Singapore O-Level G3 Math topics
Choose a taught skill to revise or use a worked example to preview it. Each Singapore G3 Math guide explains the method, offers three short checks and links to useful foundations and next practice.
For Sec 3 or Sec 4 preparation, choose content you have been taught or use the example as an introduction. An untaught topic is not a weakness. Explore how the skills connect.
Number & Algebra
Numbers and Operations
Number types and ordering, prime factors, HCF and LCM, approximation and estimation, rounding, and standard form. The existing Indices guide covers index laws in depth.
Example and three practice checks →
Ratio and proportion
Ratios, distance and area scales, direct proportion and inverse proportion. Convert quantities to the same unit before comparing them.
Example and three practice checks →
Percentage
Expressing and comparing quantities as percentages, percentages greater than 100%, percentage increase or decrease, and reverse percentages.
Example and three practice checks →
Rate and Speed
Average rate, average speed and unit conversion, including interpreting rates with consistent units in context.
Example and three practice checks →
Factorisation
Common factors, grouping, quadratic expressions and difference of two squares. This guide focuses on factorisation, not the changing-the-subject portion of the same graph objective.
Example and three practice checks →
Algebraic fractions
Multiplying, dividing, adding and subtracting algebraic fractions, including linear and quadratic denominators. Restrictions from the original denominator remain after simplification.
Example and three practice checks →
Quadratic equations
Solving by factorisation, the quadratic formula, completing the square and graphs. The examples sample algebraic methods; a graph gives approximate roots unless exact values can be established.
Example and three practice checks →
Functions and graphs
Coordinates, linear and quadratic graphs, specified power and exponential graphs, and estimating a curve gradient with a tangent. The checks focus on interpreting coordinates and quadratic features.
Example and three practice checks →
Indices
Positive, zero, negative and fractional indices and their laws. For the fractional-power examples here, bases are positive; zero cannot be raised to a negative power.
Example and three practice checks →
Simultaneous equations
Simultaneous linear equations in two unknowns by elimination, substitution and graphical interpretation. This guide teaches the two algebraic methods and explains the intersection meaning.
Example and three practice checks →
Linear inequalities
Linear inequalities in one variable and solutions on a number line. Two-variable shaded regions are outside this guide.
Example and three practice checks →
Sets and Venn diagrams
Set membership, subsets, complements, unions and intersections of two sets, with Venn diagrams. A complement is always relative to a stated universal set.
Example and three practice checks →
Matrices
Displaying and interpreting matrix data, scalar multiplication, addition and compatible matrix products. No determinants or inverses are needed here.
Example and three practice checks →
Geometry & Measurement
Angles, Triangles and Polygons
Angle types and basic angle facts, parallel-line relationships, triangle and parallelogram angle properties, and interior and exterior angle sums for convex polygons.
Example and three practice checks →
Circle properties
Chord and tangent properties, angles subtended by the same arc, semicircles and cyclic quadrilaterals. Conditions matter more than how a sketch looks. The graph also contains an alternate-segment objective, which is not included here because it is not explicitly listed in this syllabus scope.
Example and three practice checks →
Trigonometry
Pythagoras, right-triangle ratios, sine and cosine rules, triangle area and 2D/3D applications including bearings. The short checks sample right triangles and area, not the full topic.
Example and three practice checks →
Mensuration
Perimeter, area, surface area and volume, including composite figures, arcs, sectors, segments and radians. Keep length, area and volume units distinct.
Example and three practice checks →
Coordinate geometry
Gradient, distance between points, straight-line equations and geometric problems using coordinates. Coordinate methods convert geometric information into calculations.
Example and three practice checks →
Vectors
Two-dimensional vectors, translations, position vectors, magnitude, addition, subtraction, scalar multiplication and geometric reasoning. Components below are stated in words to keep direction explicit.
Example and three practice checks →
Similarity and congruence
Recognising congruent and similar figures, triangle conditions, corresponding parts and length, area and volume ratios. These examples focus on reasoning rather than compass constructions.
Example and three practice checks →
Statistics & Probability
Statistics
Data displays, mean, median, mode, grouped estimates, range, quartiles, interquartile range, standard deviation and cumulative frequency. The short checks below sample averages and spread; they do not cover every display or establish mastery.
Example and three practice checks →
Probability
Single and combined events, possibility and tree diagrams, mutually exclusive events and independent events. Count equally likely outcomes only when that assumption is justified.
Example and three practice checks →
Sources and examination years
These are search-friendly groupings within 2026 O-Level Mathematics 4052. The 2027 G3 Mathematics K310 syllabus is a separate examination document. Nine guides carry an explicit 2027 subject-content check dated 12 September 2026; each names the section checked. The remaining guides retain their 2026 scope. These 22 search groupings are not the 18 official syllabus topics and do not represent complete coverage. We do not automatically relabel the graph. Examination year, syllabus code and later admissions year are different. Compare the 2027 K310 and 2026-or-earlier 4052 examination codes.
Connections are selected from Mentora's canonical knowledge graph at revision a0c9165e. Only checked prerequisite relationships are shown; related applications are described separately. The alternate-segment objective is omitted because it is not explicitly listed in the supplied circle syllabus scope. Original practice here is separate from protected diagnostics, TYS and school-paper questions.