Stage 5 Maths: Every NSW Syllabus Outcome, Explained

Stage 5 Mathematics in NSW is 41 outcomes, MA5-ALG-C-01 through MA5-VOL-P-01, covering Years 9 and 10. Eighteen are Core and 23 are Path, which means more than half of Stage 5 Maths is optional, and which student does which is decided at the start of Year 9.

That is the whole story of this stage, and it makes it unlike every other syllabus in the NSW secondary suite. Stage 5 English has six outcomes and no Path. Stage 5 Science has 19 and no Path. Mathematics is the only subject where NSW streams inside the stage, so a student can be sitting the full English and Science syllabuses while taking barely half the maths.

This guide covers all 41 outcomes, how the Core and Path split actually works, what each of the three Path directions adds, the four outcomes that decide senior maths, a two-year teaching order, and six checks.

How the Core and Path split works

Every Stage 5 code carries a C or a P in the middle slot: MA5-ALG-C-01 is Core, MA5-ALG-P-01 is Path. Core outcomes are for every student. Path outcomes are additional, and each is tagged in its own text for the senior directions it serves: Stn for Standard, Adv for Advanced and Ext for Extension.

The tags are not exclusive and the distribution is lopsided. Of the 23 Path outcomes, 19 are tagged Advanced, seven are tagged Standard and four are tagged Extension, with several carrying more than one tag. Read that as a shape rather than a menu: the Advanced pathway is most of Path, the Standard additions are a small targeted set, and Extension is four outcomes sitting on top of Advanced.

Two consequences matter more than the arithmetic. First, Core alone is not a neutral default. A student who does Core only finishes Year 10 having met 18 of 41 outcomes, and the senior subjects that assume more than Core will be hard to enter. Second, the decision is made early. Stage 5 runs across Years 9 and 10, so the pathway a student is placed in at the start of Year 9 determines what they meet for two years, and it is made on Stage 4 evidence. Our guide to Stage 4 Maths and its 16 outcomes covers the stage that decision runs on, and how the NSW syllabuses are structured covers stages and outcomes generally.

The 18 Core outcomes

Read the Core list against the national Year 9 and 10 curriculum and the coverage is close but the emphasis differs in one visible way: financial mathematics gets two Core outcomes in NSW, where nationally it appears as a clause inside modelling descriptors. Simple interest, compound interest, depreciation, earning and spending are Core content for every NSW student, which is a defensible choice for the subject most of them will stop taking at the end of Year 10.

The 23 Path outcomes, by direction

Path outcomes extend a Core focus area or open a new one. The lettering runs on from Core, so Algebraic techniques A is Core and B and C are Path.

• Extending the algebra: MA5-ALG-P-01 and MA5-ALG-P-02 take algebraic fractions into indices and then into general manipulation, expansion and factorisation. MA5-EQU-P-01 adds monic quadratics, linear inequalities and cubics of the form ax³ = k, and MA5-EQU-P-02 adds equations of more than three steps, non-monic quadratics and simultaneous equations. MA5-IND-P-01 covers negative-integer indices with algebraic expressions and MA5-IND-P-02 covers surds and fractional indices.
• Extending the graphs: MA5-LIN-P-01 adds transformations and the midpoint, gradient and distance formulas with equations of lines. MA5-NLI-P-01 covers non-linear relationships and their transformations. MA5-FNC-P-01 introduces function notation and graphing inequalities in one and two variables. MA5-LOG-P-01 establishes the logarithm laws, and MA5-POL-P-01 covers polynomials with the factor and remainder theorems.
• Extending the geometry: MA5-GEO-P-01 establishes the conditions for congruent and similar triangles, MA5-GEO-P-02 constructs proofs using them, and MA5-CIR-P-01 proves circle theorems. Those three are the Extension core, and they are where NSW puts formal deductive proof.
• Extending measurement and trigonometry: MA5-ARE-P-01 and MA5-VOL-P-01 add pyramids, cones and spheres. MA5-TRG-P-01 adds three-dimensional problems and the sine, cosine and area rules, and MA5-TRG-P-02 covers the properties of trigonometric functions and solving trigonometric equations.
• Extending data, and two standalone topics: MA5-DAT-P-01 plans and reviews a full statistical inquiry, and MA5-PRO-P-01 covers Venn diagrams, two-way tables and conditional probability. MA5-RAT-P-01 and MA5-RAT-P-02 cover direct and inverse variation and rates of change. MA5-NET-P-01 introduces networks, planar graphs and Eulerian trails, and it is the only Path outcome tagged for Standard alone.

