Mathematics — practice questions
8% of the exam ≈5 real questions 5 free questions here
Eight percent of the weighting: areas and volumes, the Pythagorean theorem, ratios such as compression ratio and gear speed, percentages and proportions, rearranging formulas, scientific notation, rounding, metric conversion and signed numbers.
Where people lose points
- Circle area uses the RADIUS: π × r². Plugging in the diameter gives an answer four times too big.
- Compression ratio is total volume at bottom center ÷ volume at top center.
- Gear speed is inversely proportional to tooth count: a bigger driven gear turns slower.
- 1 inch = 25.4 mm exactly; divide millimeters by 25.4 to get inches.
- Subtracting a negative is adding, which matters for negative arms in weight and balance.
Drill: Mathematics
5 free questions from this domain, each with an explanation and a cited source. Timed at real exam pace.
5 questions
Pass line: 70%, same as the real exam
See the answer and explanation right after each question.
Questions and answers, explained
All 5 questions above, with the correct answer and why it is correct. Everything here is on mathematics.
What is the area of the head of a piston that is 4 inches in diameter?
Why: Area of a circle = π × r². The radius is half the diameter, 2 in: 3.1416 × 2² = 12.57 sq in. Using the diameter instead of the radius gives 50.27, four times too large.
Reference AM.I.H.K1 · FAA-H-8083-30B, Ch. 3 (Area of a Circle)
A brace forms the hypotenuse of a right triangle whose other two sides are 6 inches and 8 inches. How long is the brace?
Why: Pythagorean theorem: c² = a² + b² = 36 + 64 = 100, so c = √100 = 10 in. The hypotenuse is always shorter than the two legs added together (14).
Reference AM.I.H.K3 · FAA-H-8083-30B, Ch. 3 (Right Triangles)
A part's service limit is 240 hours, and a bulletin reduces it by 15 percent. How many hours does the bulletin remove?
Why: 15 percent of 240 = 0.15 × 240 = 36 hours. The new limit would be 240 − 36 = 204 hours, which answers a different question than the one asked.
Reference AM.I.H.K5 · FAA-H-8083-30B, Ch. 3 (Percentage)
How is 0.00045 written in scientific notation?
Why: Move the decimal point right until one nonzero digit is in front of it: four places gives 4.5. Moving right means a negative exponent, so 4.5 × 10⁻⁴. Option B equals the same number but is not in proper scientific form.
Reference AM.I.H.K8 · FAA-H-8083-30B, Ch. 3 (Scientific Notation)
A metric bolt is 50 millimeters long. About how long is it in inches?
Why: One inch is exactly 25.4 mm, so 50 ÷ 25.4 = 1.97 in. Multiplying instead of dividing, or confusing millimeters with centimeters (5.00), are the common errors.
Reference AM.I.H.K7 · FAA-H-8083-30B, Ch. 3 (Metric System; Conversions)