Higher Nationals
Internal verification of assessment decisions – BTEC (RQF)
INTERNAL VERIFICATION – ASSESSMENT DECISIONS
Programme title BTEC Higher National Diploma in Computing
Assessor Internal Verifier
Unit 18 : Discrete Mathematics
Unit(s)
Discrete mathematics in software engineering concepts
Assignment title
Student’s name
List which assessment Pass Merit Distinction
criteria the Assessor has
awarded.
INTERNAL VERIFIER CHECKLIST
Do the assessment criteria awarded match
those shown in the assignment brief? Y/N
Is the Pass/Merit/Distinctiongrade awarded
justified by the assessor’s comments on the
student work? Y/N
Has the work been assessed
accurately? Y/N
Is the feedback to the student:
Give details:
• Constructive? Y/N
Y/N
• Linked to relevant assessment criteria?
• Identifying opportunities for
improved performance?
Y/N
• Agreeing actions?
Y/N
Does the assessment decision need
amending? Y/N
Assessor signature Date
,Internal Verifier signature Date
Programme Leader signature (if
required) Date
, Confirm action completed
Remedial action taken
Give details:
Assessor signature Date
Internal Verifier
signature Date
Programme Leader
signature (if required) Date
Mahela Dissanayake Page | 3
Unit 18- Discrete Mathematics
, Higher Nationals - Summative Assignment Feedback Form
Student Name/ID
Unit Title Unit 18 : Discrete Mathematics
Assignment Number 1 Assessor
Date Received 1st
Submission Date
submission
Date Received 2nd
Re-submission Date
submission
Assessor Feedback:
LO1 Examine set theory and functions applicable to software engineering .
Pass, Merit & Distinction P1 P2 M1 D1
Descripts
LO2 Analyse mathematical structures of objects using graph theory.
Pass, Merit & Distinction P3 P4 M2 D2
Descripts
LO3 Investigate solutions to problem situations using the application of Boolean algebra.
Pass, Merit & Distinction P5 P6 M3 D3
Descripts
LO4 Explore applicable concepts within abstract algebra.
Pass, Merit & Distinction P7 P8 M4 D4
Descripts
Grade: Assessor Signature: Date:
Resubmission Feedback:
Grade: Assessor Signature: Date:
Internal Verifier’s Comments:
Signature & Date:
* Please note that grade decisions are provisional. They are only confirmed once internal and external moderation has taken place and
grades decisions have been agreed at the assessment board.
Mahela Dissanayake Page | 4
Unit 18- Discrete Mathematics
, Pearson
Higher Nationals in
Computing
Unit 18 : Discrete Mathematics
General Guidelines
1. A Cover page or title page – You should always attach a title page to your assignment. Use
previous page as your cover sheet and be sure to fill the details correctly.
2. This entire brief should be attached in first before you start answering.
3. All the assignments should prepare using word processing software.
4. All the assignments should print in A4 sized paper, and make sure to only use one side
printing.
5. Allow 1” margin on each side of the paper. But on the left side you will need to leave room for
binging.
Word Processing Rules
1. Use a font type that will make easy for your examiner to read. The font size should be 12
point, and should be in the style of Times New Roman.
2. Use 1.5 line word-processing. Left justify all paragraphs.
3. Ensure that all headings are consistent in terms of size and font style.
4. Use footer function on the word processor to insert Your Name, Subject, Assignment No,
and Page Number on each page. This is useful if individual sheets become detached for any
reason.
5. Use word processing application spell check and grammar check function to help edit your
assignment.
Mahela Dissanayake Page | 5
Unit 18- Discrete Mathematics
,Important Points:
1. Check carefully the hand in date and the instructions given with the assignment. Late
submissions will not be accepted.
2. Ensure that you give yourself enough time to complete the assignment by the due date.
3. Don’t leave things such as printing to the last minute – excuses of this nature will not be
accepted for failure to hand in the work on time.
