I was a student for more than 20 years, and I have taught hundreds of students since I became a tutor and then a lecturer. Throughout my study and teaching, I have witnessed that many of my classmates or students failed their exams. Some of them may have used time-consuming methods and have not completed all the questions, some of them may have had no idea about using appropriate formulae, or some of them may have skipped essential steps and just given the final results. All these behaviours result in losing marks. With these points in mind, using proper and efficient methods and giving correct and complete responses to questions play a significant role in sitting for the test. As a student, it is very important to analyse what the examiners are testing you in their places. For example, a question worth four marks may be broken down as one mark for showing appropriate method or formula, one mark for substituting the corresponding values into the formula, one mark for working, and one mark for finding correct value at the end. In this case, to obtain full marks at least four steps are necessary, and one or two more steps are recommended to improve the chance of obtaining full marks. In this book, I summarise all the knowledge required for standard level mathematics for the IB diploma. Some words are written in colour or bold to draw your attention where I think it is important or confusing. Some pragmatic and efficient methods for tests are introduced by some examples where students often have trouble or make mistakes based on my teaching experience. The questions from the papers in the last two years are taken as examples to show a detailed breakdown of marking including the reasons or explanations for each mark. These real test questions may also help you to realise the importance of a section if you find more questions there. In some examples, a solution is given step by step for a non-calculator question, and a shortcut by a graphing calculator is also demonstrated since a similar question may appear on Paper 2. A \textit graph calculator is used for demonstration because I think it is a little more complicated compared with the Casio calculators. The relevant pre-knowledge is also given in Chapter 1 as a brief revision. All in all, solving questions is just like giving your viewpoints by showing your reasons logically but in a mathematical way. William ZhangPhD in PhysicsPhD in Electrical Engineering