Page 1 of 115
AWS CWEng Part 1 — Fundamentals of Science and Mathematics
Exam QUESTIONS AND CORRECT ANSWERS LATEST UPDATE THIS
YEAR
AWS CWEng Part 1 — Fundamentals of Science and Mathematics
Summarized Exam Coverage
Exam Format: 35 multiple-choice questions, closed-book, 2 hours, 60%
passing score required .
Domain Weighting: Mathematics (25%), Physics (50%), Chemistry (25%)
.
Mathematics Topics: Simple calculations, special functions (exp, log),
trigonometric functions, algebraic equations (linear, quadratic,
polynomial), graphs and equations (slope, intercept, roots, derivatives),
geometry, hyperbola, parabola, complex numbers, calculus
fundamentals, statistics (normal distribution, mean, standard deviation,
variance), and simple correlation (linear regression, r²) .
, Page 2 of 115
Physics Topics: Unit conversion, mass/weight/volume/density,
force/energy/work/power, stress/strain/Hooke's Law, moment and
momentum, temperature and heat measurement (thermocouples,
pyrometers), thermal properties of materials (conductivity, expansion,
stress) .
Chemistry Topics: Symbols (elements and inorganic compounds),
molecular weight and stoichiometry, acids and bases, balancing
chemical equations, gas combustion reactions, oxidation-reduction
reactions, ideal gas law, mass balance, bulk and chemical analysis
methodologies, reactivity/toxicity/environmental effects .
250 Randomized Multiple-Choice Questions
Questions 1–50: Mathematics
1. A welding engineer calculates the cross-sectional area of a circular
weld nugget with a radius of 12 mm. What is the area in square
millimeters?
A) 144 mm²
B) 226 mm²
C) 452 mm²
D) 1,809 mm²
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Answer: C
Rationale: Area of a circle equals πr². With r = 12 mm, area = π × 144 =
452.39 mm², rounded to 452 mm². This calculation is fundamental for
determining weld cross-sectional area and calculating heat input per
unit length.
2. During a tensile test on a welded specimen, the elongation is
recorded as 22%. If the original gauge length was 50 mm, what is the
final gauge length?
A) 55 mm
B) 61 mm
C) 72 mm
D) 82 mm
Answer: B
Rationale: Final length equals original length multiplied by (1 +
elongation). Therefore, 50 mm × 1.22 = 61 mm. Elongation percentage
is a critical ductility measure for weld qualification and acceptance
criteria in welding codes.
3. A welding procedure requires a heat input of 1.5 kJ/mm. If the travel
speed is 4 mm/s, what is the arc power in kilowatts?
A) 3.0 kW
B) 6.0 kW
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C) 0.375 kW
D) 1.5 kW
Answer: B
Rationale: Heat input (kJ/mm) = Power (kW) divided by travel speed
(mm/s). Rearranging: Power = Heat Input × Travel Speed = 1.5 × 4 = 6.0
kW. Heat input calculations are essential for controlling microstructure
and mechanical properties in welding.
4. Determine the value of x in the equation 3x² − 12x + 9 = 0.
A) x = 1 or x = 3
B) x = −1 or x = −3
C) x = 2 or x = 4
D) x = 0 or x = 6
Answer: A
Rationale: Factoring: 3(x² − 4x + 3) = 3(x − 1)(x − 3) = 0. Therefore x = 1
or x = 3. Quadratic equations appear in thermal expansion calculations
and stress-strain relationships.
5. If sin θ = 0.8 and θ is in the first quadrant, what is the value of cos θ?
A) 0.2
B) 0.4
AWS CWEng Part 1 — Fundamentals of Science and Mathematics
Exam QUESTIONS AND CORRECT ANSWERS LATEST UPDATE THIS
YEAR
AWS CWEng Part 1 — Fundamentals of Science and Mathematics
Summarized Exam Coverage
Exam Format: 35 multiple-choice questions, closed-book, 2 hours, 60%
passing score required .
Domain Weighting: Mathematics (25%), Physics (50%), Chemistry (25%)
.
Mathematics Topics: Simple calculations, special functions (exp, log),
trigonometric functions, algebraic equations (linear, quadratic,
polynomial), graphs and equations (slope, intercept, roots, derivatives),
geometry, hyperbola, parabola, complex numbers, calculus
fundamentals, statistics (normal distribution, mean, standard deviation,
variance), and simple correlation (linear regression, r²) .
, Page 2 of 115
Physics Topics: Unit conversion, mass/weight/volume/density,
force/energy/work/power, stress/strain/Hooke's Law, moment and
momentum, temperature and heat measurement (thermocouples,
pyrometers), thermal properties of materials (conductivity, expansion,
stress) .
Chemistry Topics: Symbols (elements and inorganic compounds),
molecular weight and stoichiometry, acids and bases, balancing
chemical equations, gas combustion reactions, oxidation-reduction
reactions, ideal gas law, mass balance, bulk and chemical analysis
methodologies, reactivity/toxicity/environmental effects .
250 Randomized Multiple-Choice Questions
Questions 1–50: Mathematics
1. A welding engineer calculates the cross-sectional area of a circular
weld nugget with a radius of 12 mm. What is the area in square
millimeters?
A) 144 mm²
B) 226 mm²
C) 452 mm²
D) 1,809 mm²
, Page 3 of 115
Answer: C
Rationale: Area of a circle equals πr². With r = 12 mm, area = π × 144 =
452.39 mm², rounded to 452 mm². This calculation is fundamental for
determining weld cross-sectional area and calculating heat input per
unit length.
2. During a tensile test on a welded specimen, the elongation is
recorded as 22%. If the original gauge length was 50 mm, what is the
final gauge length?
A) 55 mm
B) 61 mm
C) 72 mm
D) 82 mm
Answer: B
Rationale: Final length equals original length multiplied by (1 +
elongation). Therefore, 50 mm × 1.22 = 61 mm. Elongation percentage
is a critical ductility measure for weld qualification and acceptance
criteria in welding codes.
3. A welding procedure requires a heat input of 1.5 kJ/mm. If the travel
speed is 4 mm/s, what is the arc power in kilowatts?
A) 3.0 kW
B) 6.0 kW
, Page 4 of 115
C) 0.375 kW
D) 1.5 kW
Answer: B
Rationale: Heat input (kJ/mm) = Power (kW) divided by travel speed
(mm/s). Rearranging: Power = Heat Input × Travel Speed = 1.5 × 4 = 6.0
kW. Heat input calculations are essential for controlling microstructure
and mechanical properties in welding.
4. Determine the value of x in the equation 3x² − 12x + 9 = 0.
A) x = 1 or x = 3
B) x = −1 or x = −3
C) x = 2 or x = 4
D) x = 0 or x = 6
Answer: A
Rationale: Factoring: 3(x² − 4x + 3) = 3(x − 1)(x − 3) = 0. Therefore x = 1
or x = 3. Quadratic equations appear in thermal expansion calculations
and stress-strain relationships.
5. If sin θ = 0.8 and θ is in the first quadrant, what is the value of cos θ?
A) 0.2
B) 0.4