4. You must take responsibility for managing your own time effectively.
5. If you are unable to hand in your assignment on time and have valid reasons such as illness,
you may apply (in writing) for an extension.
6. Failure to achieve at least a PASS grade will result in a REFERRAL grade being given.
7. Non-submission of work without valid reasons will lead to an automatic REFERRAL. You will
then be asked to complete an alternative assignment.
8. Take great care that if you use other people’s work or ideas in your assignment, you properly
reference them, using the HARVARD referencing system, in you text and any bibliography,
otherwise you may be guilty of plagiarism.
9. If you are caught plagiarising you could have your grade reduced to A REFERRAL or at worst
you could be excluded from the course.
Mahela Dissanayake Page | 6
Unit 18- Discrete Mathematics
,Student Declaration
I hereby, declare that I know what plagiarism entails, namely to use another’s work and to present it
as my own without attributing the sources in the correct way. I further understand what it means to
copy another’s work.
1. I know that plagiarism is a punishable offence because it constitutes theft.
2. I understand the plagiarism and copying policy of the Edexcel UK.
3. I know what the consequences will be if I plagiaries or copy another’s work in any of the
assignments for this program.
4. I declare therefore that all work presented by me for every aspects of my program, will be my
own, and where I have made use of another’s work, I will attribute the source in the correct
way.
5. I acknowledge that the attachment of this document signed or not, constitutes a binding
agreement between myself and Edexcel UK.
6. I understand that my assignment will not be considered as submitted if this document is not
attached to the attached.
Student’s Signature: Date:
(Provide E-mail ID) (Provide Submission Date)
Mahela Dissanayake Page | 7
Unit 18- Discrete Mathematics
,Assignment Brief
Student Name /ID Number
Unit Number and Title Unit 18 :Discrete Mathematics
Academic Year
Unit Tutor
Assignment Title Discrete mathematics in Computing
Issue Date
Submission Date
IV Name & Date
Submission Format:
Mahela Dissanayake Page | 8
Unit 18- Discrete Mathematics
, This assignment should be submitted at the end of your lesson, on the week stated at the front of this brief.
The assignment can either be word-processed or completed in legible handwriting.
If the tasks are completed over multiple pages, ensure that your name and student number are present on
each sheet of paper.
Unit Learning Outcomes:
LO1 Examine set theory and functions applicable to software engineering
LO2 Analyse mathematical structures of objects using graph theory
LO3 Investigate solutions to problem situations using the application of Boolean algebra
LO4 Explore applicable concepts within abstract algebra.
Assignment Brief and Guidance:
Activity 01
Part 1
1. Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and A∩B are
72, 28 and 13 respectively, find the cardinality of the set A∪B .
2. If n( A−B )=45, n( A∪B )=110 and n( A∩B )=15, then find n(B).
3. If n(A)=33, n(B)=36 and n(C)=28, find n( A∪B∪C ).
Mahela Dissanayake Page | 9
Unit 18- Discrete Mathematics
, Part 2
1. Write the multisets of prime factors of given numbers.
I. 160
II. 120
III. 250
2. Write the multiplicities of each element of multisets in part 2(1-I,ii,iii) separately.
3. Find the cardinalities of each multiset in part 2-1.
Part 3
1. Determine whether the following functions are invertible or not. If it is invertible, then find
−1
the rule of the inverse ( f ( x ) )
i . f : ℜ→ℜ+ ii . f : ℜ+ → ℜ+
1
f ( x )=x 2 f ( x )=
x
−π π
iii . f : ℜ+ → ℜ+ iv. f : [ ,
2 2 ]
→ [ −1, 1 ]
f ( x )=x 2 f ( x )=sin x
v . f : [ 0 , π ] →[ −2, 2 ]
f ( x )=2 cos x
5
f (x )= (x −32)
2. Function 9 converts Fahrenheit temperatures into Celsius. What is the
function for opposite conversion?
