OFAI FACT preparation · Mathematical Reasoning
Free OFAI FACT Math Practice Test
Practise original mathematical-reasoning questions for the Ontario firefighter FACT. Work through percentages, ratios, rates, fractions and multi-step word problems, then review every answer with a clear explanation.
Independent preparation material. These are original FACT-style questions, not questions from the live exam. Firefighter Academy is not affiliated with OFAI or FPSI.
- 15 Mathematical Reasoning items
- One of the five FACT constructs
- Part of the 110-question FACT
- Aptitude plus personal characteristics
- Practical calculations and reasoning
- Applied arithmetic and word problems
- Original questions with explanations
- Free, no account required
OFAI publicly describes this section as practical mathematical reasoning for minimally qualified firefighter candidates. Exact live questions are not published.
Interactive practice
Try 6 Free FACT Math Practice Questions
Complete the questions one at a time. Choose an answer before revealing the explanation. Use paper arithmetic and focus on setting up each problem correctly before calculating.
Question 1 of 6
PercentagesAn apparatus water tank holds 2,400 litres when full. During an operation, 35% of the water is used. How many litres remain?
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Answer key
Review the questions and worked answers
Question 1 · PercentagesAn apparatus water tank holds 2,400 litres when full. During an operation, 35% of the water is used. How many litres remain?
- A. 840 litres
- B. 1,440 litres
- C. 1,560 litres
- D. 2,040 litres
Correct answer: 1,560 litres
If 35% was used, 65% remains. Convert 65% to 0.65 and multiply: 2,400 × 0.65 = 1,560 litres. Another method is to calculate the 840 litres used and subtract it from 2,400.
Question 2 · Ratios and proportionsA training mixture uses concentrate and water in a ratio of 1:24. If 625 litres of mixture are required, how many litres should be concentrate?
- A. 24 litres
- B. 25 litres
- C. 26 litres
- D. 48 litres
Correct answer: 25 litres
The ratio contains 25 total parts: 1 part concentrate plus 24 parts water. Divide 625 by 25 to find the value of one part: 625 ÷ 25 = 25. The concentrate is one part, so 25 litres are required.
Question 3 · Rates and timeAn apparatus travels 18 kilometres in 24 minutes. What is its average speed in kilometres per hour?
- A. 36 km/h
- B. 40 km/h
- C. 45 km/h
- D. 48 km/h
Correct answer: 45 km/h
Convert 24 minutes to hours: 24 ÷ 60 = 0.4 hours. Then use rate = distance ÷ time: 18 ÷ 0.4 = 45 km/h.
Question 4 · FractionsA crew completes 3/8 of an inspection list in the morning and 1/4 in the afternoon. What fraction of the list remains?
- A. 1/8
- B. 3/8
- C. 5/8
- D. 7/8
Correct answer: 3/8
Convert 1/4 to eighths: 1/4 = 2/8. The crew completed 3/8 + 2/8 = 5/8. Subtract from the whole: 8/8 − 5/8 = 3/8 remaining.
Question 5 · AveragesFive recorded response times are 6, 8, 7, 9 and 5 minutes. What is the average response time?
- A. 6 minutes
- B. 7 minutes
- C. 7.5 minutes
- D. 8 minutes
Correct answer: 7 minutes
Add the five values: 6 + 8 + 7 + 9 + 5 = 35. Divide by the number of values: 35 ÷ 5 = 7 minutes.
Question 6 · Multi-step word problemsA supply order contains four identical boxes and 12 loose items. There are 84 items in total. How many items are in each box?
- A. 16
- B. 18
- C. 21
- D. 24
Correct answer: 18
First remove the 12 loose items: 84 − 12 = 72. The remaining 72 items are divided equally among four boxes: 72 ÷ 4 = 18 items per box.
Exam context
What Math Is on the OFAI FACT?
OFAI identifies Mathematical Reasoning as one of the five FACT constructs. It contains 15 of the assessment's 110 multiple-choice items and measures practical reasoning and calculation skills expected of a minimally qualified firefighter candidate.
OFAI does not publicly release the live question bank or a detailed list of every calculation type. Effective preparation should therefore build broad fluency with applied arithmetic and word problems rather than depend on memorizing supposed exam questions.
| Topic | What to practise |
|---|---|
| Arithmetic | Accurate addition, subtraction, multiplication and division |
| Fractions and decimals | Converting, comparing and calculating with common values |
| Percentages | Finding a percentage, percentage change and the remaining amount |
| Ratios and proportions | Scaling quantities and finding the value of one part |
| Rates | Distance, time, speed and other unit-based relationships |
| Averages | Adding a set of values and dividing by the number of values |
| Conversions | Moving carefully between compatible units |
| Multi-step word problems | Identifying relevant information and completing operations in the correct order |
These are preparation areas selected to build the practical mathematical reasoning described by OFAI. They should not be interpreted as an official or exhaustive breakdown of live FACT content.
