Year 10 Maths: Every Australian Curriculum Code, Explained

Year 10 Maths in the Australian Curriculum Version 9 is 21 content descriptions, AC9M10A01 through AC9M10ST05. It is the smallest code count in secondary and the largest conceptual jump, because four objects arrive that have no ancestor anywhere in the preceding ten years: the exponential relation, the logarithmic scale, the network, and the scatterplot.

This is a working guide to all 21 codes: what changes from Year 9, the four descriptors that decide whether senior maths is available to a student, a term-by-term order, and six checks for the end of compulsory schooling.

What changes this year

Statistics becomes bivariate, and that is the single biggest shift in the year. Every Statistics descriptor from Foundation to Year 9 asked a question about one variable at a time: how tall, how many, how often, how spread out. Three of the five Year 10 descriptors ask about the relationship between two. AC9M10ST03 constructs scatterplots and comments on the association between two numerical variables in terms of strength, direction and linearity. AC9M10ST04 constructs two-way tables and discusses possible relationships between categorical variables. AC9M10ST05 plans full investigations involving bivariate data. Nothing before this year has asked whether one thing moves with another, and it is the direct on-ramp to every senior statistics course.

The second shift is that Probability shrinks to two descriptors and both are conditional. AC9M10P01 uses the language of “if … then”, “given”, “of” and “knowing that” to describe and interpret situations involving conditional probability. That is a descriptor about words, deliberately, because conditional probability is the topic where ordinary English and mathematics disagree most sharply and where confident adults reliably get the wrong answer. Year 9 had three probability descriptors and none of them conditional.

The third is that four genuinely new mathematical objects turn up at once. Exponential relations (AC9M10A03) are a new family of function after linear in Year 8 and quadratic in Year 9. Logarithmic scales (AC9M10M02) have no ancestor at all and are the first time a student meets an axis where equal distances mean equal ratios rather than equal differences. Networks and network diagrams (AC9M10SP02) arrive with no preparation anywhere in F–9. And the scatterplot completes the set.

The fourth is quieter. Number is a single descriptor for the second year running, and AC9M10N01 is subtler than it looks: it is about the effect of using approximations of real numbers in repeated calculations, compared against exact representations. Year 9 established that measurements carry error. Year 10 asks what happens to that error when you keep calculating with it, which is the idea underneath every spreadsheet a student will ever build.

The year at a glance

Algebra, Measurement and Statistics all sit at five, which makes Year 10 the most evenly balanced year in the curriculum. There is no dominant strand to build the program around, and that is a planning problem rather than a convenience: the strands are also less connected to each other than in any previous year, so a term that runs late genuinely strands content rather than compressing it. The 21 descriptions here are the Year 10 content descriptions. Students heading toward the more demanding senior subjects usually cover extension material on top, which Victoria publishes separately as Level 10A.

Reading the codes

The pattern is unchanged: AC9M + year + strand + number, so AC9M10ST03 is Year 10 Statistics, position 3. Strand letters are N Number, A Algebra, M Measurement, P Probability, SP Space, ST Statistics. Note that the year token is now two characters, so string matching that assumed a fixed-width code will break here, which is worth knowing if you keep a scope and sequence in a spreadsheet.

Two placements will surprise anyone mapping from a textbook. Logarithms are in Measurement (AC9M10M02), not Algebra, because the descriptor is about reading and using logarithmic scales in applied contexts rather than about manipulating logarithms algebraically. And networks are in Space (AC9M10SP02), which makes sense once you see that the descriptor is about connectedness rather than about counting.

Strand by strand

Number (AC9M10N01)

One descriptor, and it is easy to skip because it does not look like a topic. AC9M10N01 recognises the effect of using approximations of real numbers in repeated calculations and compares the results with exact representations. Taught properly it takes one good lesson and pays for itself for the rest of a student’s life: round π to 3.14 and to 3.14159, run both through a calculation with several steps, and compare. The gap grows. Do it again with a rounded trigonometric ratio inside a multi-step AC9M10M03 problem and the point lands harder, because the student has just been rounding intermediate values all term. Attach this descriptor to AC9M10M04 rather than teaching it alone, since measurement error and rounding error are the same idea arriving from two directions.

Algebra (AC9M10A01 to AC9M10A05)

AC9M10A01 expands, factorises, simplifies and solves equations algebraically, applying the exponent laws to products, quotients and powers of variables and applying the distributive property. It is the merge point for three years of work: Year 8 expanded linear expressions, Year 9 expanded binomial products and factorised monic quadratics, and Year 10 assumes all of it while adding exponent laws on variables. Nothing in it is retaught.

