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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