Advanced Mathematics For Express and IP Students Secondary 4

Singapore Curriculum — suitable for enrichment alongside Australian primary and secondary learning.

This is a book for those who do not just want to pass; they want to excel. This is a book for those who do not just want to stop at grasping the concepts, but challenge themselves to master the 'killer questions' in tests and examinations. If excellence is what you are aiming for, then you have picked up the right book. Advanced Mathematics for Express and IP Students aims to be an essential practice companion to IP and O-Level students in their Mathematics learning journey. Complete with notes, examples, practice questions and worked solutions, it is everything a student needs for effective self-revision. Carefully crafted and compiled by a team of expert tutors from Future Academy (including former MOE senior teachers, top IP school HODs and distinguished scholars), this book contains insights and guidance from the perspective of experienced educators who have seen and understood the common struggles of high-ability students here. It covers all key topics meticulously, ensuring a profound understanding. It also features tailored questions of varying difficulty levels, supporting learners in their course from familiarisation to mastery. Proficient students will also benefit from the demands of challenging questions, encouraging them to think deeper and achieve greater excellence in the subject. Filled with concept guides, exam-style questions, mixed-topic mock quizzes, and step-by-step solutions, this book is designed for ease of use – whether you are a student doing independent learning or a tutor looking for quality practice questions as a teaching tool.

Sections of Advanced Mathematics for Express and IP Students include:

Introduction - Serves as a useful checklist and summary of key ideas, concepts and formulae required before attempting questions.

Examples with Solutions - Demonstrate how different concepts can be applied to common exam questions.

Practice – Builds on students' confidence in each topic as they attempt thoughtfully selected questions designed to challenge, inspire and elevate every student's learning journey.

Review – Simulates termly assessments in schools.

Step-by-step Solutions at the back of the book are written with the independent learner in mind, so that mistakes can be learnt from and rectified immediately after completing an exercise. Comprehensive and cutting-edge, yet handy and easy to use – it is with hope that this book will benefit students in their learning and propel them towards reaching their study goals.

Secondary 4 Contents

Unit 1.1 Coordinate Geometry

Unit 1.2 Binomial Theorem

Unit 1.3 Trigonometric Identities

Unit 1.4 Trigonometry Revision

Review 1

Unit 2.1 Proofs in Plane Geometry

Unit 2.2 Vectors

Unit 2.3 Differentiation (I)

Unit 2.4 Differentiation (II)

Unit 3.1 Applications of Differentiation

Unit 3.2 Integration Techniques

Unit 3.3 Integration Application to Area

Unit 4.1 Practice Paper 1

Unit 4.2 Practice Paper 2

Unit 4.3 Practice Paper 3

Solutions