AC9M10A02 solves linear inequalities and simultaneous linear equations in two variables, and interprets the solutions graphically. The graphical interpretation is the part worth protecting: a pair of simultaneous equations is two lines and the solution is where they cross, which makes no-solution and infinite-solution cases obvious rather than mysterious. AC9M10A03 recognises the connection between algebraic and graphical representations of exponential relations and solves related exponential equations, the new function family.

AC9M10A04 is the modelling descriptor, growth and decay including financial contexts, with the student choosing between linear, quadratic and exponential models and then evaluating and modifying the model. That three-way choice is the year’s hardest assessable judgement, and it is the natural home for compound interest. AC9M10A05 experiments with functions and relations using digital tools. As in Year 9, it should be taught before the formal work rather than after: twenty minutes changing the base of an exponential and watching the curve respond does more for AC9M10A03 than a week of tables.

Measurement (AC9M10M01 to AC9M10M05)

AC9M10M01 solves problems involving the surface area and volume of composite objects. Year 9 did prisms and cylinders; the new work is decomposing a solid into parts and, in the surface area case, remembering that joined faces disappear, which is the error this descriptor exists to expose. AC9M10M02 interprets and uses logarithmic scales in applied contexts involving small and large quantities and change, covered below. AC9M10M03 solves practical problems applying Pythagoras and trigonometry in right-angled triangles, including direction and angles of elevation and depression, which is the applied extension of Year 9 trigonometry and the largest single block of Measurement work.

AC9M10M04 identifies the impact of measurement errors on the accuracy of results in practical contexts, the successor to Year 9’s AC9M9M04 and the partner to AC9M10N01. AC9M10M05 models practical problems involving proportion and the scaling of objects, where the useful content is that area scales with the square of a length factor and volume with the cube, which students find genuinely surprising and which explains everything from why a scaled-up model collapses to why small animals lose heat quickly.

Probability (AC9M10P01, AC9M10P02)

AC9M10P01 uses the language of “if … then”, “given”, “of” and “knowing that” to describe and interpret situations involving conditional probability. Two descriptors is the smallest Probability strand in secondary and it is not a light year, because conditional probability is where intuition is most reliably wrong. AC9M10P02 designs and conducts repeated experiments and simulations using digital tools to model conditional probability and interpret results, which is the descriptor that rescues the first one: a student who does not believe a conditional probability result can be made to simulate it ten thousand times and watch the answer appear, and that is a more durable form of persuasion than a tree diagram.

Space (AC9M10SP01 to AC9M10SP03)

AC9M10SP01 applies deductive reasoning to proofs involving shapes in the plane and uses theorems to solve spatial problems. This is the endpoint of a line that ran through Year 8 congruence and Year 9 similarity: Year 8 established conditions, Year 9 explained relationships, and Year 10 asks for a proof, meaning a chain of statements each justified by a named theorem. The assessable object is the chain, not the answer.

AC9M10SP02 interprets networks and network diagrams used to represent relationships in practical situations and describes connectedness. It has no ancestor and no successor inside F–10, which makes it the descriptor most often quietly dropped, and it is a genuine shame because it is the most immediately applicable topic in the year: timetables, transport maps, social connections and dependency charts are all networks. AC9M10SP03 designs, tests and refines solutions to spatial problems using algorithms and digital tools, then communicates and justifies them.

Statistics (AC9M10ST01 to AC9M10ST05)

AC9M10ST01 analyses claims, inferences and conclusions of statistical reports in the media, including ethical considerations and the identification of potential sources of bias. AC9M10ST02 compares distributions for continuous numerical variables using appropriate displays including boxplots, discussing shape, centre, spread and outliers in context. The boxplot is the last new univariate display in the curriculum and it is worth teaching as a five-number summary made visible rather than as a shape to draw.

AC9M10ST03 constructs scatterplots and comments on the association between two numerical variables in terms of strength, direction and linearity. AC9M10ST04 constructs two-way tables and discusses possible relationships between categorical variables, which is the same bivariate question asked of data that has no natural ordering. AC9M10ST05 plans and conducts investigations involving bivariate data and reports findings with consideration of the limitations of any inference. That last clause is the one that separates a Year 10 investigation from a Year 9 one, and it is where the ethical content of AC9M10ST01 comes back as a requirement rather than a discussion.

The four codes that decide senior maths

AC9M10P01: the probability of A given B is not the probability of B given A

The misconception: that conditioning is symmetric, so the chance of having a disease given a positive test equals the chance of a positive test given the disease. The deeper version is that the word “given” is read as background colour rather than as an instruction to change the denominator.

