[PDF] 4048_y20_sy Mathematics O-Level for 2020 - SEAB

101372_64048_y21_sy.pdf

MOE & UCLES 2011

Singapore Examinations and Assessment Board Mathematics Singapore-Cambridge General Certificate of Education

Ordinary Level (202

) (Syllabus 4048)

CONTENTS

Page

INTRODUCTION2

AIMS 2

ASSESSM

ENT OBJECTIVES 2

SCHEME OF ASSESSMENT 3

USE OF CALCULATORS 3

SUBJECT CONTENT 4

MATHEMATICAL FORMULAE 11

MATHEMATICAL NOTATION 12

4048 MATHEMATICS GCE ORDINARY LEVEL SYLLABUS (202) 2

INTRODUCTION

The syllab

us is intended to provide students with t he fundamental mathematical knowledge and skills. The content is organised into three strands namely, Number and Algebra, Geometry and Measurement, and

Statistics and Probability. Besides conceptual understanding and skills proficiency explicated in the content

strands, development of process skills that are involved in the process of acquiring and applying mathematical

knowledge is also emphasised. These include reasoning, communication and connections, thinking skills

and heuristics, and application and modelling; and are dev eloped based on the three content strands. AIMS

The O-Level

Mathematics syllabus aims to enable all students to: •acquire mathematical concepts and skills for continuous learning in mathematics and to support learni ng in other subjec ts •develop thinking, reasoning, communication, application and metacognitive skills through a mathemati cal approach to problem-solving

•connect ideas within mathematics and between mathematics and other subjects through applications of

mathemati c s •build confidence and foster interest in mathematics.

ASSESSMENT OBJECTIVES

The asse

ssment will test candidates' abilities to: AO1 understand and apply mathematical concepts and skills in a variety of contexts

AO2 organise and analyse data and information; formulate and solve problems, including those in real-world

contexts, by selecting and applying appropriate techniques of solution; interpret mathematical results

AO3 solve higher order thinking problems; make inferences; write mathematical explanation and arguments.

4048 MATHEMATICS GCE ORDINARY LEVEL SYLLABUS (202) 3

SCHEME OF ASSESSMENT

Paper Duration Description Marks Weighting

Paper 1 2 hours There will be about 25 short answer questions. Candidates are required to answer all questions. 8050%

Paper 2 2 hours

30 minutes There will be 10 to 11 questions of varying marks and lengths. The last question in this paper will focus

specifically on applying mathematics to a real-world scenario. Candidates are required to answer all questions. 10050% NOTES 1.

Omission of essential working

will result in loss of marks. 2. Some questions may integrate ideas from more than one topic of the syllabus where applicab le. 3. Relevant mathematical formulae will be provided for candidates. 4. Candidates should have geometrical instruments with them for Paper 1 and Paper 2. 5. Unless stated otherwise within a question, three-figure accuracy will be required for answe rs. This mean s that four-figure accuracy should be shown throughout the working, including cases wher e answe rs are used in subsequent parts of the question. Premature approximation will be pena lised, whe re appropriate. Angles in degrees should be given to one decim al place. 6. SI units will be used in questions involving mass and measures. Both the 12-hour and 24-hour clock may be used for quoting times of the day. In the 24-hour clo ck, for example, 3.1

5 a.m. will be denoted

by 03 15; 3.15 p.m. by 15 15. 7. Candidates are expected to be familiar with the solidus notation for the expressi on of compound units, e.g. 5 cm/s fo r 5 centimetres per second, 13.6 g/cm 3 for 13.6 grams per cubic centimetre. 8. Unless the question requires the answer in terms of , the calculator value for or = 3.142 sh ould be use d . 9. Spaces will be provided in each question paper for working and an swers.

USE OF CALCULATORS

An approved

calculator may be used in both Paper 1 and Paper 2.

