NT-829-1-MATHS-9-E-VOL.2 Standard IX MATHEMATICS PART- 2 Government of Kerala Department of General Education State Council of Educational Research and Training (SCERT), Kerala 2019
THE NATIONAL ANTHEM Jana-gana-mana adhinayaka, jaya he Bharatha-bhagya-vidhata. Punjab-Sindh-Gujarat-Maratha Dravida-Utkala-Banga Vindhya-Himachala-Yamuna-Ganga Uchchala-Jaladhi-taranga Tava subha name jage, Tava subha asisa mage, Gahe tava jaya gatha. Jana-gana-mangala-dayaka jaya he Bharatha-bhagya-vidhata. Jaya he, jaya he, jaya he, Jaya jaya jaya, jaya he! PLEDGE India is my country. All Indians are my brothers and sisters. I love my country, and I am proud of its rich and varied heritage. I shall always strive to be worthy of it. I shall give respect to my parents, teachers and all elders and treat everyone with courtesy. I pledge my devotion to my country and my people. In their well-being and prosperity alone lies my happiness. Prepared by : State Council of Educational Research and Training (SCERT) Poojappura, Thiruvananthapuram 695 012, Kerala Website : www.scertkerala.gov.in E-mail : [email protected] Phone : 0471-2341883, Fax : 0471-2341869 Typesetting and Layout : SCERT Printed at : KBPS, Kakkanad, Kochi-30 © Department of Education, Government of Kerala
Dear children, Man invented various types of numbers to understand the world through measurements and the relations between measures. You have already seen how natural numbers and fractions evolved like this and how their operations were defined based on the physical contexts in which they were used. In this book, you can get acquainted with measures which cannot be indicated by natural numbers or fractions and the new kind of numbers used to represent them. The study of geometry also continues in this book. We discuss the relations between parallel lines, triangles and circles. We have explained how new geometric theorems and applications arise from the recognition of such relations. We have also described how the program GeoGebra can be used to present geometry in a dynamic manner. More material are made available through the Samagra portal and QR codes. With love and regards Dr. J. Prasad Director, SCERT
CONSTITUTION OF INDIA Part IV A FUNDAMENTAL DUTIES OF CITIZENS ARTICLE 51 A Fundamental Duties- It shall be the duty of every citizen of India: (a) to abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem; (b) to cherish and follow the noble ideals which inspired our national struggle for freedom; (c) to uphold and protect the sovereignty, unity and integrity of India; (d) to defend the country and render national service when called upon to do so; (e) to promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women; (f) to value and preserve the rich heritage of our composite culture; (g) to protect and improve the natural environment including forests, lakes, rivers, wild life and to have compassion for living creatures; (h) to develop the scientific temper, humanism and the spirit of inquiry and reform; (i) to safeguard public property and to abjure violence; (j) to strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavour and achievements; (k) who is a parent or guardian to provide opportunities for education to his child or, as the case may be, ward between age of six and fourteen years.
8. Polynomials....................................... 119 9. Circle Measures................................. 129 10. Real Numbers ................................... 153 11. Prisms ............................................... 165 12. Proportion ........................................ 179 13. Statistics............................................ 191
Certain icons are used in this textbook for convenience Computer Work Additional Problems Project For Discussion NSQF
Algebra of Measures The sides of a rectangle are 2 and 3 centimetres and they are extended by 1 centimetre to make a new rectangle: 1 cm 2 cm 2 cm 3 cm 3 cm 1 cm What is the perimeter of the new rectangle? Its sides are 3 and 4 centimetres and so perimeter is 14 centimetres. We can do this in a different way: The perimeter of the original rectangle is 10 centimetres. All four sides are increased by 1 centimetre; so the total increase is 4 centimetres. The new perimeter is 10 + 4 = 14 centimetres. What if each side is extended by 2 centimetres? Using the second line of thought, each side is increased by 2 centimetres, the total increase is 8 centimetres and so the new perimeter is 10 + 8 = 18 centimetres. This computation is quicker, isnt it? If each side is extended by 2 1 centimetres, the perimeter of the new rectangle is. 2 ⎛ 4 × 2 1 ⎞ + 10 = 20 centimetres ⎝⎜ 2 ⎟⎠ Thus we can see that, the perimeter of the new rectangle is 10 added to 4 times the extension of sides.
Circle Measures (6) In the figure, semicircles are drawn with the sides of a right triangle as diameters. Prove that the area of the largest semicircle is the sum of the areas of the smaller ones. Length and angle Imagine a point starting at some point on a circle and moving along the circle. The distances travelled by the point at some positions are shown below, as fractions of the circle: Since this journey is a rotation about the centre of With A as centre, draw a circle of perimeter 24. the circle, we can also say how much the point has (Just give the radius as 12/pi). Mark a point B on the cirlce. Make an angle slider α, select. Angle turned about the centre, instead of stating how with Give Size and click on B and then A give the much distance it has travelled along the circle. angle size as α. We get a new point B′. Select Circular Arc and click on A, B, B′ in order to draw Remember how we made an angle of 45o at the the arc BB′. Mark its length. See what fraction of 1 centre of a circle to get 8 of the circle, and angle the perimeter of the circle is the arc length, for different values of α. of 90o to get 1 of the circle? (The lesson, Angles 4 in Class 6). 143
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