What you will see: in a class where 30 students play sport and 12 of those also play an instrument, asked for the probability that a student plays sport given that they play an instrument, the student answers 12 out of 30. They have conditioned on the wrong event, because 30 was the number in front of them. In a medical-test question the same inversion produces the confident and badly wrong claim that a positive result on a 99% accurate test means a 99% chance of illness. And students routinely treat “P of A and B” and “P of A given B” as interchangeable, since both sentences mention both events.

The fix: make the denominator the explicit first step, always. Before any calculation, the student writes the sentence “I am now only looking at the students who…” and finishes it. Conditioning is not a formula, it is discarding part of the sample space, and once that is said out loud the arithmetic follows. Use two-way tables rather than tree diagrams as the primary tool here, because the conditioning is visible as choosing a row or a column and reading its total, which is exactly the move the student needs to make. Then use AC9M10P02 as designed: simulate the medical-test scenario with ten thousand trials and let the disagreement between the intuition and the count do the teaching. Because AC9M10P01 is written as a language descriptor, assess it as one, by asking students to translate between the four phrases and a table rather than only to compute.

AC9M10ST03: association is not causation, and a strong pattern is not a linear one

The misconception: two of them, and they compound. First, that a scatterplot showing a clear relationship shows that one variable causes the other. Second, that “strength” and “linearity” are one property, so any tight pattern gets described as strongly linear regardless of its shape.

What you will see: ice cream sales plotted against drowning incidents, and a student concludes that ice cream is dangerous, missing the temperature sitting behind both. A plot of height against age across ages 2 to 40, which is tight but obviously curved, described as “strong positive linear association”. And a plot with an obvious outlier described only by the trend, with no comment on the point that does not fit.

The fix: the descriptor names three separate things (strength, direction, linearity), so require three separate sentences, in that order, every time. A student who has to write “the association is strong / positive / clearly non-linear” cannot collapse the second and third into each other. For causation, make the lurking variable a routine question rather than a warning: after every plot, ask “what else could explain this?” and require an answer even when there is not an obvious one. Build a small stock of examples where the answer is genuinely causal, genuinely coincidental, and genuinely a third variable, and make students sort new plots into those three bins. AC9M10ST05 requires the limitations of an inference to be reported, so this is the descriptor being assessed twice.

AC9M10A03: exponential growth is not fast linear growth

The misconception: that an exponential relation is a steep straight line, so the rate is the thing that is large. Underneath it sits a persistent notation confusion between 2^x and x², which look similar and behave nothing alike.

What you will see: asked to compare 2^x and x² for large x, a student says they are about the same, or that x² is bigger because squaring is what makes things big. Asked to sketch an exponential decay curve, they draw a line reaching and crossing the horizontal axis, because a decreasing quantity must eventually hit zero. And in AC9M10A04 modelling, they pick a linear model for a population or an interest problem because the first three data points look straight, which they always do.

The fix: build a table before a graph, and make it long. Double a number twenty times next to squaring it twenty times, and let the student watch 2^x overtake and then annihilate x². The classic rice-on-a-chessboard problem earns its reputation here. For the axis-crossing error, ask what happens if you keep halving: the answer gets smaller forever and never arrives, which is a genuinely interesting fact and introduces the asymptote as an observation rather than a definition. Teach AC9M10A05 first, so students have already varied the base and seen growth flip to decay as it crosses one. And for AC9M10A04, insist that the model choice is justified by the situation rather than by the first few points: things that grow by a fixed amount are linear, things that grow by a fixed percentage are exponential, and that sentence resolves most of the choices a student will face.

AC9M10M02: on a log scale, equal steps mean equal ratios

The misconception: that an axis is an axis, so equal distances mean equal differences. This descriptor has no ancestor anywhere in F–9, so every student arrives with ten years of linear-axis experience and no reason to suspect anything else exists.

What you will see: a magnitude 6 earthquake described as twice as strong as a magnitude 3, and a magnitude 7 as one unit worse than a magnitude 6 rather than ten times worse. On a plotted log scale, a student reads a point halfway between the 10 and 100 gridlines as 55. In a pH context, a solution of pH 4 gets called “a bit more acidic” than pH 5 rather than ten times more.

The fix: introduce the scale before the mathematics, with a problem that cannot be drawn otherwise. Ask students to plot the mass of an ant, a cat, a person, a car and a whale on one axis. On a linear axis every animal but the whale sits on the origin, and the page is useless. That failure is the motivation, and once a class has hit it they will accept a different kind of axis readily. Then make the rule explicit and repeat it constantly: one step along means one multiplication, not one addition. Use the Richter, decibel and pH scales as the applied contexts the descriptor asks for, and always ask “how many times” rather than “how much more”, because the second question is the one that produces the wrong answer. Teach it directly after AC9M10A03, since a logarithmic scale is an exponential relation read backwards.

