| Level 3 in Advanced Manufacturing Engineering Certificate / Diploma / Extended Diploma |
Assignment Brief
| Student name | Group | ||||
| Qualification Title(s) & Programme number(s) | Level 3 in Advanced Manufacturing Engineering Certificate Diploma Extended Diploma | Course Code | |||
| Unit Title | Further Engineering Mathematics | Unit Code | Unit 6 Issue 4 | ||
| Tutor | Outcome | 2 & 3 | |||
| Date issued to student | As released on Moodle | Hand-in date, time and place | Electronic Submission As specified on Moodle for this group. | ||
| Please refer to your student handbook for academic regulations and assessment guidance. | |||||
| Assignment Title | Matrices and Complex Numbers | Assignment No. | 2 of 3 | ||
| Criteria covered by this assessment | ||||||||||||||||
| Criteria | P 1 | P 2 | P 3 | P 4 | P 5 | P 6 | M 1 | M 2 | M 3 | M 4 | M 5 | M 6 | D 1 | D 2 | D 3 | |
| 1st submission | ||||||||||||||||
| 2nd submission |
| Link to English and Maths (Functional Skills) where applicable. | Refer to unit SOW |
| Prepared by: | Internally Verified by: | Lead Internal Verifier: |
| Date: January 2022 | Date: February 2022 | Date: |
| Internal verifier’s name, signature and date (only where IV is required – refer to IV plan) |
| I understand that plagiarism, which includes copying from the internet, other students’ work or any other source whether referenced or not, will lead to disciplinary action (see FE Regulations). I confirm that the work I am submitting is wholly my own: Student signature: Date: |
Assessor feedback
IMPORTANT NOTE: If the feedback boxes are left blank then specific written feedback against each criterion is provided on your worksheet.
| Outcome 2 – Examine how matrices and determinants can be used to solve engineering problems Outcome 3 – Examine how complex numbers can be used to solve engineering problems | ||
| Assessment criteria | Feedback | |
| P3 | Solve given problems using routine matrices and determinant operations | Feedback is provided on marked ‘Turnitin’ documentation |
| P4 | Solve given problems using routine complex number operations | Feedback is provided on marked ‘Turnitin’ documentation |
| M3 | Solve given problems accurately, using routine and non-routine matrices and determinant operations | Feedback is provided on marked ‘Turnitin’ documentation |
| M4 | Solve given problems accurately using routine and non routine complex number operations | Feedback is provided on marked ‘Turnitin’ documentation |
| D2 | Evaluate, using technically correct language and a logical structure, engineering problems using non routine matrices, determinant and complex operations, whilst solving accurately all the given problems using routine and non routine operations | Feedback is provided on marked ‘Turnitin’ documentation |
| Student feedback (optional): | ||
| Task 1 | Solve given problems using routine matrices and determinant operations (P3) | |
Task 1.1
Using the given matrices:
a) Find A + B
b) Find A – B
c) Find 4A
c) Find the determinant of A
d) Find the inverse of B
Task 1.2
Solve the following simultaneous equation using the inverse matrix method:
| Task 2 | Solve given problems accurately, using routine and non-routine matrices and determinant operations (M3) |
Routine operations were covered in Task 1. The following task covers non-routine operations. Solutions must be fully correct and written in the correct mathematical format, with working clearly laid out in a logical manner
Task 2.1
Using the given matrices:
a) Find A X B
b) Find the determinant of A
Task 2.2
A simultaneous equation in two unknowns is defined as:
- Solve the simultaneous equations using Cramer’s rule
- Solve the simultaneous equations using Gaussian elimination and compare your answers to those obtained in part (a).
| Task 3 | Solve given problems using routine complex number operations (P4) |
Given : A = 1 + 2j B = 3 – 4j
- - A iii) 3B
- ÷ A
| Task 4 | Solve given problems accurately using routine and non routine complex number operations (M4) |
Routine operations were covered in Task 3. The following task covers non-routine operations. Solutions must be fully correct and written in the correct mathematical format, with working clearly laid out in a logical manner
Task 4.1
Given : A = 1 + 2j B = 3 – 4j
- Identify the real and imaginary part of A
- Identify the complex conjugate of A
- Perform the operations below, showing all working in rectangular form.
- A x B ii) B ÷ A
- Convert your answers for i) and ii) to polar forms showing the modulus and argument of each result using the correct engineering notation for each, and ensuring that your results agree with the answers in Task 3.1
- Using De Moivre’s theorem, work out i). (A x B)5 ii). (B ÷ A)5
| Task 5 | Evaluate, using technically correct language and a logical structure, engineering problems using non routine matrices, determinant and complex operations, whilst solving accurately all the given problems using routine and non routine operations (D2) |
Task 5.1
When Kirchhoff ’s laws are applied to an electrical circuit the currents and
are connected by the two loop equations shown. Solve the equations using Gaussian elimination to find the values of currents
and
.
27 =
-26 =
Task 5.2
The diagram below shows a parallel arrangement of two impedances Z1 and Z2, where
Z1 = 1.2+ 5.6j
Z2 = 3.5 – 9.2j
- Determine the total impedance of the circuit giving your answer in Cartesian form
- What is the magnitude of the total impedance?
- If the reactance of the impedance Z1 is increased by 10% , evaluate the effect that this will have on the magnitude of the total impedance.
In Addition to completing tasks 5.1 and 5.2, D1 requires you to:
- Correctly and efficiently manipulate formulae.
- Use mathematical methods and terminology precisely, applying relevant units when working with mathematical expressions that model engineering situations
- Present variables and values correctly and in an appropriate format, for example engineering notation or standard form.
- Perform calculations to specified numerical precision, as specified by the assessor, reflected in working and results written out to specified significant figures or decimal places. Where the significant figures/decimal places required is not specified, results must be written out to sufficient significant figures.
Student checklist (Refer to tasks for full details)
Important note: The purpose of the checklist is to help to ensure you have included all aspects of evidence required by the tasks detailed in the main body of this assignment brief. It is NOT intended as detailed instruction on what you have to do.
| Scenario(s): You are nearing the end of the second year of an engineering apprenticeship and have been moved into the design department of your company to gain further experience. Part of your new job will involve assisting with calculations and the chief designer wants you to check out your mathematical competence by giving you an assignment. | ||
| Outcome 2 – Examine how matrices and determinants can be used to solve engineering problems Outcome 3 – Examine how complex numbers can be used to solve engineering problems | ||
| Tasks (& sub-tasks where applicable): | Student tick when complete | |
| P3 | Solve given problems using routine matrices and determinants | |
| M3 | Solve given problems using non-routine matrices and determinants | |
| P4 | Solve given problems using routine complex number operations | |
| M4 | Solve given problems accurately, using non-routine complex number operations | |
| D2 | Evaluate, using technically correct language and a logical structure, engineering problems using non routine matrices, determinant and complex operations, whilst solving accurately all the given problems using routine and non routine operations |
