HKDSE Mathematics · S1–S6 · EDB curriculum
Every learning unit, S1 to S6 52 Learning Units and 219 Learning Objectives, straight from the EDB curriculum — Junior Secondary through the Compulsory Part — with the standard formula for each topic and a drill link wherever one exists.
What this is (and isn't) This page summarises EDB's own publicly-published Curriculum and Assessment Guide and Learning Content documents — not HKEAA exam material. Objective wording is cleaned and paraphrased from the official text, not a verbatim reproduction; formulas are standard textbook forms, independently verified.
See how these units depend on one another — the knowledge map → Junior Secondary (S1–S3) Compulsory Part (S4–S6) All
▸ Junior Secondary (S1–S3) ▸ Number & Algebra 14 units JS 1
Basic Computation 1.1 Recognise the tests of divisibility of 4, 6, 8 and 9. 1.2 Understand the concept of power (index notation). 1.3 Perform prime factorisation of positive integers. 1.4 Find the greatest common divisor (H.C.F.) and least common multiple (L.C.M.). 1.5 Perform mixed operations of positive integers involving multiple levels of brackets. 1.6 Perform mixed arithmetic operations of fractions and decimals. JS 2
Directed Numbers 2.1 Understand the concept of directed numbers. 2.2 Perform mixed arithmetic operations of directed numbers. 2.3 Solve problems involving directed numbers. JS 3
Approximate Values and Numerical Estimation 3.1 Recognise the concept of approximate values and significant figures. 3.2 Understand estimation strategies (rounding, over-estimation, under-estimation). 3.3 Solve related real-life problems. JS 4
Rational and Irrational Numbers 4.1 Recognise the concept of the nth root. 4.2 Recognise the concepts of rational and irrational numbers. 4.3 Perform mixed arithmetic operations of simple quadratic surds. JS 5
Using Percentages 5.1 Understand the concept of percentage change (increase and decrease). 5.2 Solve real-life problems: discount, profit/loss, growth/depreciation, simple and compound interest, successive changes, salaries tax. Formulae Compound interest:
JS 6
Rates, Ratios and Proportions 6.1 Understand rates, ratios and proportions, including direct and inverse proportion. 6.2 Solve problems involving rates, ratios and proportions, including scale problems. JS 7
Algebraic Expressions 7.1 Represent word phrases by algebraic expressions. 7.2 Represent algebraic expressions by word phrases. 7.3 Recognise number sequences (odd/even/square/triangular numbers). 7.4 Recognise the preliminary idea of functions. Formulae Triangle area (recap):
JS 8
Linear Equations in One Unknown 8.1 Solve linear equations in one unknown. 8.2 Formulate a linear equation in one unknown from a problem. 8.3 Solve problems involving linear equations in one unknown. JS 9
Linear Equations in Two Unknowns 9.1 Understand linear equations in two unknowns and their graphs. 9.2 Solve simultaneous linear equations in two unknowns graphically. 9.3 Solve simultaneous linear equations algebraically (substitution, elimination). 9.4 Formulate simultaneous linear equations from a problem. 9.5 Solve problems involving simultaneous linear equations in two unknowns. JS 10
Laws of Integral Indices 10.1 Understand the laws of positive integral indices. 10.2 Understand the definitions of zero and negative exponents. 10.3 Understand the laws of integral indices (extended to all integers). 10.4 Understand scientific notation. 10.5 Understand the binary and denary number systems. JS 11
Polynomials 11.1 Understand the concept of polynomials (terms, degree, coefficients, like/unlike terms). 11.2 Add, subtract and multiply polynomials. 11.3 Factorise polynomials (common factor, grouping, cross method). JS 12
Identities 12.1 Understand the concept of an identity. 12.2 Use identities to expand algebraic expressions. 12.3 Use identities to factorise polynomials. Formulae Difference of two squares:
Perfect square:
JS 13
Formulae 13.1 Perform operations of algebraic fractions (denominators as products of linear factors). 13.2 Substitute values into formulae. 13.3 Change the subject of a formula (not involving radicals). JS 14
Linear Inequalities in One Unknown 14.1 Understand inequalities and represent them on a number line. 14.2 Recognise the basic properties of inequalities. 14.3 Solve linear inequalities in one unknown. 14.4 Solve problems involving linear inequalities in one unknown. ▸ Measures, Shape & Space 13 units JS 15
Errors in Measurement 15.1 Recognise the concept of errors in measurement. 15.2 Recognise maximum absolute error, relative error and percentage error. 15.3 Solve problems related to measurement errors. JS 16
