Queensland · Queensland Academies · Year 7 entry

Queensland Academies entrance test maths practice

The Queensland Academies are academically selective state schools, and entry to Year 7 involves an Entrance Test of about three hours run by Edutest. Two of its five parts use numbers: a 30-minute numerical reasoning test and a 30-minute mathematics test. This page describes both from the academies' own admissions pages, then practises the skill the numerical reasoning description ends on, deduction, through logic grid puzzles we wrote. You will find nothing here about applications, shortlisting or offers, and no promise of any result.

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Format from qa.eq.edu.au · Puzzles written by us · No admissions advice

In short

Year 7 entry to a Queensland Academy includes an Entrance Test of about three hours, facilitated by Edutest. It mixes ability tests (verbal reasoning, numerical reasoning) and achievement tests (reading comprehension, mathematics, written expression). Numerical reasoning and mathematics each run 30 minutes. The academies say individual test results and parent reports are not distributed.

Strong foundations

Three courses for able upper-primary students

Maths and reasoning that serve any Year 7, wherever it is.

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Problem solving and logic

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Upper-primary maths

Number, measurement, algebra, space and data from the curriculum.

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Maths Olympiad & Competition Course course thumbnail

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Competition maths

For children who enjoy harder, unfamiliar problems.

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The Entrance Test

Five tests, about three hours, ability and achievement

From the Queensland Academies admissions site, read on 7 October 2026.

Year 7 Entrance Test components (qa.eq.edu.au)
AspectTest areaDuration
AbilityVerbal reasoning30 minutes
AbilityNumerical reasoning30 minutes
AchievementReading comprehension30 minutes
AchievementMathematics30 minutes
AchievementWritten expression15 minutes

The academies explain the difference between the two kinds of test. Ability tests "are designed to measure a child's ability to think, reason and solve problems, without necessarily relying on prior knowledge." Achievement tests "are designed to measure actual achievement or performance in some key academic areas."

Edutest marks the tests and analyses results on behalf of the Queensland Academies. The academies state that they do not distribute individual test results or parent reports.

For Year 7 entry in 2028, the academies listed applications due by 4pm, Friday 21 August 2026, and the Entrance Test on either Saturday 5 or Sunday 6 September 2026, allocated automatically. Testing takes place at the academy campuses at Toowong, Kelvin Grove and the Gold Coast, with remote testing possible in limited circumstances.

The policy's list of what to bring is short: two black or blue pens, two pencils, an eraser, a sharpener and identification.

Sources: Queensland Academies, Year 7 enrolments; Entrance Test Policy; Queensland Academies admissions. Checked on 7 October 2026. Modern Age Coders is not connected with the academies or Edutest.

The two number tests

Numerical reasoning is not the same as mathematics

The academies describe each test in a sentence. Reading them side by side explains how to think about preparation.

Descriptions quoted from the Year 7 enrolments page
TestDescription (quoted)
Numerical reasoning (ability, 30 minutes)"Measures the ability to think and reason using numbers. This includes series, matrices, arithmetical reasoning and deduction."
Mathematics (achievement, 30 minutes)"Measures year-level appropriate mathematical knowledge, including items tapping numbers, measurement, algebra, space and data."

The mathematics test checks what a child has learned at school, across the familiar strands. Good everyday teaching is the preparation for it.

Numerical reasoning is described as an ability test. Its four named ingredients, series, matrices, arithmetical reasoning and deduction, are about seeing structure in numbers rather than recalling methods.

Because ability tests aim to measure reasoning without relying on prior knowledge, we do not think drilling them is worthwhile, and the academies give no indication that families should.

What does help a young thinker is enjoying puzzles that need careful, step-by-step deduction. That is a lifelong skill, and the logic grids below are a good way to practise it.

Source: Queensland Academies, Year 7 enrolments: The Entrance Test. Checked on 7 October 2026.

Puzzles we wrote

Logic grids: deduction you can see

A logic grid lists people down one side and possibilities across the top. Each clue lets you cross out boxes. When only one box is left in a row, that answer is certain.

One fact per clue

Read each clue on its own and cross out only what it rules out. Resist guessing until the grid forces an answer.

Rows and columns both count

If a column has one box left, that value belongs to that person, even if their row still has options.

Loop back

After placing an answer, reread earlier clues. A clue that looked useless often becomes decisive later.

Original logic grid puzzles with full solutions
PuzzleCluesSolution
Ari, Bo and Cam each chose a different number: 4, 7 or 9.Ari's number is even. Bo's number is bigger than Cam's.Ari 4, Bo 9, Cam 7
Dee, Eli, Fin and Gus finished a race in places 1 to 4.Gus came second. Fin came last. Dee finished ahead of Eli.Dee 1st, Gus 2nd, Eli 3rd, Fin 4th
Three students scored 12, 15 and 18 on a quiz: Hana, Ivo and Jo.Ivo scored a multiple of 6. Jo scored 3 more than Hana. Hana did not score 15.Hana 12, Jo 15, Ivo 18
Kai, Lia and Max each own one pet: a cat, a dog or a fish. Their pets have 4, 4 and 0 legs.Kai's pet has no legs. Lia is allergic to cats.Kai fish, Lia dog, Max cat

The third puzzle carries a lesson about checking. With only its first two clues, it has two answers. "Ivo scored a multiple of 6" leaves Ivo with 12 or 18, and "Jo scored 3 more than Hana" fits both Hana 12 with Jo 15 and Hana 15 with Jo 18. So Ivo 18, Hana 12, Jo 15 works, and so does Ivo 12, Hana 15, Jo 18. The third clue, Hana did not score 15, removes the second answer and leaves exactly one.