What students need to arrive with

Year 10 leans on five Year 9 codes, and unusually for a secondary year the gaps do not surface gradually. AC9M9A02 (binomial products and monic quadratics) is the prerequisite for AC9M10A01, which assumes it completely and adds exponent laws on variables on top. AC9M9A01 (exponent laws with integer exponents extended to variables) is the prerequisite for both AC9M10A01 and AC9M10A03, and a student who still reads a negative exponent as a negative number cannot make sense of exponential decay. AC9M9A03 (gradient, midpoint and distance) is the prerequisite for AC9M10A02, since solving simultaneous equations graphically means drawing two lines accurately. AC9M9M03 (spatial problems with Pythagoras and trigonometry) is the prerequisite for AC9M10M03, which adds bearings and angles of elevation and depression to machinery that has to already work. And AC9M9ST03 (comparing distributions on centre, spread and shape) is the prerequisite for AC9M10ST02, because a boxplot is that comparison drawn.

Where any of these is shaky, spend the first three weeks going back to Year 9’s quadratics, exponent and trigonometry work rather than opening on exponentials and discovering the gap in Term 2. The exponent check is the one to run first, because it silently blocks a third of the year’s Algebra. If you are supporting a student at home, helping with maths at home without a tutor covers how to run that catch-up without turning every evening into a lesson.

What this year sets up

Year 10 is the end of the F–10 curriculum, so what follows is senior secondary rather than another year of codes. The mapping is worth knowing, because Year 10 is where subject selection happens and students routinely close doors they did not know were open.

• AC9M10A03 and AC9M10M02 (exponential relations and logarithmic scales) are the direct entry point to Mathematical Methods, where exponential and logarithmic functions carry a large part of the course. A student who never really got AC9M10A03 will find Methods unmanageable within a term.
• AC9M10A01 and AC9M10A02 (algebraic manipulation and simultaneous equations) are assumed fluency in every senior mathematics subject without exception, including the applied ones.
• AC9M10ST03, AC9M10ST04 and AC9M10ST05 (scatterplots, two-way tables and bivariate investigation) lead into the bivariate and regression work that dominates General Mathematics, and into the statistical inference strand of Mathematical Methods.
• AC9M10SP02 (networks) leads into the networks and decision mathematics module of General Mathematics, and it is the one Year 10 topic that is genuinely a taste of the senior subject rather than a prerequisite for it.
• AC9M10SP01 (deductive proof) leads into Specialist Mathematics, where proof stops being one descriptor and becomes a habit the whole subject is built on.
• AC9M10M03 and AC9M10M05 (applied trigonometry, proportion and scaling) lead into Essential Mathematics and General Mathematics, where measurement in practical contexts carries real weight.
• AC9M10N01 and AC9M10M04 (approximation in repeated calculations, and the impact of measurement error) are the numeracy backbone of every senior science subject, which is where they will be assumed rather than taught.

Victorian families following VC2 should note that Victoria publishes a Level 10A alongside Level 10, holding the extension content for students heading to the more demanding senior subjects, so the Victorian Year 10 decision is made inside the curriculum rather than alongside it. Our comparison of the Victorian and Australian curriculums covers the structural differences. NSW families should note that Year 10 is the second half of Stage 5, where the Core and Path split means the pathway decision was effectively made at the start of Year 9 rather than at the end of Year 10, see how the NSW syllabuses are structured. Our guide to which curriculum your state uses is worth a minute if you are unsure which applies.

