NSW Selective Mathematical Reasoning: What's Tested, With Free Example Questions

Of the four sections in the selective test, Mathematical Reasoning is the one parents feel most able to help with. It's also the one where good students most often come home saying "I knew how to do all of it, I just ran out of time." Both things are true, and the gap between them is what this section is really testing.

The format

The Mathematical Reasoning test is 35 multiple-choice questions in 40 minutes. That is the figure on the Department's practice-tests page and on its test-day timetable. No calculator. Like each of the other three sections, it counts for 25% of the overall score.

Forty minutes for 35 questions is a little under 70 seconds each. Some questions take fifteen seconds. The ones at the end can take three or four minutes if a child insists on finishing them. That arithmetic is the first thing worth understanding: the test is designed so that most children will not comfortably finish, and knowing when to move on is part of the skill.

What "reasoning" means here

The Department is deliberate about the name. This isn't a test of whether your child has covered the Year 6 syllabus. The content sits mostly inside what a strong Year 5 or Year 6 student has met at school. What's different is how it's asked.

A school worksheet says "find the perimeter of a rectangle 8 cm by 5 cm". The selective test gives you a rectangle made of three identical squares, tells you the perimeter of the whole shape, and asks for the area of one square. Same knowledge, but the child has to work out which tool to reach for, and usually has to take two or three steps to get there. Most questions are word problems. Many have a small diagram or table. Almost none can be done by pattern-matching to a method they've been drilled on.

This is why children who are "good at maths" at school sometimes do worse than expected. School maths rewards knowing the procedure. This test rewards recognising which procedure applies when nobody has told you.

The topics that come up most

The Department doesn't publish a topic breakdown. We tallied the questions across the official practice papers to see where the marks actually fall. It's an estimate from a handful of papers, not a syllabus, but the shape is clear.

• Measurement is the big one. Length, perimeter, area, volume and capacity together make up roughly a quarter of the questions. Perimeter problems are the single most common type we saw, often with a shape built from other shapes.
• Number sense: place value, the four operations, factors and multiples, and number patterns. These are the "what comes next" and "which number satisfies all of these conditions" questions.
• Time, data and chance: reading timetables and clocks, interpreting graphs and tables, and basic probability. Timetable questions are a reliable place to lose marks by misreading a column.
• Geometry: angles, properties of 2D shapes, and 3D shapes including nets and views.
• Fractions, ratio, algebra and money each get a few questions. Fractions are usually inside a word problem rather than asked directly.

Nothing on that list is beyond primary school. The difficulty is in the combination.

Five questions to try

These are from PrepKit's free selective maths set, chosen to show the range rather than the hardest end. Have your child do them before reading on. Each one shows the working after you answer.

Watch how your child approaches the fraction questions in particular. A child who tries to do "a quarter plus a third" in their head, gets stuck, and moves on has the maths but not the method. A child who writes the two fractions with the same denominator has the method. That second habit, writing the one line that makes the problem easy, is most of what practice for this section is teaching.

How to practise

Work from the official papers first. The Department publishes three practice tests with answers on its practice tests page. Do the first one with no clock, and go through every wrong answer together. Not "the answer was C", but what the question was actually asking and where the working went off.

Teach the two-pass habit. First pass: answer everything that's quick, and put a mark next to anything that isn't. Second pass: go back to the marked ones with whatever time is left. Children who do the questions strictly in order routinely leave four or five easy questions at the end unanswered because question 19 ate six minutes.

Always answer something. There's no penalty for a wrong answer. A guess on a four-option question is worth a quarter of a mark on average. A blank is worth nothing.

Estimate before calculating. Half the wrong answers on multiple-choice maths are arithmetic slips that an estimate would have caught. "The answer should be a bit less than 30" rules out two of the four options before any working starts.

Short and often. Ten or fifteen questions a day with a proper look at the mistakes builds more than a Saturday marathon. Mistakes are the useful part; the correct answers just confirm what was already known.

Cover the topics, don't just do the favourites. Children gravitate to the maths they like. If every practice session is number patterns, the perimeter questions will still be there on test day, and there will be more of them.

A note on pace

If your child is finishing the practice papers with time to spare and getting most of them right, they are in good shape and more drilling has diminishing returns. If they're getting most of them right but only reaching question 25, the problem is pace, not maths, and the fix is timed practice with the two-pass habit. If they're reaching the end but getting a lot wrong, slow down, go back to untimed work, and find out which topics are actually shaky. Those are three different problems and they need three different kinds of practice.

For the rest of the test, see our guide to the selective test format, what Thinking Skills tests, and how the Reading section works. For more practice, the free selective sample quiz covers Maths, Reading and Thinking Skills in about five minutes.