OC & Selective Maths: preparing for Mathematical Reasoning
Mathematical Reasoning is a third of the OC test and a quarter of the Selective test: 35 questions in 40 minutes, no calculator. It tests whether your child can use the maths they know on problems they have not seen before. Here are the topics, the methods that save time, and practice questions with answers.
What Mathematical Reasoning tests
The Department describes it as applying mathematical knowledge to new problems. The questions stay close to the primary curriculum but combine ideas and hide the method. These topics come up again and again:
Number and place value
Order of operations, factors and multiples, mental strategies, estimation.
Fractions, decimals, percentages
Fractions of amounts, equivalents, discounts, “what fraction is shaded”.
Ratio and rates
Sharing in a ratio, unit rates, speed–distance–time (Selective especially).
Measurement and time
Perimeter and area of composite shapes, volume, units, elapsed time, timetables.
Patterns and algebra
Number and shape patterns, “find the rule”, working backwards.
Data, chance and space
Graphs and tables, averages, simple probability, nets, symmetry, rotations.
OC or Selective? The OC test (Year 4) stays mostly within Year 3–4 maths, pushed hard. The Selective test (Year 6) adds more percentages, ratio, rates and multi-step problems.
Six worked examples
1. Fraction of an amount. ⅔ of a number is 24. What is ¾ of the number?
Go through one unit fraction: if ⅔ is 24, then ⅓ is 12, so the whole number is 36.
¾ of 36: a quarter is 9, so three quarters is 27.
Answer: 27
2. Working backwards. I think of a number, double it and subtract 7. The answer is 25. What was my number?
Undo each step in reverse order: 25 + 7 = 32, then 32 ÷ 2 = 16.
Answer: 16
3. Composite shapes. A 4 cm × 3 cm rectangle is cut from one corner of a 10 cm × 8 cm rectangle. Find the area and the perimeter of the L-shape that is left.
Area: 10 × 8 − 4 × 3 = 80 − 12 = 68 cm².
Perimeter: cutting a corner moves two edges inwards but does not change their total length, so it is still 2 × (10 + 8) = 36 cm.
Answer: 68 cm², 36 cm — a favourite trap, because the area changes and the perimeter does not.
4. Unit rate. 5 pens cost $3.50. How much do 8 pens cost?
One pen: $3.50 ÷ 5 = $0.70. Eight pens: 8 × $0.70 = $5.60.
Answer: $5.60
5. Speed and time. Sam walks at 4 km/h. How many minutes does it take him to walk 1.4 km?
4 km in 60 minutes means 1 km in 15 minutes. 1.4 km takes 1.4 × 15 = 21 minutes.
Answer: 21 minutes
6. Finding the rule. A row of squares is made from matchsticks: 1 square uses 4 matches, 2 squares use 7, 3 squares use 10. How many matches are needed for 20 squares?
Each new square adds 3 matches, and there is 1 extra at the start: matches = 3 × squares + 1.
3 × 20 + 1 = 61.
Answer: 61 matches
Mathematical Reasoning practice questions
Eight mixed questions. Try them without a calculator; start the timer for test pace (a little over a minute each).
Five mistakes that cost marks in Mathematical Reasoning
- Answering a different question. The question asks for Mia’s share, or “how many more”, and the child gives the other number. Underline what is asked.
- Units and time. 2 hours 15 minutes is 2¼ hours, not 2.15 hours.
- Percentages of percentages. Two discounts in a row do not simply add.
- Order of operations. Multiplication and division come before addition and subtraction.
- Not checking against the options. Multiple choice gives five answers; a quick estimate often rules out three.
A method is worth more than a trick. Our guide cancel before you multiply shows one that saves time on every fraction question.
How Mathkari teaches OC and Selective maths
Live, one-to-one, on a shared whiteboard: your child explains their method out loud, the teacher fixes the step that went wrong, and the next question tests the same idea in a new form. Timed sets come later, once the methods are secure. Maths is taught alongside Reading and Thinking Skills in our OC exam preparation and Selective exam preparation.
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Questions parents ask
Is Mathematical Reasoning the same as school maths?
It uses the maths taught at school, but the questions are less routine: several steps, hidden methods and unfamiliar wording. Knowing the content is necessary but not enough — children need practice applying it.
Can my child use a calculator in the OC or Selective test?
No. Calculators and rulers are not allowed, so mental strategies and quick written methods matter.
How much time is there per maths question?
Both the OC and Selective Mathematical Reasoning tests have 35 questions in 40 minutes — a little over a minute per question.
Do you teach maths only, or all the tests?
Both. Some families book maths only; most combine Mathematical Reasoning with Thinking Skills and Reading (and Writing for Selective).
What does “OCSC” mean?
Some families use “OCSC” as shorthand for the NSW OC (Opportunity Class) and Selective tests together. They are two separate tests run by the NSW Department of Education: the OC test in Year 4 for Year 5 entry, and the Selective High School test in Year 6 for Year 7 entry.
Is Mathkari affiliated with the NSW Department of Education?
No. Mathkari Concepts is an independent tutoring provider. Facts about the tests on this page come from the Department’s published information, and every practice question here is our own original material.
Sources
- Selective high schools and opportunity classes: placement test (NSW Department of Education)
- Get ready for the Opportunity Class Placement Test (NSW Department of Education)
- Get ready for the Selective High School Placement Test (NSW Department of Education)
- Opportunity class practice tests (NSW Department of Education)
- Selective high school practice tests (NSW Department of Education)
- Applications to open for 2027 selective school entry (NSW Government, ministerial release)
Mathkari Concepts is an independent tutoring provider and is not affiliated with or endorsed by the NSW Department of Education. All practice questions on this page are original Mathkari material.
Free Mathematical Reasoning practice papers
Every paper is attempted online and marked the moment you finish — nothing to download. The first three questions are open to everyone.
- OC Practice Mock 1 — Mathematical Reasoning (Year 3, early preparation)Year 3 · 35 questions · 40 min · free, marked instantly
- OC Practice Mock 1 — Reading (Year 3, early preparation)Year 3 · 23 questions · 40 min · free, marked instantly
- OC Practice Mock 1 — Thinking Skills (Year 3, early preparation)Year 3 · 30 questions · 30 min · free, marked instantly
- Selective Practice Mock 1 — Mathematical Reasoning (Year 5, early preparation)Year 5 · 35 questions · 40 min · free, marked instantly
- Selective Practice Mock 1 — Reading (Year 5, early preparation)Year 5 · 38 questions · 45 min · free, marked instantly
- Selective Practice Mock 1 — Thinking Skills (Year 5, early preparation)Year 5 · 40 questions · 40 min · free, marked instantly