Engineering Mathematics I: Applied Scenario Worksheet Level 6

Introduction and Purpose

In professional electrical engineering, mathematical knowledge is not applied in isolation; it must support real-world problem solving, system design, maintenance, and compliance.

This worksheet allows learners to:

• Apply mathematical reasoning in realistic electrical engineering scenarios.
• Link theoretical knowledge of calculus, algebra, and trigonometry to workplace tasks.
• Consider UK legislation and industry standards while making practical decisions.
• Develop vocational competence, bridging the gap between classroom learning and fieldwork.

The purpose of this Applied Scenario Worksheet is to give learners hands-on, reflective practice, enabling them to solve problems like a professional engineer would in a real electrical workplace.

Scenario 1: Industrial Motor Control System

Context:

You are an electrical engineer responsible for monitoring a factory motor control system. Operators have reported irregular motor acceleration during startup and occasional overload tripping.

Tasks for Learners:

1. Identify potential causes for the motor behavior using mathematical reasoning:
   • Consider how changes in voltage or load may affect motor acceleration (calculus reasoning).
   • Analyze relationships between system variables such as torque, current, and speed (algebraic reasoning).
   • Examine phase differences in AC supply that could affect motor timing (trigonometric reasoning).
2. Predict how changes in operating conditions could impact motor performance.
3. Link your analysis to relevant UK standards:
   • BS 7671 – for load distribution and wiring compliance.
   • o Electricity at Work Regulations – for safe operation during testing and adjustment.
4. Reflect on workplace actions:
   o What steps would you take to correct the problem safely?
   o How would you document observations and actions for audit and compliance?

Discussion Prompt:

• How does applying calculus and algebra reasoning support fault detection before physical intervention?
• How does considering phase angles using trigonometry help prevent motor damage?

Scenario 2: Commercial Lighting Installation

Context:

You are tasked with supervising the installation of a commercial office lighting system. Multiple circuits are planned, and there is concern about uneven load distribution and flickering lights.

Tasks for Learners:

1. Use algebra reasoning to logically assess current distribution across circuits.
2. Apply trigonometry reasoning to consider phase alignment in AC circuits to prevent flicker.
3. Use predictive reasoning (calculus conceptually) to anticipate potential load issues during peak operating hours.
4. Ensure compliance with UK regulations:
   • BS 7671 – for circuit safety and load planning.
   • Part P Building Regulations – for safe and inspected electrical installations.
   • Health and Safety at Work Act – to prevent workplace hazards during installation.
5. Reflective Questions:
   • How would you communicate your analysis to the installation team?
   • What preventative measures can be taken to ensure long-term performance and compliance?

Workplace Competency Focus:

• Observational skills, reasoning, and compliance awareness.
• Predictive planning to avoid common installation issues.

Scenario 3: Battery Backup System for Data Center

Context:

A data center relies on battery backups for emergency power. Engineers have reported rapid voltage drops and inconsistencies during testing cycles.

Tasks for Learners:

1. Apply calculus reasoning to understand how the battery discharge rate affects backup duration.
2. Use algebra reasoning to compare predicted voltage behavior against actual measurements and identify discrepancies.
3. Apply trigonometry reasoning for AC-DC converters, ensuring smooth synchronization with grid supply.
4. Connect analysis to UK regulations and standards:
   • Electricity at Work Regulations – for safe handling during testing.
   • BS 7671 – for integration of backup systems into main distribution.
   • COSHH – if batteries contain hazardous substances.
5. Reflective Questions:
   • How does predicting system behavior support preventative maintenance?
   • What documentation is required to demonstrate compliance and safety?

Workplace Competency Focus:

• Systematic troubleshooting using reasoning.
• Safety-focused decision-making in line with UK regulations.

Scenario 4: Sensor Network in Process Automation

Context:

You are overseeing a sensor network for a chemical plant. Some sensors show delayed readings, causing process alarms.

