OC Maths Reasoning: Practice Questions with Worked Solutions
The Mathematical Reasoning section of the NSW OC (Opportunity Class) test rewards clear, multi-step thinking — not memorised facts. Below are six exam-style questions with full worked solutions.
What this section is like
- 5 options (A–E) per question — not four.
- About 35 questions in 40 minutes — roughly a minute each.
- Heavily visual — grids, charts, shapes and 3D solids.
- Tests reasoning, not curriculum recall.
Try each question first, then open the solution.
6 practice questions
Look at the pattern: 2, 6, 12, 20, 30, … What is the next number?
- A.40
- B.44
- C.42
- D.36
- E.38
Answer & worked solution
Answer: C) 42
The gaps grow by 2 each time (4, 6, 8, 10), so the next gap is 12: 30 + 12 = 42.
What fraction of the grid is shaded? Give your answer in its simplest form.
- A.1/2
- B.1/4
- C.1/3
- D.2/5
- E.3/10
Answer & worked solution
Answer: D) 2/5
8 of the 20 squares are shaded. 8/20, dividing top and bottom by 4, gives 2/5.
The bar chart shows how many books each class read. How many more books did 3B read than 3C?
- A.6
- B.3
- C.27
- D.12
- E.9
Answer & worked solution
Answer: E) 9
3B read 18 and 3C read 9, so 18 − 9 = 9.
A printer prints 24 pages every 3 minutes. How long will it take to print 96 pages?
- A.9 minutes
- B.8 minutes
- C.12 minutes
- D.4 minutes
- E.16 minutes
Answer & worked solution
Answer: C) 12 minutes
24 ÷ 3 = 8 pages per minute, so 96 ÷ 8 = 12 minutes.
I think of a number, multiply it by 4, then subtract 7. The result is 25. What was my number?
- A.8
- B.7
- C.4
- D.11
- E.6
Answer & worked solution
Answer: A) 8
Work backwards: 25 + 7 = 32, then 32 ÷ 4 = 8.
How many lines of symmetry does this regular pentagon have?
- A.1
- B.2
- C.5
- D.10
- E.0
Answer & worked solution
Answer: C) 5
A regular polygon has as many lines of symmetry as it has sides. A pentagon has 5 sides, so 5 lines.
Quick exam tips
- Read the question twice — solve for what it actually asks.
- Eliminate clearly-wrong options first to save time.
- Re-check units and your answer before moving on.
Want hundreds more like these, each explained step by step? Try PrepPath OC Maths practice — with an AI Tutor for the tricky ones.
PrepPath is an independent educational platform and is not affiliated with ACARA or the NSW Department of Education. This guide is general information only — always check the official ACARA (nap.edu.au) or NSW Department of Education websites for current dates and rules.