The wording bank

Discrete mathematics

Full discrete mathematics reference

[SPEC], verbatim: "Students should use command/task words, other instructional information within questions and corresponding mark allocations to guide their responses." This section is that instruction, unpacked, for each wording VCAA actually uses.

3.1 "Prove, by mathematical induction, that …" / "Use mathematical induction to prove that …"

Both forms appear. 2023 Exam 1 Q8 and 2025 Exam 1 Q7 use "Use mathematical induction to prove that"; 2024 NHT Exam 1 Q8 and 2026 NHT Exam 1 Q2 use "Prove by mathematical induction that". There is no difference in what is required.

What must appear, in the reports' and guides' own words:

On the mark codes. VCAA publishes no glossary for M1, A1, H1 and A1* in the Assessment Guides. The conventional reading, consistent with every usage in the four published guides, is: M = method mark, A = answer/accuracy mark, H = a further intermediate mark within a multi-mark part, and the asterisk in A1* marks a part whose answer was given in the question, which is why every A1* in the corpus is annotated "ans. given", "answer given" or "working required". This is an inference from usage, not a published definition.

The four-mark and three-mark shapes, side by side:

3.2 "Use proof by contradiction to show / prove that …"

[SAMPLE] Exam 1 Q4 and Q5 are the only exemplars; there is no report, so there is no VCAA commentary. What must appear is fixed by the logic and by the model proof VCAA printed in 2024 NHT Exam 2 Section A Q1:

If the statement is an implication ("if P then Q"), the assumption is P AND not-Q — the hypothesis is retained. This is the difference between contradiction and contrapositive and it is the one place candidates reliably err.

3.3 "State the contrapositive of …" / "The contrapositive of this statement is"

Never yet set as a written question; four live multiple-choice instances (§2.11).

In a written form, the answer is one sentence, and the mark would hang on both operations being performed. Given 2024 Exam 2 Section A Q1, where 20% chose the option that performed only one of the two operations, the risk is real.

3.4 "Give a counter-example to show that …"

Never yet set as a written question; one live multiple-choice instance (§2.12). The written form would require:

One counter-example is enough, and more than one wastes time — the mirror image of the over-proving trap in 2008 Exam 1 Q8c (§2.16).

3.5 "Show that …" and "Prove that …" — the general rule

This is the highest-frequency wording in the whole subject and VCAA has restated the rule in its general comments almost every year. The rule, in the reports' own words, across fourteen years:

Three operational rules follow and they are worth more marks per minute than anything else in this document.

1. Never write the target on the first line. [RPT16 E2]: "Some students incorrectly started with the given expression with no explanation of its origin."
2. Work one side to the other, and say which. [RPT07 E2]: "Very few students worked separately on the right hand side to show that it became the left hand side."
3. Substitution is not proof. [RPT19 E2]: "rather than 'verify'". [RPT10 E1]: "just substituting the value and showing that the coefficient of j was zero was not sufficient."

3.6 "Hence …" — the companion instruction

[RPT06 E2]: "The paper also contained six 'hence' type questions. With this type of question, students must use the result obtained in the previous question part to answer the subsequent part of a question. To gain full marks, this instruction must be [followed]." [RPT09 E2]: "It needs to be emphasised that for this type of question students must use a previously established result to answer the question at hand."

The live example: 2009 Exam 1 Q8b (31%), where [RPT09 E1] records "Most students realised that the given result from Question 8a. should be used". And [RPT06 E2] on Q5c (37%): "A large number of students ignored the 'hence' requirement of this question and did not use the answer for cos(π/8)."

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Functions, relations and graphs

Full functions, relations and graphs reference

These are VCAA's recurring sentences. Learn them as instructions with a mark attached, because that is what they are.

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Algebra, number and structure

Full algebra, number and structure reference

VCAA reuses a small closed set of sentences. Learning them is worth marks, because each one names a required form and the reports are explicit that answers in the wrong form do not score.

