This book is specially designed for students who want to test their mathematical skills at a higher level. Though the Advanced Questions here are of similar or slightly higher standard than those in the A-Level examinations, students should be able to solve them. The Challenging Questions are designed to push the student’s limits, though the skills needed to solve them are within the student’s scope of knowledge. Detailed worked solutions enable students to learn from their mistakes and at the same time coach them on certain concepts.

The change in the H2 Mathematics syllabus for 2017 has necessitated this Second Edition. In the new 9758 H2 mathematics syllabus, mathematical induction, De Moivre’s Theorem, loci in complex numbers, multiple planes in vectors, recurrence relations, Poisson distribution and approximations in statistics have been dropped. In their place are at least two questions in each paper on applications of mathematics in real-world contexts. Each question will carry at least 12 marks with two such questions in Pure Mathematics and two in Statistics, making a total of 48 marks.

The application of mathematics in real-world contexts is not new. It is now more emphasised. Such questions can be found in this book in topics like AP/GP, applications of differentiation and differential equations. Too often, students do not see and appreciate the real-life applications of the mathematics that they learn in school. This change in the syllabus is a step forward to enhance students’ appreciation of the subject. While the mathematics that students learn at A-level is still considered basic for many real-life applications, it is a start. Questions in this book include solving real-world financial problems using AP/GP and carbon dating using differential equations. I hope that through these exposures, students can have a better appreciation of the mathematics that they are learning.