Manual_Mathematics_T_2020

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MAJLIS PEPERIKSAAN MALAYSIA

(MALAYSIAN EXAMINATIONS COUNCIL)

PEPERIKSAAN
SIJIL TINGGI PERSEKOLAHAN MALAYSIA (STPM)

(MALAYSIA HIGHER SCHOOL CERTIFICATE EXAMINATION)

Manual for
Mathematics (T) Coursework

Paper 4 (954/4)

STPM 2017

REMINDER:

This manual is specifically for the use of teachers or examiners only and should not be given to
unauthorised persons.

___________________________________________________________________________

This manual consists of 14 printed pages.
© Majlis Peperiksaan Malaysia 2016

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Contents

Part 1: Teacher’s Manual for Mathematics (T) Coursework Page

1. 1 Introduction 1
1.2 Aims 1
1.3 Manual for Coursework 1
1.4 Implementation 1
1.5 Assignment Reports 1
1.6 Assessment 2
1.7 Moderation 2
1.8 Assignment Record 2
1.9 Assessment Criteria 3

Part 2: Student’s Manual for Mathematics (T) Coursework 7
7
2.1 Assignment Reports 8
2.2 Viva
2.3 Assessment criteria
2.4 Assignments

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Part 1: Teacher’s Manual for Mathematics (T) Coursework

1.1 Introduction

This manual consists of the administration of Mathematics (T) coursework.

1.2 Aims

The Mathematics (T) coursework is intended to enable students to carry out mathematical
investigation and mathematical modelling so as to enhance their understanding of mathematical
processes and applications and to develop soft skills.

1.3 Manual for Coursework

1.3.1 The manual contains regulations and guidelines on the conduct and assessment of
coursework which needs to be implemented by the school as well as coursework
assignments.

1.3.2 The school authority is responsible to make copies of Part 2: Student’s Manual for
Mathematics (T) Coursework of this manual to be given to the students.

1.3.3 Students are required to complete the coursework which comprises of three
assignments: Assignment A, Assignment B and Assignment C set down in this manual.
They should carry out these assignments in the respective terms.

1.4 Implementation

1.4.1 Students must carry out each assignment individually. Plagiarism will be penalised.

1.4.2 Teachers must monitor the progress of the students’ coursework. It is, however, not
acceptable for teachers to give detailed suggestions as to how the work may be
improved to meet the assessment criteria. Examples of unacceptable assistance are as
follows:

• detailed indication of errors or omissions

• the provision of detailed outlines, analysis, discussion, or conclusion specific to the
coursework tasks

• personal intervention to improve the presentation or content of the coursework

1.5 Assignment Reports

1.5.1 All assignment reports should follow the specification in Part 2.

1.5.2 The assignment reports should be concise. The table of contents, folders, decoration and
binding are not required. References, if any, should be included at the end of the report
and cited in the texts.

1.5.3 Assignments may be written either in English or Bahasa Melayu.

1.5.4 Each student is required to write the declaration statement to confirm that the
assignment report submitted is his/her own work.

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1.5.5 The teacher is required to set the deadline for the submission of each assignment report
in the specified date.

1.5.6 Once an assignment report is submitted, it is not allowed to be revised or replaced.
Adding or removing of any material to or from the assignment report is prohibited.

1.6 Assessment

1.6.1 Assignment reports are to be marked by the teacher according to the assessment criteria
stipulated in this manual.

1.6.2 The annotation enable the teacher to distinguish as precisely as possible where the
student’s work has met the assessment criteria specified in this manual.

1.6.3 The viva for an assignment should be carried out by the teacher in the relevant term
after the assessment of the assignment reports of all students. The viva should take
about 15 minutes for each student.

1.6.4 The assessment of coursework must be completed four weeks before the STPM
examination for each term.

1.6.5 The student may be given grade ‘X’ for the subject grade for failing to send assignment
report on the specified deadline.

1.7 Moderation

1.7.1 A common standard for marking must be agreed upon if more than one teacher in the
same school is involved in assessing the assignment.

1.7.2 All components of assessment are subjected to moderation by an external moderator
appointed by the Malaysia Examinations Council (MEC). Random samples of
assignment reports may be requested.

1.8 Assignment Record

1.8.1 The teacher is required to record the marks for each assignment report and the viva in
the Assignment Record.

1.8.2 In the event that a student has transferred to another school, the principal of the former
school is responsible to submit the student’s Assignment Record to the principal of the
new school. These records must be certified by the subject teacher of the former school.

1.8.3 The moderator is required to record the marks for the assignment report moderated by
him/her in the Assignment Record.