One correction that matters. The phrase "sketch the subset of the complex plane defined by" does not occur anywhere in this corpus. A case-insensitive search for subset across all 97 Specialist Mathematics paper and report files returns zero hits, and the word appears in [SD] only in the transformations and counting topics of Units 1 and 2 ("effect of these linear transformations … on subsets of the plane", "countable and uncountable subsets of R"). VCAA's actual wordings for this task are:

• "On the Argand diagram below, sketch {z : z z̄ = 4, z ∈ C} and sketch {z : |z + z̄| = |z − z̄|, z ∈ C}" (2013 Exam 2 Section B Q2a)
• "Sketch {z : z z̄ = 4, z ∈ C} on the Argand plane below" (2025 Exam 2 Section B Q2a)
• "Sketch the circle on the Argand diagram below" (2018 NHT Exam 1 Q8a)
• "Sketch L and the graph of |z| = 2 on the argand diagram below" (2009 Exam 2 Section B Q2e)
• "Graph the circle given by |z + 1| = 2|z − i| on the Argand diagram below, labelling the intercepts with the vertical axis" (2018 Exam 2 Section B Q2c)

Set-builder notation with z ∈ C is the house style from 2012 onward; before that VCAA wrote "the relation …" or "the curves given by …". Two more house conventions worth internalising: VCAA writes "Argand diagram" in papers up to 2023 and "Argand plane" in 2025 and 2026 NHT, interchangeably; and it lowercases "argand" in several 2006–2010 papers. Neither carries meaning.

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Calculus

Full calculus reference

VCAA writes examinations from a small, stable vocabulary. Each recurring sentence carries a precise instruction about what work is required, and — critically — about what work is not. Misreading them is the single largest cause of avoidable loss in this area of study. [RPT16 E1] and [RPT17 E1] list "not reading the question carefully enough — this included not answering the question, proceeding further than required or not giving the answer in the specified form" as the first area of weakness on the whole paper, both years.

3.1 "Write down a definite integral that gives …"

Where it appears. 2008, 2009, 2010, 2013, 2014, 2015, 2016, 2017 NHT, 2018, 2018 NHT, 2021, 2021 NHT, 2022 NHT, 2023, 2023 NHT, 2024 NHT, 2025, 2026 NHT — eighteen distinct Examination 2 papers in the corpus contain the exact string "Write down a definite integral" [PAPERS].

Canonical forms.

What it demands. A complete, correct integral expression: the constant (π or 2π), the integrand, both terminals, and the differential. Nothing else. There is no credit for evaluating it — and no penalty either, except time.

Why it is set as its own part. It separates set-up from evaluation so that the two can be marked independently. The design is deliberate and it works: on 2022 Exam 2 Section B Q1d the set-up part scored 45% and the evaluation part 37% — the evaluation being harder despite being a single button press, because students who had lost π at the set-up stage compounded the error.

The variable specification is the whole question. "In terms of x", "in terms of y", "in terms of t" and "in terms of u" each demand a different, complete change of variable. 2019 Exam 2 Section B Q1e asked for t and 79% of the state scored zero [RPT19 E2].

Related phrasings that mean the same thing. - 2006 Exam 1 Q6a: "Express the volume of the solid of revolution as a definite integral." (70%) - 2017 Exam 2 Section B Q3 (two consecutive parts): "Write down an equation involving definite integrals that can be used to determine a." (2 marks) then "Hence, find the value of a, correct to two decimal places." (1 mark) - 2017 Exam 2 Section B Q3d.i: "Write down an expression involving a definite integral that gives the time taken for the skydiver to reach a speed of 30 m s⁻¹." - 2018 Exam 2 Section B Q3d: "Express the time taken for the depth to reach 0.25 m as a definite integral and evaluate this integral correct to the nearest tenth of a second." (both verbs in one part, 2 marks, 56%) - 2014 Exam 2 Section B Q4c: "By using an appropriate definite integral, find the time it takes for the tank to fill." (2 marks, 32%) - 2017 Exam 2 Section B Q1c.i: "[write] π∫₀ᵃ(f(x))² dx = π∫ₐ³(f(x))² dx" — an equation of two definite integrals defining an unknown terminal (71%).