A term-by-term order

1. Term 1: consolidate the algebra everything else assumes. AC9M10A01 expanding, factorising, simplifying and solving with the exponent laws on variables, then AC9M10A02 linear inequalities and simultaneous linear equations with the graphical interpretation kept alongside the algebraic one. Fold AC9M10N01 in here, using rounding inside multi-step solutions rather than teaching it separately. This term is where a student’s senior options are actually decided, so it is worth protecting from interruption.
2. Term 2: the new function family. AC9M10A05 experimenting with functions using digital tools first, then AC9M10A03 exponential relations and equations, then AC9M10M02 logarithmic scales immediately afterwards while exponentials are still live, because a log scale is an exponential read backwards. Close the term with AC9M10A04 modelling growth and decay, where the three-way choice between linear, quadratic and exponential is the assessable judgement.
3. Term 3: measurement and deductive geometry. AC9M10M03 practical trigonometry with bearings and angles of elevation and depression, which is the biggest block in the term, then AC9M10M01 surface area and volume of composite objects, then AC9M10M05 proportion and scaling where area scales by the square and volume by the cube, then AC9M10M04 the impact of measurement error. Finish with AC9M10SP01 deductive proofs and AC9M10SP03 spatial algorithms, which belong together.
4. Term 4: conditional probability and bivariate data. AC9M10P01 the language of conditional probability and AC9M10P02 simulating it, then AC9M10ST02 boxplots as the last univariate display, then AC9M10ST03 scatterplots and AC9M10ST04 two-way tables as one bivariate unit, then AC9M10ST01 media claims and bias, and AC9M10ST05 a full bivariate investigation to finish the compulsory curriculum. AC9M10SP02 networks fits at the start of this term or the end of the last, and needs protecting from the end-of-year squeeze because it is the descriptor most often lost.

Four orderings matter more than the rest. AC9M10A03 comes before AC9M10M02, because a logarithmic scale only makes sense once exponential growth does. AC9M10A05 comes before AC9M10A03, inverting the published order deliberately, because varying a base and watching growth flip to decay is how the family gets understood. AC9M10ST02 comes before AC9M10ST03, because a student should finish with univariate display before being asked about two variables at once. And AC9M10P01 comes before AC9M10P02, but only just: the simulation is what makes the language believable, so the gap between them should be days rather than weeks.

Assessment checkpoints

• Algebra: ask which is larger for large values of x, 2^x or x², and for a reason. 2^x, with any reference to doubling repeatedly outrunning squaring, confirms AC9M10A03. “About the same” or x² means exponential growth is being read as fast linear growth, so build the twenty-row doubling table before going further.
• Algebra: ask them to solve a pair of simultaneous linear equations and then to say what the solution means on a graph. A correct pair plus “it is where the two lines cross” confirms AC9M10A02. A correct pair with no graphical meaning attached means the descriptor has been half taught, and no-solution cases will look like arithmetic mistakes when they arrive.
• Measurement: ask how much stronger a magnitude 7 earthquake is than a magnitude 5. A hundred times confirms AC9M10M02. “Two more” or “twice as much” means the scale is being read as linear, so go back to plotting the ant and the whale on one axis.
• Probability: in a group of 30 who play sport, 12 also play an instrument, and 20 students in the class play an instrument in total. Ask for the probability that a student plays sport given they play an instrument. 12 out of 20 confirms AC9M10P01. 12 out of 30 means the conditioning went the wrong way, so make writing the “I am now only looking at…” sentence a required first step.
• Space: give a short proof to complete about a property of a parallelogram and ask for a reason beside every line. Named theorems beside each step confirm AC9M10SP01. A correct conclusion with no justifications means the answer is being assessed and the chain is not, which is the whole content of the descriptor.
• Statistics: show a scatterplot of ice cream sales against drowning incidents and ask what it shows. Naming the strong positive association and raising temperature as a lurking variable confirms AC9M10ST03 and AC9M10ST05. “Ice cream causes drowning” means association is being read as causation, and the “what else could explain this?” question needs to become routine.

Recording the alignment

Whether you are programming for a class or building evidence for a homeschool registration review, record the code on the activity as you go. At Year 10 there is a reason to be more careful than in any earlier year: this is the last set of records that exists before senior subject selection, and “statistics unit” will not tell anyone whether a student has met AC9M10ST03 or only AC9M10ST02, which is precisely the difference that matters when deciding whether General Mathematics is a reasonable choice. “AC9M10ST03, scatterplot of study hours against test score with strength, direction and linearity described, 12 October” answers that question a year later. Our guide to state-by-state registration requirements covers what reviewers ask for at the end of compulsory schooling, and teaching maths through interests covers wrapping these codes around whatever your student is currently into, which is at its hardest and most valuable in Year 10.

Sprout Lessons builds a full interactive lesson from any of these 21 codes, pitched at Year 10 and wrapped in whatever your student is into, with self-checking practice that hints rather than just marking wrong, and the exact AC9 code recorded in the lesson footer. It earns its keep most on AC9M10P01 and AC9M10M02, the two descriptors where students need many more worked contexts than a textbook chapter carries, and where the wrong intuition is confident enough that a hint at the moment of the error is worth more than a mark at the end. Try it free and generate a Year 10 Maths lesson in about a minute.

Australian Curriculum content descriptions are © ACARA and licensed under CC BY 4.0. Quoted here unmodified. ACARA does not endorse this product. Always verify against the current content descriptions and achievement standards at australiancurriculum.edu.au.

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