Mental maths for pilot aptitude tests: methods and examples

Why mental maths matters

Numerical questions are among the most commonly reported parts of cadet pilot aptitude tests. They are usually timed, and candidates commonly report that calculators are not allowed. The maths itself is rarely hard; most of it is school arithmetic. The challenge is doing it quickly and accurately under time pressure, sometimes while you are busy with something else.

Pilots use the same kind of quick sums all the time: how long to the next waypoint, how much fuel is left, when to start descending. This guide covers the topics candidates commonly report, with worked examples and a practice routine. Each example uses friendly numbers so you can check every step in your head.

Build the basics first

Speed comes from not having to think about the small steps. Before you move to harder questions, make these automatic:

Ten minutes a day on these for two weeks makes everything else faster.

• Times tables up to 12 × 12, and ideally up to 15 × 15.
• Squares from 1 to 20, and the matching square roots.
• Common fractions as percentages: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/3 ≈ 33.3%.
• Minutes as parts of an hour: 6 min = 0.1 h, 15 min = 0.25 h, 20 min = 1/3 h, 45 min = 0.75 h.
• Multiplying and dividing by 10, 100 and 1,000 without losing a zero.

Speed, distance and time

Aviation speeds are usually given in knots. One knot is one nautical mile (NM) per hour. Everything comes from one rule: distance = speed × time. Rearrange it to get speed = distance ÷ time, or time = distance ÷ speed. Change minutes into hours, or work in NM per minute, before you multiply.

A useful shortcut: divide the speed in knots by 60 to get NM per minute. At 120 knots you cover 2 NM a minute, at 180 knots 3 NM, and at 240 knots 4 NM.

• Example 1, distance: an aircraft flies at 180 knots for 20 minutes. 180 ÷ 60 = 3 NM per minute, and 3 × 20 = 60 NM.
• Example 2, time: how long does 210 NM take at 140 knots? 210 ÷ 140 = 1.5 hours, which is 90 minutes. Remember that 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes.
• Example 3, speed: you must cover 96 NM in 40 minutes. 40 minutes is 2/3 of an hour, so the speed is 96 ÷ 2/3 = 96 × 1.5 = 144 knots.

Percentages and fractions

Percentages appear in fuel, load and change questions. Break them into easy pieces: 10% is one tenth, 5% is half of that, and 1% is one hundredth.

• Example 4: a fuel tank holds 6,400 litres and is 35% full. 10% is 640, so 30% is 1,920, and 5% is 320. 1,920 + 320 = 2,240 litres.
• Percentage change: from 80 to 100 is a rise of 20, and 20 ÷ 80 = 25%. Always divide by the starting value.
• Swap trick: x% of y equals y% of x. So 8% of 50 is the same as 50% of 8, which is 4.
• A 10% rise followed by a 10% fall does not bring you back to the start: 100 becomes 110, then 99.

Units pilots use: knots, feet and nautical miles

Aviation mixes units. Height is usually in feet, distance in nautical miles and speed in knots, while everyday life in India uses metres and kilometres. These values are worth learning by heart:

Example 5, height: an aircraft cruises at 35,000 feet. Roughly how high is that in metres? 35,000 × 3 ÷ 10 = 10,500 m. The exact answer is 35,000 × 0.3048 = 10,668 m, so 'about 10.5 to 10.7 km' is sensible. If the options are far apart, the quick estimate is enough.

Example 6, descent: an aircraft must descend from 11,000 feet to 2,000 feet at 1,500 feet per minute. The height to lose is 9,000 feet, and 9,000 ÷ 1,500 = 6 minutes.

• 1 nautical mile = 1.852 km, so roughly 1.85 km. 1 NM is also about 1.15 ordinary (statute) miles.
• 1 knot = 1.852 km/h. For example, 250 knots × 1.852 = 463 km/h.
• 1 foot = 0.3048 m. Quick estimate: multiply feet by 3 and divide by 10. This comes out about 1.6% low.
• 1 metre ≈ 3.28 feet.
• 8 km ≈ 5 statute miles, a handy ratio for kilometres and miles.

Headings: arithmetic on a circle

Heading questions are sums on a 360° circle. For a turn, add degrees for a right turn and subtract for a left turn, then add or take away 360° to bring the answer between 001° and 360°. Heading 330°, turn right 60°: 330 + 60 = 390, and 390 − 360 = 030°.

The reciprocal heading is the opposite direction. Add 180° to a heading below 180°, and subtract 180° from a heading of 180° or more. The reciprocal of 070° is 250°, and the reciprocal of 290° is 110°.

Estimation tricks

In multiple-choice questions you often do not need the exact answer. Estimate first, then look at the options.

• Round to friendly numbers: 487 × 21 is close to 500 × 20 = 10,000. The exact answer is 10,227, so if only one option is near 10,000, choose it.
• Note which way you rounded. If you rounded both numbers up, your estimate is too high, so the answer is a little below it.
• Check the last digit: 37 × 43 must end in 1, because 7 × 3 = 21. That alone can rule out options. (The answer is 1,591.)
• Check the size: 600 NM for a 20-minute flight in a light aircraft is clearly wrong. A quick sense check catches many slips.
• Halve and double: 16 × 25 = 8 × 50 = 4 × 100 = 400.
• Watch hours and minutes: 2.4 hours is 2 hours 24 minutes (0.4 × 60 = 24), not 2 hours 40 minutes.

A timed practice routine

Short, regular, timed practice builds speed far better than occasional long sessions.

On FlyAptitude, the numerical reasoning section gives 20 questions in 15 minutes on Foundation and 25 questions in 14 minutes on Advanced, with no calculator. It covers arithmetic, sequences, percentages, conversions, speed–distance–time and headings. These are our own practice timings, not an official format. Track your score each week, and aim for accuracy first, then speed.

• Daily warm-up, 5 minutes: tables, squares and fraction-to-percentage facts, said out loud or written fast.
• Topic drill, 10 minutes: one topic a day, such as speed–distance–time on Monday and percentages on Tuesday.
• Timed set, 15 minutes, two or three times a week: mixed questions against the clock, without a calculator.
• Review, 5 minutes: redo every wrong answer slowly and note whether it was a gap in method or a careless slip.
• Once a week: do sums while handling something else, for example in a multitasking drill, so the skill holds up under load.