Mathematics is a basic and important discipline that contributes to the development and understanding of sciences and other disciplines. It is used by scientists, engineers, business analysts and psychologists, etc. to model, understand and solve problems in their respective fields. A good foundation in mathematics and the ability to reason mathematically is therefore essential for students to be successful in their pursuit of various disciplines.
H2 Mathematics is designed to prepare students for a range of university courses, including mathematics, sciences, engineering and related courses, where a good foundation in mathematics is required. It develops mathematical thinking and reasoning skills that are essential for further learning of mathematics. Through applications of mathematics, students also develop an appreciation of mathematics and its connections to other disciplines and to the real world.
The aims of H2 Mathematics are to enable students to:
(a) acquire mathematical concepts and skills to prepare for their tertiary studies in mathematics, sciences, engineering and other related disciplines
(b) develop thinking, reasoning, communication and modelling skills through a mathematical approach to problem-solving
(c) connect ideas within mathematics and apply mathematics in the contexts of sciences, engineering and other related disciplines
(d) experience and appreciate the nature and beauty of mathematics and its value in life and other disciplines.
There are three levels of assessment objectives for the examination.
The assessment will test candidates’ abilities to
AO1 Understand and apply mathematical concepts and skills in a variety of problems, including those that may be set in unfamiliar contexts, or require integration of concepts and skills from more than one topic.
AO2 Formulate real-world problems mathematically, solve the mathematical problems, and interpret and evaluate the mathematical solutions in the context of the problems.
AO3 Reason and communicate mathematically through making deductions and writing mathematical explanations, arguments and proofs
The use of an approved GC without a computer algebra system will be expected. The examination papers will be set with the assumption that candidates will have access to GC. As a general rule, unsupported answers obtained from GC are allowed unless the question states otherwise. Where unsupported answers from GC are not allowed, candidates are required to present the mathematical steps using mathematical notations and not calculator commands. For questions where graphs are used to find a solution, candidates should sketch these graphs as part of their answers. Incorrect answers without working will receive no marks. However, if there is written evidence of using GC correctly, method marks may be awarded.
Students should be aware that there are limitations inherent in GC. For example, answers obtained by tracing along a graph to find the roots of an equation may not produce the required accuracy.
Notwithstanding the presentation of the topics in the syllabus document, it is envisaged that some examination questions may integrate ideas from more than one topic and that topics may be tested in the contexts of problem solving and the application of mathematics.
Possible list of H2 Mathematics applications and contexts:
Applications and contexts | Some possible topics involved |
|---|---|
Kinematics and dynamics (e.g. free fall, projectile motion, collisions) | Functions; Calculus; Vectors |
Optimisation problems (e.g. maximising strength, minimising surface area) | Inequalities; System of linear equations; Calculus |
Electrical circuits | Complex numbers; Calculus |
Population growth, radioactive decay, heating and cooling problems | Differential equations |
Financial maths (e.g. banking, insurance) | Sequences and series; Probability; Sampling distributions |
Standardised testing | Normal distribution; Probability |
Market research (e.g. consumer preferences, product claims) | Sampling distributions; Hypothesis testing; Correlation and regression |
Clinical research (e.g. correlation studies) | Sampling distributions; Hypothesis testing; Correlation and regression |
The list illustrates some types of contexts in which the mathematics learnt in the syllabus may be applied and is by no means exhaustive. While problems may be set based on these contexts, no assumptions will be made about the knowledge of these contexts. All information will be self-contained within the problem.
For the examination in H2 Mathematics, there will be two 3-hour papers, each carrying 50% of the total mark, and each marked out of 100, as follows:
PAPER 1 (3 hours)
A paper consisting of 10 to 12 questions of different lengths and marks based on the Pure Mathematics section of the syllabus.
There will be at least two questions on the application of Mathematics in real-world contexts, including those from sciences and engineering. Each question will carry at least 12 marks and may require concepts and skills from more than one topic. Candidates will be expected to answer all questions.
PAPER 2 (3 hours)
A paper consisting of two sections, Sections A and B.
Section A (Pure Mathematics – 40 marks) will consist of 4 to 5 questions of different lengths and marks based on the Pure Mathematics section of the syllabus.
Section B (Probability and Statistics – 60 marks) will consist of 6 to 8 questions of different lengths and marks based on the Probability and Statistics section of the syllabus.
There will be at least two questions in Section B on the application of Mathematics in real-world contexts, including those from sciences and engineering. Each question will carry at least 12 marks and may require concepts and skills from more than one topic.
Candidates will be expected to answer all questions.
Full H2 Mathematics syllabus details can be read in the SEAB H2 Mathematics Syllabus.
