Simple properties of addition, multiplication and scalar multiplication. Chapter 9: Differential Equations In Differential Equations, you will be studying some basic concepts related to differential equation, general and particular solutions of a differential equation, formation of differential equations, number of methods to solve a question based on first order - first degree differential equation and some applications of differential equations in different areas. It is very important for every student to indulge in some other extracurricular or after school programs so that they can spend some time exploring. Click on the links below to access these handwritten notes. Questions from board papers will also be uploaded related to continuity and differentiability in the form of practice tests.
The expectations of your parents, relatives, and friends are shooting higher. Take to pass class 12 in easier way. Operation on matrices: Addition and multiplication and multiplication with a scalar. Chapter 12: Linear Programming This chapter has only two exercises in which you will study about some linear programming problems and their solutions by graphical method only, though there are many other methods also available to solve such problems. Chapter 8: Application of Integrals Here, in this chapter, you will study some specific application of integrals to find the area given under the simple curves, also, area between lines and arcs of circles, parabolas and ellipses standard forms only.
Chapter 13: Probability Probability will take you through the important concepts of conditional probability of an event given that another event has occurred, which will in turn clarify the Bayes' theorem, multiplication rule of probability and independence of events. There are five solved exercises at the end of the chapter to help the students understand every concept perfectly and do well in the exams. Derivatives of logarithmic and exponential functions. Concept of exponential and logarithmic functions. Maths plays a vital role in the success of students in class 12th boards and competitive exams.
Hence, if you study the Differential equations chapter in a detailed manner, it will help you to gain a detailed insight into all modern scientific investigations. The head quarter of the national council of education research and training is situated in New Delhi at Sri Aurobindo Marg. After that you will be learning about binary operation, composite function, inverse function and so on. The main motto of the development of the e-book is to reach each and every student or teacher or school to give the benefit of education. Chapter 11: Three Dimensional Geometry The chapter Three Dimensional Geometry will take you through the study of the direction cosines and direction ratios of a line joining two points and also about the equations of lines and planes in space under different conditions.
Based on the recommendations of the Education Commission 1964-66 , in 1968 the first national policy statement on education was issued. You should consult with your teacher regarding that. The probability is the most important chapter of this class. Apart from these exercises, there are also notes and tips for the students to understand the chapter better and perform well in the exams. Invertible matrices and proof of the uniqueness of inverse, if it exists; Here all matrices will have real entries.
Ncert maths book is very interactive and written beautifully. This chapter teaches students How to calculate determinants, the different properties of determinants, the adjoint and inverse of a matrix, the area of a triangle, the various applications of determinants and matrix, the minors and cofactors, and the determinants and matrices as equation solver. Some of the topics covered in this chapter are the degree of a differential equation, the First-degree differential equations, the general and particular solutions of a differential equation, the Methods of Solving First Order, among the others. This stage is the turning point in your life and the marks you score in this year will determine the career of yours. Getting a good grip over exhaustive details of some chapters of Maths like Calculus, differential equations etc can be of great help while understanding the derivations and concepts behind the numericals of Science.
Sample Papers with answers and solutions also will be uploaded for the till December, 2018. If you have done a chapter, the Together With Maths is very good to get proper practice. Direction cosines and direction ratios of a vector. There are also two exercises on the subject that help students gain a deep understanding of the different types of problems and questions with the brilliantly explained and detailed solutions to the questions. You can read the whole story here. It covers all the important theorems and formulas with detailed explanations to promote a better conceptual understanding in students.
Chapter 10: Vector Algebra Did you know that quantities that involve only one value magnitude , which is a real number are call scalars? Inverse Trigonometric Functions Now comes the chapter number two: inverse trigonometric functions. Here you will learn about the direction ratios of a line, skew lines, proper angle between two lines, etc. We expect that these will be useful and supportive in your studies. The solutions for each exercise have been curated and reviewed by some of the best teachers across India. It explains about the feasible and infeasible regions that are also known as bounded and unbounded. You will understand multiplication theorem, independent events, conditional, unconditional and total probability. Thus students are advised to follow these solutions and notes as not only they will help them to achieve more marks, but could also be used as the answer key to complete an assignment or homework faster.