The 2026 H2 Mathematics syllabus

 The 2026 H2 Mathematics syllabus in Singapore for the A-Level examination covers Pure Mathematics and Probability & Statistics. Here’s a detailed breakdown:

Section A: Pure Mathematics

1. Functions and Graphs:

• Study transformations of graphs, asymptotes, and properties of functions, including exponential and logarithmic functions.

2. Sequences and Series:

• Key topics include arithmetic and geometric progressions, summation of series, and sigma notation.

3. Vectors:

• Learn about vectors in 2D and 3D, vector products, and the geometry of lines and planes in 3D space.

4. Complex Numbers:

• Work with complex numbers in both Cartesian and polar forms, including their geometric interpretation and application in solving polynomial equations.

5. Calculus:

• Differentiation and integration are central to the curriculum. This includes advanced techniques like implicit differentiation, integration by parts, and solving differential equations (both first and second order). You’ll also study applications such as optimization and rates of change.

6. Differential Equations:

• Analytical solutions to first- and second-order linear differential equations are explored, including methods for solving non-homogeneous equations and modeling real-life problems like exponential growth and decay  .

Section B: Probability & Statistics

1. Probability:

• Concepts covered include discrete and continuous probability distributions (like Poisson, geometric, and normal distributions), additive properties of the Poisson distribution, and conditional probability.

2. Statistics:

• Learn about hypothesis testing for population means, contingency tables, and chi-square tests for goodness of fit and independence. The syllabus also covers confidence intervals and methods for estimation in the context of real-world applications  .

3. Hypothesis Testing and Confidence Intervals:

• Test statistical hypotheses with a focus on t-tests, non-parametric tests like the Wilcoxon matched-pair test, and the connection between hypothesis tests and confidence intervals.

4. Non-parametric Tests:

• This includes tests such as the Sign Test and the Wilcoxon matched-pair signed rank test, which are useful when assumptions about population distributions may not hold .

The syllabus emphasizes both theoretical knowledge and practical applications in mathematical modeling, data interpretation, and solving real-world problems. This ensures students are well-prepared for higher-level studies in mathematics or related fields.