Guides · Mathematical Reasoning
Short answer: no, and the Department says so plainly — the questions draw on the Year 6 curriculum and need no new or special knowledge. We wanted to know whether that held up, so we read all 105 questions in its three official practice tests against its own answer keys, and checked them against the NSW syllabus. It holds up. What the test does instead is take ordinary Year 6 content and wrap a second demand around it — a chain of steps, a reversal, a constraint, a trap. 104 of the 105 questions do this. That layer is the difficulty, and it never appears in a topic list, which is why the paper feels harder than the maths in it actually is.
Verified August 2026Every quotation traces to a Department page, a Department answer key, or the NSW syllabus.
Before anything else: the Department publishes three complete Mathematical Reasoning practice tests free, each with a question paper, an answer key, and a full explained-answers document. They are the closest thing to the real paper that exists, because the same people make both.
The explained answers are the part almost nobody reads, and they are the most useful document in the whole set. They show the method the test writers intend — which, as you will see below, is usually simpler than the method an adult reaches for. Work through those three papers before paying anyone for anything, including us.
Two statements, from two different official documents, and they need reading together.
On content
Source: NSW Department of Education, selective high school practice tests (accessed 16 August 2026).
On what is being measured
Source: NSW Department of Education, policy PD-2002-0006-06, section 4.2 (accessed 16 August 2026).
Our reading of the pair — and it is our reading, not a sentence the Department has written — is that Year 6 content is the raw material, and what earns marks is what your child does with it. That distinction explains almost everything about how the paper feels.
We read every question in the three official practice tests alongside the Department's explanation of it. Exactly one question comes close to being a bare calculation, and even that one asks your child to work out what the smallest four-digit number is before multiplying anything. Every other question adds a layer:
| What the question adds | What it looks like |
|---|---|
| A chain of steps | Three or more operations in sequence, often with a unit change buried in the middle |
| Two or more unknowns | Two quantities you cannot find separately until you relate them to each other |
| Several claims to test | Three statements about a graph or a set of fractions; decide which combination is true |
| Working backwards | The result is given; the starting number is not |
| A constraint to satisfy | Find the largest number that is also a multiple of something and has distinct digits |
| A trap to notice | A trailing zero, a transposed unit, a bar chart that shows cumulative totals rather than weekly ones |
None of that is content you can be taught in a lesson and then own. It is a habit of reading a question twice before starting — which is, inconveniently for everybody, built slowly.
Sixteen questions across the three papers give your child two or more unknown quantities at once. In Year 8 every one of these is a simultaneous-equations problem, and this is where the belief that selective candidates need to be pushed ahead into high-school algebra comes from. It is worth knowing that the Department's own answer keys never once use algebra to solve them. Across all 105 questions, not a single pronumeral appears. Four methods cover all sixteen, and a Year 6 child can learn every one.
Two totals differ by exactly one known thing. Subtract them, and the difference names it.
The difference between the two totals is 41 − 27 = 14 points. Two stars and two hearts = 14 points… so one star and one heart = 7.
Practice Test 1, question 34
Write every unknown as a multiple of the smallest one, then divide the total by the number of units.
Mon is 2× Tues, and Tues is 2× Wed. So Mon is 4× Wed… altogether equal 7× Wed. 420 ÷ 7 = 60.
Practice Test 2, question 22
Draw the relationship instead of writing it. Once it is drawn, the arithmetic is usually obvious.
We need to split 12 into two numbers, so that one number is twice the other.
Practice Test 2, question 16
Try a candidate, see how it fails, adjust. Unglamorous, fast, and endorsed by the people who write the test.
Alternatively, we could use trial and improvement. Let's try the number 1 in position X… This doesn't work… We could try 2…
Practice Test 1, question 33
The most useful sentence in the official material
On question 33 of the first practice test, having solved it by inspection, the Department adds: "Alternatively, we could use trial and improvement." The people who write the test are telling you, in print, that guessing sensibly and adjusting is a legitimate way through. Children who think they are cheating by trying numbers are usually the ones who freeze.
The Year 6 curriculum in NSW is Stage 3, which spans Years 5 and 6 together. We checked the test against all twenty Stage 3 content areas. There are two places where the paper asks for something the syllabus does not contain — and in both, what is new is the shape of the question, not the mathematics needed to answer it.
