This module provides the foundational mathematical knowledge required for aircraft maintenance engineering. It covers arithmetic operations, algebraic manipulation, geometry, trigonometry, and unit conversions — all applied to practical aeronautical contexts such as engine performance calculations, structural measurements, fuel computations, and maintenance tolerances. The syllabus is divided into four main areas: Arithmetic (1.1), Algebra (1.2), Geometry (1.3), and Trigonometry (1.4), with knowledge levels ranging from basic overview (Level 1) to detailed theoretical understanding (Level 3).
1.1 Arithmetic
Fractions, Decimals, and Percentages
Aircraft maintenance frequently requires working with fractional quantities, particularly when measuring fuel levels, calculating remaining service life, or interpreting inspection findings.
Key operations:
Addition/subtraction of fractions: Find a common denominator before adding or subtracting.
Multiplication of fractions: Multiply numerators together and denominators together.
Division of fractions: Multiply by the reciprocal of the divisor.
Fraction to decimal conversion: Divide the numerator by the denominator.
Example — Fuel quantity: A 200-litre tank is ¾ full. Current fuel = ¾ × 200 = 150 litres. Additional fuel required = 200 − 150 = 50 litres.
Example — TBO fraction: An engine has 1,500 hours TBO with 400 hours since overhaul. Remaining = 1,500 − 400 = 1,100 hours. Fraction remaining = 1,100 / 1,500 = 11/15 ≈ 0.733.
Ratios and Proportions
Ratios express the relationship between two quantities and are fundamental to engine parameters such as compression ratio and gearbox reduction ratios.
Maintenance inspections often involve multiple measurements of the same parameter. The arithmetic mean and range provide essential information about measurement consistency.
Arithmetic mean = sum of all values / number of values
Range = maximum value − minimum value
Example — Crankshaft journal measurements (mm): 49.98, 50.02, 50.00, 50.04
Mean = (49.98 + 50.02 + 50.00 + 50.04) / 4 = 200.04 / 4 = 50.01 mm
Range = 50.04 − 49.98 = 0.06 mm
Example — Runout measurements (mm): 0.02, 0.03, 0.01, 0.04, 0.02
Mean = 0.12 / 5 = 0.024 mm
Tolerances and Deviations
Manufacturing specifications include nominal dimensions with allowable tolerances. Deviation is calculated as:
Deviation = measured value − nominal value
Example: Nominal diameter = 45.80 mm, tolerance ±0.05 mm, measured = 45.72 mm
Deviation = 45.72 − 45.80 = −0.08 mm
Since |−0.08| > 0.05, the measurement is outside tolerance
1.2 Algebra
Solving Linear Equations
Algebraic manipulation is essential for rearranging formulas used in maintenance calculations.
Example: Solve 3x − 7 = 2x + 5
Subtract 2x from both sides: x − 7 = 5
Add 7 to both sides: x = 12
Example: Solve 3(x − 4) + 2x = 5x − 12
Expand: 3x − 12 + 2x = 5x − 12
Simplify: 5x − 12 = 5x − 12
Both sides identical → equation holds for all real values of x (identity)
Exponents and Indices
Exponent rules are fundamental for engineering notation and scientific calculations.
Multiplication rule: aᵐ × aⁿ = a^(m+n)
Example: 2³ × 2² = 2^(3+2) = 2⁵ = 32
Other key rules:
Division: aᵐ ÷ aⁿ = a^(m−n)
Power of a power: (aᵐ)ⁿ = a^(m×n)
Negative exponent: a⁻ⁿ = 1/aⁿ
Zero exponent: a⁰ = 1
Linear Relationships
Many aeronautical relationships are linear, such as temperature lapse rates with altitude.
Example — Temperature lapse: At 500 m, temperature = 15°C. Lapse rate = 2°C per 500 m.