Part 4
Mahela Dissanayake Page | 10
Unit 18- Discrete Mathematics
Internal verification of assessment decisions – BTEC (RQF)
INTERNAL VERIFICATION – ASSESSMENT DECISIONS
Programme title BTEC Higher National Diploma in Computing
Assessor Internal Verifier
Unit 18 : Discrete Mathematics
Unit(s)
Discrete mathematics in software engineering concepts
Assignment title
Student’s name
List which assessment Pass Merit Distinction
criteria the Assessor has
awarded.
INTERNAL VERIFIER CHECKLIST
Do the assessment criteria awarded match
those shown in the assignment brief? Y/N
Is the Pass/Merit/Distinctiongrade awarded
justified by the assessor’s comments on the
student work? Y/N
Has the work been assessed
accurately? Y/N
Is the feedback to the student:
Give details:
• Constructive? Y/N
Y/N
• Linked to relevant assessment criteria?
• Identifying opportunities for
improved performance?
Y/N
• Agreeing actions?
Y/N
Does the assessment decision need
amending? Y/N
Assessor signature Date
,Internal Verifier signature Date
Programme Leader signature (if
required) Date
, Confirm action completed
Remedial action taken
Give details:
Assessor signature Date
Internal Verifier
signature Date
Programme Leader
signature (if required) Date
Mahela Dissanayake Page | 3
Unit 18- Discrete Mathematics
, Higher Nationals - Summative Assignment Feedback Form
Student Name/ID
Unit Title Unit 18 : Discrete Mathematics
Assignment Number 1 Assessor
Date Received 1st
Submission Date
submission
Date Received 2nd
Re-submission Date
submission
Assessor Feedback:
LO1 Examine set theory and functions applicable to software engineering .
Pass, Merit & Distinction P1 P2 M1 D1
Descripts
LO2 Analyse mathematical structures of objects using graph theory.
Pass, Merit & Distinction P3 P4 M2 D2
Descripts
LO3 Investigate solutions to problem situations using the application of Boolean algebra.
Pass, Merit & Distinction P5 P6 M3 D3
Descripts
LO4 Explore applicable concepts within abstract algebra.
Pass, Merit & Distinction P7 P8 M4 D4
Descripts
Grade: Assessor Signature: Date:
Resubmission Feedback:
Grade: Assessor Signature: Date:
Internal Verifier’s Comments:
Signature & Date:
* Please note that grade decisions are provisional. They are only confirmed once internal and external moderation has taken place and
grades decisions have been agreed at the assessment board.
Mahela Dissanayake Page | 4
Unit 18- Discrete Mathematics
, Pearson
Higher Nationals in
Computing
Unit 18 : Discrete Mathematics
General Guidelines
1. A Cover page or title page – You should always attach a title page to your assignment. Use
previous page as your cover sheet and be sure to fill the details correctly.
2. This entire brief should be attached in first before you start answering.
3. All the assignments should prepare using word processing software.
4. All the assignments should print in A4 sized paper, and make sure to only use one side
printing.
5. Allow 1” margin on each side of the paper. But on the left side you will need to leave room for
binging.
Word Processing Rules
1. Use a font type that will make easy for your examiner to read. The font size should be 12
point, and should be in the style of Times New Roman.
2. Use 1.5 line word-processing. Left justify all paragraphs.
3. Ensure that all headings are consistent in terms of size and font style.
4. Use footer function on the word processor to insert Your Name, Subject, Assignment No,
and Page Number on each page. This is useful if individual sheets become detached for any
reason.
5. Use word processing application spell check and grammar check function to help edit your
assignment.
Mahela Dissanayake Page | 5
Unit 18- Discrete Mathematics
,Important Points:
1. Check carefully the hand in date and the instructions given with the assignment. Late
submissions will not be accepted.
2. Ensure that you give yourself enough time to complete the assignment by the due date.
3. Don’t leave things such as printing to the last minute – excuses of this nature will not be
accepted for failure to hand in the work on time.
4. You must take responsibility for managing your own time effectively.
5. If you are unable to hand in your assignment on time and have valid reasons such as illness,
you may apply (in writing) for an extension.
