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Our aim is to help students learn subjects like physics, maths and science for students in school , college and those preparing for competitive exams. All right reserved. All material given in this website is a property of physicscatalyst. Features of the data Statistics deals with collection, presentation, analysis and interpretation of numerical data.
Arranging data in a order to study their salient features is called presentation of data. Data arranged in ascending or descending order is called arrayed data or an array Range of the data is the difference between the maximum and the minimum values of the observations Table that shows the frequency of different values in the given data is called a frequency distribution table A frequency distribution table that shows the frequency of each individual value in the given data is called an ungrouped frequency distribution table.
A table that shows the frequency of groups of values in the given data is called a grouped frequency distribution table The groupings used to group the values in given data are called classes or class-intervals. The number of values that each class contains is called the class size or class width. The lower value in a class is called the lower class limit.
The higher value in a class is called the upper class limit. Class mark of a class is the mid value of the two limits of that class. A frequency distribution in which the upper Byjus Class 10 Maths Real Numbers Today limit of one class differs from the lower limit of the succeeding class is called an Inclusive or discontinuous Frequency Distribution.
A frequency distribution in which the upper limit of one class coincides from the lower limit of the succeeding class is called an exclusive or continuous Frequency Distribution Bar Graph: A bar graph is a pictorial representation of data in which Byjus Class 10 Maths Real Numbers Update rectangular bars of uniform width are drawn with equal spacing between them on one axis, usually the x axis.
The value of the variable is shown on the other axis that is the y axis. Histogram: A histogram is a set of adjacent rectangles whose areas are proportional to the frequencies of a given continuous frequency distribution Mean The mean value of a variable is defined as the sum of all the values of the variable divided by the number of values.
Once it is understood, the next step is to study the various terms related to arithmetic progression. This is the general form of an AP. Exercise 5. Moving ahead to the next section, students will find a detailed description on the n th term of an AP. Various solved examples are given to make the problems of this chapter more comprehensible. In exercise 5. A few diagrammatic questions are also given which makes the exercise interesting.
Later, a summary of the chapter is provided followed by a note to the reader. Factors like congruency and similarity are known to everyone. But going deep into the same, a short description of similar figures is given. Certain factors are stated that helps in recognizing whether the figures are similar or not.
An activity is given to make this concept more clear. The next section is on the topic- Similarity of Triangles. Basic proportionality theorem and its converse are important theorems to be studied in this chapter.
The next section deals with different criteria that are used to prove the similarity of triangles: AAA similarity criterion AA similarity criterion SSS similarity criterion SAS similarity criterion Several theorems and activities are also given in this section.
Exercise 6. The next section deals with Pythagoras theorem and has an exercise based on the same. In the end, there is an optional exercise that is not from the examination point of view and the summarization of key points is done. This chapter lays emphasis on how to find the distance between the two points whose coordinates are given, and to find the area of the triangles formed by three given points.
Last, but not least students will also learn how to find the coordinates of the points which divide a line segment joining two given points in a given ratio. In the first section, readers will learn about the distance formula. It is explained in detail with the help of a diagram.
Solved examples are given to make the concept more understandable to students. Moving further, section formula is given and a special case of finding the mid-point of the line segment is also explained which is important from the Byjus Class 10 Maths Real Numbers 2019 examination point of view.
In the last section, area of a triangle is discussed followed by solved example and exercise. An optional exercise is given at the end of the chapter. After that, the chapter is concluded in 5 points for a quick revision. In this chapter, students will study the trigonometric ratios of the angles.
The discussion of the trigonometric ratios will be restricted to acute angles only. In section 8. Solved examples are given to explain how to find trigonometric ratios and how to prove certain given relations. Table 8. Students must learn these values as they are the most important part of this chapter and are essential to solve the problems.
Exercise 8. The next part of the chapter is about trigonometric identities. Three important identities are highlighted in this section. In the end key points of chapter are discussed. Mathematics NCERT Grade 10, Chapter 9: Some applications of trigonometry - In this chapter students will study about some ways in which trigonometry is used in life around us.
Trigonometry is the most ancient subjects studied by scholars all over the world. In section 9. Various terms are explained in this part of the chapter. This chapter contains only one exercise. This is a vast exercise containing 16 questions. In the first few questions, the height of various objects is unknown and students have to calculate the same.
In some questions, the width of the object is to be calculated. Other questions demand calculation of the distance between two objects. A short summarization of the chapter is done in the end. The first section discusses the topic- Tangent to a Circle. This section is explained with the help of two activities followed by the theorem that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
A few remarks are mentioned at the end of the section which should not be ignored. Exercise The next section is about the number of tangents from a point on a circle. Three different cases are discussed in this section and later the theorem that related to the lengths of tangents from an external point to a circle is explained.
The last exercise of the chapter is After that few questions are based on proving the given statement. Finally, the conclusion of the chapter is given in 3 points. Following constructions are to be studied in Byjus Class 10 Maths Real Numbers Utc this chapter: To divide a line segment in the given ratio.
To construct a triangle similar to the given triangle as per the given scale factor. To construct the pair of tangents from an external point to a circle. The division of a line segment is explained first. Given steps help in understanding the construction in a better and effective manner. The steps of construction are followed by justification which give an insight into the logic used behind the construction. This is followed by the construction of tangents to a circle.
In this section student will not only draw tangents to circle but will also measure their lengths , construct tangents inclined to each other at some angle etc. In the end, a summary of the chapter is provided.
Mathematics NCERT Grade 10, Chapter Areas related to circles - We all are familiar with the methods of finding perimeters and areas of simple plane figures such as rectangles , squares, parallelograms, triangles, and circles. The first section is about the perimeter and area of a circle. One solved example is discussed in this section. First exercise Second section deals with areas of sector and segment of a circle. Two examples are discussed in this section to make the concept clear to students.
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