Complimentary: 3 topical papers to be selected from
■ 2021/22 RI (with solutions)
• Equations and Inequalities
• Functions
• Vectors 1
• Vectors 2
• Vectors 3
• Differentiation Techniques
• Differentiation Applications
• Maclaurin Series and Binomial Expansion
• Graphing Techniques
• Arithmetic and Geometric Series
• Summation of Series
• Complex Numbers
• Integration Techniques
• Integration Applications
• Differential Equations
• Permutations and Combinations
• Probability
• Discrete Random Variables
• Binomial Distribution
• Normal Distribution
• Sampling
• Hypothesis Testing
• Correlation and Regression
The Graphing Calculator (GC) problem solving techniques recorded in this book are a collection of the Author's personal tips and tricks he has been using in his lessons since 2006, when the GC was officially introduced to the JC1 students, the pioneer batch who were approved to use the GC in the 2007 A Level Math examinations in Singapore.
Over the last 14 years, the calculator model and even the operating system (OS) of each model is continuously being updated by the manufacturer while the Author continues to devise innovative and efficient methods of solving examination questions in response.
To many, the GC has absolutely no use in topics like Vectors, Partial Fractions and Power Series, just to name a few. However, as the reader will discover in this book from Chapter 4 onwards, through the Author's mastery and creative use of the GC, seemingly unrelated calculations can be carried out via the approved functions of the GC, in a much more efficient manner than any non-GC methods. This not only significantly reduces the time spent by the candidate in the examination hall (when time is not on his side), but also detects any mistakes due to carelessness since the answers can now be verified by the GC.
This book is written with the following aims.
★ To recapitulate the essential knowledge of O level mathematics which are often forgotten (even by students with Additional Mathematics background) but are needed at A level.
★ To offer innovative ways of using the GC to more effectively and efficiently solve problems during examinations when time is critical, and to check answers to detect careless mistakes.
★ To summarise the critical concepts of each chapter and serve as a comprehensive exam revision guide that includes useful topics not taught under the current syllabus, including Cover-up Rule, sum and roots of a polynomial (of order higher than 2), L’Hôpital’s Rule, Thin Shell Method, Riemann Sums and De Morgan’s Laws.
As far as possible, the problems discussed in this book are extracted from actual questions from past Cambridge GCE A Level H2 mathematics examinations to demonstrate the practicality of the tips.