MATHEMATICS SYLLABUS ADVANCED SUBSIDIARY LEVEL SYLLABUS CODE: 8227

[Pages:33]Republic of Namibia MINISTRY OF EDUCATION, ARTS AND CULTURE

NAMIBIA SENIOR SECONDARY CERTIFICATE (NSSC)

MATHEMATICS SYLLABUS ADVANCED SUBSIDIARY LEVEL

SYLLABUS CODE: 8227 GRADES 12

FOR IMPLEMENTATION IN 2021 FOR FIRST EXAMINATION IN 2021

Ministry of Education, Arts and Culture National Institute for Educational Development (NIED) Private Bag 2034 Okahandja Namibia

? Copyright NIED, Ministry of Education, Arts and Culture, 2020 Mathematics Syllabus Advanced Subsidiary Level Grade 12

ISBN: 978-99945-2-247-7

Printed by NIED Website:

Publication date: December 2020

TABLE OF CONTENTS

1. INTRODUCTION............................................................................................................1 2. RATIONALE ..................................................................................................................2 3. AIMS .............................................................................................................................2 4. ADDITIONAL INFORMATION.......................................................................................3 5. LEARNING CONTENT ...................................................................................................4 6. ASSESSMENT OBJECTIVES ........................................................................................14 7. SCHEME OF ASSESSMENT .........................................................................................15 8. GRADE DESCRIPTIONS ..............................................................................................16 9. LIST OF MATHEMATICAL FORMULAE, NOTATIONS AND OTHER RELEVANT

INFORMATION (MF9) .................................................................................................22

1. INTRODUCTION

The Namibia Senior Secondary Certificate Advanced Subsidiary (NSSCAS) level syllabus is designed as a one-year course leading to examination after completion of the Namibia Senior Secondary Certificate Ordinary (NSSCO) level. The syllabus is designed to meet the requirements of the National Curriculum for Basic Education (NCBE) and has been approved by the National Examination, Assessment and Certification Board (NEACB).

The National Curriculum Guidelines, applicable at the stage of senior secondary education (Grades 10-12) and at equivalent stages of non-formal education, as a part of life-long learning, recognise the uniqueness of the learner and adhere to the philosophy of learnercentred education.

The Namibia National Curriculum Guidelines:

recognise that learning involves developing values and attitudes as well as knowledge and skills;

promote self-awareness and an understanding of the attitudes, values and beliefs of others in a multilingual and multicultural society;

encourage respect for human rights and freedom of speech; provide insight and understanding of crucial "global" issues in a rapidly changing

world which affects quality of life: the AIDS pandemic, global warming, environmental degradation, distribution of wealth, expanding and increasing conflicts, the technological explosion and increased connectivity; recognise that as information in its various forms becomes more accessible, learners need to develop higher cognitive skills of analysis, interpretation and evaluation to use information effectively; seek to challenge and to motivate learners to reach their full potential and to contribute positively to the environment, economy and society.

Thus the Namibia National Curriculum Guidelines should provide opportunities for developing essential skills across the various fields of study. Such skills cannot be developed in isolation and they may differ from context to context according to a field of study. The skills marked with an * are relevant to this syllabus.

The skills are: communication skills * numeracy skills * information skills * problem-solving skills * self-management and competitive skills * social and cooperative skills * physical skills* work and study skills * critical and creative thinking*

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2. RATIONALE

Mathematics is a dynamic, living and cultural product. It is more than an accumulation of facts, skills and knowledge. The learning of mathematics involves conceptual structures, strategies of problem solving and attitudes towards and appreciation of mathematics. Mathematical knowledge and mathematical methods of inquiry constitute an essential part of and contribute to all modern science and engineering.

Todays learners will live and work in an era dominated by computers, by worldwide communication and by a global economy. Mathematics is the key to success in this world where the economy requires workers who are prepared to absorb new ideas, to perceive patterns and to solve unconventional problems.

The senior secondary curriculum strives to prepare learners to function effectively in the 21st century by providing a basis to use mathematics in their personal and professional lives.

3. AIMS

The aims of the syllabus are the same for all learners. These are set out below and describe the educational purposes of a course in Mathematics for the NSSCAS examination. They are not listed in order of priority.

