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Indices are an essential foundation that students need as part of their preparation for the O Level Maths paper. The Laws of Indices spell out the rules behind determining how indices work when applied in various mathematical scenarios, and this handy article will outline everything you need to master them. What are Indices? Index numbers (or indices, which is the plural form of index) refer to the powers, or exponents, of numbers. A power indicates how many times a number is multiplied by itself, and is expressed as such: xa In the above example, “x” is the base, while the smaller “a” is the power or exponent. The base is the number being raised to the power, multiplying itself by “a” times. As such, 22 is essentially 2 × 2, and the answer is 4. Understanding the Laws of Indices The Laws of Indices outline how students should approach mathematical expressions that involve indices. There are six Laws of Indices covering varying scenarios. The Power of One Any number that has an power of one is itself. As such: 21 = 2 While it is not one of the Laws of Indices, this elementary rule is still fundamental to learning about indices. The Power of Zero If a number is raised to the index of zero, then the answer is simply 1. 20 = 1 Multiplying Similar Bases When multiplying two numbers with similar bases but different powers, you can proceed to add the powers and raise them to that same base. xa × xb = xa + b To illustrate this with a sample: 23 × 25 = 23 + 5 = 28 Dividing Similar Bases Conversely, when dividing two numbers of similar bases and different powers, you will subtract the second power from the first power. xa ÷ xb = xa – b Here is a simple example: 26 ÷ 23 = 26 – 3 = 23 Multiplying Same Index, Different Bases When multiplying two different bases that have the same indices, you will need to multiply both bases and raise the index to the new sum. xa × ya = (x × y)a For example: 23 × 33 = (2 × 3)3 = 63 Dividing Same Index, Different Bases Conversely, when dividing two different bases with the same indices, you will divide both bases and raise the index to this new sum. You can express this division of bases in fractions. xa ÷ ya = (x⁄y)a For example: 33 ÷ 53 = (3⁄5)3 Bracketed Indices If there is a power outside a bracket containing a base with a different power, you can multiply both powers together like so: (xa)b = xab For example: (22)3 = 22 × 3 = 26 If, however, there are two numbers in the bracket without a power, it is instead solved like this: (xy)a = xaya To make this clearer, consider the following example: (3x)2 = 32x2 = 9x2 Negative Indices A negative power is the reciprocal: the numerator is one and the denominator is the base with a positive power, like so: x–a = 1 / xa Fractions and Indices If a fraction has an power, you will apply the power to both the numerator and the denominator. (x / y)a = xa / ya If a fraction has a negative power, then it becomes the reciprocal of the fraction to the positive power, as illustrated in the following example: (x / y)–a = (y / x)a = ya / xa Should you encounter a base number with a fraction index, then the denominator becomes the root of the number or letter: x1/a = a √ x Meanwhile, a negative, fractional power is one over a root: x–1/a = (x1/a)–1 = 1 / a √ x The Importance of the Laws of Indices Understanding the laws of indices is a key part of mathematical learning. Not only does it teach students how to simplify the multiplication of a number by itself over a certain number of times, but it also serves as an entry point to more complex algebraic expressions. More specifically, they are instrumental in ensuring students understand and solve questions on differentiation and integration. Mastering this fundamental set of mathematical principles will help students do well in the more advanced O Level Maths topics that follow. At Matrix Math, we can guide students to success with personalised tutoring to help them apply the laws of indices correctly. We use valuable revision materials to help them further their understanding and strengthen their mathematical foundation. Contact us today to discover how we can prep students towards success. Read Also: Mastering O Level Maths in Singapore: A Guide to Success with Matrix Math Tuition Center Is O-Level Math Tuition Important and Necessary in Singapore? What Does O-Level Grading Mean To Students?