The time-as-an-integral idiom is worth isolating. When a question gives dh/dt = F(h) and asks for a time, the answer is t = ∫_{h₁}^{h₂} 1/F(h) dh — reciprocate and integrate with respect to the dependent variable. [RPT14 E2] on Q4c (32%): "Many students did not attempt this question. A number attempted to find t in terms of h, instead of using a definite integral. Some attempted to integrate dh/dt with respect to h."

3.2 "Using a suitable substitution" / "Using the substitution u = …"

Where it appears. "Suitable substitution" occurs in 2006, 2007, 2008, 2010, 2012, 2015, 2016, 2017, 2018, 2018 NHT, 2019, 2019 NHT, 2020, 2021 NHT and 2023 NHT [PAPERS]. "Using the substitution" with an explicit substitution occurs in 2009, 2014, 2022, 2022 NHT, 2024 NHT, 2025 and 2026 NHT.

Two distinct instructions, and the difference matters.

What VCAA does when it supplies the substitution. It removes the only creative step and then makes the bookkeeping the entire question. Every distractor in the Section A family is a specific bookkeeping failure. In the u² = x + 1 variants (2024 NHT Exam 2 Section A Q8) and x³ − 1 = u² (2026 NHT Exam 2 Section A Q9), the substitution is given implicitly, so differentiating it is itself a step: 2u du = dx and 3x² dx = 2u du.

The corollary a 45+ candidate must internalise. If VCAA has not supplied a substitution, and the integrand is a standard form, then a substitution is probably wrong. [RPT19 E1] lists among areas of weakness: "not recognising and writing down the anti-derivative of standard functions leading to unnecessary use of substitutions in integration problems (Questions 1 and 8)." [RPT21 E1]: "Use of a substitution was unnecessary in this situation and in attempting to use a substitution, some students introduced errors into their working."

3.3 "Hence" and "Hence, or otherwise"

"Hence" alone is mandatory. It means: use the immediately preceding result. Examples: 2006 Exam 1 Q1b "Hence find the exact value of dy/dx when y = 1"; 2006 Exam 2 Section B Q1e "Hence find an expression for the rate of change of the area"; 2009 Exam 1 Q5c "Hence evaluate the gradient of the curve at the point (1, 1)"; 2014 Exam 1 Q5c and Q7c "Hence evaluate …"; 2017 Exam 1 Q8a "and, hence, estimate the positive value of x when y = 0"; 2017 Exam 2 Section B Q3 "Hence, find the value of a, correct to two decimal places."

The reports mark the instruction. [RPT06 E2] on Q1e (22%): "Some did not use 'hence' and tried to use dA/dx to find dA/dt, which was a far more complicated approach." [RPT14 E1] on Q7c (26%): "Some ignored the word 'hence'." [RPT17 E1] on Q8a (17%): students who computed the answer from part b rather than reading it off the graph were penalised because "part a. used the word 'hence'".

"Hence, or otherwise" is permissive but signposted. It appears in 2023 Exam 2 twice — Q3b.ii "Hence or otherwise, find the curved surface area of the solid correct to three decimal places" and Q4e.ii "Hence or otherwise, find the size of the fish population in pond 2 and the value of t when the rate of growth of the population is a maximum" — and in 2024 NHT Exam 1 Q3b and Q9d, and 2022 Exam 1 Q1b. It licenses an alternative route, but the "hence" route is always the short one, and on a 1-mark part there is no time for the alternative.

A further wrinkle worth knowing. [RPT17 E1], on show-that questions generally: "Students should be reminded that they can use a given value in the remaining part(s) of a question whether they were able to derive it or not." A failed "show that" does not forfeit the rest of the question.

