Mathematical Reasoning in the NSW OC test

  • 35 questions
  • 40 minutes
  • About 70 sec per question
  • Multiple choice

What it tests

Applying the maths your child already learns at school to new problems. Word problems with five answer options. No calculator or ruler.

Question types you’ll practise

Multi-step problems

Several small calculations that build to the answer.

Measurement

Units, length, area and time.

Number

Place value, fractions and patterns.

Chance and data

Likelihood and reading information.

A sample question

Mathematical Reasoning · sampleFree mock, question 1

A canteen sells fruit cups for 25c, muffins for 35c, and juices for 45c.

Mia buys one item and pays with a $1 coin. She receives change made up of exactly three coins, and all three coins are different values.

Which item could Mia have bought?

  1. A fruit cup only
  2. B muffin only
  3. C juice only
  4. D fruit cup or muffin only
  5. E muffin or juice only

Worked solution

Answer: D. Australian coins are 5c, 10c, 20c and 50c. Mia pays $1 = 100c. If she buys a fruit cup for 25c, her change is 100c - 25c = 75c. 75c can be made with exactly three different coins: 50c + 20c + 5c = 75c. So a fruit cup is possible. If she buys a muffin for 35c, her change is 100c - 35c = 65c. 65c can be made with exactly three different coins: 50c + 10c + 5c = 65c. So a muffin is possible. If she buys a juice for 45c, her change is 100c - 45c = 55c. Check all possible sums of three different coins: 5c + 10c + 20c = 35c 5c + 10c + 50c = 65c 5c + 20c + 50c = 75c 10c + 20c + 50c = 80c None of these equals 55c, so a juice is not possible. Therefore, Mia could have bought the fruit cup or muffin only.

Pacing

There are 35 questions in 40 minutes, so a question that takes three minutes costs two others. A full timed mock shows where the time goes.

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