The PSLE is drawing closer, and students are understandably anxious about how they will fare. Frequent practice and revision will help them see through even the more difficult questions, but even with plenty of preparation, some students may still make mistakes. Minimising these mistakes is vital to scoring a good grade, so here are several handy tips to help students avoid these costly mistakes during the PSLE Maths exam. Careless Mistakes Whether it is due to inattentiveness, a lack of focus, or overconfidence, careless mistakes can cost a student precious marks. Given the time constraints, a student may rush through the question and misread parts of it, missing out on key details they need to solve the problem at hand. It could also be a miscalculation when they misinterpret a number, forget to include measurement units, or even place a decimal point in the wrong position. These errors can be easily avoided by double-checking, even triple-checking, the calculations and answers before proceeding. It also helps to underline or highlight crucial parts of a question and understand what is needed of them to solve it effectively. Incorrect Formulae Given the exam’s time-sensitive nature, students may accidentally apply the wrong mathematical formula to a question that leads to an incorrect answer. It could happen when a student accidentally mixes up the formulae for similar topics, such as perimeter and area, and fails to double-check their work. This occurrence may be a result of insufficient practice with the relevant formulae, as revision allows students to gain a practical understanding of how to use these formulae accurately. Visual aids and real-life examples are great ways to test their formulae applications, and even writing the formula next to the relevant question can provide. Shortcuts Shortcuts can be handy tools that can help students save time when solving problems, but these are still very situational to specific questions. Moreover, using shortcuts can mean students will miss precious method marks that they would otherwise get when writing the complete workings and formulae, even if the answer is wrong. Without these workings, a student may not be able to score the marks they would otherwise receive. When in doubt, it is a good idea to avoid using shortcuts unless the student has tested it multiple times and found it to lead to the right answer. It would also be better to provide the workings, too, to ensure students can score full marks on a question. Poor Illustrations Modelling mathematical problems can offer valuable insight to solving a maths question. As a visual aid, it can offer a clearer understanding of what the question wants from them by breaking it down into components that allow a student to easily find the answer. However, poorly illustrated models, whether due to mixing up models, drawing them poorly, or missing labels, only demonstrate a student’s inability to express their problem-solving skills effectively, even if it was a careless mistake. Frequent model revisions can give a student the confidence they need to draw clear, concise illustrations that tell the examiner that they understood the question. It does not need to be meticulously modelled, but it must be properly labelled and provide sufficient clarity and context that leads to the right answer. Poor Time Management Students need to make every minute count during the PSLE Maths paper, especially when time is not on their side. Not having a plan to answer each question can end up costing valuable time that could otherwise be used to solve other, harder (or even easier) questions. Coupled with the stress they feel as the exam’s end approaches, and there will be occasions where they will rush the final hurdle of questions and make plenty of mistakes along the way. Time can be on a student’s side if they are careful. Students need to quickly assess the questions and prioritise the ones they can solve with confidence, and then slowly work their way through the rest. If a question stumps a student’s progress, they should move on to another question and come back later. It also helps to set a time limit during revision sessions, thereby giving them much-needed practice to completing the paper even when under a time constraint. Lack of Preparation Early and continuous preparations are what students need to help them thrive during the PSLE Maths paper. However, there will be students going through various difficulties that impede their progress. For some, they may have trouble understanding the subject and are too shy or embarrassed to ask for help. For others, they may feel stressed out by the preparations they need to succeed. Whatever it is, students who do not prioritise regular revisions and practice will only end up having a much harder time preparing for the PSLE Maths paper. That can then lead to careless mistakes, mixed up formulae, and other issues that prevent students from getting a good grade. Overcome Mistakes with Personalised PSLE Maths Tuition At Matrix Math, we can guide students to success with personalised tutoring that improves their confidence and competency. We use valuable revision materials to help them further their understanding and strengthen their mathematical foundation. Contact us today to discover how we can prep students towards success. Read Also: Understanding the PSLE Scoring System: A Guide for Parents and Students Overcoming the Hurdles of the PSLE Math Paper: What Makes It So Challenging? 10 Things to Note Before PSLE Math Exam Effective Tips To Prepare Your Child For PSLE and Score Well PSLE Math Preparation: Harness The Power Of Return On Learning