigonometric identitiesStructure

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Probability and dataProbability and data

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Sets, notation and Venn diagramsStructure

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Test independence and solve event problemsStructure

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Random variables and data typesStructure

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Histograms, polygons, mode and medianStructure

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Probability distributionsProbability and data

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Sample spaces, events and probability rulesStructure

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Conditional probability and restricted sample spacesStructure

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Data distributions yr12Probability and data

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Frequency tables and cumulative dataStructure

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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.

Preliminary in the NSW source sequence · Year 11.

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 11

6 lessons in this selection

Learning tree for Mathematics Extension 1 — Years 11–12 · Year 11 37 skills · 5 topics

Stage 6 · Year 11

Further work with functions
1. Reciprocal functions: points, signs and asymptotesA starting point: builds on no earlier skill
2. Secant, cosecant and cotangentNot written yetA starting point: builds on no earlier skill
3. Two different absolute-value transformationsNot written yetA starting point: builds on no earlier skill
4. Adding and subtracting graphs with shared domainsNot written yetA starting point: builds on no earlier skill
5. One-to-one functions and reflection in y=xNot written yetA starting point: builds on no earlier skill
6. Find inverses and retain their domainsNot written yetA starting point: builds on no earlier skill
7. Choosing a branch before finding an inverseNot written yetA starting point: builds on no earlier skill
8. Composition checks and inverse intersectionsNot written yetA starting point: builds on no earlier skill
9. Linear and quadratic curves from a parameterNot written yetA starting point: builds on no earlier skill
10. Parametric circles: elimination and tracingNot written yetA starting point: builds on no earlier skill
11. Cubic inequalities through sign intervalsNot written yetA starting point: builds on no earlier skill
12. Rational inequalities without unsafe multiplicationNot written yetA starting point: builds on no earlier skill
13. Distance, compound inequalities and outside intervalsNot written yetA starting point: builds on no earlier skill
Polynomials
1. Polynomial degree, cancellation and end behaviourNot written yetA starting point: builds on no earlier skill
2. Zeroes, multiplicity and polynomial sketchesNot written yetA starting point: builds on no earlier skill
3. Polynomial division with a checked remainderNot written yetA starting point: builds on no earlier skill
4. Why substitution gives a linear-divisor remainderA starting point: builds on no earlier skill
5. Factor theorem and complete real factorisationA starting point: builds on no earlier skill
6. Quadratic and cubic zeroes from coefficientsNot written yetA starting point: builds on no earlier skill
7. Quartic zeroes and connected coefficient problemsNot written yetA starting point: builds on no earlier skill
Permutations and combinations
1. Factorials and the multiplication principleA starting point: builds on no earlier skill
2. Permutations as ordered selectionsA starting point: builds on no earlier skill
3. Restrictions and repeated objects in a lineA starting point: builds on no earlier skill
4. Circular arrangements and rotational equivalenceNot written yetA starting point: builds on no earlier skill
5. Unordered selections and Pascal identitiesNot written yetA starting point: builds on no earlier skill
6. Choose, arrange and split cases carefullyNot written yetA starting point: builds on no earlier skill
7. Probabilities from equally likely counted outcomesNot written yetA starting point: builds on no earlier skill
The binomial theorem
1. Pascal’s triangle and the binomial theoremNot written yetA starting point: builds on no earlier skill
2. Finding coefficients and constant termsNot written yetA starting point: builds on no earlier skill
3. Simplifying and proving coefficient identitiesNot written yetA starting point: builds on no earlier skill
4. New identities from counting and established resultsNot written yetA starting point: builds on no earlier skill
Further trigonometry
1. Finding a route through a three-dimensional diagramNot written yetA starting point: builds on no earlier skill
2. Deriving and applying sum and difference identitiesNot written yetA starting point: builds on no earlier skill
3. Choosing the useful double-angle formNot written yetA starting point: builds on no earlier skill
4. Solve trig equations without dropping solutionsNot written yetA starting point: builds on no earlier skill
5. From a cos x+b sin x to a single sinusoidNot written yetA starting point: builds on no earlier skill
6. Build, solve and evaluate a periodic modelNot 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.

Further work with functionsAlgebra and functions

Choose a lesson to see its structure.

Reciprocal functions: points, signs and asymptotesStructure

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PolynomialsAlgebra and proof

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Why substitution gives a linear-divisor remainderStructure

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Factor theorem and complete real factorisationStructure

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Permutations and combinationsAlgebra and proof

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Factorials and the multiplication principleStructure

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Permutations as ordered selectionsStructure

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Restrictions and repeated objects in a lineStructure

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Curriculum details for Mathematics Extension 1 — Years 11–12

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

Preliminary in the NSW source sequence · Year 11.

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