CAAS SAR-66 AML Module 1 — Mathematics

Simplify the arithmetic fraction addition: 3/8 + 5/16.

• A11/16
• B8/24
• C13/16
• D7/8

Convert an aircraft structural rivet length of 45.0 inches into millimeters (1 inch = 25.4 mm).

• A114.3 mm
• B1143.0 mm
• C11.43 mm
• D11430 mm

An aircraft fuel tank contains 150 US gallons of Jet A-1 fuel. How many liters is this equivalent to? (1 US gallon = 3.78541 liters).

• A39.63 liters
• B56.78 liters
• C567.81 liters
• D5678.1 liters

A hydraulic fluid mixture requires a ratio of mineral oil to chemical additive of 7 : 3. If 21.0 liters of mineral oil are used, how many liters of additive must be added?

• A9.0 liters
• B6.3 liters
• C14.0 liters
• D4.5 liters

An aircraft main fuel tank has a maximum capacity of 4,500 liters. If the tank is filled to 84% of its total capacity, how many liters of fuel are in the tank?

• A3,600 liters
• B3,780 liters
• C3,850 liters
• D756 liters

What is the principal square root of 0.0064?

• A0.8
• B0.08
• C0.008
• D0.032

An engine's oil consumption over 4 consecutive flights was recorded as 1.2 L, 1.5 L, 0.9 L, and 1.4 L. What was the average oil consumption per flight?

• A1.30 L
• B1.20 L
• C1.25 L
• D5.00 L

Express the decimal value 0.375 as a fully simplified fraction.

• A3/8
• B3/7
• C7/16
• D37/100

Convert a maximum takeoff mass of 2,500 pounds (lb) to kilograms (kg). (1 lb = 0.453592 kg).

• A5,511.56 kg
• B1,133.98 kg
• C11,339.8 kg
• D113.40 kg

Find the area of a rectangular aircraft skin access panel measuring 35 cm long by 20 cm wide.

• A110 cm²
• B350 cm²
• C700 cm²
• D1400 cm²

Divide the fraction 7/12 by 14/15 and express the result in simplest form.

• A5/8
• B49/90
• C5/6
• D3/4

An engine accessory gearbox drive gear has 24 teeth and drives a pump gear with 72 teeth. What is the gear ratio of driven gear to driving gear?

• A1:3
• B3:1
• C4:1
• D2.5:1

An aircraft engine turbine inlet temperature (TIT) increases from 750°C to 810°C during acceleration. What is the percentage increase in temperature?

• A8.0%
• B7.4%
• C8.5%
• D6.0%

An aircraft main hydraulic system operates at a pressure of 3,000 PSI. Convert this pressure into bar. (1 PSI = 0.0689476 bar).

• A43,511 bar
• B206.84 bar
• C20.68 bar
• D2068.4 bar

Calculate the volume of a cylindrical hydraulic fluid reservoir with internal diameter 20 cm and height 40 cm. (Use V = π r² h, π ≈ 3.14159).

• A12,566 cm³ (12.57 L)
• B50,265 cm³ (50.27 L)
• C8,000 cm³ (8.00 L)
• D25,133 cm³ (25.13 L)

An aircraft engine burns 840 kg of fuel in 2 hours and 20 minutes. At this steady fuel burn rate, how much fuel is consumed in 3 hours and 45 minutes?

• A1,350 kg
• B1,260 kg
• C1,420 kg
• D1,500 kg

Evaluate the arithmetic expression: (0.4)³ + ∛(0.125).

• A0.189
• B0.564
• C0.640
• D0.525

Evaluate (14.28 × 3.5) / 1.7 and round the result to 3 significant figures.

• A29.4
• B29.40
• C29.5
• D28.9

A raw sheet of aircraft aluminum alloy weighs 48.0 kg. If 1/6 is trimmed off during machining and 1/4 of the remaining sheet is removed for weight reduction holes, what is the mass of the final part?

• A28.0 kg
• B30.0 kg
• C32.0 kg
• D24.0 kg

Convert a fastener torque value of 180 lb-in into Newton-meters (N·m). (1 lb-in = 0.112985 N·m).

• A15.93 N·m
• B20.34 N·m
• C203.4 N·m
• D2.03 N·m

Calculate the surface area of a trapezoidal elevator trim tab with parallel sides of 80 cm and 60 cm, and height of 25 cm. [Area = (a + b) / 2 × h].

• A1,750 cm²
• B3,500 cm²
• C1,400 cm²
• D2,000 cm²

Three aircraft maintenance checks have recurring schedules: Check A every 12 days, Check B every 18 days, and Check C every 30 days. If all 3 checks are performed today, after how many days will they all coincide again?

• A90 days
• B180 days
• C360 days
• D60 days

Three residual lengths of aircraft safety wire measure 72 cm, 108 cm, and 144 cm. What is the greatest common length into which all three wires can be cut into equal pieces with no wire left over?

• A18 cm
• B36 cm
• C12 cm
• D54 cm

A 20.0-liter anti-icing solution consists of 40% glycol and 60% water. How many liters of pure glycol must be added to increase the solution to 50% glycol?