A good puzzle needs exactly one solution, and looking for a second one is part of the work, not an extra. Students who learn to ask "could anything else also fit?" become much more careful readers of clues, in puzzles and in every subject where conclusions are drawn from evidence.

A grid, solved slowly

Walking through the race puzzle

Seeing every step once makes the method easy to repeat.

Draw a grid with Dee, Eli, Fin and Gus down the side and places 1, 2, 3 and 4 across the top. The first clue, Gus came second, fills one box outright: tick Gus under 2 and cross out every other box in Gus's row and in the place 2 column. The second clue, Fin came last, does the same for Fin and place 4.

Now only places 1 and 3 remain, and only Dee and Eli remain to fill them. The final clue, Dee finished ahead of Eli, decides it: ahead means a smaller place number, so Dee takes 1 and Eli takes 3. Every box in the grid is now either ticked or crossed, and each clue can be checked against the finished grid in a few seconds.

Notice that no step involved guessing. Each tick was forced by a clue or by the boxes already crossed out. That is what deduction means, and it is why logic grids are a calm, confidence-building way for young students to practise reasoning: when a child cannot place an answer, the grid shows exactly which clue to reread.

About the academies

What kind of schools these are

Facts only, from the academies' own pages; no advice about whether to apply.

The Queensland Academy for Science, Mathematics and Technology describes itself as an academically selective state school that offers the International Baccalaureate programmes exclusively, with the Middle Years Programme in Years 7 to 9 and the Diploma Programme in Years 10 to 12. The admissions site serves all three Queensland Academies, and the Entrance Test Policy names their campuses at Toowong, Kelvin Grove and the Gold Coast. Whether a selective school suits a particular child is a family decision, and one we deliberately leave to families and the schools.

Number series

Series and simple matrices we wrote

The academies name series and matrices as part of numerical reasoning. These original examples show the kinds of structure worth noticing.

Original number patterns with the rule explained
PatternNext termRule
3, 7, 15, 31, ...63Double and add 1
2, 5, 10, 17, 26, ...37Add 3, 5, 7, 9, then 11: the gaps are consecutive odd numbers
81, 27, 9, 3, ...1Divide by 3 each time
1, 1, 2, 3, 5, 8, ...13Add the two previous terms
A 3 by 3 grid with rows 2, 3, 6 / 4, 5, 20 / 7, 2, ?14In each row the third number is the first two multiplied

For every series, the habit is the same: write the gaps underneath, then the gaps between the gaps if needed. The second pattern hides its rule until the gaps are written out; the fourth needs a different idea altogether, looking back two terms. Trying more than one kind of rule, and checking it on every term rather than only the first two, is what turns pattern spotting into reasoning.

Deduction, step by step

Four stages for young reasoners

Children grow into careful deduction over years of puzzles and discussion.

From guessing to proving
StageThe child canSecure when
1. Single cluesUse one clue to rule something outCrosses out the right boxes for each clue
2. Combining cluesUse two clues togetherSolves the race puzzle without trial and error
3. Checking uniquenessLook for a second solutionSpots that the quiz puzzle first had two answers
4. ExplainingWrite why each answer is forcedExplains a solution in clear sentences

Balance and wellbeing

Ability tests aim to measure reasoning rather than practice, so heavy preparation has little point and adds pressure.

Puzzles enjoyed as a family build the same thinking without any stress.

Other states

The NSW Year 7 test is described on NSW selective test maths.

For NAPLAN in the primary years, see NAPLAN Year 5 numeracy.

Courses for Years 5 and 6

Maths and reasoning courses

Grouped by focus. Each card links to a full syllabus.

I

Reasoning

Deduction and patterns

QAE / R / 01

Problem solving and computational thinking

Logic and patterns, step by step.

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II

Curriculum maths

Number to data
III

Ahead

Secondary readiness

QAE / A / 03

IB mathematics

For much later, for families interested in IB.

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Questions about the Queensland Academies test

Queensland families ask

What is in the Queensland Academies Year 7 Entrance Test?

Five tests over about three hours: verbal reasoning, numerical reasoning, reading comprehension, mathematics and written expression, facilitated by Edutest.

How long are the maths parts?

Numerical reasoning and mathematics each take 30 minutes, according to the academies' Year 7 enrolments page.

What is numerical reasoning?

The academies describe it as measuring the ability to think and reason using numbers, including series, matrices, arithmetical reasoning and deduction.

How is it different from the mathematics test?

Mathematics is an achievement test of year-level knowledge across numbers, measurement, algebra, space and data. Numerical reasoning is an ability test of reasoning with numbers.

What is a logic grid?

A table listing people against possibilities, in which each clue lets you cross out boxes until only one answer remains for each person.

Do families receive test results?

The academies say they do not distribute individual test results or parent reports.

Where is the test held?

The policy names the QASMT campus at Toowong, QACI at Kelvin Grove and QAHS on the Gold Coast, with remote testing in limited circumstances.

Can you help with applications or shortlisting?

No. We give no admissions, application or school-choice advice.

Will lessons improve my child's result?

We promise no result. We teach maths and reasoning that are valuable on their own terms.

What time would lessons be in Brisbane?

We agree a weekly time after the free trial. Brisbane is four and a half hours ahead of India time all year.

Related pages

More for Queensland families

Maths, NAPLAN and coding.

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NAPLAN Year 5 numeracy

Upper-primary numeracy.

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Maths challenges

Puzzles to try at home.

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