# H2 Math Syllabus 2024

Embarking on the H2 Math journey is a significant academic endeavor that demands clarity, understanding, and strategic preparation. The following are the syllabus content from the H2 math syllabus 2024 (SEAB).

## H2 Math Syllabus Content

 Topic/Sub-topics Content SECTION A: PURE MATHEMATICS Functions and Graphs   –    Topic 1.1—Functions   –    Topic 1.2—Graphs and Transformations –    Topic 1.3—Equations and inequalities Include: • concepts of function, domain and range • use of notations • finding inverse functions and composite functions • conditions for the existence of inverse functions and composite functions • domain restriction to obtain an inverse function • relationship between a function and its inverse. Sequences and Series –    Topic 2.1—Sequences and Series Include: • concepts of sequence and series for finite and infinite cases • sequence as function y = f(n) where n is a positive integer • relationship between un (the nth term) and Sn (the sum to n terms) • sequence given by a formula for the nth term • use of Σ notation • sum and difference of two series • summation of series by the method of differences • convergence of a series and the sum to infinity • formula for the nth term and the sum of a finite arithmetic series • formula for the nth term and the sum of a finite geometric series • condition for convergence of an infinite geometric series • formula for the sum Vectors –    Topic 3.1—Basic properties of vectors in two and three dimensions –    Topic 3.2— Scalar and vector products in vectors –    Topic 3.3 — Three Dimension Vector Geometry Include: • addition and subtraction of vectors, multiplication of a vector by a scalar, and their geometrical interpretations • use of notations • magnitude of a vector • unit vectors • distance between two points • collinearity • use of the ratio theorem in geometrical applications   Include: • concepts of scalar product and vector product of vectors and their properties • angle between two vectors • geometrical meanings of | a • nˆ | and | a × nˆ |, where nˆ is a unit vector Exclude triple products a • b × c and a × b × c .   Include: • vector and cartesian equations of lines and planes • finding the foot of the perpendicular and distance from a point to a line or to a plane • finding the angle between two lines, between a line and a plane, or between two planes • relationships between (i) two lines (coplanar or skew) (ii) a line and a plane (iii) two planes   Exclude: • finding the shortest distance between two skew lines   • finding an equation for the common perpendicular to two skew lines Introduction to Complex numbers –    Topic 4.1—Complex numbers expressed in cartesian form –    Topic 4.2—Complex numbers expressed in polar form Include: • extension of the number system from real numbers to complex numbers • complex roots of quadratic equations • conjugate of a complex number • four operations of complex numbers • equality of complex numbers • conjugate roots of a polynomial equation with real coefficients representation of complex numbers in the Argand diagram • complex numbers expressed in the form r(cos θ + i sin θ), or reiθ where r > 0 and – π < θ ⩽ π • calculation of modulus (r) and argument (θ) of a complex number • multiplication and division of two complex numbers expressed in polar form Calculus Topic 5.1—Differentiation Topic 5.2— Maclaurin series Topic 5.3—Integration techniques Topic 5.4 — Definite integrals Topic 5.5 — Differential equations     – Include: • graphical interpretation of (i) f′(x) > 0, f′(x) = 0 and f′(x) < 0 (ii) f″(x) > 0 and f″(x) < 0 • relating the graph of y = f′(x) to the graph of y = f(x) • differentiation of simple functions defined implicitly or parametrically • determining the nature of the stationary points (local maximum and minimum points and points of inflexion) analytically, in simple cases, using the first derivative test or the second derivative test • locating maximum and minimum points using a graphing calculator • finding the approximate value of a derivative at a given point using a graphing calculator  • finding equations of tangents and normals to curves, including cases where the curve is defined implicitly or parametrically • local maxima and minima problems • connected rates of change problems Exclude finding non-stationary points of inflexion and finding second derivatives of functions defined parametrically.     List of tested topics pdf

 SECTION B: PROBABILITY AND STATISTICS Probability and Statistics –    Topic 6.1—Probability   –    Topic 6.2—Discrete random variables –    Topic 6.3—Normal distribution –    Topic 6.4- Sampling –    Topic 6.5- Hypothesis Testing –    Topic 6.6- Correlation and Linear Regression Include: Refer to syllabus link Above

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