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:

  1. 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.
  2. 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.
  3. Task 1c: Beam deflection:

    • Use the given formula to calculate the percentage change in deflection when the span increases by 2.5%.
  4. Task 1d: Noise level calculation:

    • Calculate the maximum allowable SPL for a new machine given existing SPL data.
  5. 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)