Singapore A-Level H2 Mathematics
syllabus 9758
77 of 102 skills covered
✓ covered · ◐ partial · ○ not yet · — excluded
H2 Mathematics (9758)
| skill | lessons | ||
|---|---|---|---|
| 1 | Function, domain and range | Function Notation, Domain and Range | ✓ covered |
| 2 | Inverse and composite functions | Inverse Functions, Composite Functions | ✓ covered |
| 3 | Conditions for existence of inverse/compositeinverse-functions shows the reversal; the one-to-one (horizontal-line) condition and the range⊆domain condition for fg are not stated | Inverse Functions | ◐ partial |
| 4 | Domain restriction to obtain an inversenot taught | ○ not yet | |
| 5 | Graph of a one-to-one function and its inverse | Inverse Functions | ✓ covered |
| 6 | Graphing a function with a graphing calculatorgraphing-calculator content — deferred until the planned graphing tool ships (owner ruling 2026-08-25; these rows then join the exam-item batches) | ○ deferred | |
| 7 | Characteristics of conics and rational functionsStill missing: | Zeros and Vertical Asymptotes, Holes Where a Factor Cancels, Horizontal Asymptotes by Degree, Slant Asymptotes by Long Division, The Equation of an Ellipse, The Equation of a Hyperbola | ◐ partial |
| 8 | Equations of asymptotes, axes of symmetry, value restrictionsStill missing: | ◐ partial | |
| 9 | Transformations af(x), f(x)+a, f(x+a), f(ax) and combinationsMissing: | Transforming Graphs, Stretching a Graph Vertically, Stretching a Graph Horizontally | ◐ partial |
| 10 | y = \|f(x)\|, y = f(\|x\|), y = 1/f(x) related to y = f(x)Missing: y = 1/f(x) from y = f(x) | Taking the Modulus of a Whole Expression, Replacing x with a Modulus, The Graph of y = |x|, Reciprocal Graphs | ◐ partial |
| 11 | Simple parametric equations and their graphs | Parametric Equations | ✓ covered |
| 12 | Formulating equations/systems/inequalities from a problem | Forming Equations, Writing Formulas from Words | ✓ covered |
| 13 | Solving an equation with a graphing calculatorgraphing-calculator content — deferred until the planned graphing tool ships (owner ruling 2026-08-25; these rows then join the exam-item batches) | ○ deferred | |
| 14 | Solving a linear system with a graphing calculatorgraphing-calculator content — deferred until the planned graphing tool ships (owner ruling 2026-08-25; these rows then join the exam-item batches) | ○ deferred | |
| 15 | Inequalities f(x)/g(x) > 0 | Solving a Rational Inequality, Solving a Quadratic Inequality | ✓ covered |
| 16 | \|x\| and \|x−a\| < b ⟺ a−b < x < a+b | Solving Absolute Value Inequalities, Absolute Value, Solving Absolute Value Equations | ✓ covered |
| 17 | Solving inequalities graphicallygraph-intersections finds intersections; the inequality-from-a-graph step is missing | Intersections of Graphs | ◐ partial |
| 18 | Sequence and series, finite and infinite | Term-to-Term Rules, Sigma Notation, The Sum to Infinity | ✓ covered |
| 19 | Sequence as y = f(n) | The nth Term, Term-to-Term Rules | ✓ covered |
| 20 | Relationship between uₙ and Sₙarithmetic-series/geometric-series build Sₙ; recovering uₙ = Sₙ − Sₙ₋₁ is not taught | The Sum of an Arithmetic Series, The Sum of a Geometric Series | ◐ partial |
| 21 | nth-term formula and uₙ₊₁ = f(uₙ) recurrences | The nth Term, Recurrence Relations | ✓ covered |
| 22 | Sum and difference of two series | Sigma Notation | ✓ covered |
| 23 | Convergence of a series and sum to infinity | The Sum to Infinity, Two Infinite Sums, Opposite Fates | ✓ covered |
| 24 | nth term and sum of a finite arithmetic series | The Sum of an Arithmetic Series | ✓ covered |
| 25 | nth term and sum of a finite geometric series | Geometric Sequences, The Sum of a Geometric Series | ✓ covered |
| 26 | Convergence condition for an infinite GP; sum to infinity | The Sum to Infinity | ✓ covered |
| 27 | Vector addition, scalar multiplication, geometry | Adding Vectors, Subtracting Vectors, Scalar Multiplication | ✓ covered |
| 28 | Position, displacement and direction vectors | Position Vectors, Vectors | ✓ covered |
| 29 | Magnitude; unit vectors | Magnitude of a Vector, Unit Vectors | ✓ covered |
| 30 | Distance between two points; collinearity | The Distance Between Two Points, Collinear Vectors | ✓ covered |
| 31 | Ratio theoremvector-geometry-proofs does midpoints and two-thirds splits by hand; the ratio theorem as a named result is not stated | Vector Proofs with Midpoints | ◐ partial |
