Math Problem Statement
1.0 unit-15-further-math - AS 01 24-25.pdf
237.22 KB
Solution
The document appears to be a BTEC assignment brief for "Further Mathematics in Construction." It includes multiple mathematical problems related to construction engineering, requiring algebraic and trigonometric techniques. Here’s a breakdown of the key tasks:
Tasks Overview:
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Task 1a: Solve construction-related problems:
- Calculate the perimeter and area of a site based on a given shape.
- Determine the volume of soil for a ditch with specified dimensions.
- Calculate the height of a mobile phone mast using trigonometry.
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Task 1b: Beam design problems:
- Find the centroidal axes for given sections (I Section and Unequal Angle).
- Identify the neutral axis on diagrams.
- Calculate the moment of inertia and section modulus.
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Task 1c: Beam deflection:
- Use the given formula to calculate the percentage change in deflection when the span increases by 2.5%.
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Task 1d: Noise level calculation:
- Calculate the maximum allowable SPL for a new machine given existing SPL data.
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Evidence:
- Provide a detailed report with clear calculations, supported by diagrams where necessary.
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Math Problem Analysis
Mathematical Concepts
Algebra
Trigonometry
Geometry
Statics
Formulas
Area and perimeter of polygons
Volume of a prism
Trigonometric height calculation
Centroid calculation for sections
Moment of inertia formula
Beam deflection formula: δ = (5wL⁴) / (384EI)
Sound Pressure Level (SPL) calculation
Theorems
Trigonometric identities
Parallel axis theorem for moment of inertia
Suitable Grade Level
Undergraduate (Civil Engineering Level 1-2)
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