Two things are worth noticing in that list. Conditional probability is Path. Nationally it is compulsory Year 10 content in AC9M10P01 and AC9M10P02, and in NSW a Core-only student never meets it. So is the full statistical inquiry in MA5-DAT-P-01, which nationally is AC9M10ST05. And proof is Path and Extension-tagged, where the national curriculum makes deductive reasoning about plane shapes compulsory in AC9M10SP01. If you are comparing frameworks, those three are the sharpest divergences and all run the same way: NSW makes optional what the national curriculum requires of everyone.

Reading the codes

The pattern is MA + stage + focus area + C or P + number, so MA5-TRG-P-01 is Stage 5, Trigonometry, Path, outcome 1. The letter after the focus area in the name (Trigonometry A, B, C, D) runs in sequence across Core and Path together, so Trigonometry A and B are Core and C and D are Path.

One practical warning for anyone building a scope and sequence. The Path tags are inside the outcome text rather than the code, so you cannot filter a pathway from the code alone. A programme that selects Path outcomes by code will pick up Extension-only material such as circle geometry for a Standard class.

The four outcomes that decide senior maths

MA5-ALG-C-01: you cannot cancel across a plus sign

The misconception: that cancelling is something you do to matching symbols anywhere in a fraction, rather than to common factors of the whole numerator and the whole denominator. This is Core, so every NSW student meets it, and it is the single most common algebraic error in Stage 5.

What you will see: (x + 3) ÷ 3 simplified to x. Or (x² + 2x) ÷ x simplified to x² + 2 by cancelling only one of the two x terms. In addition, 1/x + 1/y written as 1/(x + y), which is the same misunderstanding pointed the other way: the student is operating on the parts because the parts are what is visible.

The fix: make factorising a mandatory step before any cancelling, with no exceptions, because a fraction factorised top and bottom makes the legal cancellation obvious and the illegal one impossible. Kill the addition error with numbers rather than argument: ask for 1/2 + 1/3, then ask whether 1/5 is a plausible answer for adding two positive things, and let the student reject it. Keep a numerical counter-example permanently available for the cancelling error too, since substituting x = 3 into (x + 3)/3 gives 2 rather than 3 and settles it in one line. MA5-ALG-P-01 and MA5-ALG-P-02 both build directly on this, so a Path student who has not fixed it will compound the error rather than outgrow it.

MA5-TRG-C-01: label the sides from the angle you are using

The misconception: that sine, cosine and tangent are calculator buttons, and that SOHCAHTOA is the content rather than a mnemonic for it. A student holding this cannot say why the ratio does not depend on the size of the triangle, and therefore cannot tell when the method applies.

What you will see: opposite and adjacent assigned relative to the right angle or to the bottom of the page rather than to the angle in use, so the same triangle yields different answers depending on which angle is marked. The ratios applied confidently to a triangle with no right angle. And in MA5-TRG-C-02 bearings problems, a correct ratio applied to a diagram drawn with north in the wrong place, which is a reading failure rather than a trigonometry one.

The fix: establish the constancy of the ratios before naming them. Have students draw three or four right-angled triangles containing the same angle at deliberately different sizes, measure, and compute opposite divided by adjacent for each. The answers cluster, the class has discovered tangent, and the calculator button becomes a lookup for work they have already done. Then make marking the angle in use a required first step, and rotate the page so it sits bottom-left, because the labels are defined relative to the angle and nothing else. For bearings, require the north arrow to be drawn before anything is calculated. MA5-GEO-C-01 similarity is the underlying reason the ratios are constant, so teach the two in the same term.

MA5-FIN-C-02: compound interest is repeated multiplication

The misconception: that compound interest is simple interest with an extra step, so the two are computed the same way and compounding just adds a bit. Underneath it is the percentage error that survives from Stage 4: treating a percentage change as an amount rather than as an operation on the current value.

What you will see: compound interest calculated as simple interest and then adjusted upward by guesswork. Or the formula applied correctly with no sense of what it means, so a student cannot say why the balance curve bends. On depreciation the same student often subtracts the same amount each year, which is straight-line depreciation applied where the question asked for reducing balance.

The fix: build it before formalising it. Take $1000 at 10% and do five years by hand in a table, multiplying by 1.1 each time, and let students see the amount added grow each year while the rate stays fixed. Then show the formula as shorthand for the column they just built, rather than as a new object. The multiplier framing is what carries it: growth is ×1.1, depreciation is ×0.9, and once both are multipliers the difference between reducing balance and straight line is visible rather than verbal. This is Core content, and for most NSW students it is the most directly useful maths in the stage, so it is worth the time it takes.