The entire algebraic content of Stage 3 is three lines, and the operative one is: "determine a rule describing the relationship between the bottom number and the top number in a table". One input, one output, one relationship, described in words. The word "pronumeral" does not appear anywhere in Stage 3. A scenario with two unknowns constrained by two relationships is a structure the syllabus never introduces — yet it turns up in all four past papers we have analysed, and sixteen times across the three practice tests.
This is the single best argument for practising with real papers rather than school-style worksheets. Not because the maths is beyond your child, but because the arrangement will be unfamiliar the first time and ordinary by the fifth.
Stage 3 probability is careful about its own boundary. The syllabus specifies determining the make-up of a collection by "sampling objects and returning them to the collection before the next sample (sampling with replacement)". The 2023 paper asks question 7 like this: a bag of 7 black and 6 white marbles, two taken out — one black, one white — and then, in the paper's own words, "She does not put them back in the bag."
In a Year 9 classroom that is conditional probability. For a Year 6 child it is a counting job: eleven marbles left, five of them white, so five elevenths. The difficulty is noticing that the bag changed — not knowing a rule about dependent events. Across seven papers we have examined, this happens once.
If the content is Year 6 and the difficulty is the wrapper, then drilling topics is the wrong instinct — your child is unlikely to be missing the arithmetic. Three things follow.
And the honest ceiling on all of this: roughly one applicant in four receives a place — in 2025, 17,559 applications for 4,227 Year 7 places. Those figures come out of the independent review of the 2025 test; the year-by-year table is in the NSW Selective Test guide. The arithmetic guarantees that most capable, well-prepared children will miss out, and they are fine. Preparation makes the paper familiar. It cannot make the odds something they are not.
The content is not harder; the questions are. The Department states that "the questions draw upon concepts from the NSW curriculum up to Year 6 that your child learns at school" and that "the test will not need your child to know any new or special knowledge". We read all 105 questions in its three official practice tests and found that true of the content — but 104 of the 105 ask for something beyond the calculation itself: a chain of steps, a reversal, a constraint to satisfy, or a trap to notice. That second layer is where the difficulty lives.
No. Sixteen questions across the three official practice tests involve two or more unknown quantities, which in later years would be solved with simultaneous equations. In every single case the Department's own published answer key solves them without algebra — using a bar diagram, the unitary method, elimination by subtraction, or trial and improvement. On one question its answer key says outright: "Alternatively, we could use trial and improvement." Pronumerals do not appear anywhere in the Stage 3 syllabus, and they do not appear in the answer keys either.
Two things, and both are about the shape of a question rather than the maths inside it. First, problems with two unknown quantities at once: the whole of Stage 3 algebraic reasoning is describing a single one-in-one-out rule in words, so two unknowns constrained by two relationships is a structure Stage 3 never covers. Second, one 2023 paper asks a probability question where marbles are removed and not put back; the Stage 3 syllabus specifies sampling "returning them to the collection before the next sample (sampling with replacement)". Both are still answerable with Year 6 arithmetic.
The 35 questions cluster into nine recurring families: number sense, fractions and probability, algebra-style reasoning, time and date, measurement and scales, 2D geometry, 3D and spatial reasoning, data and graphs, and combinatorics and logic. The proportions hold reasonably steady from paper to paper. Our question-types guide breaks all nine down with worked examples.
The Department publishes three complete Mathematical Reasoning practice tests free on its selective high school practice tests page, each with a question paper, an answer key and a full explained-answers document. The explained answers are the most useful and least used part: they show the method the test writers intend, which is usually simpler than the one an adult reaches for. Work through those before paying anyone for anything.
The Department's position is that "coaching or tutoring for the placement test is not necessary" and that "there is no credible research that shows coaching helps a child gain entry". On the specific worry behind this question — that a Year 6 class will not have covered the syllabus by early May — the syllabus is written in two-year stages, and NSW leaves schools to sequence Stage 3 as they see fit. So no one can tell you what your child has already covered without asking their teacher. That is a reasonable question to ask at a parent-teacher night, and a cheaper one than a term of tutoring.