3.4 "Show that" — and what counts as showing

Frequency. "Show that" occurs 105 times across the corpus text files [PAPERS]. [RPT23 E2], [RPT16 E2] and [RPT10 E2] count three, four and seven instances respectively on a single Examination 2.

What it demands. [RPT17 E1]: "showing a given result. This was required in Question 10a. In such questions, the onus is on students to include sufficient relevant working to demonstrate that they know how to derive the result." [RPT18 E1]: "students are reminded that they must present sufficient evidence that the result has been shown."

The reports are candid that this is routinely gamed. [RPT11 E1]: "as often happens in a 'show that' question, some students were unable to do the relevant algebra yet somehow still managed to give the result stated." [RPT12 E1] on Q9c (35%): "As often happens in a 'show that' type of question, some students were unable to do any convincing algebra, yet still managed to obtain the result stated." [RPT13 E1] on Q5a: "Some students who did have a constant of integration were unable to evaluate it. Nevertheless, this did not stop them from 'showing' the given result."

The mechanical rule. On an n-mark "show that", write at least n distinct lines of algebra between the starting point and the stated result. [RPT08 E2]: "As it was a 'show that' question, the most common error was the omission of a suitable intermediate expression." [RPT25 E2] on 2025 Exam 2 Section B Q3b: "Many responses did not show sufficient development of the formula to be awarded the method marks."

Variants. - "Use integration to show that …" — 2025 Exam 1 Q3a, 2025 Exam 1 Q4a ("Use integration to show that E(T) = ½"). - "Use calculus to show that …" — 2006 Exam 2 Section B, 2026 NHT Exam 2 Section B Q3b.i ("Given that the volume of the solid of revolution is π logₑ(k), use calculus to show that k satisfies the equation k² − 4k + 3 = 0"). - "Use calculus to solve …" — 2025 Exam 2 Section B Q3d. [RPT25 E2]: "'Use calculus' means students are required to show the steps needed to find the solution to gain all 3 marks." On a technology-active paper this phrase forbids deSolve. - "Use implicit differentiation to find …" — 2023 Exam 1 Q4. The method is prescribed. - "Verify by differentiation and substitution into the left side …" — 2016 Exam 2 Section B Q3d. The direction of work is prescribed.

3.5 How VCAA asks for an expression rather than an evaluation

This is the family of instructions that tells you to stop.

"Find an expression for" versus "find the value of" is the commonest misread in Section B. 2006 Exam 2 Section B Q1e asks for dA/dt "in terms of x"; the next part asks for the exact value of x at the maximum. Two parts, two different objects.

"In the form" is not decoration. [RPT16 E1] and [RPT17 E1] both list "not giving the answer in the specified form" among the paper's leading weaknesses. [RPT17 E1] on Q8b (36%): "Most students had the correct integration after separating variables but made no attempt to express the answer with integers as required." [RPT09 E1] on Q10b (23%): "A high proportion of students either ignored the instruction regarding integers or did not know how to proceed." Recent examples of the demanded forms: V = 2π(logₑ(a) + b) (2020), ay³ + by + cx² + d = 0 (2017), Q = a/(16 + 2t)^{b/c} (2018), π((a√b)/c − d) (2023), aπ/b (2024 NHT), logₑ(a/b) (2017), a/(b + cπ) (2018), π√a/b (2023).

3.6 The exactness instruction, and its negation

Every Examination 1 front page since 2010 carries [PAPERS]:

"Unless otherwise specified, an exact answer is required for each question."

and the 2006–2009 papers the equivalent "A decimal approximation will not be accepted if an exact answer is required to a question."