1.8.4 The total marks for each student must be submitted to MEC via electronic submission
by the specified date.

1.8.5 All the assignment reports and assignment records are evidence, and should be kept and
destroyed under secure conditions six months after the released of the STPM result in
the following year.

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1.9 Assessment Criteria

1.9.1 The assignment reports should be graded based on the assessment criteria below.

Assessment criterion Description Mark Max mark
3−4 4
(a) Introduction Provides sufficient description to 1−2 8
the given problem. 7−8
5−6 10
Provides limited description to 3−4
the given problem. 1−2
9 − 10
Uses correct mathematical 7−8
methods to address the given 5−6
problem. 3−4
1−2
(b) Methodology Uses some correct mathematical
methods to address the given
problem.

Uses limited correct mathematical
methods to address the given
problem.

Uses inappropriate mathematical
methods to address the given
problem.

Performs correct mathematical
calculations to obtain correct
results.

Performs correct mathematical
calculations to obtain some
results.

(c) Results Performs some correct
mathematical calculations to
obtain some results.

Performs some correct
mathematical calculations but
fails to obtain results.

Performs incorrect mathematical
calculations and fails to obtain
results.

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Assessment criterion Description Mark Max mark
5−6
Provides sufficient discussion of
outcomes related to the given
problem.

(d) Conclusion Provides some discussion of 3−4 6
outcomes related to the given
problem.

Provides incorrect discussion of 1−2
outcomes related to the given
problem.

Presents mathematical 11 − 12
information clearly using
appropriate representation,
terminology and notation.

Presents mathematical 9 − 10
information satisfactory using
appropriate representation,
terminology and notation.

(e) Communication Presents mathematical 7−8 12
information satisfactory using 5−6
some appropriate representation,
terminology and notation.

Presents mathematical
information fairly using some
appropriate representation,
terminology and notation.

Presents mathematical 3−4
information fairly using in
appropriate representation,
terminology and notation.

Presents mathematical 1−2
information poorly using
inappropriate representation,
terminology and notation.

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1.9.2 The viva should be carried out based on the assessment criteria below.

Assessment criterion Description Mark Max mark
13 −14
(a) Understanding of Provides complete and correct
the assignment explanations and critical
discussions using appropriate
terminology

Provides complete and correct 11 − 12
explanations using appropriate
terminology

Provides some correct 9 − 10 14
explanations using appropriate 7−8
terminology

Provides some correct
explanations using some
appropriate terminology

Provides few correct explanations 5−6
using some appropriate
terminology

Provides few correct explanations 3−4
using inappropriate terminology

Provides incorrect explanations 1−2
using inappropriate terminology

(b) Communication Presents explanations clearly and 5−6
effectively

Presents explanations 3−4 6
satisfactorily

Presents explanations 1−2
ambiguously or inconsistently

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Assignment Record

MATHEMATICS (T) COURSEWORK
PAPER 4 (954/4) STPM 2017

Session S / I/ C no.
Name of school/ institute
Name of candidate
Centre no./Index no.

Study term Assessment criterion Mark allocated Teacher’s mark Moderator’s mark
Third
First 1. Assignment Report 4
Second (a) Introduction 8
Third (b) Methodology 10
(c) Results 6
(d) Conclusion 12
(e) Communication
14
2. Viva 6
(a) Understanding of the assignment 60
(b) Communication
Total mark 4
8
1. Assignment Report 10
(a) Introduction 6
(b) Methodology 12
(c) Results
(d) Conclusion 14
(e) Communication 6
60
2. Viva
(a) Understanding of the assignment 4
(b) Communication 8
Total mark 10
6
1. Assignment Report 12
(a) Introduction
(b) Methodology 14
(c) Results 6
(d) Conclusion 60
(e) Communication 180

2. Viva
(a) Understanding of the assignment
(b) Communication
Total mark
Overall total mark

*TEACHER’S/EXAMINER’S OR/AND MODERATOR’S DECLARATION

*I/We certify that the marks and details recorded above are correct.

Study term First Second
Teacher’s signature
Name
Date
Hand phone number

Moderator’s signature
Name
Date
Hand phone number

*Delete which is not appropriate.

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Part 2: Student’s Manual for Mathematics (T) Coursework

2.1 Assignment Reports

2.1.1 A complete assignment report should be structured as follows:

(a) Introduction
• description of the problem (including the title)

(b) Methodology
• the application of appropriate method or strategy to address the given
problem
• the generation or collection of relevant data and information, where
appropriate

(c) Results
• mathematical calculations and results with mathematical reasoning
• interpretation of results

(d) Conclusion
• discussion of outcomes

2.1.2 Focus should be on the successful application of appropriate mathematics, not
necessarily difficult techniques. The assignment reports should be written in the passive
voice using correct mathematical language, terminology and notation.

