Mathematics
Core content
Aviation mathematics is applied arithmetic, not abstract theory. You must handle fractions, decimals, ratios, proportion, percentages, powers and roots, simple algebra, geometry, and right-angle trigonometry. Be able to transpose a formula before substituting numbers, calculate areas and volumes of common shapes, use Pythagoras, and apply sine, cosine and tangent. Units matter: convert mm to inches, litres to gallons, knots to m/s, and keep track of squared and cubed units. Graphs and tables often appear as rate or conversion questions.
Traps
Common errors include ignoring order of operations, rounding too early, applying a percentage to the wrong base, and using the calculator in radian mode for degree problems. A 10 percent increase followed by a 10 percent decrease does not return to the original value: 100 becomes 110, then 99. Ratios must be set up with matching units on each side. When a question asks for a length, check whether the answer is plausible in the units requested.
Worked example
A cable tension rises by 12 percent and then falls by 12 percent. Starting at 100 units: 100 x 1.12 = 112; 112 x 0.88 = 98.56. The net change is a fall of 1.44 percent, not zero. Rule of thumb: carry one extra significant figure through the working and round only at the end.
Key points
- Transpose formulas before substituting values.
- Keep units consistent and convert before calculating.
- Percent changes are multiplicative, not additive.
- Check whether the calculator is in degree or radian mode.
- A plausible-answer check catches most unit and decimal errors.