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Mathematical Techniques in a Manufacturing Engineering

MEM30012A – Apply mathematical techniques in a manufacturing engineering or related environment


Instructions to Learner

Assessment instructions


Prior to commencing the assessments, your trainer/assessor will explain each assessment task and the terms and conditions relating to the submission of your assessment task. Please consult with your trainer/assessor if you are unsure of any questions. It is important that you understand and adhere to the terms and conditions, and address fully each assessment task. If any assessment task is not fully addressed, then your assessment task will be returned to you for resubmission. Your trainer/assessor will remain available to support you throughout the assessment process.

Written work

Assessment tasks are used to measure your understanding and underpinning skills and knowledge of the overall unit of competency. When undertaking any written assessment tasks, please ensure that you address the following criteria:

  • Address each question including any sub-points
  • Demonstrate that you have researched the topic thoroughly
  • Cover the topic in a logical, structured manner
  • Your assessment tasks are well presented, well referenced and word processed
  • Your assessment tasks include your full legal name on each and every page.

Active participation

It is a condition of enrolment that you actively participate in your studies. Active participation is completing all the assessment tasks on time.


Plagiarism is taking and using someone else’s thoughts, writings or inventions and representing them as your own. Plagiarism is a serious act and may result in a learner’s exclusion from a course. When you have any doubts about including the work of other authors in your assessment, please consult your trainer/assessor. The following list outlines some of the activities for which a learner can be accused of plagiarism:

  • Presenting any work by another individual as one’s own unintentionally
  • Handing in assessments markedly similar to or copied from another learner
  • Presenting the work of another individual or group as their own work
  • Handing in assessments without the adequate acknowledgement of sources used, including assessments taken totally or in part from the internet.

If it is identified that you have plagiarised within your assessment, then a meeting will be organised to discuss this with you, and further action may be taken accordingly.


Collusion is the presentation by a learner of an assignment as their own that is, in fact, the result in whole or in part of unauthorised collaboration with another person or persons. Collusion involves the cooperation of two or more learners in plagiarism or other forms of academic misconduct and, as such, both parties are subject to disciplinary action. Collusion or copying from other learners is not permitted and will result in a “0” grade and NYC.

Assessments must be typed using document software such as (or similar to) MS Office. Handwritten assessments will not be accepted (unless, prior written confirmation is provided by the trainer/assessor to confirm).

Competency outcome

There are two outcomes of assessments: S = Satisfactory and NS = Not Satisfactory (requires more training and experience).

Once the learner has satisfactorily completed all the tasks for this module the learner will be awarded “Competent” (C) or “Not yet Competent” (NYC) for the relevant unit of competency.

If you are deemed “Not Yet Competent” you will be provided with feedback from your assessor and will be given another chance to resubmit your assessment task(s). If you are still deemed as “Not Yet Competent” you will be required to re-enrol in the unit of competency.

Additional evidence

If we, at our sole discretion, determine that we require additional or alternative information/evidence in order to determine competency, you must provide us with such information/evidence, subject to privacy and confidentiality issues. We retain this right at any time, including after submission of your assessments.


We will treat anything, including information about your job, workplace, employer, with strict confidence, in accordance with the law. However, you are responsible for ensuring that you do not provide us with anything regarding any third party including your employer, colleagues and others, that they do not consent to the disclosure of. While we may ask you to provide information or details about aspects of your employer and workplace, you are responsible for obtaining necessary consents and ensuring that privacy rights and confidentiality obligations are not breached by you in supplying us with such information.



Assessment appeals process

If you feel that you have been unfairly treated during your assessment, and you are not happy with your assessment and/or the outcome as a result of that treatment, you have the right to lodge an appeal. You must first discuss the issue with your trainer/assessor. If you would like to proceed further with the request after discussions with your trainer/assessor, you need to lodge your appeal to the course coordinator, in writing, outlining the reason(s) for the appeal.

Recognised prior learning

Candidates will be able to have their previous experience or expertise recognised on request.

Special needs

Candidates with special needs should notify their trainer/assessor to request any required adjustments as soon as possible. This will enable the trainer/assessor to address the identified needs immediately.



