Year 10: Singapore O-Level Mathematics 4052

Listed Mathematics sub-topics at O-Level based on the Singapore Examinations and Assessment Board (SEAB). Checked against the source on 2 October 2026.

Sub-topics from the Singapore–Cambridge GCE O-Level Mathematics syllabus (4052) for the 2026 examination. Year 10 is Secondary 4, at the end of which the papers are sat. There are two papers of 90 marks each, both 2 hours 15 minutes and each worth half the grade: Paper 1 is about 26 short answer questions, and Paper 2 is 9 to 10 longer ones, the last of which applies mathematics to a real-world scenario. Column vectors, which the syllabus sets as a two-row bracket, are written inline here as (x, y).

18sub-topics
133skills mapped
94%have practice

Coverage is the percentage of listed sub-topics with at least one linked practice skill; it does not measure how fully every part of an entry is practised. A skill can practise more than one sub-topic, so some appear more than once below.

Number and algebra

N1Numbers and their operationsprimes 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 × 10ⁿ, where n is an integer, and 1 ⩽ A < 10 • positive, negative, zero and fractional indices • laws of indices
N2Ratio and proportionratios involving rational numbers • writing a ratio in its simplest form • map scales (distance and area) • direct and inverse proportion
- Finding values based on ratios
N3Percentageexpressing 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
- Evaluate percentages
N4Rate and speedaverage rate and average speed • conversion of units (e.g. km/h to m/s)
N5Algebraic expressions and formulaeusing letters to represent numbers • interpreting notations: − ab as a × b − a/b as a ÷ b or a × 1/b − a² as a × a, a³ as a × a × a, a²b as a × a × b, … − 3y as y + y + y or 3 × y − 3(x + y) as 3 × (x + y) − (3 + y)/5 as (3 + y) ÷ 5 or 1/5 × (3 + y) • evaluation of algebraic expressions and formulae • translation of simple real-world situations into algebraic expressions • recognising and representing patterns/relationships by finding an algebraic expression for the nth term • addition and subtraction of linear expressions • simplification of linear expressions such as: −2(3x − 5) + 4x; 2x/3 − 3(x − 5)/2 • use brackets and extract common factors • factorisation of linear expressions of the form ax + bx + kay + kby • expansion of the product of algebraic expressions • changing the subject of a formula • finding the value of an unknown quantity in a given formula • use of: − (a + b)² = a² + 2ab + b² − (a − b)² = a² − 2ab + b² − a² − b² = (a + b)(a − b) • factorisation of quadratic expressions ax² + bx + c • multiplication and division of simple algebraic fractions such as: (3a/4b²)(5ab/3); (3a/4) ÷ (9a²/10) • addition and subtraction of algebraic fractions with linear or quadratic denominator such as: 1/(x − 2) + 2/(x − 3); 1/(x² − 9) + 2/(x − 3); 1/(x − 3) + 2/(x − 3)²
N6Functions and graphsCartesian coordinates in two dimensions • graph of a set of ordered pairs as a representation of a relationship between two variables • linear functions (y = ax + b) and quadratic functions (y = ax² + bx + c) • graphs of linear functions • the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients) • graphs of quadratic functions and their properties: − positive or negative coefficient of x² − 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 = axⁿ, where n = −2, −1, 0, 1, 2, 3, and simple sums of not more than three of these • graphs of exponential functions y = kaˣ, where a is a positive integer • estimation of the gradient of a curve by drawing a tangent
N7Equations and inequalitiessolving linear equations in one variable • solving simple fractional equations that can be reduced to linear equations such as: x/3 + (x − 2)/4 = 3; 3/(x − 2) = 6 • solving simultaneous linear equations in two variables by − substitution and elimination methods − graphical method • solving quadratic equations in one unknown by − factorisation − use of formula − completing the square for y = x² + px + q − graphical method • solving fractional equations that can be reduced to quadratic equations such as: 6/(x + 4) = x + 3; 1/(x − 2) + 2/(x − 3) = 5 • formulating equations to solve problems • solving linear inequalities in one variable, and representing the solution on the number line
N8Set language and notationuse of set language and the following notation: Union of A and B, A ∪ B; Intersection of A and B, A ∩ B; Number of elements in set A, n(A); ‘… is an element of …’, ∈; ‘… is not an element of …’, ∉; Complement of set A, A′; The empty set, ∅; Universal set, ℰ; A is a subset of B, A ⊆ B; A is not a subset of B, A ⊈ B; A is a (proper) subset of B, A ⊂ B; A is not a (proper) subset of B, A ⊄ B • union and intersection of two sets • Venn diagrams
N9Matricesdisplay of information in the form of a matrix of any order • interpreting the data in a given matrix • product of a scalar quantity and a matrix • problems involving the calculation of the sum and product (where appropriate) of two matrices
No practice for this one yet.

Geometry and measurement

G1Angles, triangles and polygonsright, 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 • construction of simple geometrical figures from given data using compasses, ruler, set squares and protractors, where appropriate
G2Congruence and similaritycongruent 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 • properties and construction of perpendicular bisectors of line segments and angle bisectors • 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
- Congruent triangles
G3Properties of circlessymmetry 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
G4Pythagoras’ theorem and trigonometryuse 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 ½ab sin C for the area of a triangle • 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
G5Mensurationarea 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 cm² and m², and between cm³ and m³ • 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)
G6Coordinate geometryfinding 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
G7Vectors in two dimensionsuse of notations: (x, y) as a column vector, AB with an arrow above it, a in bold, and the magnitudes |AB| and |a| • representing a vector as a directed line segment • translation by a vector • position vectors • magnitude of a vector (x, y) as √(x² + y²) • 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
- Vector arithmetic
- Position vectors and ratios

Statistics and probability

S1Data handling and analysissimple concepts in collecting, classifying and tabulating data • 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 • drawing simple inference from statistical diagrams • 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
S2Probabilityprobability 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)

Other Year 10 skills

Year 10 skills not currently linked to an entry on this page. These may include revision, extension practice, or skills still awaiting a curriculum mapping.