Maths for Class IX
- Number system
- Coordinate Geometry
All the topics again have subtopics, and Algebra and Geometry are divided into two parts in Algebra I, II and Geometry I, II. Read the syllabus thoroughly before revision.
Every student will have the NCERT or textbook, and handwritten class notes, to prepare for. But a student also needs revision notes to have better practice and quick revision before exams. The exam carries 80 marks and 3 hours duration, so practice to complete all the questions in time.
Preparing Revision Notes
Decide on the style of notes, whether to have chapter wise or division wise. The best-suggested method is to go with Division wise revision. Follow the below steps, and try to prepare notes.
Write down the formulae from each chapter with topic headings. It is much easier to find all the formulae in one place while revising. Also, write down beside the formulae if they are applicable in multiple chapters.
For surface and volumes, formulae for cuboid, cylinder, cone, sphere, can be written as a tabular form. For Algebra, list out all the formulae starting from two variables to three variables.
Write down the theorems in a brief manner, for topics like triangles, circles. Draw the diagram and make two important points for every theorem. For theorems like remainder and factor, write down the formula and statement, and make very brief sentences for proof of the statement.
Lines & Angles:
For this chapter, RS Aggarwal Class 9 chapter 7 Solutions serves as the best revision notes for Lines and angles. Foundation or basics is more important for a student to ace any exam, RS Agarwal notes give a student an ability to solve tricky questions, and when a student perfectly understands the concept of the further chapters like Heights and distances, drawing Geometrical figures, and graphs. Also in Trigonometry which will be discussed in later classes, we use angles. It is better to gain a good knowledge of this chapter, and while making revision notes, try to draw and understand. All the questions in previous papers are like, for example. A diagram is given and asks a student to prove the angle of some ABC = pqr. All the solutions for NCERT are given in the RS Agarwal solutions book or pdf.
Geometry is mostly considered a difficult topic in mathematics for many students, because of the theorems or angles or the triangles involved in it. It will be easier for a student if revised well. Firstly, consider reading the syllabus and analysing the previous papers thoroughly. Then, write down the list of the theorems in a brief way, and all the questions mostly asked in Geometry class 9 are proving theorems.
Statistics and Probability:
This chapter carries three and four marks questions which cannot be skipped as optional. It is quite a simple and easy chapter compared to geometry or others, with not much pressure to learn formulae.
Finding out mean, median, and mode for the given data, are the frequent questions asked in exams. There are just three formulae for three methods, and data will be given. Make a revision note in such a way that you do not repeat the same data.
Follow up with the previous year questions and NCERT books, and prepare notes for revision.
Probability has questions based on cards, dies, or balls, in revision notes, try to write one question for each type. Note the frequency and cumulative frequency in the Statistics chapter. Also, make a note of the difference between bar and pie diagrams separately.
For all the Geometrical shapes
Keep note of the data or the formulae for the shapes each separately, like triangles, circles and quadrilaterals. For example, Triangles are of Isosceles, Equilateral, Right angle and Scalene types.
Also, they are classified with angle, right angle, acute angle and obtuse angle triangles. Questions are based on congruent triangles, where angles and sides of the triangles are given and finding the other sides or angles. Have a brief note on the congruent triangle theorem.
The Quadrilateral shapes like Rectangle, rhombus, parallelogram and trapezium, draw the figurines and make notes on the sides and angles. Note the formulae for area, perimeter and volumes for each of them. From the previous papers pick questions and solve them for revision purposes.
Simple Points to remember while making revision notes:
- Do not write the complete notes or content from the textbooks or class notes.
- For every chapter note down the definition, and related content to it. For example, Circle: Definition, Diagram, radius, diameter, chord, circumference, arc, and theorem.
- While writing theorem, remember the points like Statement to be proved, diagram, data and construction with statements and reasons.
While briefly noting down in the revision notes, remember to write them stepwise in exams.
- Algebra carries more marks, as it os two parts, one dealing with polynomials and the other with linear equations.
Polynomials are all about the formulae and the simplification of the equations. Like x2 + x – 12 and 3x + 5x, performing arithmetic operations like subtraction, multiplication or division on polynomials and making notes on factorization method.
- For number systems, the law of exponents and rationalization problems are asked in the exam.
- Always make tabular forms for formulae to have a glance.
- Use diagrams for Geometry, that is two parts, one is Euclid Geometry and the other is the constructions.
- Do not write every problem in the revision notes, maintain it like a brief copy of the class notes. Write one problem for one method.
- For linear equations, make a graph of linear equations of two variables, for example, a question is given with coordinate points of x and y and asks the student to draw the graph and statements regarding that. Note down the Statements like equations of a line parallel to x and y-axis, where x=0 or y=0.
- For the chapter Heron’s formula, write down, for example, the area of the triangle, its da diagram and the formula given by Heron by taking sides of the triangle and calculating it.
Follow the steps and have clear and concise notes which will be much useful while preparing for the final exams.