What Mathematical Reasoning tests
Mathematical Reasoning is multiple choice. Depending on the year level, students have around 40 minutes for 28 to 35 questions, roughly a minute to a minute and a half per question, before any time is left over to check answers.
Multiple choice, four options. Question count varies by year level.
ACER describes the section as assessing comprehension, interpretation and analysis of mathematical information. At junior secondary level that covers number, measurement, space, time, logical relations and problem solving. At middle and senior secondary level, maths and science content is combined, so questions also involve inferring, predicting and drawing conclusions from information presented as numbers, text, diagrams, graphs and tables.
Nowhere in that description does it say "advanced maths content." It says comprehend, interpret, infer, reason. That's effectively the whole section in one sentence.
Why it's harder than it looks
The maths in most of these questions is genuinely simple, multiplication, exponents, basic division. What catches students out isn't the maths, it's the reading.
Mathematical Reasoning on HAST is rarely traditional school maths. Especially at middle and senior secondary level, a lot of questions are built around science content (astronomy, geology, chemistry, physics, biology) or an invented scenario (a computer network sending data packets, a lock made of symbols), where the maths is the tool used to work through information sitting inside an unfamiliar setting.
That's genuinely the point of the section. It's testing whether a student can take numerical information wrapped in an unfamiliar context and reason through it properly, not whether they've memorised a specific topic from the regular maths syllabus.
This doesn't mean content knowledge is irrelevant. Recognising an exponent pattern, converting units, understanding rates, a student who's never seen those ideas is going to struggle regardless of how carefully they read. But once that foundation is in place, the thing that actually separates a correct answer from an incorrect one is almost always a reading issue, not a maths one.
How it scales by year level
Like the rest of the HAST, Mathematical Reasoning difficulty and content scale with the year level a student is applying to enter.
Junior Secondary (Year 8 entry, for students currently in Year 7): content draws mainly on number, measurement, space, time, logical relations and problem solving. Fewer questions combine maths with science content directly.
Middle and Senior Secondary (Year 9–12 entry): maths and science are combined more often. Questions are more likely to sit inside an invented scenario or draw on scientific context (astronomy, chemistry, biology, physics) as the setting for the reasoning being tested.
Practice materials should match the year level a student is actually applying for. A question built for Year 11 entry will assume more from a student than one built for Year 8 entry, even where the underlying skill being tested is the same.
Worked example
Question
Each of 4 coins has two sides. By flipping one or more coins, but without changing their positions, different patterns can be made. The pattern shown is head, tail, head, tail. Including the one shown, how many different patterns can be made?
Correct answer: D
Working through it. Strip away the coin story and the actual question is: how many different sequences can be made from four positions, where each position independently has two possible states. That's 2⁴, which is 16. The correct answer is D.
Why the other options exist
A (4) is what you get by misreading the question and answering with the number of coins rather than the number of patterns. Under time pressure, echoing back a number already sitting in the question stem happens more often than it should.
B (8) is a calculation mistake rather than a reading mistake. Thinking of it as "four coins, two sides each" and multiplying (4 × 2 = 8) treats the relationship as additive when it's exponential, each extra coin doubles the number of possible arrangements, it doesn't just add two more options.
C (12) doesn't map cleanly onto a specific mistake. Not every wrong option in this test represents a deliberate trap, some exist just to round out four choices, and trying to reverse-engineer a reason for every option wastes time in the actual exam.
The phrasing trap worth knowing about. The question says "by flipping one or more coins." Read quickly, that can sound like it excludes flipping zero coins, meaning the original head, tail, head, tail arrangement shouldn't count. Following that logic gives 15, which isn't even one of the four options, a useful signal to reread rather than lock in an answer. The very next sentence, "including the one shown," is the question explicitly confirming the starting pattern does count. That's a deliberate check on whether a student reads the whole question or stops halfway through.
Try it yourself
Attempt the two questions below before checking the explanations. Both are Bing's Academy practice questions modelled on real HAST style and difficulty, not actual past papers, one continues directly from the coin question above, the other introduces a new scenario.
This question is also a useful example of a wider HAST pattern: questions are often grouped in sets of two or three sharing the same stimulus paragraph. All the detail about packets failing and the rate halving isn't needed for either question above, it's there for follow-up questions built on the same scenario. A comprehension mistake made while reading the setup the first time doesn't go away when the question number changes, it can cost marks across the whole set. Reading a shared stimulus carefully the first time is worth the extra fifteen or twenty seconds.
Common traps
Patterns worth watching for across the section, not just in the examples above:
- Answering the wrong thing. A number from the question stem (like the number of coins) isn't automatically the answer to the question being asked.
- Multiplying where the relationship is exponential. Doubling-type relationships get multiplied incorrectly more often than they get correctly identified as powers.
- Small qualifying phrases changing the whole answer. Words like "including" or "at least" can flip what's actually being asked. Reading the full question before committing to an answer matters more in this section than most others.
- Treating a shared stimulus as fully re-readable each time. When multiple questions share one setup, understand it properly once rather than skimming it fresh (and incompletely) for each question in the set.
Getting ready for Mathematical Reasoning
Don't prepare for this section as if the challenge is the calculation. Treat it as a comprehension test that happens to use numbers, because that's closer to what it's actually designed to measure.
Read the whole question before committing to an answer. Small qualifying phrases carry real weight in this section.
When given a long stimulus, work out what the specific question needs before doing any working. Not all of the information provided is relevant to every question attached to it.
Build reading speed under real time constraints, not just untimed accuracy. With roughly a minute to a minute and a half per question, the skill being tested as much as the maths itself is extracting the right information quickly. Students who read a stimulus once, retain what matters, and only return to it if a later question needs something new, consistently perform better on timing than students who reread the full passage each time.
Match practice materials to the actual year level being applied for. A student applying for Year 8 entry doesn't need Year 11-level content combining maths and science, and vice versa.
Preparing with Bing's Academy
At Bing's Academy, we build HAST Mathematical Reasoning practice around the same principle this guide is built on: the maths is rarely the hard part. We work with students specifically on reading speed and comprehension under timed conditions, not just running through content drills, because that's where marks are actually being lost.
If you're considering HAST preparation for your child, get in touch and we'll talk through where they're currently at and what realistic preparation looks like.
For more on the HAST exam overall, including the application process and supporting documentation, see our HAST transfer guide, or for more practice with the other reasoning section, see our guide to abstract reasoning in the HAST exam.
John 'Bing' Huang
Founder, Bing's Academy