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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 2016

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 2015

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Contents

Page

Part 1: Teachers Manual for Mathematics (T) Coursework

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: Students Manual for Mathematics (T) Coursework

2.1 Assignment Reports 7

2.2 Viva 7

2.3 Assessment criteria 8

2.4 Assignments

RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016

Part 1: Teachers 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: Students 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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RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016 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

students 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 students 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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RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016 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

(a) Introduction

Provides sufficient description to the given problem. 3 4

4 Provides limited description to the given problem. 1 2

(b) Methodology

Uses correct mathematical methods to address the given problem.

7 8

8

Uses some correct mathematical methods to address the given problem.

5 6

Uses limited correct mathematical methods to address the given problem.

3 4

Uses inappropriate mathematical methods to address the given problem.

1 2

(c) Results

Performs correct mathematical calculations to obtain correct results.

9 10

10

Performs correct mathematical calculations to obtain some results.

7 8

Performs some correct mathematical calculations to obtain some results.

5 6

Performs some correct mathematical calculations but fails to obtain results.

3 4

Performs incorrect mathematical calculations and fails to obtain results.

1 2

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Assessment criterion Description Mark Max mark

(d) Conclusion

Provides sufficient discussion of outcomes related to the given problem.

5 6

6 Provides some discussion of outcomes related to the given problem.

3 4

Provides incorrect discussion of outcomes related to the given problem.

1 2

(e) Communication

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

11 12

12

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

9 10

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

7 8

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

5 6

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

3 4

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

1 2

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RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016 1.9.2 The viva should be carried out based on the assessment criteria below.

Assessment criterion Description Mark Max mark

(a) Understanding of the assignment

Provides complete and correct explanations and critical discussions using appropriate terminology

13 14

14

Provides complete and correct explanations using appropriate terminology

11 12

Provides some correct explanations using appropriate terminology

9 10

Provides some correct explanations using some appropriate terminology

7 8

Provides few correct explanations using some appropriate terminology

5 6

Provides few correct explanations using inappropriate terminology 3 4

Provides incorrect explanations using inappropriate terminology 1 2

(b) Communication Presents explanations clearly and effectively 5 6

6 Presents explanations satisfactorily 3 4

Presents explanations ambiguously or inconsistently 1 2

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Assignment Record

MATHEMATICS (T) COURSEWORK PAPER 4 (954/4) STPM 2016

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

Study term Assessment criterion Mark allocated Teachers mark Moderators mark

First

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

Total mark 60

Second

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

Total mark 60

Third

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

Total mark 60 Overall total mark 180

*TEACHERS/EXAMINERS OR/AND MODERATORS DECLARATION

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

Study term First Second Third Teachers signature Name Date Hand phone number Moderators signature Name Date Hand phone number

*Delete which is not appropriate.

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Part 2: Students 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 (a) Introduction 4 (b) Methodology 8 (c) Results 10 (d) Conclusion 6 (e) Communication 12 2. Viva (a) Understanding of the assignment 14 (b) Communication 6 Total mark 60

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MAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAY SIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAM

AJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIA

MAJLIS PEPERIKSAAN MALAYSIA (MALAYSIAN EXAMINATIONS COUNCIL)

SIJIL TINGGI PERSEKOLAHAN MALAYSIA

(MALAYSIA HIGHER SCHOOL CERTIFICATE)

Instruction to candidates:

This question paper consist of 4 printed pages.

Majlis Peperiksaan Malaysia 2015

MAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIAMAJLISPEPERIKSAANMALAYSIA

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954/4 STPM 2016 MATHEMATICS (T)

COURSEWORK

PAPER 4

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 Modelling (60 marks)

Term 2: Assignment B - Mathematical Investigation (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 needed. Carry out all tasks and make sure that you check your work carefully to ensure that the work you produce is accurate and correct.