Candidate Details

Assessment – MEM30032A – Produce basic engineering drawings

Please complete the following activities and hand in to your trainer/assessor for marking. This forms part of your assessment for MEM30012A – Apply mathematical techniques in a manufacturing engineering or related environment

Name:              _____________________________________________________________

Email:              _____________________________________________________________


I declare that no part of this assessment has been copied from another person’s work with the exception of where I have listed or referenced documents or work and that no part of this assessment has been written for me by another person. I also understand the assessment instructions and requirements and consent to being assessed.

Signed:             ____________________________________________________________

Date:                ____________________________________________________________

If activities have been completed as part of a small group or in pairs, details of the learners involved should be provided below:

This activity workbook has been completed by the following persons and we acknowledge that it was a fair team effort where everyone contributed equally to the work completed. We declare that no part of this assessment has been copied from another person’s work with the exception of where we have listed or referenced documents or work and that no part of this assessment has been written for us by another person.

Learner 1:        ____________________________________________________________

Signed:             ____________________________________________________________

Learner 2:        ____________________________________________________________

Signed:             ____________________________________________________________

Learner 3:        ____________________________________________________________

Signed:             ____________________________________________________________



Question Assessment:

Q-1 Fill the below mentioned table. Write units and M L T form of the given quantity.

Quantity Base unit Units MLT
mass Kg Kilograms [M]
length M Meter [L]
time S Second [T]
velocity M/s Meter per second [L T-1]
acceleration M/s2 Meter per second squares [L T-2]
area A2 Area Square [L2]
volume A3 Area cube [L3]
force N Newton
[M L T-2]
power W Watt [M L2 T-3]
work J Joule [M L2 T-2]
pressure Pascal Pascal [M L-1 T-2]
current i Ampere I
resistance Ω Ohm ML²T⁻³I⁻².
potential difference V Volt  [M1 L2 T-3 I-1].
Q-2 A number that can be written in the form of p/q is called
A-2 This is known as the Rational Number
Q-3 The product of two rational numbers is
A-3 It always comes out to be a Rational Number
Q-4 Write 5630 in Scientific Notation.
A-4 The 5630 in scientific notation is written in the appropriate number as 5.63 × 103.
Q-5 Write 0.00725 in Scientific Notation.
A-5 This would be written in the appropriate like 7.25 × 10-3.
Q-6 Write 5.75 × 104 in engineering notation.
A-6 This would be written in the appropriate manner of 57.5*103
Q-7 Use approximation and estimation methods to solve:



A-7 7
Q-8 Use the correct order of the algebraic expression and calculate the value of x:

x = 1800 ÷ [10{(12−6) +(24−12)}]

A-8 1620 is the value of x
Q-9 Convert angles from degree to radian and radian to degree.

a)      45 degrees

b)      36 degrees

c)      88 degrees

d)     1.73 radians

e)      2.33 radians

A-9 a) π/4 rad

b) π/5 rad

c) 22π/45 rad

d) 99.129 degrees

e) 133.509 degrees

Q-10 A fence is built around the perimeter of a field. What is the total length of the fence and if Milan want to color the whole ground, how much area that he will need to paint?
A-10 Permitter of field = 2(l+b) =

2(5+10) = 30 m

Area of field= l*b

5*10= 50 m

Q-11 What is the perimeter of this shape?
A-11 Perimeter of this shape is = 8+15+20+10+12+5=  70m
Q-12 Calculate the area of the trapezium:
A-12 The area of the Trapezium is 35 cm
Q-13 Find the area and volume of this square-based pyramid:
A-13 After applying the formula, we have to find out the height i.e., h = 5.45 cm

The volume comes out to be 45.41

Area = A≈84.96

Q-14 Calculate the volume and total surface area of the cone (to 1 decimal place).
A-14 Volume = (1/3) πr²h = 37.68 cm3

Total Surface area = πr(r+l)= 66 cm2

Q-15 Plot the point with cylindrical coordinates (4,,−2) and express its location in rectangular coordinates.




Q-16 Find the height of the glacier.
A-16 Height of Glacier is 14.14
Q-17 Find the slope of the line connecting two dots and angle with the horizontal axis.
A-17 m= (8-2)/(11-3)= 6/8= ¾= 0.75
Q-18 In triangle ABC, B = 21°, C = 46° and AB = 9cm. Solve this triangle using Sine Rule.
A-18 A= 11.517cm

B= 4.484cm.

