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Chapter 15 - Probability. If you practice it regularly, then you will better understand all the concepts of the chapter. Still, if you find yourself in any problem, our expert teachers will always help you. Along with this, you can take help from our online videos, lectures, topic lessons, other learning materials, etc.
A circle is a chapter in which students learned about the existence of tangents to a circle and their properties. In this chapter, all concepts are explained in detail, such as Tangent, Number of a tangent from a point on a circle, Tangents to a circle, and others. No doubt, Circle is a very important topic in board exams as well as competitions.
Those students who have a goal to crack IIT, JEE, or any medical exam after their 12th, then they should not ignore this chapter at any condition. Many questions are asked from this topic. It includes lots of diagrams, figures, and lucid language, which is not easy to understand for a student without any guidance.
The five sections are introduction to coordinate geometry, formula to calculate distance between two pints, finding the coordinate of the point dividing the line in a particular ratio called section formula and finding the area of triangle in the form of coordinates of their vertices.
Exercise 7. It helps you to find the distance between any two points given on a plane. Section Formula deals with finding the coordinates of a point dividing the line in the particular ratio.
What is Coordinate Geometry. We have studied number lines to mark any point. Descartes invented the idea of placing two perpendicular lines to each other on a plane, and locating points on the lines of the plane. The perpendicular lines may be in any direction but usually one line is horizontal and the other vertical. Coordinate Geometry is the branch of mathematics that helps us to exactly locate a given point with the help of an ordered pair of numbers.
Coordinate geometry is the Ch 2 Maths Class 10 Vedantu Model combination of geometry and algebra to solve the problems. Coordinate geometry is also said to be the study of graphs.
Graphs are visual representations of our data. It can be in different forms like bar graphs, histograms, line graphs, etc. Terms Related to Coordinate Geometry. While studying coordinate geometry the students must be aware of some important terms related to coordinate geometry they are well explained in this chapter.
From this figure, let us understand some important terms used in the coordinate formula of geometry. Axes of Coordinates. In the above figure OX and OY are called X-axis and Y-axis respectively and both together are known as axes of coordinates. The point of intersection of the axes is called the origin; it is O. The distance of any point on the plane from the Y-axis is called the abscissa. The distance of any point on the plane from the X-axis is said to be ordinate. Coordinate of the Origin.
It has zero distance from both the axes. Therefore the coordinates of the origin are 0, 0. The axes divide the plane into four parts. These four parts are said to be quadrants. The plane is called the coordinate plane or the XY-plane and the axes are called the coordinate axes. In the first quadrant, both the coordinates are positive. In the second quadrant, the y-coordinate is positive and x-coordinate is negative. In the third quadrant, both the coordinates are negative.
In the fourth quadrant, the y-coordinate is negative and the x-coordinate is positive. Distance Formula. In chapter 7 Maths Class 10 we learn about distance formulas for finding distance between two points.
Finding the distance between the two points by using formula when the two coordinates of the points are given.
Section Formula. Section formula helps us in finding the coordinates of the point dividing the line in the ratio m:n. If P is the point dividing the line AB in the ratio m:n where coordinates of A x 1 , y 1 and B x 2 , y 2. Area of Triangle. It will let us find the area of any triangle in terms of coordinates of its vertices. This formula will also be used in finding the area of quadrilaterals. All the basic formulas of coordinate geometry will help you to solve your geometry and algebra problems.
Chapter 7 maths Class 10 provides you the list of all formulas of coordinate geometry to solve all the related problems. General Form of a Line. Where A , B, C are real numbers and x and y are variables. Slope Intercept Form of a Line. Where x and y are variables, Ch 2 Maths Class 10 Vedantu Wine c is constant and m is the slope. Point-Slope Form. The slope of a Line Using Coordinates.
The slope of a Line Using General Equation. Intercept-Intercept Form. Distance between two points O x 1, y 1 and B x 2, y 2. For Parallel Lines,. For Perpendicular Lines,. Angle between Two Lines. Area of a Triangle. Perpendicular Distance from a Point to a Line. It is very important to get acquainted with these basic formulas of coordinate geometry.
Chapter 7 Maths Class 10 coordinate formulas have been proven very helpful for students to solve the problems at a competitive level.
Historical Facts. Rene Descartes, the Great French Mathematician of the seventeenth century, liked to lie in bed and think. One day, when lying in the bed he solved the problem of describing the position of a point in a plane.
This chapter is all about constructing various geometric figures. The students will learn to divide a line segment, and how to draw tangents to a circle. The methods of construction are well explained in the chapter to clear the concepts. As the name suggests, the chapter is about the perimeter and area of a circle. The concepts of finding the area of a sector and segment of a circle is clarified here. This chapter further explains how to find the area of the figures that contains a circle or part of a circle.
In the five Exercises of this chapter, finding the surface area of any object which is made up of two or more different solid shapes. The solid shapes include cuboid, cone, sphere, hemisphere and cylinder.
Then, there are questions on finding the volume of the objects that are again made up of two different solid shapes. Also, there are questions which ask about the conversion from one shape to another. This chapter further explains how to find the volume, curved surface area and total surface area of a frustum of a cone.
This is another interesting chapter where the students learn about the numerical representation of data, grouped or ungrouped. They further learn about finding the mean, median and mode of the given data. In the next Exercise, they will learn about the cumulative frequency distribution and drawing cumulative frequency curves. It elaborates and explains the difference between experimental probability and theoretical probability.
The chapter is full of examples to clear the concept of probability to the learners. Students can download the PDF easily and start going through the chapters. You will find clear categorisation and step by step solutions of all the questions with a clear conclusion. This will help you to understand how you can write answers in your exams to help you score well. The exam is of marks where 80 marks is for theory whereas 20 marks is given for internal assessment.
To understand the marking scheme in a better way, you should understand the exam pattern clearly. To score good in the exam, you should know how much mark is awarded for each question and each step of the question. Every year, just before the board exams, the board releases sample papers and marking schemes so that all the doubts of the students are cleared. The number of questions are increased and the marks per question are reduced.
This marking scheme will be helpful to the students as the maximum number of questions will become objective or very short answer type as the marks per question has reduced. CBSE focuses on all-round development of Class 10 students to prepare them for their further education. To perform well in Class 10 then becomes fairly important. CBSE marking scheme is stepwise so you have scored accordingly.
Therefore students should write each step clearly and give a proper conclusion at the end of the answer. The unit wise marks weightage of the mathematics paper is as follows:. The paper has four sections.
There are a total of 30 questions for 80 marks. Number System. Coordinate geometry. Statistics and probability. The question paper design will be:. Sl No. Type of Questions.
Total Marks. Memory: Terms, answers, basic concepts and recalling of facts. Understanding: Compare, organize, interpret, translate, describe and stating main ideas. Apply: Solving problems by applying the knowledge, facts, theorems and rules in different ways. Analyse: Analyse the information provided and making inferences. Evaluate: Opine about the validity of quality of work and validity of ideas. Create: Creating alternative solutions of the given problem and grouping the elements.
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