Grade - 9

Mathematics

Grade - 9

Government of Nepal Ministry of Education

Curriculum Development Centre

Publisher: Government of Nepal

Ministry of Education

Curriculum Development Center

? All rights reserved in Publisher

First Edition

:

2070 BS

Revised Edition :

2075 BS

Price:

75/-

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any other form or by any means for commercial purpose without the prior permission in writing of the Curriculum Development Centre.

Preface

The curriculum and curricular materials have been developed and revised on a regular basis with the aim of making the education objective-oriented, practical, relevant and job oriented. It is necessary to instill the feelings of nationalism, national integrity and democratic spirit in students and equip them with morality, discipline and self reliance so as to develop in them social, personal skills and the basic competencies of language, mathematics, science, information and communication technology, environment and health, and soft skills. Education should help them appreciate and make them aware of arts and aesthetics; preserve and promote social norms, values and ideals; equip them with creative skills and have due respect for ethnicity, languages, religions, cultures, disabilities, regional diversity and human rights so as to make them capable of playing the role of responsible citizens. This textbook is the translated version of the Mathematics textbook of grade 9 which had been developed in line with the Secondary Level Mathematics Curriculum, 2014.

In bringing out the textbook in this form, the contribution of the Executive Director of CDC Mr. Baburam Paudel, Prof. Dr. Min Bahadur Shrestha, Prof. Dr. Lekh Nath Sharma, Baikunth Khanal, Bijaya Baniya, Barun Baidya, Goma Shresth, Damber Dhog Angdembe and Pusp Raj Dhakal is highly acknowledged. The book is translated in to English by a team of Krishna Bahadur Bista, Nisha Parajuli, Rajkumar Mathema and Rajyalaxmi Shrestha. The subject matter and language of this book were edited by Chandra Kanta Bhusal and Harish Pant. The layout and illustrations of the book were done by Jayram Kuikel. CDC extends sincere thanks to all those who have contributed to develop this textbook.

This book contains a variety of learning materials and exercises which will help learners to achieve the competency and learning outcomes set in the curriculum. Each unit deals with all mathematical skills and the subject matters required to practise various learning activities. There is uniformity in the presentation of the activities which will certainly make it convenient for the students. The teachers, students and other stakeholders are expected to make constructive comments and suggestions to make it a more useful learning material.

Government of Nepal Ministry of Education Curriculum Development Centre

S.No

Unit

Contents

1.

Sets

2.

Profit and Loss

3.

Commision and Taxation

4.

Home Arithmetic

5.

Area

6.

Solids

7.

Algebric Expressions

8.

Indices

9.

Ratio and Proportion

10.

Linear Equations

11.

Quadratic Equations

12.

Triangles

13.

Parallelograms

14.

Construction

15.

Similarity

16.

Circles

17.

Trigonometry

18.

Statistics

19.

Probability

Answers

Page No.

1 11 18 35 48 63 76 81 87 96 103 110 128 142 152 159 166 179 202 211

Lesson

1

Sets

1.0 Review

The given figure represents a set of students who take part in the game on the ocassion of annual day of a school. Answer the following questions by studying the figure.

(a) How many members are there in the sets B and F in total? List them out.

(b) How many subsets can be formed from the set F? (c) How many members are there in the set B? (d) Who are the common members of both sets B and F? (e) Who are not the members of any sets B and F?

F

B

U

Chhiring

Bittu

Maya

Dorje Aasha Dolma

Hari

Suntali

Ram

Harka

(f) How many members are there in the given Venn diagram all together?

Chhiring, Dorje, Hari, Maya and Aasha are the members of football team. It can be written as F = {Chhiring, Dorje, Hari, Maya, Aasha} and the members of basketball team as B = {Bittu, Dolma, Suntali, Maya, Aasha} by using listing method.

The teams of the members who take part in football and basketball are donated by English alphabet capital letters 'F' and 'B' respectively.

A well defined collection of the objects is called set.

In the above Venn diagram, Ram and Harka are not the members of sets F and B. In this discussion the set that contains all the members of the given figure is called universal set. It is denoted by U. All the members of F and B are also the members of U. So, F and B are proper subsets of universal set U.

A set from which all subsets are formed in a particular context is called universal set of the subsets. The sets which are formed from an universal set are called subsets.

German mathematician George Cantor (1844-1918) developed the ideas of set as mathematical theory in ninteenth century. John Euler Venn developed the method of representing the sets by closed figures called Venn diagrams. Now, we use Venn diagrams to represent set, set relations and set operations in a simplified form.

Mathematics, Grade-9

1

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