2.1.3 Each student must write the declaration statement and attached to the assignment
report:

Declaration
This is to certify that the assignment report submitted is based on my own work.
Signature:......................................
Name:
I/C Number:
Date:

2.2 Viva

2.2.1 Each student is required to attend a viva session for an assignment in each term
conducted by the subject teacher after the assessment of the assignment reports of all
students.

2.2.2 Students are expected to demonstrate the understanding of the assignments as reflected
in their assignment reports.

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2.3 Assessment criteria

Students will be assessed via the assignment reports and viva based on the assessment criteria
below:

Assessment criterion Mark allocated
1. Assignment Report
4
(a) Introduction 8
(b) Methodology 10
(c) Results 6
(d) Conclusion 12
(e) Communication
2. Viva 14
(a) Understanding of the assignment 6
(b) Communication 60
Total mark

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MAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIA

MAJLIS PEPERIKSAAN MALAYSIA

(MALAYSIAN EXAMINATIONS COUNCIL)

SIJIL TINGGI PERSEKOLAHAN MALAYSIA

(MALAYSIA HIGHER SCHOOL CERTIFICATE)

Instruction to candidates:

This paper consists of three assignments. You will have to complete the tasks for each
assignment in the respective terms.
Term 1: Assignment A - Mathematical Investigation (60 marks)
Term 2: Assignment B - Mathematical Modelling (60 marks)
Term 3: Assignment C - Mathematical Modelling (60 marks)
The maximum marks for this paper is 180.

It is important that you work independently from other candidates and make sure that you
hand in is your unaided work.

Read the tasks carefully to make sure that you understand what is required.

Perform all tasks and make sure that you check your work carefully to ensure that the work
you produce is accurate and correct.

This question paper consist of 4 printed pages. [Turn over
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2.4 Assignments

Assignment A: Function (Investigation)

A function is a relation whereby every input gives a unique (exactly one) output. There are four
possible ways to represent a function; verbally, numerically, visually and algebraically.

1 Discuss, with examples, the differences between a relation and a function.

2 Give at least five different representations of a simple discrete function.

3 Give at least three different representations of a continuous function.

4 Consider the algebraic function

f : x a a(x − b)n + c.

Describe, with sketch graphs, the function f for different values of a, b and c for n = 1, 2 and 3.

5 Repeat task 4 with the trigonometric function

g : x ! asin[n(x −b)]+ c.

6 Repeat task 4 with an exponential or logarithmic function of your own choice.

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Assignment B: Mathematical Modelling

In the applications in science and technology, some definite integrals obtained are difficult to evaluate

by the usual integration techniques. It is a common practice to approximate a definite integral by

integrating the first few terms of the series expansion of the integrand. The period T of a pendulum of

l released α radians with the by T =4 l π 1 dθ ,
2 2 1 − k 2 sin2 θ
∫length
at an angle vertical given g0

where k = sin α and g is the acceleration due to gravity.
2

1 (a) Using the Maclaurin theorem, find the first two non-zero terms in the series expansion

of 1 .
1 − k 2 sin2 θ

(b) Show that the period of the pendulum is given by T1 ≈ 2π ℓ ⎜⎝⎜⎛1 + π2 sin 2 α ⎟⎞⎟⎠ .
g 24 2

( )2 − 1 α
Using binomial expansion of 1 − k 2 sin2 θ 2 , where k ≈ 2 , show that the period of the

pendulum is T2 ≈ 2π ℓ ⎜⎜⎝⎛1 + α2 ⎠⎟⎟⎞ .
g 16

3 Tabulate T1 and T2 for a one meter pendulum, with g =10 m s−2 for different values of α in

each of following cases;

(a) 0.01 ≤ α ≤ 0.50 ,

(b) 1.0 ≤ α ≤ 2.5.

Comment on your results.

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Assignment C: Mathematical Modelling

It is reported that Malaysian youths spend many hours daily to access the social media such as
Facebook and WhatsApp. This phenomenon leads to deterioration of social ties and values.

In this assignment, you are required to conduct a study on the time spent daily by the students in your
school to access the social media.

1 (a) Discuss the various sampling techniques that can be used to collect data.

(b) Choose a suitable sampling technique to collect data on time spent daily (in minutes) for a
random sample of n students.

2 Construct three confidence intervals for the mean time spent daily by students in your school to
access the social media. Interpret your results.

3 Determine whether the average time spent daily by the students in your school to access the
social media is at least three hours.

4 State any assumptions made in Task 2 and Task 3. Discuss the validity of your results.

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