What Mathematical Reasoning tests
Mathematical Reasoning is multiple choice. Students have 40 minutes for 28 to 35 questions. The number of questions depends on the version of the test (ACER, 2026). That is roughly a minute to a minute and a half per question, if you leave no time to check answers.
Multiple choice, four options. The number of questions depends on the version of the test.
ACER says the section tests how well students understand, interpret and analyse mathematical information (ACER, 2026). At the junior level (Year 7 students), that covers number, measurement, space, time, logical relations and problem solving. At the middle and senior levels (Years 8 to 10), maths and science are combined. Questions also ask students to infer, predict and draw conclusions. The information comes as numbers, text, diagrams, graphs and tables.
Nowhere in that description does it say "advanced maths content." It says comprehend, interpret, infer. That's the whole section in one sentence.
Why reading matters more than maths
The maths in most of these questions is simple: multiplying, powers, dividing. What catches students out is the reading.
Mathematical Reasoning in the HAST is rarely like school maths. This is especially true at the middle and senior levels. Many questions are set in science (astronomy, geology, chemistry, physics, biology) or in a made-up situation (a computer network sending data packets, a lock made of symbols). The maths is a tool for working through information in an unfamiliar setting.
That is the point of the section. It tests whether a student can take numbers set in an unfamiliar situation and reason through them. It does not test whether they have memorised a topic from the school maths course.
This doesn't mean content knowledge is irrelevant. A student who has never met powers, unit conversions or rates will struggle however carefully they read. But once a student has those basics, a wrong answer is almost always a reading problem, not a maths one.
How it changes by 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 7 students, for Year 8 entry): mainly number, measurement, space, time, logical relations and problem solving.
Middle and Senior Secondary (Years 8 to 10, for Year 9, 10 or 11 entry): ACER's tests at these levels include mathematics and science, so more questions sit in a science setting or an invented scenario.
Practice materials should match the year level a student is applying for. A question written for Year 11 entry expects more of a student than one for Year 8 entry, even when it tests the same skill.
Worked example
Tap the picture to see it full size.
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?
Show the answer
Working through it. Without the coin story, the question is: how many different patterns can you make from four positions, when each position can be one of two things, whatever the others are? That's 2⁴, which is 16. The correct answer is D.
Why the other options exist
A (4) comes from misreading the question and answering with the number of coins, not the number of patterns. Under time pressure, students repeat a number from the question more often than they should.
B (8) is a maths mistake, not a reading one. "Four coins, two sides each" tempts you to work out 4 × 2. But each extra coin doubles the number of patterns, so the answer is 2 × 2 × 2 × 2, which is 2⁴.
C (12) doesn't map cleanly onto a specific mistake. Not every wrong option is a trap. Some are there to make up four choices. Working out a reason for each one wastes time in the test.
The phrasing trap worth knowing about. The question says "by flipping one or more coins." Read quickly, that can sound as if flipping no coins at all does not count. Then the starting pattern, head, tail, head, tail, would not count either. That logic gives 15, which is not one of the options. That is a signal to reread. The very next sentence begins "including the one shown." That tells you clearly that the starting pattern does count. It checks, on purpose, whether a student reads the whole question or stops halfway.
Try it yourself
Attempt the two questions below before checking the explanations. Both are practice questions in the HAST style. The first follows on from the coin question. The second is new.
Tap the picture to see it full size.
Each of the 5 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 and head.
Including the one shown, how many different patterns can be made?
Show the answer
The answer is C. Five positions, each with two possible states (head or tail), gives 2⁵ = 32. This is the same idea as the worked example, with one more coin. One extra coin doubles the total. It does not add a fixed amount. Also notice that “flipping one or more coins” can sound as if the unchanged pattern does not count. That would give 31, which is not one of the options, so it is a sign to reread. “Including the one shown” is what confirms the starting pattern counts.
Why not the others
- A (10) works out 5 × 2 = 10, as if each coin added two patterns. But each extra coin doubles the number of patterns, so the answer is 2 × 2 × 2 × 2 × 2, which is 2⁵.
- B (25) comes from squaring the number of coins, 5² = 25, instead of using 2 as the base. That shortcut happens to work for 4 coins, because 4² and 2⁴ both equal 16. It fails here: 5² is 25, but 2⁵ is 32. A wrong method that gives the right answer once will fail later.
- D (40) does not match a particular mistake. It is likely just a fourth believable number, not a deliberate trap.
Computer data is made up of bits. The bits can be sent over an internet network along copper wire. The data is sent in packets. One megabit is 1 million bits.
- Each packet is 1,500 bits in size.
- Packets are sent one at a time.
- When sent along copper wire, packets are sent at an initial rate of 15,000,000 bits per second.
- If a packet fails to send, it is sent again instantly at half the initial rate. If it fails again, the rate is halved again, and so on.
How long would it take to send a 30-megabit file at the initial rate?
Show the answer
The answer is A. 30 megabits is 30,000,000 bits. Divide by the initial rate of 15,000,000 bits per second and the answer is 2 seconds. The packet size in the setup is not needed here. That detail belongs to a different question that uses the same setup.
Why not the others
- B (20 seconds) starts correctly by working out how many packets the file needs (30,000,000 ÷ 1,500 = 20,000 packets). But it then divides by 1,000 packets per second instead of 10,000 (15,000,000 ÷ 1,500). The method is right, but the wrong number was carried across.
- C (45 seconds) comes from misreading the packet size, 1,500 bits, as 1.5, and multiplying the file size by it (30 × 1.5). That number isn’t relevant to this particular question at all.
- D (450 seconds) multiplies the two headline numbers straight from the setup, 30 and 15 (from 15,000,000), without working through what either one actually represents.
The second question shows a common HAST pattern. Two or three questions often share one stimulus. The detail about failed packets and the rate halving is not needed for this question. It is there for the next ones in the set. Misreading the setup can cost marks on every question in the set. So read a shared stimulus carefully the first time, even if it takes an extra fifteen or twenty seconds.
Common traps
Patterns worth watching for across the section, not just in the examples above:
- Answering the wrong thingA number from the question stem (like the number of coins) isn't automatically the answer to the question being asked.
- Multiplying when it should be a powerWhen each step doubles, the answer is a power of 2, not a times table.
- Small qualifying phrases changing the whole answerWords like "including" or "at least" can flip what's 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 timeWhen multiple questions share one setup, understand it properly once rather than skimming it fresh (and incompletely) for each question in the set.
How to prepare
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 designed to measure.
- Read the whole question before committing to an answerSmall qualifying phrases carry real weight in this section.
- When given a long stimulus, work out what the specific question needs before doing any workingNot all of the information provided is relevant to every question attached to it.
- Build reading speed under real time constraints, not just untimed accuracyWith roughly a minute to a minute and a half per question, finding the right information quickly is tested as much as the maths. In our experience, some students read a stimulus once, keep what matters, and go back only when a later question needs something new. They finish in time more often than students who reread it for every question.
- Match practice materials to the actual year level being applied forA student applying for Year 8 entry doesn't need Year 11-level content combining maths and science, and vice versa.