MA5-PRO-C-01: without replacement changes the second branch

The misconception: that a multistage experiment is just several single-stage ones, so the probabilities on the second stage are the same as the first. It holds for with-replacement problems, which is why it survives: the rule works often enough to feel reliable.

What you will see: a tree diagram for drawing two counters from a bag without replacement, with identical fractions on both levels. The total probability then fails to sum to 1 on the second stage, and students routinely do not notice, because the check is not part of the procedure they were taught.

The fix: make the denominator the visible thing. Write the number remaining on every branch before any fraction is filled in, so the change from 10 to 9 is on the page before the probability is. Then make the sum-to-one check compulsory at every level of the tree, which catches the error automatically and costs nothing. Run the same question both ways, with and without replacement, on the same numbers in the same lesson, because the contrast is what teaches it. Note that conditional probability is Path in NSW (MA5-PRO-P-01), so a Core-only student meets without-replacement here and never meets the conditional language that explains it, which makes this outcome carry more weight than its size suggests.

What students need to arrive with

Stage 5 leans on Stage 4 hard, and four outcomes carry most of it. MA4-ALG-C-01 (generalising number properties and operating with expressions) is the prerequisite for MA5-ALG-C-01 and everything Path built on it. MA4-EQU-C-01 (two-step linear equations and quadratics of the form ax² = c) is the prerequisite for MA5-EQU-C-01, which raises the ceiling to three steps with an algebraic fraction. MA4-PYT-C-01 (Pythagoras) is the prerequisite for MA5-TRG-C-01, and MA4-FRC-C-01 (fractions, decimals and percentages) is the prerequisite for both financial mathematics outcomes.

The one to check first is the percentage work, because it is quick and it predicts trouble in the Core content most NSW students will actually use. Ask for 15% of 80, then ask what percentage 12 out of 80 is: a student who can do the first and not the second has half of MA4-FRC-C-01 and will struggle through both financial outcomes. Our guide to Stage 4 Maths and its 16 outcomes covers what should have been established, and helping with maths at home without a tutor covers supporting a Year 9 student without turning every evening into a lesson.

What this sets up

Stage 5 ends compulsory Mathematics, and Stage 6 splits into Mathematics Standard, Advanced, Extension 1 and Extension 2. The Path tags exist to feed those directly, which is why the Year 9 placement decision matters so much.

• Standard is reachable from Core plus the Standard-tagged Path outcomes, which are a small set: the measurement extensions, variation and rates of change, the statistical inquiry, and networks.
• Advanced assumes most of the Advanced-tagged Path outcomes, and 19 of the 23 Path outcomes carry that tag. The algebra chain (MA5-ALG-P-01, MA5-ALG-P-02), the equation chain (MA5-EQU-P-01, MA5-EQU-P-02), indices and surds, functions and logarithms are the ones it is hardest to arrive without.
• Extension assumes the proof outcomes: MA5-GEO-P-01, MA5-GEO-P-02 and MA5-CIR-P-01, plus polynomials. Those four are where NSW puts formal deductive argument, and nothing in Core prepares for them.
• MA5-FIN-C-01 and MA5-FIN-C-02 feed the financial mathematics that carries real weight in Mathematics Standard, and they are the outcomes most likely to matter to a student who stops at Year 10.

Families comparing frameworks should note that the national curriculum makes several things compulsory that NSW makes optional. Conditional probability is AC9M10P01 nationally and MA5-PRO-P-01 here; deductive proof is AC9M10SP01 nationally and Path here; the full statistical investigation is AC9M10ST05 nationally and MA5-DAT-P-01 here. See Year 10 Maths under the Australian Curriculum and Year 9 Maths under the Australian Curriculum. Victoria bands Level 10 with a separate 10A for extension, which is closer to the NSW model than the national one, see Year 10 Maths under the Victorian Curriculum. Our guide to which curriculum your state uses is worth a minute if you are unsure which applies.

A two-year teaching order

What follows sequences the Core outcomes across two years, with the Path work attached to the Core focus area it extends rather than taught as a separate block, which is how the lettering is designed to be used.