The aims are to enable students to:

1. develop their mathematical knowledge and skills in a way which encourages confidence and provides satisfaction and enjoyment;

2. develop a feel for number and measurement, carry out calculations and understand the significance of the results obtained;

3. develop an understanding of spatial concepts and relationships; 4. develop their ability to apply mathematics, in the contexts of everyday situations and

of other subjects that they may be studying; 5. develop an understanding of mathematical principles; 6. develop their ability to analyse problems logically, recognise when and how a situation

may be represented mathematically, identify and interpret relevant factors and, where necessary, select an appropriate mathematical method to solve the problem; 7. use mathematics as a means of communication with emphasis on the use of clear expression; 8. develop the abilities to reason logically, to classify, to generalise and to prove; 9. experience a sufficiently wide range of mathematical topics and methods so that they can develop their appreciation of the power, elegance and structure of the subject; 10. acquire the mathematical background necessary for further study in this or related subjects.

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4. ADDITIONAL INFORMATION

4.1 Guided learning hours The NSSCAS level syllabuses are designed on the assumption that learners have about 180 guided learning hours per subject over the duration of the course (1 year), but this is for guidance only. The number of hours required to gain the qualification may vary according to local conditions and the learners prior experience of the subject. The National Curriculum for Basic Education (NCBE) indicates that this subject will be taught for 9 periods of 40 minutes each per 7-day cycle, or 6 periods of 40 minutes each per 5-day cycle, over a year. 4.2 Recommended prior learning It is recommended that learners who are beginning this course should have previously completed Mathematics at Namibia Senior Secondary Certificate Ordinary (NSSCO) level. 4.3 Progression NSSCAS level Mathematics provides a suitable foundation for the study of mathematics related courses in higher education. Depending on the local university entrance requirement, it may permit or assist progression directly to university courses in Mathematics or other related course in higher education. Equally it is suitable for learners intending to pursue careers or further study in Teaching, Science, Engineering, Medicine, Statistics etc. 4.4 Grading and reporting NSSCAS results are shown by one of the grades a, b, c, d or e indicating the standard achieved, grade a being the highest and grade e the lowest. ,,Ungraded indicates that the candidate has failed to reach the minimum standard required for a pass at NSSCAS level. 4.5 Support materials and approved textbooks Copies of NSSCAS syllabuses, recent specimen material, question papers and examiner reports are sent to all schools. Assessment manuals in subjects, where applicable are sent to schools. Approved learning support materials are available on the Senior Secondary Textbook Catalogue for Schools. The Textbook Catalogue is available on nied.edu.na

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5. LEARNING CONTENT The learning content for Mathematics NSSCAS level covers the following topics

Theme 1: Mathematics 1

Topic 1: Topic 2: Topic 3: Topic 4: Topic 5: Topic 6: Topic 7: Topic 8: Topic 9:

Equations, expressions, identities and inequalities Sequences and series Graphs and functions Coordinate geometry Circular measure Trigonometry Vectors in three dimensions Differentiation Integration

Theme 2: Mathematics 2

Topic 1: Topic 2: Topic 3: Topic 4: Topic 5: Topic 6:

Algebra Logarithmic and exponential functions Trigonometry Differentiation Integration Numerical solutions of equations

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Theme 1: Mathematics 1 Knowledge of the content of NSSCO Mathematics is prescribed, and learners may be required to demonstrate such knowledge in answering questions.

GENERAL OBJECTIVES Learners will:

SPECIFIC OBJECTIVES Learners should be able to:

Topic 1: Equations, expressions, identities and inequalities

gain further understanding for manipulating quadratic expressions and solving quadratic equations

complete the square for a quadratic function and use the solution to determine the turning point (vertex) of a graph of a quadratic function and sketch the graph

find the discriminant of a quadratic polynomial ax2 + bx + c and interpret the nature and the number of real roots of the related equation f(x) = ax2 + bx + c

interpret the difference between identities and equations and use identities to determine unknown coefficients in polynomials

recognise and solve equations in x which are quadratic in some function of x e.g. x4 ? 5x2 + 4 = 0 for k = x2

find the equation of a graph (quadratic and cubic) given sufficient information

solve quadratic inequalities in one unknown

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