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  • 2027 test, 2028 entry

What is in the selective Mathematical Reasoning test?

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Mathematical Reasoning is one of the four sections of the selective test: 35 multiple-choice questions in 40 minutes, worth 25% of the result. It asks your child to use maths they already learn at school to solve problems they have not seen before, with no calculator.

Facts checked Last updated Sources

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How many questions are there, and how long does my child get?

Your child has a little over a minute for each question. Mathematical Reasoning has 35 multiple-choice questions in 40 minutes, and is worth 25% of the test. These are the Department's current figures. If it changes them for the 2027 test (Year 7 entry in 2028), we will update this page.

Mathematical Reasoning at a glance, from the Department's test pages
WhatSelective Mathematical Reasoning
Questions35 questions
Time40 minutes
Share of the test result25%
Answer options5 options per question
CalculatorNo calculators
Working outTwo A4 sheets of working paper
  • Every Mathematical Reasoning question is multiple choice with five possible answers. In any multiple-choice maths question, a wrong option can match the result of a common slip, so it can look convincing.
  • Calculators are not allowed in any part of the test. Every calculation is done in your child's head or on paper, so practise working by hand.
  • Each student is given two A4 sheets of paper for working out at the start of the test, and can ask for more. Use it for working out.

In plain terms, the time is tight but not a race. A child who gets stuck on one question for three or four minutes loses time that two or three other questions needed. Moving on and coming back later is a skill worth practising.

What maths does the section cover?

It covers the maths your child already learns in primary school, used in new ways. Mathematical Reasoning is based on maths concepts your child already learns at school. No extra maths study is needed. The questions draw on concepts from the NSW curriculum up to Year 6, and the Department says students do not need extra knowledge.

The name matters: this is a reasoning test, not a test of how many facts your child has memorised. A question might use ideas a Year 5 or Year 6 child knows well, such as fractions, area or reading a graph, but put them in a situation your child has not seen before. The hard part is usually working out what to do, not doing the sum.

The Department's practice page does not give a topic-by-topic list for this section. Its practice tests and sample questions are the clearest guide to what the questions look like.

What kinds of problem should my child expect?

Reasoning problems usually need more than one step, and many are built around a diagram, a table or a pattern. The table below is our own description of the shapes these problems tend to take, with a way to approach each. It is not a Department list and it does not copy any test questions.

Kinds of reasoning problem and how to approach them (our own summary)
Kind of problemWhat it asks your child to doA way to approach it
Multi-step word problemsRead a short situation, decide which steps to take and in what order, then combine the results.Write down what is known and what is asked before working anything out.
Diagrams and shapesUse a drawing (a plan, a shape or a grid) to work out a length, an area or a position.Copy the diagram onto working paper and mark every measurement on it.
Tables and graphsPull the right numbers out of a table or graph, then compare or combine them.Check the labels and units first; many slips come from reading the wrong row.
Patterns and rulesFind the rule behind a sequence or arrangement and use it to predict a later step.Test the rule on two or three steps you can see before trusting it.
Working backwards and checking optionsStart from a result and find what must have come before, or test the answer options.Estimate first to rule out options that are far too big or too small.

Across all of them, the same habits help: read the whole question, note the units, do the working on paper, and check the answer against the question before choosing an option.

What does reasoning through a multi-step problem look like?

It looks like breaking one question into small steps you can check. Here is a question we made up ourselves to show the thinking. It is not from the Department or from any real test.

Worked example

Our example: the path around a garden bed

A rectangular garden bed is 6 m long and 4 m wide. A path 1 m wide runs all the way around it. What is the area of the path? Options: (A) 11 square metres, (B) 20 square metres, (C) 24 square metres, (D) 35 square metres, (E) 48 square metres.

A garden bed with a path around itA rectangle 6 metres by 4 metres for the bed, inside a larger rectangle 8 metres by 6 metres. The 1 metre path fills the gap between them.8 m (whole, with path)6 mBed: 6 m by 4 m(24 square metres)Path, 1 m wideWhole area: 8 × 6 = 48 square metres
  1. Draw it. The path adds 1 m on both ends of the length and on both sides of the width.
  2. Find the size of the whole shape, bed and path together: 6 + 1 + 1 = 8 m long and 4 + 1 + 1 = 6 m wide.
  3. Whole area: 8 × 6 = 48 square metres. Bed area: 6 × 4 = 24 square metres.
  4. The path is what is left: 48 − 24 = 24 square metres. The answer is C.
  5. Check another way: two long strips of 8 × 1 = 8 each, plus two short strips of 4 × 1 = 4 each, make 8 + 8 + 4 + 4 = 24. The answers agree.
  6. Look at the wrong options. 48 is the whole area, and 35 and 11 come from adding the path to only one side. Each matches a slip, which is why checking matters.

The maths here is simple multiplication and subtraction. What the question tests is whether your child pictures the shape correctly and plans the steps. That is the skill to practise, and talking through a problem aloud like this is a good way to build it.

