Source: MOE 2023 O level Math Syllabus
The syllabus prepares students adequately for O Level Math Syllabus 2023, where a strong foundation in algebraic manipulation skills and mathematical reasoning skills are required. The content is organised into three strands, namely, Algebra, Geometry and Trigonometry, and Calculus. Besides conceptual understanding and skill proficiency explicated in the content strand, the development of process skills, namely, reasoning, communication and connections, thinking skills and heuristics, and applications and modelling are also emphasised. The 2023 O-Level Mathematics syllabus assumes knowledge of O-Level Mathematics.
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), squares, cubes, square roots and cube roots by prime factorisation · negative numbers, integers, rational numbers, real numbers, and their four operations · calculations with calculator · representation and ordering of numbers on the number line · use of the symbols <, >, ⩽, ⩾ · approximation and estimation (including rounding off numbers to a required number of decimal places or significant figures and estimating the results of computation) · use of standard form A ´ 10^{n}, where n is an integer, and 1 ⩽ A < 10 · positive, negative, zero and fractional indices · laws of indices |
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 percentage · reverse percentages |
N4 | Rate and speed | · average rate and average speed
· conversion of units (e.g. km/h to m/s) |
GEOMETRY AND MEASUREMENT | ||
G1 | Angles, triangles and polygons | · right, acute, obtuse and reflex angles
· vertically opposite angles, angles on a straight line and angles at a point · angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles · properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties · classifying special quadrilaterals on the basis of their properties · angle sum of interior and exterior angles of any convex polygon · properties of perpendicular bisectors of line segments and angle bisectors · construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate |
Topic/Sub-topics | Content | |
G2 | Congruence and similarity | · congruent figures and similar figures
· properties of similar triangles and polygons: * corresponding angles are equal * corresponding sides are proportional · enlargement and reduction of a plane figure · scale drawings · determining whether two triangles are * congruent * similar · ratio of areas of similar plane figures · ratio of volumes of similar solids · solving simple problems involving similarity and congruence |
G3 | Properties of circles | · symmetry properties of circles:
* equal chords are equidistant from the centre * the perpendicular bisector of a chord passes through the centre * tangents from an external point are equal in length * the line joining an external point to the centre of the circle bisects the angle between the tangents · angle properties of circles: * angle in a semicircle is a right angle * angle between tangent and radius of a circle is a right angle * angle at the centre is twice the angle at the circumference * angles in the same segment are equal * angles in opposite segments are supplementary |
G4 | Pythagoras’ theorem and trigonometry | · use of Pythagoras’ theorem
· determining whether a triangle is right-angled given the lengths of three sides · use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles · extending sine and cosine to obtuse angles · use of the formula 1 ab sin C for the area of a triangle 2 · use of sine rule and cosine rule for any triangle · problems in two and three dimensions including those involving angles of elevation and depression and bearings |
G5 | Mensuration | · area of parallelogram and trapezium
· problems involving perimeter and area of composite plane figures · volume and surface area of cube, cuboid, prism, cylinder, pyramid, cone and sphere · conversion between cm^{2} and m^{2} , and between cm^{3} and m^{3} · problems involving volume and surface area of composite solids · arc length, sector area and area of a segment of a circle · use of radian measure of angle (including conversion between radians and degrees) |
Topic/Sub-topics | Content | |
G6 | Coordinate geometry | · finding the gradient of a straight line given the coordinates of two points on it
· finding the length of a line segment given the coordinates of its end points · interpreting and finding the equation of a straight line graph in the form y = mx + c · geometric problems involving the use of coordinates |
G7 | Vectors in two dimensions | · use of notations: æ x ö , AB , a, AB and a
ç ÷ è y ø · representing a vector as a directed line segment · translation by a vector · position vectors · magnitude of a vector æ x ö as x ^{2} + y ^{2} ç ÷ è y ø · use of sum and difference of two vectors to express given vectors in terms of two coplanar vectors · multiplication of a vector by a scalar · geometric problems involving the use of vectors |
G8 | Problems in real- world contexts | · solving problems in real-world contexts (including floor plans, surveying, navigation, etc.) using geometry
· interpreting the solution in the context of the problem |
Topic/Sub-topics | Content | |
STATISTICS AND PROBABILITY | ||
S1 | Data analysis | · analysis and interpretation of:
* tables * bar graphs * pictograms * line graphs * pie charts * dot diagrams * histograms with equal class intervals * stem-and-leaf diagrams * cumulative frequency diagrams * box-and-whisker plots · purposes and uses, advantages and disadvantages of the different forms of statistical representations · explaining why a given statistical diagram leads to misinterpretation of data · mean, mode and median as measures of central tendency for a set of data · purposes and use of mean, mode and median · calculation of the mean for grouped data · quartiles and percentiles · range, interquartile range and standard deviation as measures of spread for a set of data · calculation of the standard deviation for a set of data (grouped and ungrouped) · using the mean and standard deviation to compare two sets of data |
S2 | Probability | · probability as a measure of chance
· probability of single events (including listing all the possible outcomes in a simple chance situation to calculate the probability) · probability of simple combined events (including using possibility diagrams and tree diagrams, where appropriate) · addition and multiplication of probabilities (mutually exclusive events and independent events) |