Applied Trade Mathematics
Applied Trade Mathematics
The Applied Trade Mathematics domain tests practical calculation: perimeter, area, volume, mass, angles, offsets, cut lengths, weld consumption, heat input, and cost. Questions are usually word problems tied to a shop task, so units and rounding matter.
Core rules
- Rectangle: A = L × W; P = 2(L + W). Circle: A = πr²; C = πd. Triangle: A = ½bh.
- Volume: prism = base area × length; cylinder = πr²h. Mass = volume × density. Keep units consistent (mm, cm, m).
- Right triangles: a² + b² = c²; sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent.
- Pipe and plate layouts use centreline lengths, bend allowance, and kerf. Add or subtract kerf depending on whether the dimension is outside or inside.
- Heat input (kJ/mm) = (voltage × current × 60) / (travel speed in mm/min × 1000). Use arc efficiency only if the question supplies it.
- Weld metal volume and consumable weight: volume × density, then allow for deposition efficiency and waste.
Worked example
A weld is made at 25 V and 200 A with a travel speed of 250 mm/min. Heat input = (25 × 200 × 60) / (250 × 1000) = 300,000 / 250,000 = 1.2 kJ/mm. If travel speed doubles to 500 mm/min, heat input halves to 0.6 kJ/mm, assuming voltage and current stay constant. This is why faster travel reduces heat input and can change HAZ hardness and distortion. If the question gives inches per minute, convert to mm/min first (1 in = 25.4 mm).
Traps
- Mixing radius and diameter.
- Using travel speed in in/min without converting.
- Forgetting that heat input is inversely proportional to travel speed.
- Adding kerf when the dimension is already a finished size.
- Rounding too early; carry units through the calculation.
- Using density in kg/m³ with dimensions in mm without converting.