Where can my child practise Mathematical Reasoning?

The Department publishes its own practice tests, and they are the place to start. The Department offers 2 types of practice test: online computer-based tests and PDF tests.

  • The online practice tests simulate the real test, so your child can get used to the test software and its tools.
  • In the online practice tests each response is worth 1 mark; questions that ask for several responses are worth more.
  • The Department publishes 3 PDF sample tests, each with Reading, Mathematical Reasoning, Thinking Skills and a Writing sample question.
  • The PDF practice tests come from older paper-based versions of the test, so they do not reflect the current format.
  • For students with disability, practice materials are available in large print, black-and-white or braille.

Use the online tests to get used to the screen and the timing, and the PDF questions for extra problems to talk through on paper. Find them on the Department's selective practice test page.

On preparation, the Department's position is plain: The Department says coaching or tutoring for the placement test is not necessary, and that extra paid coaching will not give a child an advantage.

How does it fit with the other sections and the OC test?

The Selective High School Placement Test is a computer-based test with 4 sections: Reading, Mathematical Reasoning, Thinking Skills and Writing. Alongside Mathematical Reasoning, the other three are Reading, Thinking Skills and Writing. Thinking Skills also involves problem solving; its page explains how it differs. How the whole test day runs is on how the selective test works, and the timing of the 2027 test is on selective test dates.

The opportunity class test has its own Mathematical Reasoning section, for younger children. It is explained on the OC Mathematical Reasoning page, and the two tests are compared side by side on OC vs selective. For everything else about the selective test, start at the selective high schools guide.

Sources

Each fact on this page, the page we checked it against and the source's own words. An “Expected” date is our estimate from past years, not the Department's.

  1. Selective high school practice tests

    NSW Department of Education · page last updated 20 March 2026

    • Mathematical Reasoning: 35 questions, 40 minutes, 25%PublishedChecked
      The source's words
      “Mathematical Reasoning Test | 35 | 40 | Multiple-choice | 25%”
    • Mathematical Reasoning: five optionsPublishedChecked
      The source's words
      “For the Mathematical Reasoning Test you will have 40 minutes to answer 35 questions. The questions are all multiple choice with five possible answers.”
    • No calculatorsPublishedChecked
      The source's words
      “Students cannot use a calculator during this, or any other, test.”
    • Mathematical Reasoning: school maths applied to problemsPublishedChecked
      The source's words
      “Remember that these concepts are based on what your child already learns at school. They do not have to study any extra maths concepts to prepare.”
    • Concepts up to Year 6PublishedChecked
      The source's words
      “The questions draw upon concepts from the NSW curriculum up to Year 6 that your child learns at school. We review all questions to make sure students do not need any extra knowledge.”
    • Four sections, all on computerPublishedChecked
      The source's words
      “The Selective High School Placement Test is a computer-based test that has 4 sections. All questions (multiple-choice and the writing question) are answered using the computer.”
    • Official practice: online and PDFPublishedChecked
      The source's words
      “There are 2 types of practice test: - online computer-based practice tests - PDF practice tests.”
    • Online practice simulates the real testPublishedChecked
      The source's words
      “The online computer-based practice tests will simulate the actual placement tests. This helps your child get familiar with the test software and its tools.”
    • Practice marking: 1 mark per responsePublishedChecked
      The source's words
      “Each individual response is worth 1 mark. Some questions ask for multiple responses and so are worth more than 1 mark.”
    • Three PDF sample testsPublishedChecked
      The source's words
      “Sample practice test 3 | Section | Links to practice tests |”
    • PDF tests are from the old paper testPublishedChecked
      The source's words
      “The PDF practice tests below are from older paper-based versions of the test. So they do not reflect the current test format.”
    • Accessible practice materialsPublishedChecked
      The source's words
      “For students with disability, practice materials are available in different formats. For example, we can provide test material in: - large print - black-and-white - braille.”
    • The Department says coaching is not necessaryPublishedChecked
      The source's words
      “It is important to know that coaching or tutoring for the placement test is not necessary.”
  2. Placement test

    NSW Department of Education · page last updated 18 August 2026

    • Two A4 sheets of working paperPublishedChecked
      The source's words
      “each student will be given two A4 pieces of paper for working out at the start of the test. They may ask for more paper if needed.”
  3. Selective high schools and opportunity classes placement procedures (PD-2002-0006-06)

    NSW Department of Education · page last updated 5 November 2025

    • Practice scores are not consideredPublishedChecked
      The source's words
      “Results of practice and sample tests do not show how a student will perform in the test and selection committees do not consider performance on sample or practice tests.”

Quotes from NSW Department of Education pages are © State of New South Wales (Department of Education), used under CC BY 4.0.

Not affiliated with the NSW Department of Education. SelectiveReady (ABN 53 930 169 401) is an independent practice product. Every fact here is checked against the Department's own pages, and changes are logged.

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