The negation is always explicit, and always precise about the precision: "correct to two decimal places" (291 occurrences of "correct to" across the corpus [PAPERS]), "correct to the nearest integer", "correct to one decimal place", "correct to the nearest tenth of a second", "correct to three decimal places". [RPT24 E2]: "Answers must be left in exact form unless a specific number of decimal places is required." [RPT23 E2] on Q3b.ii (55%): "Incorrect rounding … was a frequent final response. Students are reminded to set their calculators to display sufficient decimal places." [RPT25 E2] on Q3f: "Several responses left the answer as a decimal, rather than in exact form as required by the question." [RPT15 E2] on Q1e: "A significant number of students did not give their answer correct to three decimal places."

3.7 The technology-selection wordings (Examination 2 only)

[RPT25 E2] on Section A Q11: "Use the DEsolve functionality on CAS to solve the given differential equation and then find the domain of the solution. Alternatively, use separation of variables to solve the differential equation manually." [RPT25 E2] on Section B Q1b.i: "Students must make sure variables are defined if they are being used in formulas." [RPT24 E2] on Q1b.i: "Students were expected to write an expression for … within the definite integral instead of stating the generic formula. Many students made transcription errors when transferring their answer from their CAS to the script."

The rule that follows: on Examination 2, a written response must show the instantiated integral — π∫₀¹(2 − sin²x)dx, not V = π∫y²dx.

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Space and measurement

Full space and measurement reference

VCAA reuses a small number of sentences almost verbatim. Learning the sentence is learning the task.

3.1 The resolute wordings — three distinct sentences

Two further variants exist and are pure traps: - "The vector resolute of a = 2i − j + 3k that is perpendicular to b = i + j − k is" (2019 NHT Exam 2 Section A) — the perpendicular one is still called a vector resolute. - "The magnitude of the component of the force F that acts in the direction d" (2020 Exam 2 Section A Q14, pct 76) and "The component of the force F = ai + bj … in the direction of the vector w = i + j" (2015 Exam 2 Section A Q15, pct 49) — "component" here means the resolute, and whether it is the scalar or the vector one is settled by the word "magnitude".

3.2 "Show that the acceleration … is given by"

Five live instances in the corpus [PAPERS]:

• 2008 Exam 2 Section B Q2a: "Show that the acceleration of the skier is 4.5 m/s²." (pct 91)
• 2010 Exam 1 Q2a: "Show that the acceleration of the body is given by dv/dt = (v − 4)/2." (pct 92)
• 2017 NHT Exam 2 Section B Q5b: "Show that the acceleration of the 5 kg mass is 4 m s⁻²."
• 2019 NHT Exam 2 Section B Q5dii: "Show that the acceleration of the pallet down the plane is given by g(5 − t)/(t + 290) m s⁻², for t ∈ [0, 5)."
• 2022 Exam 2 Section B Q5a: "Show that the acceleration of the object is given by (8 − k) m s⁻²." (pct 72)

What it demands. Not the answer — the answer is printed. It demands the chain: a labelled force or model statement, an equation of motion or an acceleration form, and the algebra connecting them. [RPT16 E2] on the rocket: "As this was a 'show that' question, students needed to show clear progress from an equation of motion to the required differential equation. Some students did not include the weight force in the initial equation; drawing a diagram showing forces could have benefited these students." [RPT25 E2] generalises it: "'Show that' questions require clear steps of working that lead to the given answer."

The cognate wordings behave identically: "Show that the speed of the particle … can be expressed as" (2025 Exam 2 Section B Q4d, pct 35.56 — [RPT25 E2]: "Another 'show that' question which required working that shows the use of trigonometric identities that are given on the formula sheet"), and "Show that the Cartesian equation of the path of the particle is" (T25).