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RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016 2.4 Assignments Assignment A: Mathematical Modelling Parametric equations express a set of related quantities as explicit functions of an independent variable, known as a parameter. An equation, relating variables x and y in Cartesian coordinates, can be expressed by parametric equations which describe a position on the curve. 1 The parametric equations of a plane curve are defined by

x = et, y = t2 1, 2 t 2. Tabulate the values t, x and y, and plot the curve. 2 (a) Find three sets of parametric equations for the curve whose equation is (y 1)2 = x 49. (b) Is it possible to choose x = t2 as the parametric equation for x? Can you start with any choice for the parametric equation for x?

(c) Can you start with any choice for the parametric equation for y? 3 Suppose that the position of a particle at time t is given by

x1 = 2 sin t, y1 = 3 cos t, 0 t 2, and the position of another particle is given by

x2 = cos t 2, y2 = 1 + sin t, 0 t 2, (a) Sketch the paths of the particles on the same coordinate axes.

(b) How many points of intersection are there?

(c) Determine whether there is any point where the particles collide.

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RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016 Assignment B: Mathematical Investigation The concept of a limit plays a central role in calculus. For example, continuity, derivative and integral require this concept. In this assignment, you are required to explore the concept of a limit. 1 (a) Draw an equilateral triangle inscribed in a circle of radius x cm. Express the area of the triangle A3 in term of x.

(b) Repeat 1(a) with square, regular pentagon, regular hexagon, , regular polygon with n sides in the circle of radius x cm.

(c) Determine the value of 2nA

x correct to three decimal places when n is large.

2 A function f is defined by (x) = k fk1

(1 ) xkx+ . (a) (i) Tabulate the values x and f1(x) when x equals to 0.1, 0.01, 0.001, . Deduce value of

f1(x). 0

limx

(ii) Tabulate the values x and f (x) for k = 2, 3 and 4, when x equals to 0.1, 0.01, 0.001, . Deduce value of fk (x).

k

0limx

(b) Show that ( )10

lim 1 lim 1x

xx x

k kxx

+ = + .

3 A function g is defined by g(t) = 1

1 d ,( 1)

t

xx x + where t > 1. (a) Suppose t is an integer, estimate g(t) using the trapezium rule with

(i) t 1 strips, (ii) 2(t 1) strips, (iii) 4(t 1) strips. In each case, express g(t) in terms of and determine g(t). t lim

t

(b) Suppose t is a real number, find g(t) using integration and determine g(t). limt

(c) Comment on your findings.

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RESTRICTED MATHEMATICS (T) COURSEWORK STPM 2016 Assignment C: Mathematical Modelling Parents often wonder how tall their kids would be. Would they be short, average, or tall? Is height inherited? The height, in cm, of a person can be predicted from ones parents heights using the following formulae:

For girl: 12

(fathers height + mothers height) 6.35

For boy: 12

(fathers height + mothers height) + 6.35

1 (a) Select a random sample of 50 upper secondary students of the same gender from your school. Describe how to ensure the randomness of your sample.

(b) Record the heights of the students and their parents in centimeters. 2 Determine suitable confidence intervals for the mean height of the students using a normal distribution. Interpret your results. 3 (a) Calculate the predicted heights of the students based on of the formulae given above.

(b) Classify the predicted heights into three categories (short, average and tall). 4 (a) Carry out a suitable hypothesis test to determine whether the students actual heights can be modeled by the predicted heights by category.

(b) What can you say about the formula given?

(c) Comment on whether the height of a person is inherited from ones parents.

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SIJIL TINGGI PERSEKOLAHAN MALAYSIA (STPM)STPM 2016PagePart 1: Teachers Manual for Mathematics (T) Coursework11111 1.6 Assessment 2 1.7 Moderation

223Part 2: Students Manual for Mathematics (T) Coursework

1.3 Manual for Coursework1.5 Assignment Reports 1.6 Assessment

Assessment criterionAssessment criterionAssessment criterion