Arc Lengths and Areas of Sectors 16.1 Understand the formula for arc length of a circle. 16.2 Understand the formula for the area of a sector. 16.3 Solve problems involving arc lengths and sector areas, including composite figures. Formulae Arc length:
Sector area:
JS 17
3-D Figures 17.1 Recognise right prisms, cylinders, pyramids, cones, polyhedra and spheres. 17.2 Recognise the sections (uniform cross-sections) of 3-D figures. 17.3 Sketch 2-D representations of 3-D figures. JS 18
Mensuration 18.1 Recognise the formulae for volumes of prisms, cylinders, pyramids, cones and spheres. 18.2 Find surface areas of prisms, cylinders, pyramids, cones and spheres. 18.3 Recognise how lengths, areas and volumes scale in similar figures, including frustums. 18.4 Solve problems involving volumes and surface areas. Formulae Cylinder volume:
Cone volume:
Sphere volume:
Sphere surface area:
Cylinder curved surface area:
JS 19
Angles and Parallel Lines 19.1 Understand adjacent angles on a line, vertically opposite angles and angles at a point. 19.2 Understand corresponding, alternate and interior angles formed by a transversal. 19.3 Recognise the conditions for two lines to be parallel. 19.4 Recognise angle properties associated with parallel lines. 19.5 Understand interior and exterior angle properties of triangles. JS 20
Polygons 20.1 Understand the concept of regular polygons. 20.2 Understand the formula for the sum of interior angles of a polygon. 20.3 Understand the formula for the sum of exterior angles of a convex polygon. 20.4 Recognise which polygons tessellate the plane. 20.5 Construct equilateral triangles and regular hexagons with compasses and straightedge. Formulae Sum of interior angles:
Sum of exterior angles:
JS 21
Congruent Triangles 21.1 Understand the concept of congruent triangles. 21.2 Recognise the conditions for congruent triangles (SSS, SAS, ASA, AAS, RHS). 21.3 Understand the base-angles property of isosceles triangles. 21.4 Understand the converse condition for isosceles triangles. 21.5 Construct angle/perpendicular bisectors, perpendicular and parallel lines, special angles and squares. JS 22
Similar Triangles 22.1 Understand the concept of similar triangles. 22.2 Recognise the conditions for similar triangles (AA, 3 sides proportional, 2 sides + included angle). 22.3 Recognise the concept of similar 2-D figures. JS 23
Quadrilaterals 23.1 Understand the properties of parallelograms. 23.2 Understand the properties of rectangles, rhombuses and squares. 23.3 Understand the conditions for a quadrilateral to be a parallelogram. 23.4 Use these properties/conditions in simple geometric proofs. 23.5 Understand the mid-point theorem and the intercept theorem. JS 24
Centres of Triangles 24.1 Understand the properties of angle bisectors and perpendicular bisectors of a triangle. 24.2 Understand the concurrence of angle bisectors (incentre) and perpendicular bisectors (circumcentre). 24.3 Recognise the concurrence of medians (centroid) and altitudes (orthocentre). JS 25
Pythagoras' Theorem 25.1 Understand Pythagoras' theorem. 25.2 Recognise the converse of Pythagoras' theorem. 25.3 Solve problems related to Pythagoras' theorem and its converse. Formulae Pythagoras' theorem:
JS 26
Rectangular Coordinate System 26.1 Recognise the rectangular coordinate system. 26.2 Find distances between points on a horizontal or vertical line. 26.3 Find areas of polygons in the coordinate plane. 26.4 Recognise the effect of translation, reflection and rotation on a point. 26.5 Understand the distance formula. 26.6 Understand the mid-point formula and the internal-division-point formula. 26.7 Understand the slope formula. 26.8 Recognise the slope relations for parallel and perpendicular lines. 26.9 Use coordinate geometry to perform simple geometric proofs. Formulae Distance formula:
Mid-point formula:
Slope formula:
JS 27
Trigonometry 27.1 Understand sine, cosine and tangent of angles between 0° and 90°. 27.2 Understand the properties of trigonometric ratios. 27.3 Understand exact values of trig ratios for 30°, 45° and 60°. 27.4 Solve problems related to plane figures. 27.5 Solve problems involving gradients, angles of elevation/depression and bearings. Formulae Tangent identity:
Pythagorean identity:
▸ Data Handling 4 units JS 28
Organisation of Data 28.1 Recognise discrete and continuous data. 28.2 Organise ungrouped data. 28.3 Organise data into groups (frequency distribution tables). JS 29