3.3 "Find the distance travelled by the particle"

Six instances, and the wording is always precise about which distance:

• 2009 Exam 2 Section B Q1b: "Calculate the distance travelled by the car during the first nine seconds of its motion." (pct 76)
• 2009 Exam 2 Section B Q1c: "Calculate, correct to the nearest 0.1 m, the distance travelled by the car while it is decelerating." (pct 71)
• 2009 Exam 2 Section B Q3gi: "Write down a definite integral of the form ∫√(a + bt²) dt which represents the distance travelled by the child." (pct 28)
• 2012 Exam 2 Section B Q3eii: "Find the total distance travelled from when the car starts to accelerate to when it comes to rest." (pct 30)
• 2012 Exam 2 Section A Q18: "The distance travelled by the particle in the first 2 seconds of its motion is given by".
• 2022 Exam 2 Section B Q4d: "How far does the ball travel during the first four seconds after passing through O?" (pct 45)

What it demands. For motion along a curve, ∫|ṙ(t)| dt. For rectilinear motion that changes direction, ∫|v| dt — split at the turning points. Never |r(t₂) − r(t₁)|, which is displacement. [RPT07 E2] on Q4e (pct 18): "A common erroneous approach was to work out |r(60)| − |r(0)| instead of |r(60) − r(0)|" — and even the corrected version is the displacement, which was what that particular question wanted. Read which one is being asked.

3.4 The i–j–k conventions

VCAA sets the basis explicitly, in one of four standard sentences, and the sentence tells you what the components mean:

Consequences that are examined: "height above ground" is the k (or j) component only, never |r|. [RPT09 E2] on Q3a: "A common error was to find |r(0)| rather than the magnitude of its vertical component." [RPT15 E2] on Q4ai: "A number of students attempted to solve |r(t)| = 60, failing to realise that only the k component was 60." "Lands" means the vertical component equals zero.

Notation in the written papers uses an under-tilde (a̰) for vectors and an over-arrow for displacements between named points; the corpus text extraction drops both, which is why archived question text often reads as scalars. VCAA does penalise notation: [RPT07 E2] — "Lack of tildes indicating what should be vectors was common"; [RPT13 E2] lists among the paper's weaknesses "lack of proper vector notation, in particular the confusion of scalar 0 with null vector 0."

3.5 Other recurring sentences

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Data analysis, probability and statistics

Full data analysis, probability and statistics reference

VCAA reuses a small number of sentences almost verbatim. Learn them as triggers; each one names a specific deliverable.

3.1 The hypothesis-statement sentence

What it demands. Two lines, in the notation H₀: and H₁:, each about μ, with H₀ an equality. Nothing else — no p-value, no conclusion. The word "suitable" is not an invitation to editorialise.

The direction is always in the stem's preceding sentence. "to test whether the mean level of pollutant has increased" → H₁: μ > 1.1. "The ranger thinks that the true mean mass is less than this" → H₁: μ < 12. "to test whether the machine is working properly and is still producing packets with a mean mass of 375 grams. … A two-tailed test at the 5% level of significance is to be carried out" → H₁: μ ≠ 375. When VCAA wants two tails it says "two-tailed"; when it wants one it says "one-tailed" or "one-sided" and names a direction.

3.2 The critical-value sentence

What it demands. A number on the scale of the sample mean, to the stated accuracy. "Smallest … for H₀ not to be rejected" is an upper-tail critical value on a lower-tail test; "largest … for H₀ not to be rejected" is a lower-tail critical value on an upper-tail test. Draw the picture before touching the calculator.

3.3 The conclusion sentence, and what a complete conclusion must contain

What the reports say a complete conclusion must contain. Assembling the eight report comments quoted under Type 21, a full-mark conclusion has three components, and VCAA's published sample answers show all three:

1. The numerical comparison, with both numbers present. [RPT25 E2]'s model answer: "as 0.0023 < 0.01 (the significance level)". [RPT18 E2]'s: "As p = 0.0092 < 0.05, reject H₀." Writing only "p is small" or only "p < α" without the figures is where marks go. [RPT18 E2] also records responses that wrote 0.0092 > 0.05 — a comparison stated backwards.
2. The decision about H₀. "Reject H₀" or "do not reject H₀". VCAA's own older sample answers use "accept" ([RPT17 E2]: "p > 0.05, accept the dairy's claim") but the 2023–2025 answers use "reject / not reject", and "fail to reject" is safest.
3. The translation into the context, answering the literal question asked. [RPT24 E2]: "some students did not fully answer the question regarding whether or not the machine should be paused." [RPT25 E2]: "Responses needed to comment on the company's claim and also quote the significance level." [RPT19 E2]'s model answer: "As p < 0.05 reject H₀. The sample suggests the machine is not working properly."