4048 MATHEMATICS GCE ORDINARY LEVEL SYLLABUS (202) 4

SUBJECT CONTENT

Topic/Sub-topics Content

NUMBER AND ALGEBRA

N1 Numbers and their

operations •primes and prime factorisation •finding highest common factor (HCF) and lowest common multiple (LCM), squ ares, cubes, square roots and cu be roots by prime factorisatio n • negative numbers, integers, rational numbers, real numbers, and th eir four operation s • cal culations with calculator •representation and ordering of numbers on the number line • use of the symbols <, >, င, စ •approximation and estimation (including rounding off numbers to a require d numbe r of decimal places or significant figures and estimating the results of comp utation) •use of standard form A × 10 n , where n is an integer, and 1 င A < 10 •positive, negative, zero and fractional indice s • laws of indice s

N2 Ratio and

proportion •ratios involving rational numbers • writing a ratio in its simplest form • map scales (distance and area ) • direct and inverse proportion N3 Percentage •expressing one quantity as a percentage of another • comparing two quantities by percentage •percentages greater than 100% •increasing/decreasing a quantity by a given percentag e •reverse percentage s N4 Rate and speed •average rate and average speed •conversion of units (e.g. km/h to m/s)

4048 MATHEMATICS GCE ORDINARY LEVEL SYLLABUS (202) 5

Topic/Sub-topics Content

N5 Algebraic

expressions and formulae •using letters to represent numbers •interpreting notations: ab as a × b ba as a ÷ b or a × b1 a 2 as a × a, a 3 as a × a × a, a 2 b as a × a × b,

3y as y + y + y or 3 × y

3(x + y) as 3 × (x + y)

53y+ as (3 + y) ÷ 5 or51 × (3 + y

) •evaluation of algebraic expressions and formulae •translation of simple real-world situations into algebraic expression s • recognising and representing patterns/relationships by finding an algebr aic expre ssion for the n th term • addition and subtraction of linear expression s •simplification of linear expressions such as:

2(3x 5) + 4

x () 253
32xx
•use brackets and extract common factor s •factori sation of linear expressions of the form ax + bx + kay + kby •expansion of the product of algebraic expression s • changing the subject of a formula •finding the value of an unknown quantity in a given formula • use of: (a + b) 2 = a 2 + 2ab + b 2 (a b) 2 = a 2 2ab + b 2 a 2 b 2 = (a + b)(a b) • factorisation of quadratic expressions ax 2 + bx + c •multiplication and division of simple algebraic fractions such as: 35
43
2 ab ba 109
43
2 aa÷ •addition and subtraction of algebraic fractions with linear or quadrat ic denomi nator such as : 32
21
+xx 32
91
2 +xx () 2 32
31
+xx

4048 MATHEMATICS GCE ORDINARY LEVEL SYLLABUS (202) 6

Topic/Sub-topics Content

N6 Functions and

graphs •Cartesian coordinates in two dimensions •graph of a set of ordered pairs as a representation of a relationship between two variabl es • linear functions (y = ax + b) and quadratic functions (y = ax 2 + bx + c) • graphs of linear function s • the gradient of a linear graph as the ratio of the vertical chan ge to the hori zontal change (positive and negative gradi ents) • graphs of quadratic functions and their propertie s: positive or negative coefficient of x 2 maximum and minimum points symmetry • sketching the graphs of quadratic functions given in the form: y = - (x p) 2 + q y = (x p) 2 + q y = - (x a)(x b ) y = (x a)(x b) • graphs of power functions of the form y = ax n , where n = 2, 1, 0, 1, 2, 3, and sim ple sums of not more than three of these •graphs of exponential functions y = ka x , where a is a positive integer • estimation of the gradient of a curve by drawing a tang ent N7 Equations and inequalities •solving linear equations in one variable •solving simple fractional equations that can be reduced to linear equations such as: 342
3=+xx

623=x

•solving simultaneous linear equations in two variables by substitution and elimination method s grap hical method •solving quadratic equations in one unknown by factori sation use of formul a completing the square for qpxxy++= 2 grap hical method s • solving fractional equations that can be reduced to quadratic equ ations su ch as:

346+=+xx

532

21=+xx

•formulating equations to solve problem s • solving linear inequalities in one variable, and representing the solu tion on the numbe r line

4048 MATHEMATICS GCE ORDINARY LEVEL SYLLABUS (202) 7

Topic/Sub-topics Content

N8 Set language and

notation •use of set language and the following notation: Unio n of A and

BA Ӣ B

Intersection of A and

BA

ӡ B

' is an element of '