Presentation of Data 29.1 Recognise stem-and-leaf diagrams and histograms. 29.2 Interpret stem-and-leaf diagrams and histograms. 29.3 Interpret statistical charts representing two different data sets in daily life. 29.4 Recognise frequency polygons/curves and cumulative frequency polygons/curves. 29.5 Interpret frequency/cumulative-frequency polygons and curves (medians, quartiles, percentiles). 29.6 Choose appropriate statistical charts to present data. 29.7 Recognise the uses and abuses of statistical charts in daily life. JS 30
Measures of Central Tendency 30.1 Understand mean, median and mode/modal class. 30.2 Calculate mean, median and mode of ungrouped data. 30.3 Calculate mean, median and modal class of grouped data. 30.4 Recognise the uses and abuses of mean, median and mode. 30.5 Understand the effect of adding/multiplying by a constant on mean, median and mode. 30.6 Recognise the concept of weighted mean. JS 31
Probability 31.1 Recognise certain, impossible and random events. 31.2 Recognise the concept of probability (sample space, Venn diagrams). 31.3 Calculate probabilities by listing the sample space and counting. 31.4 Solve problems involving probability. 31.5 Recognise the concept of expectation. ▸ Further Learning Unit 1 units JS 32
Inquiry and Investigation 32 Discover and construct knowledge through inquiry activities; develop the ability to communicate, reason and conceptualise mathematics. ▸ Compulsory Part (S4–S6) ▸ Number & Algebra 9 units CP 1
Quadratic Equations in One Unknown 1.1 Solve quadratic equations by the factor method. 1.2 Form a quadratic equation from given roots. 1.3 Solve a quadratic equation graphically, by reading the x-intercepts of y = ax²+bx+c. 1.4 Solve quadratic equations using the quadratic formula. 1.5 Relate the discriminant to the nature of the roots. 1.6 Solve problems involving quadratic equations. 1.7 Relate the sum and product of roots to the coefficients, and use these relations to form equations. 1.8 Appreciate the development of number systems, including the complex numbers. 1.9 Add, subtract, multiply and divide complex numbers of the form a ± bi. Formulae Quadratic formula:
Discriminant:
Sum and product of roots:
CP 2
Functions and Graphs 2.1 Recognise functions, domains, co-domains, and independent/dependent variables. 2.2 Represent functions using tables, algebra and graphs. 2.3 Understand features of quadratic-function graphs (vertex, axis of symmetry, direction of opening). 2.4 Find the maximum/minimum of a quadratic function algebraically (completing the square). CP 3
Exponential and Logarithmic Functions 3.1 Understand the definitions of rational indices. 3.2 Understand the laws of rational indices. 3.3 Understand the definition and properties of logarithms, including change of base. 3.4 Understand the properties and graph features of exponential and logarithmic functions. 3.5 Solve exponential and logarithmic equations. 3.6 Appreciate applications of logarithms (e.g. Richter scale, decibel scale). Formulae Log laws:
Change of base:
CP 4
More about Polynomials 4.1 Perform division of polynomials. 4.2 Understand the remainder theorem. 4.3 Understand the factor theorem. 4.4 Find the H.C.F. and L.C.M. of polynomials. 4.5 Add, subtract, multiply and divide rational functions (algebraic fractions). CP 5
More about Equations 5.1 Solve simultaneous equations (one linear, one quadratic) graphically. 5.2 Solve simultaneous equations (one linear, one quadratic) algebraically. 5.3 Solve fractional, exponential, logarithmic and trigonometric equations reducible to quadratics. 5.4 Solve problems involving equations reducible to quadratic equations. CP 6
Variations 6.1 Understand direct and inverse variation and their real-life applications. 6.2 Understand the graphs of direct and inverse variation. 6.3 Understand joint and partial variation and their applications. Formulae Direct variation:
Inverse variation:
CP 7
Arithmetic and Geometric Sequences and their Summations 7.1 Understand the concept and properties of arithmetic sequences. 7.2 Understand the general term of an arithmetic sequence. 7.3 Understand the concept and properties of geometric sequences. 7.4 Understand the general term of a geometric sequence. 7.5 Use the summation formulae for arithmetic and geometric sequences. 7.6 Understand the sum-to-infinity formula for certain geometric sequences. 7.7 Solve related real-life problems (growth, depreciation, interest). Formulae Arithmetic general term:
Geometric general term:
Arithmetic sum:
Geometric sum:
Sum to infinity:
CP 8