A conclusion missing any one of the three has lost the mark in at least one archive year. The safe sentence is:

"As p = 0.0023 < 0.01, reject H₀ at the 1% level of significance. The sample provides evidence that the mean volume dispensed is less than 750 mL, so the company's claim is supported."

3.4 The p-value sentence

• "Find the p value for this test correct to three decimal places." (2024 E2 Q6b.i)
• "Determine the p value for this test. Give your answer correct to four decimal places." (2025 E2 Q6f.i; 2026 NHT E2 Q6d.i)
• "Write down an expression for the p value of the statistical test and evaluate your answer correct to four decimal places." (2018 E2 Q6c; 2019 NHT E2 Q6c; 2017 NHT E2 Q6b)

"Write down an expression … and evaluate" is a two-part instruction worth two marks: the conditional-probability statement p = Pr(X̄ < 145 | μ = 150) earns one and the value 0.0092 earns the other. Omitting the expression halves the mark.

3.5 The Type II error sentence

Four registers, all meaning the same thing:

1. Named: "find the probability of a type II error for the test" (2024 E2 Q6c; 2024 NHT E2 Q6f; [SAMPLE] E2 Q7).
2. Semi-named: "what is the probability that H₀ will be accepted at the 5% level of significance?" (2018 E2 Q6f); "find the probability that the null hypothesis would be incorrectly accepted" (2021 E2 Q6e).
3. Conditional-probability notation: "If the mean level of pollutant in the river, μ, is in fact 1.2 mg/L after the spill, find Pr(X̄ < 1.163 | μ = 1.2)." (2016 E2 Q6e).
4. Fully contextual, no statistical vocabulary at all: "find the probability that the company will conclude that the service has not reduced the mean volume of water in an Apa bottle" (2025 E2 Q6h); "find the probability that the snowboarder … will conclude that the wax is ineffective" (2026 NHT E2 Q6e); "what is the probability that the inspectors will not query the manufacturer's claim if the mean volume … is in fact 749.5 mL and not the claimed 750 mL?" (2023 NHT E2 Q6b.ii).

Register 4 is the dangerous one. Nothing in the sentence says "error", "hypothesis" or "Type II". The tell is always the phrase "is in fact" or "the true mean … is" followed by a value different from μ₀.

3.6 The simulation-count sentence

• "In how many of these confidence intervals would the actual mean mass … be expected to lie?" (2023 E2 Q6b)
• "In how many of these confidence intervals would the population mean volume dispensed by the machine be expected to lie?" (2024 E2 Q6f)
• "In how many of these confidence intervals would the engineers expect the value of the true mean volume dispensed to be included?" (2025 E2 Q6c)
• "If the manufacturer took 200 such samples, how many of the 99% confidence intervals would be expected to contain the value of the population mean?" (2025 NHT E2 Q6d)

3.7 Accuracy instructions, which are marks

Every statistics part in 2023–2025 carries an explicit accuracy instruction: "correct to four decimal places", "correct to three decimal places", "correct to one decimal place", "correct to the nearest integer", "give your answers in millilitres". [RPT24 E2] states the general rule: "Answers must be left in exact form unless a specific number of decimal places is required." [RPT17 E2] on Q6a: "many students either did not express their answer as a percentage or did not give the required level of accuracy"; on Q6c: "A significant proportion of otherwise correct answers were not given in the required form."

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