Q-19 In triangle ABC, B = 60°, C = 60° and AB = 10 cm. Solve this triangle using sine rule.
A-19 So, AC = 20.78 and A= 74 degrees and BC= 20
Q-20 Solve the triangle ABC given C = 40°, b = 23cm and a = 19cm.
A-20 A≈140.45cm²
A-21 X= √1418.143
Q-22 Draw a line passing through (3,3) and (6,12), Find the slope of the line.
A-22 The slope of the line is (m)= 3
Q-23 Find the solution of the equation x + 3y = 20, and 3x – 6y = 30 using graph.
A-23 X= 14 and y= 2



Q-24 Find the equation of the line whose slope is 3 and passing through (1,2).
A-24 C= -1 and whereas

Y= 3x+(-1)

Y-3x+1= 0

Q-25 Solve the linear equation algebraically and graphically:

4x – 5y = 22, x + 2y = 12

Find the length and midpoint of these lines in the between [0,4]

A-25 X= 8 and y= 2



Q-26 Solve the equation and get the intersection points of the given curves.

y = x + 1, y = x2 – 1.

A-26 The point of intersection is (2,3) and (1,2).
Q-27 y = -x2 + 4 and y = c, If the system above has exactly one solution, what is the value of c?
A-27 C= -x2+4=

At x= 0

C= 4

At x= 1


At x=2

C= -4+4= 0

And so on.

Q-28 Solve the given equation simultaneously.

y = x + 3, y = x2 + 3x.

A-28 At x= ( -3 ) and also y = 0

At x= ( 1 ) and also y = 4

This would become (-3,0) and (1,4).

Q-29 Football: Age of Professional Players How old are professional football players? The 11th Edition of The Pro Football Encyclopaedia gave the following

information. Random sample of pro football player ages in years:

24 23 25 23 30 29 28 26 33 29

24 37 25 23 22 27 28 25 31 29

25 22 31 29 22 28 27 26 23 21

25 21 25 24 22 26 25 32 26 29

Compute the mean, median, and mode of the ages.

A-29 The mean is 26.25, the Median is 25.5 and also Mode is 25.
Q-30 Big Blossom Greenhouse was commissioned to develop an extra large rose for the

Rose Bowl Parade. A random sample of blossoms from Hybrid A bushes yielded

the following diameters (in inches) for mature peak blooms.

2 3 3 8 10 10

Find the sample variance and standard deviation

A-30 The sample variance is 14.

The standard deviation is 3.74

Q-31 Suppose two pizza restaurants advertise a 20-minute average delivery time. We’re starving and both look equally good! However, we know the mean does not tell the entire story!


Let’s assess their standard deviations to choose the restaurant. Imagine we obtain their delivery time data. One restaurant has a SD of 10 minutes while the other has a value of 5. How does this affect deliveries? We can wait upto 30 mins for the food then what will be the probability of getting food after 30 mins.

A-31 Variance is 201

The standard deviation is 14.177



Question assessment checklist – for assessor

This should be used by the trainer/assessor to document the learner’s skills, knowledge and performance as relevant to the unit activity. Indicate in the table below if the learner is deemed satisfactory (S) or not satisfactory (NS) for the activity or if reassessment is required.

Marking checklist Performance Criteria




Yes         No

(Please circle)

Assessor’s comments here:
The learner’s performance was: Not yet satisfactory Satisfactory


Competency record to be completed by assessor

This should be used by the trainer/assessor to document the learner’s skills, knowledge and performance as relevant to the overall unit. Indicate in the table below if the learner is deemed competent or not yet competent for the unit or if reassessment is required.

Learner’s name
Assessor’s name
Unit of Competence

(Code and Title)

Has the learner completed all required assessments to a satisfactory standard?     Yes         No

(Please circle)

Has sufficient evidence and information been provided by the learner to prove their competency across the entire unit?     Yes         No

(Please circle)

Learner is deemed: Not yet competent Competent
If not yet competent, date for re-assessment:           
Comments from trainer/assessor:
Assessor Signature:                                                                              Date: