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ASP11 · 10% of the exam

Mathematical Calculations practice questions

10 free Mathematical Calculations questions for the Associate Safety Professional (ASP) (ASP11) exam, each with the correct answer and an explanation for every option.

Start the questionsFree 10-question ASP11 quiz

What this domain covers

The calculations a safety professional uses day to day: incident rates, unit conversions, basic statistics and probability, and applied physics and engineering formulas.

Exam weight
10%
On a real exam
≈ 20 questions
In our bank
60 questions

Topics that come up most

  • Incident and severity rates on a 200,000-hour basis
  • Unit conversions and concentration (ppm and mg/m³)
  • Descriptive statistics and probability
  • Forces, mechanics and Ohm's law
  • Engineering economics and cost-benefit analysis

How to study it

Do practice problems with the BCSP reference sheet open so you know where each formula is and which units it expects; most mistakes come from units, not algebra.

Sample Mathematical Calculations questions

Try each one before opening the answer. Original questions written to the official exam objectives.

  1. Question 1

    A room measures 20 ft × 30 ft × 10 ft. A ventilation system supplies 1,200 cfm of air. The air changes per hour is about:

    • A120
    • B0.2, dividing cfm by room volume
    • C2
    • D12
    Show answer and explanation

    Answer: D) 12

    • AIncorrect. That's off by a factor of 10.
    • BIncorrect. The flow must be converted to per hour.
    • CIncorrect. That isn't the calculation.
    • DCorrect. (1,200 × 60) ÷ 6,000 ft³.

  2. Question 2

    During one year, a site recorded 10 OSHA-recordable cases. Four of them were days-away, restricted, or transferred (DART) cases. Employees worked a total of 160,000 hours. What is the site's DART rate?

    • A5.0
    • B12.5
    • C7.5
    • D2.5
    Show answer and explanation

    Answer: A) 5.0

    The DART rate equals (DART cases x 200,000) / total hours worked. Here that is 4 x 200,000 / 160,000 = 5.0.

    • ACorrect. DART rate = (DART cases x 200,000) / hours worked = (4 x 200,000) / 160,000 = 5.0 per 100 full-time workers.
    • BIncorrect. This uses all 10 recordable cases, which gives the total recordable case (TRC) rate, not the DART rate.
    • CIncorrect. This uses the 6 recordables that were not DART cases. The DART rate counts only the 4 DART cases.
    • DIncorrect. This uses 100,000 hours as the base. OSHA's base is 200,000 hours, which equals 100 full-time employees working 40 hours a week for 50 weeks.

  3. Question 3

    Using the 4-to-1 rule, a ladder reaching a support point 16 ft high should have its base about how far from the wall?

    • A1 ft
    • B16 ft, the same as the height
    • C4 ft
    • D8 ft
    Show answer and explanation

    Answer: C) 4 ft

    • AIncorrect. That's too steep.
    • BIncorrect. That's far too shallow an angle.
    • CCorrect. One foot out for every four feet up.
    • DIncorrect. That's too shallow.

  4. Question 4

    A mechanic pushes with 40 lb of force at a right angle to a wrench handle, 18 in. from the center of the bolt. What torque is applied to the bolt?

    • A60 ft-lb
    • B720 ft-lb
    • C27 ft-lb
    • D58 ft-lb
    Show answer and explanation

    Answer: A) 60 ft-lb

    Torque equals force times the perpendicular distance from the pivot. Convert 18 in. to 1.5 ft, then 40 lb × 1.5 ft = 60 ft-lb.

    • ACorrect. Torque = force × perpendicular lever arm. 18 in. = 1.5 ft, so 40 lb × 1.5 ft = 60 ft-lb.
    • BIncorrect. 40 × 18 = 720 is in in-lb, not ft-lb. Converted to feet it is 720 ÷ 12 = 60 ft-lb.
    • CIncorrect. This divides the force by the lever arm (40 ÷ 1.5 ≈ 27). Torque is the product of force and distance, not the quotient.
    • DIncorrect. This adds the force and the distance (40 + 18). Adding quantities with different units gives a meaningless result. Torque multiplies them.

  5. Question 5

    A 2,000-lb load is lifted with a two-leg sling. Each leg makes a 30° angle with the horizontal. The tension in each leg is about:

    • A4,000 lb
    • B1,000 lb, half the load per leg
    • C1,155 lb, the tension at 60°
    • D2,000 lb
    Show answer and explanation

    Answer: D) 2,000 lb

    • AIncorrect. That doubles it again.
    • BIncorrect. Low angles increase leg tension.
    • CIncorrect. That's for a 60° angle.
    • DCorrect. Load ÷ (2 × sin 30°).