| 32 | Scalar **and vector** product and their propertiesthe-dot-product and the-vector-product now give both products, with a·b = 0 for perpendicular, a × b = −(b × a) and a × a = 0; distributivity over addition is still not stated | The Dot Product, The Vector Product | ◐ partial |
| 33 | Angle between two vectors | The Angle Between Vectors | ✓ covered |
| 34 | Geometrical meanings of \|a·n̂\| and \|a × n̂\|line | The Distance from a Point to a Plane, Parallelogram Area from the Vector Product | ◐ partial |
| 35 | Vector and cartesian equations of lines **and planes** | The Vector Equation of a Line, The Vector Equation of a Plane, The Cartesian Equation of a Plane | ✓ covered |
| 36 | Foot of perpendicular; distance from a point to a line/planeplane | The Distance from a Point to a Plane | ◐ partial |
| 37 | Angle between two lines / line and plane / two planes | The Angle Between Vectors, The Angle Between a Line and a Plane, The Angle Between Two Planes | ✓ covered |
| 38 | Relationships between lines, lines and planes, planesthe-intersection-of-a-line-and-a-plane classifies the line-plane cases (meets once / parallel and clear / lies inside); skew and coplanar lines, and plane-plane intersections, are still absent | The Intersection of a Line and a Plane | ◐ partial |
| 39 | Extension from real to complex numbers | Roots of Negative Numbers, The Imaginary Unit | ✓ covered |
| 40 | Complex roots of quadratic equations | Complex Roots of a Quadratic | ✓ covered |
| 41 | Modulus, argument, conjugate | The Modulus of a Complex Number, The Argument of a Complex Number, Complex Conjugates | ✓ covered |
| 42 | Four operations; equality of complex numbers | Adding Complex Numbers, Multiplying Complex Numbers, Dividing Complex Numbers | ✓ covered |
| 43 | Conjugate roots of real-coefficient polynomial equations | Complex Roots of a Quadratic, Complex Roots of a Cubic | ✓ covered |
| 44 | Representation on the Argand diagram | The Argand Diagram | ✓ covered |
| 45 | Geometrical effects of conjugation, negation, ±, × iMissing: | The Imaginary Unit, Complex Conjugates, Adding Complex Numbers | ◐ partial |
| 46 | Graphical interpretation of f′ and f″ signs | Increasing and Decreasing Functions, Points of Inflection | ✓ covered |
| 47 | Relating the graph of y = f′(x) to y = f(x)curve-sketching-with-derivatives goes f → shape; reading a *given* f′ graph back to f is not taught | Curve Sketching with Derivatives | ◐ partial |
| 48 | Implicit and parametric differentiation | Implicit Differentiation, Parametric Differentiation | ✓ covered |
| 49 | Nature of stationary points analytically | The First Derivative Test, The Second Derivative Test | ✓ covered |
| 50 | Locating max/min and derivative values with a GCgraphing-calculator content — deferred until the planned graphing tool ships (owner ruling 2026-08-25; these rows then join the exam-item batches) | ○ deferred | |
| 51 | Tangents and normals, incl. implicit/parametric curves | Tangents and Normals to Curves, Implicit Differentiation, Parametric Differentiation | ✓ covered |
| 52 | Local maxima and minima problems | Optimization Problems | ✓ covered |
| 53 | Connected rates of change | Related Rates | ✓ covered |
| 54 | Standard Maclaurin expansions | Maclaurin Series | ✓ covered |
| 55 | Deriving the first terms by repeated differentiation | Maclaurin Series | ✓ covered |
| 56 | Range of x for which a standard series convergesMissing | Binomial Series for a Negative or Fractional Index, Expanding (a + bx) to a Rational Power, The Sum to Infinity, Maclaurin Series | ◐ partial |
| 57 | Maclaurin series as an approximation | Maclaurin Series | ✓ covered |
| 58 | Small-angle approximations | Small-Angle Approximations, The Limit of sin x over x | ✓ covered |
| 59 | ∫ f′(x)[f(x)]ⁿ and ∫ f′(x)e^f(x) | Integrals of f′ over f, Integration by Substitution | ✓ covered |
| 60 | ∫ sin²x, cos²x, tan²x | Integrating sin² and cos², Integrating sec²x, sec x tan x and tan x | ✓ covered |
| 61 | ∫ 1/(a²+x²), 1/√(a²−x²), 1/(a²−x²), 1/(x²−a²) | Integrals That Give tan⁻¹ and sin⁻¹, Integration by Partial Fractions | ✓ covered |
| 62 | Integration by a given substitution | Integration by Substitution | ✓ covered |
| 63 | Integration by parts | Integration by Parts | ✓ covered |
| 64 | Definite integral as a limit of sum and as area | The Definite Integral, Area Under a Curve | ✓ covered |
| 65 | Areas incl. between two curves and below the axis | Area Between Two Curves, Area Below the Axis | ✓ covered |
| 66 | Volume of revolution about x- or y-axis | Volumes of Revolution | ✓ covered |
