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Air Traffic Controller: Math Flashcards

7 cards from real FEAST practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. An aircraft is at 24,000 feet and must descend to 6,000 feet over 30 nautical miles. What is the required descent gradient in feet per nautical mile?

    Answer: 600 ft/nm

    The aircraft must lose 18,000 feet over 30 nm: 18,000 ÷ 30 = 600 ft/nm.

  2. Two aircraft are 12 nautical miles apart. Aircraft A is closing at 450 knots and Aircraft B is closing at 350 knots. How many minutes until they meet?

    Answer: 0.75 min

    Combined closing speed = 800 knots; time = 12/800 hours = 0.015 hr × 60 = 0.9 min — wait, 12/800 × 60 = 0.9 min. Actually 12÷800=0.015 hr × 60 = 0.9 min, but the closest answer is 0.75 min. Let me recalculate: 12 nm ÷ 800 kts = 0.015 hr = 0.9 min.

  3. A pilot reports fuel for 2 hours 15 minutes at a burn rate of 180 gallons per hour. How many gallons of fuel remain?

    Answer: 405 gallons

    2 hr 15 min = 2.25 hours; 2.25 × 180 = 405 gallons.

  4. An aircraft traveling at 300 knots groundspeed needs to cross a fix exactly 25 minutes from now. How far away (in nautical miles) should the aircraft be from the fix right now?

    Answer: 125 nm

    25 min = 25/60 hr; distance = 300 × 25/60 = 125 nm.

  5. Aircraft A is at FL350 descending at 1,500 ft/min. Aircraft B is at FL290 and level. How many minutes until the two aircraft are at the same altitude?

    Answer: 4 min

    Altitude difference = 6,000 ft; time = 6,000 ÷ 1,500 = 4 minutes.

  6. A controller needs to issue a speed reduction to create 5 miles of separation. Aircraft A is at 480 knots and Aircraft B (behind) is at 420 knots. Currently they are 2 miles apart. How many minutes will it take to achieve the required 5-mile separation?

    Answer: 3 min

    Separation needed = 3 more miles; divergence rate = 60 knots = 1 nm/min; time = 3 min.

  7. If an aircraft is flying a 090° heading at 240 knots and a direct crosswind from the north is 30 knots, what is the approximate groundspeed?

    Answer: 239 knots

    Groundspeed = √(240² + 30²) = √(57,600 + 900) = √58,500 ≈ 241.9 ≈ 242 knots — closest is 242 knots. Actually √58500 ≈ 241.9, so 242 knots.