Altitude difference to 2,500 m = 2,000 m
Number of 500-m intervals = 2,000 / 500 = 4
Temperature drop = 4 × 2°C = 8°C
Temperature at 2,500 m = 15 − 8 = 7°C
1.3 Geometry
Areas of Common Shapes
Rectangle: Area = length × width
Example — Rotor blade: Length = 3.5 m, chord = 0.25 m
Area = 3.5 × 0.25 = 0.875 m²
Circle: Area = π × r² = π × (d/2)²
Example — Hydraulic hose: Internal diameter = 12 mm
Area = 3.14 × (6)² = 3.14 × 36 = 113.04 mm²
Cylinder Volume and Engine Displacement
The swept volume of a cylinder is calculated using:
Spark timing in degrees BTDC can be converted to time:
Time per revolution = 60 / RPM (seconds)
Time for angle θ = (θ / 360) × time per revolution
Example: Fires at 25° BTDC, engine at 3,000 RPM
Time per revolution = 60 / 3,000 = 0.02 s = 20 ms
Time for 25° = 20 ms × (25/360) = 1.39 ms
Units and Conversions
SI Base Units
Quantity
Unit
Symbol
Length
metre
m
Mass
kilogram
kg
Time
second
s
Force
newton
N
Pressure
pascal
Pa
Energy
joule
J
Power
watt
W
Common Conversions
Torque:
1 ft-lb = 1.356 N·m
1 N·m = 0.7376 lb-ft
Example: 20 ft-lb = 20 × 1.356 = 27.12 N·m
Example: 25 N·m = 25 × 0.7376 = 18.44 lb-ft
Example: 25 ft-lb = 25 × 1.356 = 33.9 N·m
Pressure:
1 psi = 6.895 kPa
1 bar = 100 kPa
Example: 60 psi = 60 × 6.895 = 413.7 kPa
Volume:
1 US gallon = 3.785 litres
Example: 45 L/h ÷ 3.785 = 11.89 US gal/h
Temperature:
A difference of 1°C = 1 K
Absolute zero = −273.15°C
Example: Temperature drops from +15°C to −5°C
Drop = 15 − (−5) = 20°C = 20 K
Derived Quantities
Density: ρ = mass / volume
Example: Fuel density = 0.8 kg/L, tank capacity = 200 L
Mass = 200 × 0.8 = 160 kg
Example — Fuel consumption: 42 L/h, density = 0.72 kg/L
Mass flow = 42 × 0.72 = 30.24 kg/h
Per minute = 30.24 / 60 = 0.504 kg/min
Pressure and Force: Force = Pressure × Area
Example: Piston area = 80 cm² = 0.008 m², pressure = 50 bar = 5,000 kPa = 5,000,000 Pa
Force = 5,000,000 × 0.008 = 40,000 N = 40 kN
Speed: Speed = distance / time
Example: 150 nautical miles in 1 hour 15 minutes (1.25 hours)
Speed = 150 / 1.25 = 120 knots
Common Relationships Between Concepts
168.Engine performance: Power, torque, and RPM are interrelated through angular velocity. Increasing RPM at constant power reduces torque.
169.Engine geometry: Bore, stroke, and number of cylinders determine total displacement. Compression ratio links swept and clearance volumes.
170.Drive train: Engine RPM, gearbox reduction ratio, and rotor RPM are directly proportional.
171.Temperature and altitude: Lapse rates create linear temperature changes with altitude, affecting engine performance and density altitude calculations.
172.Measurement analysis: Mean values indicate central tendency while range indicates measurement spread — both essential for wear assessment and tolerance verification.
173.Unit systems: Many maintenance manuals mix SI and imperial units; accurate conversion is critical for correct torque application, pressure settings, and fuel calculations.
Typical Exam Focus Points
Torque/power/RPM calculations using the formula P = T × ω
Compression ratio calculations from swept and clearance volumes
Unit conversions between N·m and ft-lb, psi and kPa, litres and US gallons
Cylinder displacement calculations using V = (π/4) × D² × L
Angular velocity conversion from RPM to rad/s
Pythagoras' theorem applications in structural measurements
Algebraic manipulation of linear equations and identities
Exponent rules for engineering notation
Arithmetic mean and range calculations for inspection data
Ratio and proportion problems applied to gearboxes and fuel mixtures
Temperature difference conversions between Celsius and Kelvin
Fraction and percentage applications for fuel quantities and service life calculations
Speed/distance/time calculations for flight planning and performance verification
Regulatory References
Regulation (EU) No 1321/2014, Annex III (Part-66): Establishes the basic knowledge requirements for aircraft maintenance licences.
Appendix I to Part-66: Defines the Module 1 Mathematics syllabus with knowledge levels:
Level 1: Familiarisation with basic concepts
Level 2: General knowledge with practical application
Level 3: Detailed theory with in-depth understanding
AMC/GM to Part-66: Provides acceptable means of compliance and guidance material for examination standards and question formats.