Refresher
Quick FACT Math Formulas and Relationships
- Percentage = part ÷ whole × 100
- Percentage of a number = decimal form × whole
- Rate = distance ÷ time
- Distance = rate × time
- Average = sum of values ÷ number of values
- Ratio share = total quantity ÷ total number of parts
The most useful skill is not memorizing a large formula sheet. It is recognizing what the question gives you, what it asks for and which relationship connects the two.
Method
How to Solve Firefighter Math Questions More Reliably
- 1
Read the final sentence first.
Identify exactly what unit and value the question wants.
- 2
Separate useful numbers from background details.
Not every number in a word problem necessarily belongs in the calculation.
- 3
Write the relationship before calculating.
For example: rate = distance ÷ time.
- 4
Estimate the approximate answer.
An estimate helps eliminate impossible answer choices and catches misplaced decimals.
- 5
Check the unit and reasonableness.
A mathematically correct calculation can still answer the wrong question or use the wrong unit.
Prepare for the conditions, not just the content
Practise clean paper arithmetic and confirm the current test-day rules directly with OFAI before your appointment. Policies and administration details can change.
Whole exam
Math Is One Part of the Complete FACT
Mathematical Reasoning accounts for 15 questions, but the FACT also assesses Reading Ability, Map Reading, Writing Ability and Personal Characteristics. Improving math is useful, but complete preparation should cover the entire assessment rather than one comfortable or difficult section.
Reading Ability
15
Mathematical Reasoning
15
Map Reading
10
Writing Ability
10
Personal Characteristics
60
Total
110
multiple-choice items
Writing a CPS-style test instead? Practise CPS mechanical aptitude questions. Mechanical aptitude is a CPS-style topic — it is not a FACT section.
Full preparation
Turn One Math Drill Into Complete FACT Preparation
Full access adds timed FACT simulations, section-level performance tracking, complete practice banks and detailed explanations so you can identify weaknesses before test day — including 165+ math and calculation questions.
- Complete FACT-style question bank (470+)
- Timed simulations
- Detailed explanations
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- Unlimited practice for 12 months
Questions
OFAI FACT Math Questions: Frequently Asked Questions
Does the OFAI FACT include math?
Yes. OFAI identifies Mathematical Reasoning as one of the five FACT constructs. The section contains 15 items focused on practical reasoning and calculation skills.
How many math questions are on the FACT?
OFAI currently lists 15 Mathematical Reasoning items. The complete FACT contains 110 multiple-choice items across aptitude and personal-characteristics measures.
What math should I practise for the FACT?
Build fluency with applied arithmetic, fractions, decimals, percentages, ratios, rates, averages, conversions and multi-step word problems. OFAI describes the construct broadly and does not publish the live question bank, so preparation should develop transferable mathematical reasoning.
Can I use a calculator on the OFAI FACT?
Prepare to complete the calculations accurately by hand and confirm the current test-day rules directly with OFAI before your appointment. Administrative policies can change.
Are these real OFAI FACT questions?
No. Every question on this page is original preparation material. The questions are designed to practise relevant mathematical-reasoning skills and are not copied or recalled from a live examination.
What score do I need on the math section?
OFAI reports the complete FACT result as pass or fail and does not publish a separate public math cut-off. Aim for consistent accuracy across every FACT section rather than targeting an unofficial minimum.
Is the free practice timed?
The six questions on this page are designed as a focused skill check. Firefighter Academy's complete practice experience includes timed simulations for candidates who want to practise pacing as well as accuracy.
How is FACT math different from CPS mechanical aptitude?
FACT Mathematical Reasoning tests practical calculation and problem-solving. Mechanical aptitude can appear in CPS-style formats and focuses on concepts such as gears, pulleys, levers and force. Confirm which test your target department requires before preparing.
Opportunities
Current Ontario firefighter recruitments
Testing requirements vary by department and recruitment cycle. Confirm which aptitude test a posting requires before you prepare or book.
Transparency
Sources and Methodology
The FACT structure and official item counts on this page are based on current information published by the Ontario Fire Administration Inc. Practice topics, strategies and questions were independently developed by Firefighter Academy to build practical mathematical-reasoning skills. No live examination questions are reproduced.
OFAI — Firefighter Aptitude and Character Test
Last substantively reviewed: August 2026
Firefighter Academy is an independent preparation platform and is not affiliated with, endorsed by, or connected to OFAI, FPSI or any fire department. Verify all testing requirements with the administering body and the department you are applying to before booking.