| 67 | Approximate definite integral with a graphing calculatorgraphing-calculator content — deferred until the planned graphing tool ships (owner ruling 2026-08-25; these rows then join the exam-item batches) | ○ deferred | |
| 68 | dy/dx = f(x)g(y), incl. reduction by a given substitutionseparable-differential-equations covers the separable form; reduction to it by a supplied substitution is not taught | Separable Differential Equations | ◐ partial |
| 69 | Formulating a differential equation from a situation | Forming Differential Equations | ✓ covered |
| 70 | Interpreting a DE and its solution in context | Forming Differential Equations, Separable Differential Equations | ✓ covered |
| 71 | Addition and multiplication principles | Adding and Multiplying Choices | ✓ covered |
| 72 | Permutations and combinations | Permutations, Combinations | ✓ covered |
| 73 | Arrangements in a line **or in a circle**, with repetition/restrictioncircular arrangements are absent | Permutations, Repeats and Restrictions | ◐ partial |
| 74 | Addition and multiplication of probabilities | The Addition Rule for Overlapping Events, Independent Events | ✓ covered |
| 75 | Mutually exclusive and independent events | Mutually Exclusive Events, Independent Events | ✓ covered |
| 76 | Tables, Venn, tree diagrams and P&C for probabilities | Possibility Diagrams, Venn Diagrams, Tree Diagrams | ✓ covered |
| 77 | Conditional probabilities | Conditional Probability, Conditional Probability from Tables | ✓ covered |
| 78 | P(A′), P(A∪B), P(A\|B) formulae | Complementary Events, The Addition Rule for Overlapping Events, Conditional Probability Notation | ✓ covered |
| 79 | Discrete RVs: distributions, expectations, variances | Random Variables, Probability Distributions, Expected Value, Variance | ✓ covered |
| 80 | Binomial distribution and conditions for suitability | The Binomial Distribution, Modeling with a Binomial | ✓ covered |
| 81 | Mean and variance of the binomial | Binomial Mean and Variance | ✓ covered |
| 82 | Continuous RVs; normal model; N(μ, σ²) | Continuous Variables, The Normal Distribution | ✓ covered |
| 83 | Standard normal distribution | Standardizing, Reading the Z-Table | ✓ covered |
| 84 | P(X < x₁) given x₁, μ, σ | Reading Normal Probabilities | ✓ covered |
| 85 | Symmetry of the normal curve | The Normal Distribution | ✓ covered |
| 86 | Relationship between x₁, μ, σ from a given probability | Inverse Normal | ✓ covered |
| 87 | E(aX + b), Var(aX + b) | Transforming a Random Variable | ✓ covered |
| 88 | E(aX + bY), Var(aX + bY) | Combining Normals | ✓ covered |
| 89 | Population and simple random sample | Populations and Samples, Sampling Methods | ✓ covered |
| 90 | E(X̄) = μ, Var(X̄) = σ²/n | Mean and Variance of X-bar, Standard Error | ✓ covered |
| 91 | Distribution of X̄ from a normal population | The Sampling Distribution | ✓ covered |
| 92 | Central Limit Theorem | The Central Limit Theorem, Applying the Theorem | ✓ covered |
| 93 | Unbiased estimates, incl. from summarised datapoint-estimates, unbiased-variance; the Σx / Σx² / Σ(x−a) computational forms are absent | Point Estimates, Unbiased Sample Variance | ◐ partial |
| 94 | H₀/H₁, test statistic, critical region, level, p-value | Null and Alternative Hypotheses, Critical Regions, P-Values | ✓ covered |
| 95 | Hypothesis test for a population mean | The Z-Test | ✓ covered |
| 96 | 1-tail and 2-tail tests; interpretation | One-Tailed and Two-Tailed, P-Values | ✓ covered |
| 97 | Scatter diagram to judge a linear relationship | Scatter Plots, Correlation | ✓ covered |
| 98 | Correlation coefficient; interpreting r | Pearson’s Correlation Coefficient, Spearman’s Rank Correlation | ✓ covered |
| 99 | Linear regression; least squares; the regression equation | The Least-Squares Regression Line | ✓ covered |
| 100 | Interpolation and extrapolation | Interpolation and Extrapolation, Predicting from a Regression Line | ✓ covered |
| 101 | Regression line for prediction, with model commentary | Predicting from a Regression Line, Correlation Is Not Causation | ✓ covered |
| 102 | Square/reciprocal/log transformation to achieve linearitystraightening-growth-with-logs and straightening-a-power-law (2026-08-26) cover the log and log-log transforms; square and reciprocal transformations are absent | Straightening Growth with Logarithms, Straightening a Power Law | ◐ partial |
Other syllabuses: Singapore PSLE Mathematics · Singapore O-Level Mathematics · SAT Math · GCSE Mathematics (Higher)