# Mathematics

MATSEC Mathematics SEC 23 Syllabus.

SEC Mathematics Syllabus 2018

SEC 'O' Level Mathematics Past Papers

Introduction

Mathematics furnishes the prime means by which information can be organised, communicated and manipulated. It is also an ever-expanding body of facts, skills, concepts and strategies used in the solution of a wide range of problems. As a consequence, when implementing this syllabus, teachers of Mathematics should emphasize two important aspects of the teaching and learning of mathematics:

• Utilitarian Aspect of Mathematics Teaching and Learning

Mathematics is useful. It equips individuals with the necessary knowledge to help them understand and interact with the world around them. Moreover, it forms the basis of science, technology, architecture, engineering, commerce, industry and banking. It is also increasingly being used in the medical sciences, biological sciences, economics and geography. This pervasiveness makes Mathematics one of the most important subjects in the school curriculum.

• Aesthetic Aspect of Mathematics Teaching and Learning

Mathematics is an evolving body of knowledge that is characterised by its order, precision, conciseness and logic. It should offer the individuals intellectual challenge, excitement, satisfaction and wonder.

Aims

When implementing this syllabus, teachers should aim to enable candidates to:

1. Understand and appreciate the place and purpose of Mathematics in society and apply mathematical concepts to situations arising in their own lives;
2. Apply mathematical knowledge and understanding to solve problems;
3. Think and communicate mathematically - precisely, logically and creatively;
4. Develop a positive attitude to Mathematics, including confidence and perseverance;
5. Develop an ability to work independently and co-operatively when doing Mathematics; Appreciate the interdependence of the different branches of Mathematics;
6. Acquire a secure foundation for the further study of Mathematics; Use Mathematics across the curriculum; and,
7. Make efficient, creative and effective use of appropriate technology in Mathematics.

Assessment Objectives

The examination will, in general, test:

1. The candidate’s ability to recall, understand and apply mathematical knowledge  in a wide context;
2. The candidate’s ability to understand and analyse a problem, select an appropriate strategy, apply suitable knowledge and techniques to solve it, verify and interpret the results; and,
3. The candidate’s ability to understand, interpret and evaluate mathematical ideas that are presented in oral, written and visual forms.

In particular, the candidate will be required to demonstrate the ability to:

1. Communicate, conjecture, reason and prove mathematically; Understand the nature of numbers and make use of them;
2. Understand the nature of algebraic relationships and make use of them;
3. Understand the nature and properties of shape, space and measures and make use of them; Understand the nature of statistics and process, represent and interpret data; and,
4. Understand the nature of probability and calculate the probabilities of events.

During the course candidates should be given opportunities to:

1. Use calculators and computer software including spreadsheets, LOGO, a dynamic geometry package and computer algebra system;
2. Use computers as a source of large samples, as a tool for exploring graphical representations, and as a means for simulating events;
3. Develop a feel for numbers;
4. Develop and use a range of methods of computation, namely, mental, pencil-and-paper, calculator and computer methods, and apply these to a range of problems;
5. Develop and use a range of methods for approximation of numbers and apply these to a range of problems; Develop and use a range of methods for estimation of measures and apply these to a range of problems;
6. Explore a variety of situations which lead to the expression of relationships;
7. Consider how relationships between number operations underpin the techniques for manipulating algebraic expressions;
8. Consider how algebra can be used to model real-life situations and to solve problems; Explore shape and space through drawing and practical work;
9. Use computers to generate and transform graphic images and to solve problems; Formulate questions that can be solved using statistical methods;
10. Undertake purposeful inquiries based on data analysis;
11. Engage in practical and experimental work in order to appreciate principles which govern random events; and,
12. Look critically at some of the ways in which representations of data can be misleading and conclusions can be uncertain.

Scheme of Assessment

The examination will consist of two papers, Paper I and Paper II, each of 2 hours duration. There will be two versions of Paper II: Paper IIA and Paper IIB. Candidates who intend to further their study in Mathematics and Science subjects at Intermediate Level and Advanced Level are STRONGLY advised to sit for Paper IIA.

Questions will be set in English and must be answered in English.

Candidates are expected to abide by the following principles of good mathematical practice:

1. inclusion of justifications in solutions whenever appropriate;
2. specification of the number of decimal places/significant figures being used whenever numbers are rounded up or down, and
3. inclusion of all appropriate steps in solutions to problems.

Paper I

This paper is to be taken by all candidates and will cover the Core Syllabus content only.

It will be divided into two Sections, A and B.

Section A (Non-Calculator Section)

1. It will consist of eighteen to twenty short questions to be answered in 20 minutes. The paper will carry a total of 20 marks.
2. Calculators and protractors are not allowed.
3. Questions will typically involve numerical calculations, approximations, estimations, data and graphical interpretations, application of formulae, recall and applications of properties of shapes, recall and applications of mathematical facts
4. To answer these questions, particularly those involving numerical calculations, candidates are advised to choose and use the more efficient techniques (mental and pencil-and-paper). They are expected to have a range of strategies to aid mental calculations of unknown facts from facts that can be rapidly recalled.

Section B (Calculator Section)

1. It will consist of nine to eleven compulsory graded questions to be answered in one hour and forty minutes.
2. The questions may have different mark allocations which will be stated on the paper and will carry a total of 80 marks.
3. Candidates are allowed to use mathematical instruments and scientific calculators with statistical functions.
4. Programmable calculators are not allowed.
5. Candidates are allowed to use transparencies for drawing transformations.

Paper II

There will be two versions of this paper (IIA or IIB). Candidates will be required to indicate on the registration form which version they wish to sit for. No change in the choice of paper will be allowed after the registration period. In the September supplementary session only Paper I and Paper IIB will be offered.

1. Candidates are allowed to use mathematical instruments and scientific calculators with statistical functions. Programmable calculators are not allowed.
2. Candidates are allowed to use transparencies for drawing transformations.

Paper IIA will consist of nine to eleven compulsory questions with varying mark allocations per question which will be stated on the paper, carrying a total of 100 marks. The questions in this paper will cover the content in both the Core and the Extension parts of the syllabus. A typical problem in this paper will be more difficult to solve than a typical Paper I problem. The time allowed for this Paper is two hours.

Paper IIB will consist of twenty to twenty-eight questions with varying mark allocations stated on the paper and will carry a total of 100 marks. The questions in this paper will cover the content in that part of the syllabus indicated as Core. A typical problem in this paper will be easier to solve than a typical Paper I problem. The time allowed for this Paper is two hours.

The overall weighting ( 5%) for each of the four main components of the syllabus is shown below:

 Number Algebra Shape, Space & Measures Data Handling Paper I and Paper IIA 25% 35% 30% 10% Paper I and Paper IIB 35% 20% 35% 10%

Results

Candidates sitting for Paper I and Paper IIA may qualify for Grades 1, 2, 3, 4 or 5. The results for candidates who do not obtain at least a Grade 5 shall remain Unclassified (U).

Candidates sitting for Paper I and Paper IIB may qualify for Grades 4, 5, 6, or 7. The results for candidates who do not obtain at least a Grade 7 shall remain Unclassified (U).

The following descriptions are meant to provide a general indication of the standards of achievement normally shown by candidates earning particular grades. However, the final grade awarded will reflect the extent to which the candidates have met the assessment objectives overall.

1. An understanding of complex non-routine problems; o Logical reasoning and valid conclusions;
2. An overall high performance in all areas of the syllabus
3. A high level of presentation (providing evidence of effective and clear communication through writing and diagrams); and,
4. Correct computations and solutions.