6. Failure to achieve at least a PASS grade will result in a REFERRAL grade being given.
7. Non-submission of work without valid reasons will lead to an automatic REFERRAL. You will
then be asked to complete an alternative assignment.
8. Take great care that if you use other people’s work or ideas in your assignment, you properly
reference them, using the HARVARD referencing system, in you text and any bibliography,
otherwise you may be guilty of plagiarism.
9. If you are caught plagiarising you could have your grade reduced to A REFERRAL or at worst
you could be excluded from the course.
Mahela Dissanayake Page | 6
Unit 18- Discrete Mathematics
,Student Declaration
I hereby, declare that I know what plagiarism entails, namely to use another’s work and to present it
as my own without attributing the sources in the correct way. I further understand what it means to
copy another’s work.
1. I know that plagiarism is a punishable offence because it constitutes theft.
2. I understand the plagiarism and copying policy of the Edexcel UK.
3. I know what the consequences will be if I plagiaries or copy another’s work in any of the
assignments for this program.
4. I declare therefore that all work presented by me for every aspects of my program, will be my
own, and where I have made use of another’s work, I will attribute the source in the correct
way.
5. I acknowledge that the attachment of this document signed or not, constitutes a binding
agreement between myself and Edexcel UK.
6. I understand that my assignment will not be considered as submitted if this document is not
attached to the attached.
Student’s Signature: Date:
(Provide E-mail ID) (Provide Submission Date)
Mahela Dissanayake Page | 7
Unit 18- Discrete Mathematics
,Assignment Brief
Student Name /ID Number
Unit Number and Title Unit 18 :Discrete Mathematics
Academic Year
Unit Tutor
Assignment Title Discrete mathematics in Computing
Issue Date
Submission Date
IV Name & Date
Submission Format:
Mahela Dissanayake Page | 8
Unit 18- Discrete Mathematics
, This assignment should be submitted at the end of your lesson, on the week stated at the front of this brief.
The assignment can either be word-processed or completed in legible handwriting.
If the tasks are completed over multiple pages, ensure that your name and student number are present on
each sheet of paper.
Unit Learning Outcomes:
LO1 Examine set theory and functions applicable to software engineering
LO2 Analyse mathematical structures of objects using graph theory
LO3 Investigate solutions to problem situations using the application of Boolean algebra
LO4 Explore applicable concepts within abstract algebra.
Assignment Brief and Guidance:
Activity 01
Part 1
1. Let A and B be two non-empty finite sets. If cardinalities of the sets A, B, and A∩B are
72, 28 and 13 respectively, find the cardinality of the set A∪B .
2. If n( A−B )=45, n( A∪B )=110 and n( A∩B )=15, then find n(B).
3. If n(A)=33, n(B)=36 and n(C)=28, find n( A∪B∪C ).
Mahela Dissanayake Page | 9
Unit 18- Discrete Mathematics
, Part 2
1. Write the multisets of prime factors of given numbers.
I. 160
II. 120
III. 250
2. Write the multiplicities of each element of multisets in part 2(1-I,ii,iii) separately.
3. Find the cardinalities of each multiset in part 2-1.
Part 3
1. Determine whether the following functions are invertible or not. If it is invertible, then find
−1
the rule of the inverse ( f ( x ) )
i . f : ℜ→ℜ+ ii . f : ℜ+ → ℜ+
1
f ( x )=x 2 f ( x )=
x
−π π
iii . f : ℜ+ → ℜ+ iv. f : [ ,
2 2 ]
→ [ −1, 1 ]
f ( x )=x 2 f ( x )=sin x
v . f : [ 0 , π ] →[ −2, 2 ]
f ( x )=2 cos x
5
f (x )= (x −32)
2. Function 9 converts Fahrenheit temperatures into Celsius. What is the
function for opposite conversion?
Part 4
Mahela Dissanayake Page | 10
Unit 18- Discrete Mathematics
