Unit 34 Further Mathematics for Construction (M/618/8110) Assignment Brief 2026

Unit 34 Further Mathematics for Construction Assignment Brief

Qualification	Higher National Diploma in Construction and the Built Environment
Module Code	P5E34
Module Title	Further Mathematics for Construction
Unit code	M/618/8110
Unit level	5
Credit value	15

Submission Requirement

Font	Times New Roman
Font Size	12 font
Spacing	Single Line Spacing
Margin	2 cm (Left-side only)
Printing	1-Sided
Number of Words (Approx.)	1) At least 2 pages answer of each question (400-500 words) excluding diagrams or pictures

Learning Outcomes

By the end of this unit, students will be able to:

LO1 Apply instances of number theory in practical construction situations

LO2 Solve systems of linear equations relevant to construction applications using matrix methods

LO3 Approximate solutions of contextualised examples with graphical and numerical methods

LO4 Review models of construction systems using ordinary differential equations.

Assignment Brief and Guidance

Scenario

A multi-disciplinary Engineering Consultancy has contracted you as an Engineering Mathematics tutor
to support the recruits of Apprentice Engineers. They have asked you to produce a workbook for the apprentices.

Part A

Task 1

Complete the following arithmetic and then convert to the identified number system

1011001₂ × 101100₂, convert the answer to Octal number system
4A6₁₆ + 3C4F₁₆ Convert to Denary number system

Task 2

Using complex numbers determine the magnitude and direction of the resultant force for the force system below.

Task 3

P2/P3

A delta-connected impedance ZA of an electrical circuit is given by:

ZA = (Z1Z2 + Z2Z3 + Z3Z1) / Z2

Determine ZA given:

Z1 = (10 + 0i) Ω
Z2 = (0 − 10i) Ω
Z3 = (10 + 10i) Ω

Give your answer in polar, cartesian and exponential form.

Task 4

If z1 = 12∠125° and z2 = 3∠72°

Determine:

z1z2
z1 / z2

Task 5

P2/P3

If v = Ve^i(ωt+α) and i = Ie^i(ωt+β)
then show that the impedance (z) is given by

z = V/I [ cos(α − β) + i sin(α − β) ]

Task 6

An electro mechanical circuit will perform repetitive cycles of operation,
hence the total impedance of the circuit is given by the complex equation.
Simplify this equation to give ZT in cartesian and polar form.

ZT = (3 + 5i)⁵ × (6 + 3.6i)³

Task 7

Check that the following identities are valid using De Moivre’s Theorem:

cos 3θ = cos³θ − 3cosθsin²θ

sin 3θ = 3cos²θsinθ − sin³θ

Task 9

P10

The settlement of soil in a foundation is described by a second-order differential equation.

Find the general solution for the depth of settlement.
Determine the particular solution given the stated boundary conditions.

Task 10

P10

The deflection of a beam under a varying load can be modelled by the differential equation.
Find the general equation for the deflection.

Task 11

P10

In coastal engineering, the behaviour of waves in a medium can be modelled by a differential equation.
Determine a general solution for the equation when:

f(x) = 3cos(kx)

Task 12

P11

Using Laplace transform determine the particular solution for the differential equation
given the boundary condition y(0) = 0.

Task 13

P11

In a building’s heating system, the temperature T(t) of a room is modelled by a second-order differential equation.
Solve using Laplace transforms and determine T(t) given:

T(0) = 20
T'(0) = 5

Task 14

M4/D4

Analyse how first-order differential equations are used to solve structural or environmental problems.
Evaluate first- and second-order differential equations when generating solutions to construction problems.

Learning Outcomes and Assessment Criteria

Pass	Merit	Distinction
LO1 Apply instances of number theory in practical construction situations		D1 Test the correctness of a trigonometric identity using de Moivre’s Theorem.
P1 Apply addition and multiplication methods to numbers that are expressed in different base systems. P2 Solve construction problems using complex number theory.P3 Perform arithmetic operations using the polar and exponential form of complex numbers.	M1 Deduce solutions of problems using de Moivre’s Theorem.
LO2 Solve systems of linear equations relevant to construction applications using matrix methods
P4 Ascertain the determinant of a 3 × 3 matrix. P5 Solve a system of three linear equations using Gaussian elimination.	M2 Determine solutions to a set of linear equations using the inverse matrix method.

Pass	Merit	Distinction
LO3 Approximate solutions of contextualised examples with graphical and numerical methods		D2 Validate all analytical matrix solutions using appropriate computer software.D3 Critique the use of numerical estimation methods, commenting on their applicability and the accuracy of the methods.
P6 Estimate solutions of sketched functions using a graphical estimation method. P7 Identify the roots of an equation using two different iterative techniques.P8 Determine the numerical integral of construction functions using two different methods.	M3 Evaluate construction problems to formulate mathematical models using numerical and graphical methods.
LO4 Review models of construction systems using ordinary differential equations
P9 Determine first-order differential equations using analytical methods. P10 Determine second-order homogeneous and non-homogenous differential equations using analytical methods.P11 Calculate solutions to linear ordinary differential equations using Laplace transforms.	M4 Analyse how first-order differential equations are used to solve structural or environmental problems. D4 Evaluate first- and second-order differential equations when generating the solutions to construction problems.

Recommended Resources

Print resources

BIRD, J. (2017), Higher Engineering Mathematics, Routledge

SINGH, K. (2011), Engineering Mathematics Through Applications, Macmillan International Higher Education

STROUD, K., BOOTH, D. (2001), Engineering Mathematics, Industrial Press Inc.