H1 Mathematics

H1 Mathematics provides students with a foundation in mathematics and statistics that supports further studies in business and social sciences. It is suitable for students without a G3 Additional Mathematics background.

Syllabus Aims

The syllabus aims to enable students to:

• Acquire mathematical concepts and skills for tertiary studies in business and social sciences.
• Develop thinking, reasoning, communication, and modeling skills through mathematical problem-solving.
• Connect mathematical ideas and apply them in business and social science contexts.
• Appreciate the value of mathematics.

Content Strands

The syllabus covers three content strands:

• Functions and Graphs: This strand builds a foundation for algebraic and quantitative reasoning. It includes exponential and logarithmic functions, graphing techniques, and methods for solving equations and inequalities.
• Calculus: This strand introduces tools for analyzing and modeling change. It covers basic differentiation and integration, including applications like finding optimal values and areas under curves.
• Probability and Statistics: This strand focuses on modeling chance and making inferences from data. It covers counting techniques, probability, binomial and normal distributions, sampling, hypothesis testing, correlation, and regression.

Exam Format

The H1 Mathematics examination consists of a single 3-hour paper worth 100 marks, divided into two sections:

• Section A (Pure Mathematics - 40 marks): Around 5 questions based on the Pure Mathematics section of the syllabus.
• Section B (Probability and Statistics - 60 marks): 6 to 8 questions based on the Probability and Statistics section of the syllabus.

At least two questions, one in each section, will focus on real-world applications of mathematics, particularly in business and social sciences. Each application question will be worth at least 12 marks and may involve concepts from multiple topics.

Detailed Syllabus Content (2024)

Section A: Pure Mathematics

• 1. Functions and Graphs
• 1.1 Exponential and logarithmic functions and Graphing techniques (Includes the concept of a function, exponential growth and decay, laws of logarithms, and using graphing calculators. Excludes finding domain and range and change of base.)
• 1.2 Equations and inequalities (Includes conditions for quadratic roots, solving simultaneous equations, and graphical methods. Excludes certain complex inequality problems.)
• 2. Calculus
• 2.1 Differentiation (Includes derivatives of standard functions, chain rule, and applications to tangents and optimization. Excludes derivatives from first principles and products/quotients.)
• 2.2 Integration (Includes integration as the reverse of differentiation, definite integrals, and area calculations. Excludes integration by parts and complex area calculations.)

Section B: Probability and Statistics

• 3. Probability and Statistics
• 3.1 Probability (Includes counting principles, permutations and combinations, conditional probability. Excludes complex probability scenarios.)
• 3.2 Binomial distribution (Includes the concept of binomial distribution and its mean and variance. Excludes normal approximation.)
• 3.3 Normal distribution (Includes properties of the normal distribution, standard normal distribution, and related calculations. Excludes normal approximation to binomial.)
• 3.4 Sampling (Includes concepts of population and sample, sample mean, Central Limit Theorem, and unbiased estimates. Excludes stratified sampling.)
• 3.5 Hypothesis testing (Includes null and alternative hypotheses, test statistics, and p-values. Excludes Type I and Type II errors and complex hypothesis tests.)
• 3.6 Correlation and Linear regression (Includes scatter diagrams, correlation coefficients, and least squares regression. Excludes hypothesis tests and transformations for linearity.)