Inequalities and Linear Programming 8.1 Solve compound linear inequalities in one unknown. 8.2 Solve quadratic inequalities graphically. 8.3 Solve quadratic inequalities algebraically. 8.4 Represent linear inequalities in two unknowns graphically. 8.5 Solve systems of linear inequalities in two unknowns. 8.6 Solve linear programming problems. CP 9
More about Graphs of Functions 9.1 Sketch and compare graphs of constant, linear, quadratic, trigonometric, exponential and logarithmic functions. 9.2 Solve f(x) = k using the graph of y = f(x). 9.3 Solve inequalities f(x) > k, f(x) < k, f(x) ≥ k and f(x) ≤ k using the graph of y = f(x). 9.4 Understand transformations of f(x): f(x)+k, f(x+k), k·f(x), f(kx). ▸ Measures, Shape & Space 5 units CP 10
Equations of Straight Lines 10.1 Understand the equation of a straight line (from two points, or slope + a point, or slope + intercept). 10.2 Understand the possible intersection of two straight lines. CP 11
Basic Properties of Circles 11.1 Understand properties of chords and arcs of a circle. 11.2 Understand angle properties of a circle (angle at centre, angles in the same segment, angle in a semicircle). 11.3 Understand properties of a cyclic quadrilateral. 11.4 Understand tests for concyclic points and cyclic quadrilaterals. 11.5 Understand properties of tangents and the tangent–chord angle (alternate segment theorem). 11.6 Use the basic properties of circles in simple geometric proofs. CP 12
Loci 12.1 Understand the concept of a locus. 12.2 Describe and sketch loci satisfying given conditions. 12.3 Describe loci with algebraic equations (lines, circles, parabolas). CP 13
Equations of Circles 13.1 Understand the equation of a circle (from centre + radius, or three points). 13.2 Find the intersection of a straight line and a circle, including tangent equations. CP 14
More about Trigonometry 14.1 Understand sine, cosine and tangent functions, their graphs and periodicity. 14.2 Solve trigonometric equations of the form a sinθ = b, a cosθ = b, a tanθ = b (0°–360°). 14.3 Understand the area-of-triangle formula ½ab sin C. 14.4 Understand the sine rule and cosine rule. 14.5 Understand Heron's formula. 14.6 Understand the concept of projection. 14.7 Understand the angle between a line and a plane, and between two planes. 14.8 Understand the theorem of three perpendiculars. 14.9 Solve 2-D and 3-D problems involving angles and distances. Formulae Triangle area:
Sine rule:
Cosine rule:
Heron's formula:
▸ Data Handling 4 units CP 15
Permutations and Combinations 15.1 Understand the addition rule and multiplication rule in counting. 15.2 Understand the concept and notation of permutation. 15.3 Solve problems on permutation of distinct objects without repetition. 15.4 Understand the concept and notation of combination. 15.5 Solve problems on combination of distinct objects without repetition. Formulae Permutations:
Combinations:
CP 16
More about Probability 16.1 Use set language (union, intersection, complement) and Venn diagrams. 16.2 Understand the addition law of probability, mutually exclusive and complementary events. 16.3 Understand the multiplication law of probability and independent events. 16.4 Understand the concept and notation of conditional probability. 16.5 Use permutations and combinations to solve probability problems. Formulae Addition law:
Multiplication law (independent):
Conditional probability:
CP 17
Measures of Dispersion 17.1 Understand the concept of dispersion. 17.2 Understand range and inter-quartile range. 17.3 Construct and interpret box-and-whisker diagrams. 17.4 Understand standard deviation for grouped and ungrouped data. 17.5 Compare dispersion of data sets using appropriate measures. 17.6 Apply standard deviation to standard scores and the normal distribution. 17.7 Understand the effect of adding/multiplying by a constant on dispersion. Formulae Standard deviation:
Standard score:
CP 18
Uses and Abuses of Statistics 18.1 Recognise sampling techniques and questionnaire design principles. 18.2 Recognise uses and abuses of statistical methods in daily-life activities. 18.3 Assess statistical investigations presented in different sources (news media, research reports). ▸ Further Learning Unit 2 units CP 19
Further Applications 19 Solve more sophisticated real-life and mathematical problems integrating multiple areas of mathematics (e.g. financial problems, survey data analysis, Ptolemy's/Ceva's theorems). CP 20
Inquiry and Investigation 20 Discover and construct knowledge through inquiry activities; develop the ability to communicate, reason and conceptualise mathematics.