The curriculum set for High school level Mathematics primarily focuses on boosting the capacity of students to apply Mathematics in solving day-to-day life problems and studying the subject as a separate core discipline. Carrying out experiments with numbers and forms of geometry, framing hypotheses and verifying these with further observations form an inherent part of Mathematics learning at this stage of education. The 9th-grade syllabus of Mathematics includes the study of the number system, algebra, geometry, trigonometry, mensuration, statistics, graphs and coordinate geometry, and is structured to consolidate the concepts learnt in the lower classes and further develop on those to reach new theories and conclusions. Mathematics has been included as a core subject in the curriculum to enhance the reasoning and logical skills of the students along with overall development. The syllabus yearns to initiate an interest in the students to study Mathematics as a separate discipline. Another objective of the curriculum is to acquaint students with different aspects of Mathematics used in daily life and to build an interest in mathematics as a problem-solving tool in various fields further in the course of their education or career. The teaching of Mathematics should be imparted carefully so as to enable students to understand the concepts well enough in order to solve questions correctly and also to remember them while learning new ones in further classes. It can be done by including various activities which may involve the use of concrete materials, models, patterns, charts, pictures, posters, games, puzzles and experiments. The NCERT curriculum makes sure of this with specific instructions for teachers to incorporate activities during the classes to make learning fun for students. The curriculum has textbooks prescribed for the purpose of helping students study the concepts properly along with having enough questions to work out and evaluate themselves on how well they have understood the topics. It also helps in preparing the students to formulate answers with the right steps for the sole purpose of scoring more marks in the exam.
The first unit of the class 8 Mathematics curriculum deals with the review of the representation of natural numbers, integers and also rational numbers on the number line. You can make use of a resource like RS Aggarwal Solutions Class 9 Chapter 1 Real Numbers for more. It contains portions that include rational numbers as recurring/ terminating decimals along with teaching the occurrence of various operations on real numbers. The unit gives adequate examples of non-recurring or non-terminating decimals and touches upon the existence of non-rational numbers which are also called irrational numbers such as and their representation on the number line. Rationalization of real numbers of different types and their combinations along with laws of exponents with integral powers and rational exponents with positive real bases are also incorporated. Mathematics exams are usually the ones that demand utmost focus and concentration from the students. To crack maths exams, there is a foremost need to practice solving question papers prior to the exams. The formulas and concepts from each chapter are to be properly understood and is a complete necessity towards solving problems. Instead of y hearting formulas, students can look for proper and simple derivations behind each of it which will help students understand why and where a formula is applied. It will also guide students during the exam if they forget a particular formula. Once these are clear, the only thing left to do to score better is to start working out as many questions as possible from each topic. Just like all other chapters, the Number system also has a set of exercise questions the students can try solving along with its answers. They can also look through some question papers and try solving questions that are exclusively from this chapter and crisis check it with the answers key. Apart from working on these questions thoroughly, students can go through references books that are available online and as printed books. R D Sharma and RS Agarwal’s solutions for class 9 Mathematics for chapter 1 are available online as pdf which the students can refer to get proper and detailed answer keys. Once students start solving at least a few questions from each type, with practice most questions will be internalized and they will be able to answer them spontaneously without even having to think properly and try different methods to see which one works out. This will help students save a lot of time. Students always face the hurdle of not getting enough time to finish the whole paper for subjects like Mathematics. Therefore it is completely necessary for students to develop speed and it is possible only by working out each question more than once with the required steps.
This will also lead to an increase in the student’s accuracy in calculations as students automatically tend to remember the result for some operations by practising to get the precise answer for each question. While solving questions, it is important for students to work on at least a few HOTS questions and also application-based questions. These carry a certain weightage of marks in every exam and solving a few of them beforehand will give students a heads up and also help them get familiarized with the pattern of this type of question. In addition to this once, all the chapters are done studying the entire syllabus, they can try working on mock tests. Many websites today have such a facility where the students can take mock tests which will provide the students with a question paper and the students will solve it within a time frame just like how the real exam will be. This will help students to prioritize certain questions and will give an idea on how best to attend to questions within the time frame. Students can sort to solve previous years’ questions papers on their own in such a manner also. The advantage of using previous years’ question papers is that there will already be an authorized answer key for it and therefore will assist the students in correcting the answer by themselves. This will help students find their mistakes and rework them over and over again until they get it right.