Mathematics
What you must understand
CAR-66 mathematics is applied arithmetic for maintenance, not abstract algebra. Be fluent with fractions, decimals, percentages, ratio and proportion, powers and roots, scientific notation, and unit conversion. Understand basic algebra (transposition, substitution), simple geometry (perimeter, area, volume of cylinders and rectangular solids), trigonometry (sine, cosine, tangent, Pythagoras) and the meaning of significant figures and rounding. Airmanship numeracy matters: torque values, tolerances, clearances and mass-and-balance arithmetic all depend on it.
Traps in questions
- Unit mixing: millimetres versus centimetres versus inches inside one calculation. Convert before you compute.
- Order of operations: multiplication and division before addition and subtraction; brackets first.
- Percentage change versus percentage of: a 20% increase then a 20% decrease does not return to the original value.
- Rounding too early: carry full precision, round only at the end to the stated significant figures.
- Ratio direction: "fuel to air 1:15" versus "air to fuel 15:1" - read which is asked.
Worked example
A cylinder has bore 80 mm and stroke 100 mm. Volume = π × r² × h = π × 40² × 100 = π × 1600 × 100 ≈ 502,655 mm³. In cm³ divide by 1000 → ≈ 502.7 cm³. Rule of thumb: keep a running unit check - mm³ ÷ 1000 = cm³, cm³ ÷ 1000 = litres.
Rule of thumb
If an answer looks off by a factor of 10, 100 or 1000, suspect a unit slip before reworking the whole problem.