Tasks for Learners:

1. Identify patterns using trigonometric reasoning to analyze periodic sensor behavior.
2. Apply algebra reasoning to model relationships between sensor inputs and system responses.
3. Conceptually apply calculus reasoning to predict timing adjustments required for accurate process monitoring.
4. Consider UK regulatory compliance:
   • HSWA – to ensure safe sensor testing and maintenance.
   • Electricity at Work Regulations – to handle electrical components safely.
   • BS 7671 – to verify wiring and signal distribution are compliant.
5. Reflective Questions:
   • How do you prioritize which sensors to troubleshoot first?
   • How do mathematical reasoning and compliance standards interact in process safety decisions?

Workplace Competency Focus:

• Applying multi-concept reasoning for complex systems.
• Documenting observations and interventions for regulatory compliance.

Scenario 5: Fault Analysis in Industrial Panel

Context:

An industrial electrical panel is experiencing repeated breaker trips during peak load periods.

Tasks for Learners:

1. Use algebra reasoning to logically deduce which circuits or components could be causing overloads.
2. Apply conceptual calculus reasoning to understand the rate of load increase and predict potential failure points.
3. Consider phase differences (trigonometry reasoning) in AC supply to identify imbalances.
4. Apply UK compliance requirements:
   • BS 7671 – for safe panel operation and load planning.
   • Electricity at Work Regulations – for safe handling during analysis.
   • Health and Safety at Work Act – for worker safety.
5. Reflective Questions:
   • How do these reasoning strategies prevent future breakdowns?
   • What steps would you document to show safe and compliant troubleshooting?

Workplace Competency Focus:

• Problem-solving using multi-layered reasoning.
• Predictive maintenance planning.
• Compliance-focused reporting.

Scenario Analysis Table

Scenario	Mathematical Concept Applied	Workplace Application	UK Regulation	Competency Focus
Motor Control	Calculus, Algebra, Trigonometry	Predict motor behavior, prevent overload	BS 7671, Electricity at Work	Fault analysis, safe operation
Lighting Installation	Algebra, Trigonometry, Predictive Reasoning	Load distribution, prevent flicker	BS 7671, Part P, HSWA	Planning, compliance, observation
Battery Backup	Calculus, Algebra, Trigonometry	Predict discharge, synchronize AC/DC	BS 7671, Electricity at Work, COSHH	Maintenance, safety, documentation
Sensor Network	Algebra, Trigonometry, Calculus	Accurate process readings	HSWA, Electricity at Work, BS 7671	Troubleshooting, prediction, compliance
Industrial Panel	Algebra,Calculus, Trigonometry	Fault detection,overload prevention	BS 7671, Electricity at Work, HSWA	Problem-solving, reporting, preventive planning

Learner Reflection and Task

Task Brief

You are required to demonstrate your ability to perform accurate manual engineering calculations. Instead of writing a report, you must complete Technical Calculation Worksheets and produce Analytical Graphs for two specific workplace scenarios.

Activity 1: Motor Control Analysis (Calculus & Graphs)

• Context: Refer to Scenario 1: Industrial Motor Control System. The motor is overheating due to a high rate of current rise during startup.
• Worksheet Requirement (Calculus):
  • Given the current equation I (t) = 100(1 – e-t/ T)
  • use Calculus (differentiation) to calculate the Rate of Change at time
  • Determine the time constant required keeping the rate of rise below a safe threshold.
• Graphing Requirement:
  • Produce a Graph/Chart plotting Current (A) vs. Time (s) for the startup phase.
  • Visually identify and annotate the point where the acceleration stabilizes.

Activity 2: Battery Backup Discharge (Algebra & Analytical Interpretation)

• Context: Refer to Scenario 3: Battery Backup System. You need to verify if the battery bank can support the data center load for the required 3-hour statutory period.
• Worksheet Requirement (Algebra):
  • Use Algebraic equations to calculate the total energy capacity (kWh) required vs. the actual capacity of the battery bank.
  • Calculate the specific Voltage Drop across the DC bus bars at full load current.
• Analytical Interpretation:
  • Compare your calculated values against the manufacturer’s data sheet. Provide a brief Analytical Interpretation (100-200 words) summarizing whether the system is compliant or if it needs re-sizing.

Submission Guidelines / Evidence for Portfolio

To achieve the credits for this unit, you must upload the following specific evidence to your learner portal. Ensure these are distinct from previous submissions:

Evidence Type: “Algebraic, trigonometric, and calculus calculation worksheets”