• A4.0 liters
• B2.0 liters
• C5.0 liters
• D3.0 liters

An emergency pneumatic blowout bottle is spherical with an internal radius of 15.0 cm. Calculate its total internal volume. [V = (4/3) π r³, π ≈ 3.14159].

• A14,137 cm³ (14.14 L)
• B28,274 cm³ (28.27 L)
• C10,603 cm³ (10.60 L)
• D4,241 cm³ (4.24 L)

Express the product of (4.2 × 10⁵) and (3.0 × 10⁻²) in standard scientific notation.

• A12.6 × 10³
• B1.26 × 10⁴
• C1.26 × 10³
• D1.26 × 10⁵

An aircraft flies a leg of 600 nautical miles at a groundspeed of 300 knots, and the return leg of 600 nautical miles at a groundspeed of 400 knots. What is the average groundspeed for the total 1,200 NM distance?

• A350.0 knots
• B342.9 knots
• C340.0 knots
• D345.5 knots

Jet A-1 aviation fuel has a relative density (specific gravity) of 0.80 kg/L. What is the mass in kilograms of 3,500 liters of Jet A-1?

• A2,800 kg
• B4,375 kg
• C3,500 kg
• D2,400 kg

Simplify the fraction expression: [(2/3 + 1/4) ÷ (5/6 - 1/2)].

• A11/6
• B11/4 (2.75)
• C3/2
• D9/4

Convert a temperature reading of 50°C into degrees Fahrenheit (°F). [F = (9/5) C + 32].

• A90°F
• B112°F
• C122°F
• D130°F

A wing flap fairing consists of a rectangular section measuring 1.20 m by 0.80 m connected to a semi-circular cap with a diameter of 0.80 m. What is the total surface area of the fairing?

• A1.211 m²
• B1.463 m²
• C1.161 m²
• D1.086 m²

An engine oil scavenging flow rate is 4.5 US gallons per hour. Express this flow rate in cubic centimeters per second (cm³/s). (1 US gal = 3785.41 cm³, 1 hour = 3,600 s).

• A17.03 cm³/s
• B4.73 cm³/s
• C2.84 cm³/s
• D8.52 cm³/s

A hollow tubular aluminum strut has an outer radius R = 5.0 cm, an inner radius r = 4.0 cm, and length L = 120 cm. Calculate the volume of aluminum metal in the strut. [V = π (R² - r²) L].

• A3,393 cm³
• B9,425 cm³
• C6,032 cm³
• D1,357 cm³

An avionics component depreciates in value by 10% each year for 3 consecutive years. If its initial purchase value was S50,000, what is its book value after 3 years?

• AS35,000
• BS36,450
• CS37,500
• DS40,500

An aircraft structural fitting is cast from an alloy containing copper, zinc, and nickel in the ratio 5 : 3 : 2 by weight. If the total mass of the fitting is 14.5 kg, what is the weight of zinc contained in the part?

• A7.25 kg
• B4.35 kg
• C2.90 kg
• D5.80 kg

Technician A can complete a wire harness overhaul in 6.0 hours working alone. Technician B can complete the same task in 4.0 hours working alone. How long will it take to complete the job if both work together at their constant rates?

• A2.4 hours (2 h 24 m)
• B2.5 hours (2 h 30 m)
• C5.0 hours (5 h 00 m)
• D3.0 hours (3 h 00 m)

Calculate the value of: [(3/4 - 1/3) / (1/2 + 1/6)] × √(144 / 25).

• A1.25
• B1.50
• C1.75
• D2.00

An environmental control system heat exchanger absorbs 450 British Thermal Units (BTU) of heat energy. Convert this energy to kilojoules (kJ). (1 BTU = 1,055.06 Joules).

• A474.78 kJ
• B426.60 kJ
• C527.53 kJ
• D47.48 kJ

A conical fuel drain collector has a frustum shape with top radius R = 12.0 cm, bottom radius r = 8.0 cm, and vertical height h = 15.0 cm. Calculate its total internal volume in liters. [V = (1/3) π h (R² + R r + r²), π ≈ 3.14159].

• A6.79 L
• B4.78 L
• C3.02 L
• D5.53 L

An engine mounting bolt has a nominal length specification of 75.00 mm ± 0.15 mm. If a manufactured bolt measures 75.12 mm, what is its percentage deviation from nominal length?

• A0.16%
• B0.20%
• C0.12%
• D1.60%

Evaluate the algebraic expression: 3a² - 2ab + b² for a = 4 and b = -2.

• A68
• B36
• C52
• D44

Solve the linear equation for x: 5x - 7 = 3x + 9.

• A1
• B4
• C8
• D16

Simplify the expression using the laws of indices: (x⁴ · x⁵) / x³.

• Ax⁶
• Bx²⁰/3
• Cx⁷
• Dx⁸

Convert the binary number (110101)₂ into its decimal equivalent.

• A45
• B53
• C55
• D27

What is the value of log₁₀(100,000)?

• A4
• B5
• C6
• D10

Expand and simplify the algebraic expression: 4(2x - 3) - 3(x - 5).

• A5x + 3
• B5x - 27
• C11x + 3
• D5x - 3

Solve the fractional algebraic equation for y: y/4 + 3 = 9.

• A1.5
• B12
• C24
• D36