Air Traffic Controller / FAA ATSA Exam Numerical, Analytical, and Logical Reasoning Syllabus

Numerical, Analytical, and Logical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Numerical, Analytical, and Logical Reasoning in Air Traffic Controller / FAA ATSA Exam, not a summary of it.

1. 1

   Applied Arithmetic and Mental Math

   3 topics

   • Speed-Distance-Time Calculations
     • Computing ground speed, ETA, and closure time
     • Unit conversions (knots, nautical miles, minutes)
   • Rates, Ratios, and Proportions
     • Rate-of-climb/descent and altitude-change timing
   • Rapid Estimation
     • Rounding and approximation under time limits
2. 2

   Deductive and Inductive Logic

   3 topics

   • Conditional and Rule-Based Reasoning
     • Applying if-then operational rules to scenarios
   • Sequencing and Ordering
     • Determining valid orders from constraints
   • Pattern Recognition in Data
     • Inferring the next term or missing value
3. 3

   Information Prioritization and Problem Solving

   3 topics

   • Multi-Variable Decision Tasks
     • Weighing competing constraints (separation, fuel, priority)
   • Data Extraction Under Pressure
     • Pulling relevant values from tables and data blocks
   • Error Checking and Verification
     • Catching inconsistencies before committing an answer

Numerical, Analytical, and Logical Reasoning flashcards for Air Traffic Controller / FAA ATSA Exam

25 of 51 cards from the Numerical, Analytical, and Logical Reasoning deck — real questions with worked answers.

1. What is the fundamental formula relating speed, distance, and time?

   Speed = Distance ÷ Time. Rearranged: Distance = Speed × Time, and Time = Distance ÷ Speed.

2. An aircraft travels 450 miles in 1.5 hours. What is its average speed?

   300 mph (450 ÷ 1.5).

3. How do you convert a speed from miles per hour to miles per minute?

   Divide the mph value by 60. For example, 300 mph = 5 miles per minute.

4. Two aircraft are 200 miles apart flying directly toward each other at 250 mph and 350 mph. How long until they meet?

   20 minutes. Combined closing speed = 600 mph; 200 ÷ 600 hr = 1/3 hr = 20 min.

5. When two objects move in the same direction, how do you find the rate at which the gap changes?

   Subtract the slower speed from the faster speed (relative/closure speed = difference of speeds).

6. How long does it take to cover 60 miles at 480 mph?

   7.5 minutes. 60 ÷ 480 hr = 0.125 hr × 60 = 7.5 min.

7. In speed-distance-time problems, why must units be consistent before calculating?

   Speed, distance, and time must use matching units (e.g., mph with hours, or knots with hours) or the result will be wrong; convert one to match the others first.

8. What is a knot, and how does it relate to distance and time?

   One knot equals one nautical mile per hour. So distance in nautical miles = speed in knots × time in hours.

9. Define a 'rate' in the context of reasoning problems.

   A rate is a ratio comparing two quantities with different units, expressing how much of one quantity occurs per unit of another (e.g., miles per hour, planes per minute).

10. What is the difference between a ratio and a proportion?

    A ratio compares two quantities (a:b); a proportion is an equation stating that two ratios are equal (a/b = c/d).

11. How do you solve a proportion such as 3/4 = x/20?

    Cross-multiply: 3 × 20 = 4 × x, so 60 = 4x, giving x = 15.

12. If a controller handles 12 aircraft in 4 minutes at a steady rate, how many can be handled in 10 minutes?

    30 aircraft. Rate = 3 per minute × 10 = 30.

13. A scale shows 1 inch = 25 nautical miles. How many nautical miles is 3.5 inches?

    87.5 nautical miles (3.5 × 25).

14. How do you split a quantity in a given ratio, e.g., 60 in the ratio 2:3?

    Add the parts (2+3=5), divide the total by that sum (60÷5=12 per part), then multiply: 2×12=24 and 3×12=36.

15. If 5 workers complete a task in 8 hours, how long would 10 workers take at the same rate (inverse proportion)?

    4 hours. Doubling workers halves the time (work is constant: 5×8 = 10×4 = 40 worker-hours).

16. What does 'directly proportional' mean?

    As one quantity increases, the other increases at the same ratio; their quotient stays constant (y = kx).

17. What does 'inversely proportional' mean?

    As one quantity increases, the other decreases proportionally; their product stays constant (xy = k).

18. What is rapid estimation and why is it useful on the ATSA?

    Rapid estimation is quickly approximating an answer using rounding and mental math to save time and check plausibility; it is useful because many timed items only require a close enough answer to pick the correct choice.

19. How would you quickly estimate 312 × 19?

    Round 19 to 20: 312 × 20 = 6240, then subtract one 312 to get ~5928 (exact = 5928).

20. What is the rounding rule for estimating numbers ending in 5 or higher in a place value?

    Round up if the digit being dropped is 5 or more; round down if it is 4 or less.

21. To estimate a percentage like 18% of 250 quickly, what mental shortcut works?

    Use 10% (25) plus half of that for 5% (12.5) plus a bit; or approximate to 20% of 250 = 50, then trim slightly to ~45 (exact = 45).

22. When estimating a division like 587 ÷ 29, what is a fast approach?

    Round to 600 ÷ 30 = 20 as a quick estimate (exact ≈ 20.2).

23. In a timed test, when should you estimate rather than calculate exactly?

    When the answer choices are far apart or the question asks 'approximately,' estimation is faster and sufficient; calculate exactly only when choices are close.

24. What is conditional (if-then) reasoning?

    Reasoning where a conclusion depends on whether a stated condition is met; if the condition (antecedent) is true, the result (consequent) follows.

25. In rule-based reasoning, what is the correct order when multiple rules apply?

    Apply rules in their stated priority or sequence; check each condition against the facts and act only on rules whose conditions are satisfied, respecting precedence.

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