BTEC Unit 4002 (A/651/0708) Assignment Brief
| Programme Title | Pearson BTEC Level 4 Higher National Diploma in Electrical and Electronic Engineering for England Pearson BTEC Higher National Diploma in Electrical and Electronic Engineering for England: 610/1222/1 |
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| Student Name/ID Number | |
| Unit Number and Title | 4002: Engineering Mathematics (A/651/0708) Level 4 / 15 Credits |
| Academic Year | 2025-2026 |
| Unit Tutor | |
| Assignment Title | Assignment 1 – Mathematical Methods and Applications of Statistical & Probability Techniques |
| Issue Date | 14/01/2026 |
| Submission Date | 27/02/2026 |
| Submission Format | Written report with correct calculations and working out shown. |
| Unit Learning Outcomes | LO1. Apply a variety of mathematical concepts to a range of engineering and manufacturing sector problems.
LO2. Investigate applications of statistical & probability techniques to interpret, organise, and present data. |
| 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 Highfields GreenTech Manufacturing Ltd, a company specialising in sustainable energy systems. The company is developing a new wind turbine prototype and needs mathematical analysis to support design, quality assurance and performance prediction.
You have been asked to prepare a technical report that applies mathematical and statistical methods to real engineering data and problems. |
| Recommended Resources | Please note that the resources listed are examples for you to use as a starting point in your research – the list is not definitive. |
Assignment Activity and Guidance
Task 1
The wind turbine blade length L is given by the formula:
L = k · (P1/2) / (ρ1/2 · V3/2) where P is power output, ρ is air density, V is wind speed, and k is a dimensionless constant.
Use dimensional analysis to confirm the consistency of the formula and determine the dimensions of k.
Task 2
The turbine’s maintenance costs over 5 years are modelled as an arithmetic progression: Year 1 = £800, increasing by £120 each year.
Task: Calculate total maintenance costs over 5 years.
The efficiency of the turbine improves each year by 5% of the previous year’s value (geometric progression). If Year 1 efficiency is 82%, calculate efficiency in Year 5.
Task 3
- The voltage output from the turbine is modelled by:V(t) = 240 sin(100π t) + 50 e–0.1tFind V(0.01) and solve for t when V(t) = 200.
- The current output from the turbine is modelled by:I(t) = 5 e–0.4tDetermine the time t when the current falls to 1 A.
- The displacement of one of the cables in the turbine is modelled by the equation:cosh(2x) = 5Solve the equation for x.
Task 4
You are given weekly energy output (in kWh) for 10 turbines:
[420, 435, 410, 440, 430, 425, 438, 415, 442, 428]
Calculate mean, mode, median, and standard deviation. Present the data in a histogram.
Task 5
Faults in the turbine electronic controller occur at an average rate of 2 per month (Poisson).
Calculate probability of exactly 3 faults in a month.
If 10 turbines are tested, and each has a 95% chance of passing quality check (binomial), find probability at least 8 pass.
Blade length is normally distributed with mean 3.2m and SD 0.15m. Find probability a blade is between 3.0m and 3.4m.
Task 6
- An AC motor drive connected to the wind turbine is supplied from a 50 Hz source. The circuit contains resistance and inductance, causing the voltage and current to be out of phase.
If the AC circuit consists of:- Resistance R = 12 Ω
- Inductive reactance XL = 9 Ω
- Supply voltage is: V = 230 ∠ 0° V
a. Calculate the magnitude of the current.
b. Justify the method used. - The wind turbine frame supports loads at multiple mounting points. Forces must be balanced to prevent structural deformation and premature failure.
The loads F1, F2, F3 must satisfy:F1 + F2 + F3 = 18 kN2F1 + F2 = 10 kNF2 + 3F3 = 14 kN
a. Write the system in matrix form.
b. Solve the system to determine the load carried by each column.
c. Justify the method used. - The vertical profile of a suspended cable is modelled by:y(x) = a cosh(x/a)where a = 40 m
x is the horizontal distance from the lowest point.
a. Calculate the cable height at x = 20 m.
b. Explain why hyperbolic functions are used.
Task 7
Claim: New blade material increases average output to above 430 kWh. Sample data (12 turbines): mean = 432 kWh, SD = 8 kWh.
Perform a t-test at 5% significance, state H0 and H1, and interpret the result in an engineering context.
Task 8
Using the energy output data from Task 4, create a one-page visual summary for management. Include:
a. A bar chart comparing turbine performance.
b. A summary table of key statistics.
c. A short paragraph explaining trends and recommendations.
Learning Outcomes and Assessment Criteria
| LO1. Apply a variety of mathematical concepts to a range of engineering and manufacturing sector problems. LO2. Investigate applications of statistical & probability techniques to interpret, organise, and present data. |
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| Pass | Merit | Distinction |
| 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. P4. Investigate engineering data by calculating mean, mode, median, and standard deviation. P5. Calculate probabilities within Poisson, binomially and normally distributed engineering random variables. |
M1. Use three mathematical concepts to solve engineering/manufacturing problems, justifying your chosen methods.
M2. Conduct an engineering hypothesis test and interpret the results. |
D1. Present data as meaningful information using appropriate methods that can be understood by a non-technical audience. |
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