Unit 4002 Engineering Mathematics (A/651/0708) Assignment Brief 2026
Unit 4002 Assignment Brief
| Programme Title | Pearson BTEC Level 4 Iligher National Diploma in Electrical and Electronic Engineering for England
Pearson BTEC Iligher National Diploma in Electrical and Electronic Engineering for England: 610/1222/1 Pearson BTEC Higher National Certificate in Mechanical Engineering for England: 610/1231/2 Pcarson BTEC Iligher National Diploma in Mechanical Engineering for England: Pearson BTEC Iligher National Certificate in Manufacturing Engineering for England: 610/1229/4 Pearson BTEC Higher National Diploma in Manufacturing Engineering for England:610/1230/(). |
| Unit Number | 4002 |
| Unit Title | Engineering Mathematics |
| Unit Reference Number | A/651/0708 |
| Unit Level | 4 |
| Credits | 15 |
| Assignment Title | Assignment 2 — Analytical & Computational Methods and Calculus |
Learning Outcomes
By the end of this unit students will be able to:
LO1 Apply a variety of mathematical methods to a range of engineering and manufacturing sector problems
LO2 Investigate applications of statistical and probability techniques to interpret, organise, and present data
LO3 Use analytical and computational methods for solving engineering and manufacturing sector problems by relating sinusoidal wave and vector functions to their respective applications
LO4 Examine how differential and integral calculus can be used to solve engineering and manufacturing sector problems.
Transferable Skills and Competencies Developed
Cognitive skills – Problem solving, critical thinking / analysis, decision making, effective communication, digital literacy, numeracy.
Intra-personal skills – Plan prioritise, self-management, independent learning.
Vocational Scenario
You work as a Junior Engineer at I lighfields GreenTech Manu [acturing Ltd, a company spectalising In sustainable energy systcnns. Thc conopany is dcvcloping a new wind turbinc prototype and needs tuathetnatical analysis to support design, quality assurance and performancc predict ion.
You have been asked to prepare a technical report that applies mathematical and statistical methods to real engineering data and probletns.
Task 1
In a pneumatic system, a piston oscillates up and down with its position defined as
S = 0.5 sin(3mt) [meters]
a. Find the period time for the piston to finish one cycle.
b. Find the maximum displacement of the piston from the centre point.
c. Write the function of the displacement if the frequency of the oscillation was doubled and maximum displacement halved.
Task 2
In an AC circuit, a resistor and an inductor are connected in series with voltages defined as:
= 15sin(2t)
= 23sin(2t +-)
d. Using addition of vectors, find the total voltage and its phase angle, measured in degrees, with regards to the current.
e. How would the voltage change if a capacitor was added to the circuit connected in series and its voltage is defined as:
= 9sin(2t -E)2
g. Using graph paper or software, sketch the resistor and the inductor’s voltage sinewaves and model their combination. Analyse how the results would vary from the analytical model.
Task 3
System A emits simultaneously two sound signals which are defined mathematically as: = O.5cos(t)
S2 = sin(t) cos(300 )
Systclll B reads the signals as one conibined sound. Using cornponncl angle i(lcntltlcs, find a function of a single wavc read by systetn B which of thc two smcwavcs cmlttcd by systcll)
Task 4
Three different cotnpanies were connpared with regards to their power consumption in thc first year of operation. Their power consun)ption in Megawatts (M W) was recorded and approx Imatcd With the following functions:
Company l: Cl = 21n(M6 10)
Conpny 2: c02 —0.5M 2 + 10M – 8)
Cotnpany 3 : CN = 20si n -M
a, Sketch or present using software, the power consumption of each company between I st and 1 2’h month of operation.
b. Using differential method, determine which company had the highest increase rate (rate of change) in power consumption after 6 months of operation.
c. Using integral calculus, compare the total energy consumed by company 2 and company 3 between the 5 th and the 10th
d. Using higher order derivatives, find when (if ever) in the first 18 months of operation the power consumption of those companies would reach its highest point and when (if ever) in the first 18 months it would be predicted to fall to the minimum.
Task 5
Power consumption of a company tends to grow exponentially in the morning hours following a curve Pm = e 3t (MW) and then starts falling exponentially in the afternoon following a curve pa = 0 • 05t (MW) . using integration methods, formulate prediction how much energy is used in the first 2 hours of the shift and how much would be used in the last 2 hours, considering the shift starts at 8am and finishes at 4pm.
Learning Outcomes and Assessment Criteria
| Pass | Merit | Distinction | ||
| LO1 Apply a variety of mathematical methods to a range of engineering and manufacturing sector problems | LO1 and LO2 | |||
| P1 Apply dimensional analysis techniques to solve complex engineering/manufacturing problems.
P2 Generate answers from engineering arithmetic and geometric progressions. P3 Determine solutions of engineering equations using exponential, logarithmic, trigonometric, and hyperbolic functions. |
M1 Use three mathematical concepts to solve engineering/ manufacturing problems, justifying your chosen methods. | D1 Present data as meaningful information using appropriate methods that can be understood by a nontechnical audience. | ||
| LO2 Investigate applications of statistical and probability techniques to interpret, organise, and present data | ||||
| P4 Investigate engineering data by calculating mean, mode, median, and standard deviation.
P5 Calculate probabilities within Poisson, binomially and normally distributed engineering random variables. |
M2 Conduct an engineering hypothesis test and interpret the results. | |||
| Pass | Merit | Distinction | ||
| LO3 Use analytical and computational methods for solving engineering and manufacturing sector problems by relating sinusoidal wave and vector functions to their respective applications | ||||
| P6 Solve engineering/
manufacturing problems relating to sinusoidal functions. P7 Use appropriate methodology to determine engineering parameters of data represented in vector form. |
M3 Use compound angle identities to combine individual sine waves into a single wave, and illustrate graphically. | D2 Apply engineering mathematical software to confirm the analytical solutions for at least three engineering/ manufacturing problems involving sinusoidal and vector functions. | ||
| LO4 Examine how differential and integral calculus can be used to solve engineering and manufacturing sector problems | ||||
| P8 Examine rates of change for a range of mathematical functions.
P9 Use integral calculus to determine a range of mathematical functions. |
M4 Solve a range of complex engineering/ manufacturing problems using both differential and integral calculus. | D3 Evaluate a range of engineering/ manufacturing problems that involve secondorder derivatives and the concept of maxima and minima. | ||
Engineering Mathematics Assignment Help for BTEC Engineering Students
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