  6. Question 6

    A worker uses a 6-ft shock-absorbing lanyard tied to an anchor at the height of the harness's dorsal D-ring. The deceleration distance is 3.5 ft, D-ring shift and harness stretch are taken as 1 ft, the D-ring sits 5 ft above the worker's feet, and a 2-ft safety factor is used. What is the minimum clearance required below the anchor?

    • A9.5 ft
    • B15.5 ft
    • C18.5 ft
    • D17.5 ft
    Show answer and explanation

    Answer: D) 17.5 ft

    Required fall clearance is the sum of free fall, deceleration distance, D-ring shift/harness stretch, D-ring height above the feet, and a safety factor: 6 + 3.5 + 1 + 5 + 2 = 17.5 ft.

    • AIncorrect. This adds only the lanyard length and the deceleration distance (6 + 3.5). It leaves out D-ring shift, D-ring height, and the safety factor.
    • BIncorrect. This adds the lanyard, deceleration, D-ring shift, and D-ring height (6 + 3.5 + 1 + 5) but leaves out the 2-ft safety factor.
    • CIncorrect. This uses a full 6-ft body height instead of the 5-ft D-ring-to-feet distance. Only the distance from the D-ring down to the feet counts.
    • DCorrect. Free fall 6 + deceleration 3.5 + D-ring shift 1 + D-ring height 5 + safety factor 2 = 17.5 ft.

  7. Question 7

    Two independent safeguards each have a 0.01 chance of failing on demand. The chance both fail is:

    • A0.02
    • B0.0001
    • C0.01
    • D0.5
    Show answer and explanation

    Answer: B) 0.0001

    • AIncorrect. That adds the probabilities.
    • BCorrect. 0.01 × 0.01.
    • CIncorrect. Both must fail.
    • DIncorrect. Recheck the multiplication.

  8. Question 8

    The mean of the values 4, 6, 8, 10 and 12 is:

    • A10
    • B8
    • C6
    • D40
    Show answer and explanation

    Answer: B) 8

    • AIncorrect. Recheck the sum.
    • BCorrect. 40 ÷ 5 = 8.
    • CIncorrect. Recheck the sum.
    • DIncorrect. That's the sum.

  9. Question 9

    Type A soil's maximum allowable slope of ¾H:1V corresponds to an angle of about:

    • A45°
    • B53°
    • C34°
    • D90°
    Show answer and explanation

    Answer: B) 53°

    • AIncorrect. That's 1:1 for Type B.
    • BCorrect. Measured from horizontal.
    • CIncorrect. That's 1½:1 for Type C.
    • DIncorrect. That's a vertical wall.

  10. Question 10

    A worker's measured noise dose is 200% for an 8-hour shift. Under OSHA's 5-dB exchange rate, the 8-hour TWA is:

    • A100 dBA, adding 10 dB for the doubled dose
    • B180 dBA, doubling the 90 dBA criterion
    • C93 dBA, adding 3 dB for the doubled dose
    • D95 dBA
    Show answer and explanation

    Answer: D) 95 dBA

    • AIncorrect. That overstates it.
    • BIncorrect. Decibels don't double linearly.
    • CIncorrect. OSHA uses a 5-dB exchange rate.
    • DCorrect. Each doubling of dose adds 5 dB to 90 dBA.

Mathematical Calculations: FAQs

How much of the ASP11 exam is Mathematical Calculations?

Mathematical Calculations is 10% of the ASP11 exam by the official exam guide's weighting, which on a 200-question form works out to roughly 20 questions. The real exam's exact split varies by form.

What does the Mathematical Calculations domain cover?

The calculations a safety professional uses day to day: incident rates, unit conversions, basic statistics and probability, and applied physics and engineering formulas.

How should I study Mathematical Calculations for ASP11?

Do practice problems with the BCSP reference sheet open so you know where each formula is and which units it expects; most mistakes come from units, not algebra.

Where can I practise more Mathematical Calculations questions?

This page has 10 free Mathematical Calculations questions with answers. The ExamWize ASP11 question bank has 60 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Other ASP11 topics

Also: 15 free questions across all topics, the ASP11 cheat sheet and the study guide.

Get Mathematical Calculations exam-ready

The full ASP11 bank has 60 Mathematical Calculations questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full ASP11 practice examsTake the free diagnostic

Not affiliated with BCSP; questions are original, written from the official exam outline, and never copied from the real exam.