1. Year 9, Semester 1: algebra and equations. MA5-ALG-C-01 algebraic fractions and expansion, then MA5-EQU-C-01 three-step equations, then MA5-IND-C-01 indices. Path classes continue straight into MA5-ALG-P-01, MA5-EQU-P-01 and MA5-IND-P-01 rather than waiting, because the chains are continuous and breaking them costs more than it saves. This block is the foundation of everything else in the stage.
2. Year 9, Semester 2: lines, then trigonometry. MA5-LIN-C-01 midpoint, gradient and length, then MA5-LIN-C-02 gradient and intercept form, with MA5-LIN-P-01 for Path. Then MA5-GEO-C-01 similarity, immediately followed by MA5-TRG-C-01 and MA5-TRG-C-02, because similarity is why the trigonometric ratios are constant and teaching them apart wastes the connection.
3. Year 10, Semester 1: measurement, magnitude and money. MA5-ARE-C-01 surface area and MA5-VOL-C-01 volume of composite solids, with MA5-ARE-P-01 and MA5-VOL-P-01 for Path. Then MA5-MAG-C-01 scientific notation and significant figures, which pairs naturally with the measurement work. Finish with MA5-FIN-C-01 and MA5-FIN-C-02, built from a hand-calculated table before the formula.
4. Year 10, Semester 2: curves, data and chance. MA5-NLI-C-01 and MA5-NLI-C-02 quadratic and exponential relationships, with MA5-NLI-P-01, MA5-FNC-P-01 and MA5-LOG-P-01 for Path. Then MA5-DAT-C-01 and MA5-DAT-C-02 including bivariate data, and MA5-PRO-C-01 multistage chance. Extension classes take MA5-GEO-P-01, MA5-GEO-P-02 and MA5-CIR-P-01 through this semester alongside, since proof needs sustained time rather than a block.

Three orderings matter more than the rest. MA5-ALG-C-01 comes first, because algebraic fractions underpin the equation work and both Path algebra chains. MA5-GEO-C-01 comes immediately before MA5-TRG-C-01, because similarity is the reason the ratios work. And MA5-FIN-C-02 comes after MA5-IND-C-01, since compound interest is repeated multiplication and lands far better once indices are familiar.

Assessment checkpoints

• Algebraic techniques: ask them to simplify (x + 3) ÷ 3. “It does not simplify” confirms MA5-ALG-C-01. An answer of x means cancelling is being applied across a plus sign, so make factorising a mandatory step and substitute x = 3 to show the answer would be 2.
• Trigonometry: draw a right-angled triangle, mark an angle that is not the right angle, and ask which side is opposite. Correct labelling relative to the marked angle confirms MA5-TRG-C-01. Labelling relative to the right angle means the ratios have been learned as a picture, and rotating the triangle will confirm it.
• Financial mathematics: ask what $1000 at 10% compound becomes after two years. $1210 confirms MA5-FIN-C-02. $1200 is simple interest, and a student who cannot say why the second year adds more than the first has the formula without the idea.
• Probability: two counters drawn from a bag of ten without replacement. Ask for the second-stage probabilities. Denominators of 9 confirm MA5-PRO-C-01. Denominators of 10 mean the without-replacement condition is not reaching the tree, so write the number remaining on each branch before any fraction.
• Equations: give a three-step linear equation containing one algebraic fraction. A correct solution confirms MA5-EQU-C-01, which is the Core ceiling. If it is comfortable, the student is ready for the Path chain; if the fraction is what breaks it, that is MA5-ALG-C-01 rather than an equations problem.
• Pathway check: ask a Year 9 student which senior maths they are aiming at, and check it against the Path outcomes they are actually being taught. A student aiming at Advanced who is doing Core only is on a path that will not reach it, and Year 9 is when that is still cheap to fix.

Recording the alignment

Whether you are programming for a class or building evidence for a NESA home schooling registration, record the outcome on the activity as you go, and for Stage 5 Maths record the pathway alongside it. With 23 of 41 outcomes optional, a portfolio that lists outcomes without indicating which pathway was being followed does not show whether the programme was complete, because completeness depends on which set was in scope.

Record the year as well, since Stage 5 spans Years 9 and 10 and the codes do not distinguish them. And if a student changes pathway partway through, note the date, because the outcomes met before and after the change are different sets and a reviewer cannot infer that from the codes. Our guide to state-by-state registration requirements covers what NSW reviewers ask for at the end of compulsory schooling, and teaching maths through interests covers wrapping these outcomes around whatever your student is currently into.

Sprout Lessons builds a full interactive lesson from any of these 41 outcomes, pitched at Stage 5 and wrapped in whatever your student is into, with self-checking practice that hints rather than just marking wrong, and the exact NSW outcome recorded in the lesson footer. It earns its keep most on MA5-ALG-C-01 and MA5-FIN-C-02, where students need many more worked variations than one worksheet carries, and where the hint at the moment of the error is worth more than the mark at the end. Try it free and generate a Stage 5 Maths lesson in about a minute.

Outcome codes reference the NSW Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales. Outcome descriptions are paraphrased here, not reproduced. The syllabus can be accessed directly at curriculum.nsw.edu.au. NESA does not endorse this product. Always verify against the current syllabus outcomes and content.

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