Maths OTBA Class IX for SA-II 2014-15

MATHEMATICS OPEN TEXT BASED ASSESSMENT QUESTION BANK for Summative Assessment -II

CLASS – IX 2014 – 15

CBSE OPEN TEXT MATERIAL AND CBSE SAMPLE QUESTIONS INCLUDING SOME PROBABLE QUESTIONS THEME WISE

Prepared by

M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli Prepared by: M. S. KumarSwamy, TGT(Maths)

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PREFACE It gives me great pleasure in presenting the Question Bank for Open Text Based Assessment (OTBA) for Class IX Mathematics for Summative Assessment (SA) - II. It is in strictly according to the latest guidelines issued by CBSE (Circular No. Acad-45/2014, dated 21 November, 2014) for OTBA to be held with SA-II in March 2015. The CBSE has short listed text material for class IX in the subject areas of English, Hindi, Mathematics Science and Social Science. This short listed text is in the form of an article, a case study, a picture or a cartoon or a problem/situation. The question paper in each main subject will have a separate section of 10 marks for Open Text Based Assessment (OTBA). The OTBA aims to strengthen students’ analytical and theoretical skills by moving away from the trend of rote learning. I avail this opportunity to convey my sincere thanks to respected sir, Shri S. Vijay Kumar, Director, KVS ZIET Gwalior, respected madam Smt. R. Kalavathi, Deputy Commissioner, KVS RO Hyderabad, respected sir Shri Isampal, Deputy Commissioner, KVS RO Bhopal, respected sir Shri P. V. Sairanga Rao, Deputy Commissioner, KVS RO Varanasi, respected sir Shri P. Deva Kumar, Deputy Commissioner, KVS RO Ahmedabad, respected sir Shri Sirimala Sambanna, Assistant Commissioner, KVS RO Hyderabad, respected sir Shri. K. L. Nagaraju, Assistant Commissioner, KVS RO Bangalore, respected sir Shri.Gangadharaiah, Assistant Commissioner, KVS RO Bangalore and respected Shri M.K. Kulshreshtha, Assistant Commissioner, KVS RO Chandigarh for their blessings, motivation and encouragement in bringing out this notes in such an excellent form. I also extend my special thanks to respected sir Shri. P. S. Raju, Principal, KV Gachibowli, respected Smt. Nirmala Kumari M, Principal, KV Mysore & respected Shri. M. Vishwanatham, Principal, KV Raichur for their kind suggestions and motivation while preparing this Question Bank. I would like to place on record my thanks to respected sir Shri. P. K. Chandran, Principal, presently working in KV Bambolim. I have started my career in KVS under his guidance, suggestions and motivation. Inspite of my best efforts to make this notes error free, some errors might have gone unnoticed. I shall be grateful to the students and teacher if the same are brought to my notice. You may send your valuable suggestions, feedback or queries through email to [email protected] that would be verified by me and the corrections would be incorporated in the next year Question Bank.

M. S. KUMARSWAMY Prepared by: M. S. KumarSwamy, TGT(Maths)

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DEDICATED TO MY FATHER

LATE SHRI. M. S. MALLAYYA

Prepared by: M. S. KumarSwamy, TGT(Maths)

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THEME – 1 : ATITHIDEVO BHAVAH OPEN TEXT MATERIAL ABSTRACT: Atithidevo Bhavah is a verse in Sanskrit. It means to consider the guest as god. This statement is drawn from an ancient scripture which has been the ethos of Indian culture. Recently, this verse has found its place in the tagline of Ministry of Tourism in order to improve the treatment of the foreign tourists visiting the country due to the popularity the country has gained in the recent times as a popular and favorite tourist destination. The concept of Atithidevo bhav is deep rooted in our Indian culture and is carried forward with same spirit as it used to in ancient times. The text gives an insight into the number of foreign tourists arrivals in India during different seasons which is supported with data. The concept also gets reinforced when the statistics show that tourists of all age groups from across the globe love to visit India. India is a beautiful country rich in diversity. The majestic Himalayas, the sparkling ocean, the dry desert, the dancing river, the enticing lagoons or the magical back waters, all appeal to nature lovers. People come from far off countries to a new beautiful vision of glory of nature. Its rich history, cultural and geographical diversity makes it an international tourism attraction. There are many places which attract the interest of the tourists in India. Many foreign tourists from different parts of the world come to explore the natural and the heritage beauty of this Nation. Tourists come for different purposes such as weddings, shopping, tourism, business, education, adventure, family reunions, etc. SEASONALITY IN FOREIGN TOURIST ARRIVALS IN INDIA India experiences three major seasons - Winter, Summer and Monsoon. In 2011 over six lakh tourists had visited various tourist destinations such as Agra, Jaipur, Udaipur, Kashmir valley, Goa, Mysore and Thiruvanantha-puram in the winter season. In 2012, the minimum number of foreign tourists visited India during the month of May and maximum during the months of December.


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The following graph clearly shows that the highest FTAs in India were in October December and January-March during 2012.

India is ranked as the 38th country in the world in terms of foreign tourist arrivals. The most represented countries are the United Kingdom and the United States. In 2012 Maharashtra, Tamil Nadu and Delhi were the most popular states for foreign tourists. Domestic tourists visited the states of Uttar Pradesh, Andhra Pradesh and Tamil Nadu most frequently.

Delhi, Mumbai, Chennai and Agra have been the four most visited cities of India by foreign tourists during the year 2012. Worldwide, Chennai is ranked 41 by the number of foreign tourists, while Delhi is ranked at 50, Mumbai at 57, Agra at 65 and Kolkata at 99.


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FOREIGN TOURISTS ARRIVALS (FTAS) IN INDIA It can be observed clearly that the FTAs in India have been increasing from all regions during the year 2012. The growth was maximum from Eastern Europe followed by Africa, East Asia, Australia, Central and South America. Table-2: Number of FTAs from different regions of the world (in lakhs approximately) Region/Country

Eastern Europe

Africa

East Asia

Australia

Central and South America

2011

27

23

47

23

6

2012

31

26

53

24

7

MODES OF TRAVEL OF FOREIGN TOURISTS ARRIVALS (FTAS) IN INDIA Travel by ‘air’ has been found to be the most preferred mode of transport. In 2012, out of the 6.58 million foreign tourist arrivals in India, majority arrived by air(92%), followed by land(7 %) and sea(1%). Arrivals through land routes comprised tourists mainly from Bangladesh and Pakistan. Figure-2: Arrival of Foreign Tourists in India.

Air travel has been the most preferred mode of travel for the FTAs over the years, accounting for above 80% share in each year during this period. During last three years from 2010 onwards, the percentage of FTAs travelling to India by air has remained more than 90%. The share of arrivals through land check-post has been above 10% during 2001 to 2008; however, it has been gradually declining over the last 3 years. Arrivals through sea routes remain less than 1% from 1996 to 2012.


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AGE DISTRIBUTION OF FTAS IN INDIA Table-3: The percentage distribution of FTAs in India according to age groups during 1996- 2012: Age-group (in years) % Distribution by Age group (in years)

0 – 15

15 – 25

25 – 35

35 – 45

45 – 55

55 – 65

65 & above

11

8

16

21

20

14

10

During the year 2012, sex-wise distribution of the FTAs comprises of 58.7% males and 41.3% females. The government's proposal to infuse over Rs 1,000 crore in developing India as an attractive tourism destination is being seen as a window to draw more foreign tourists and foreign exchange, besides enhancing air connectivity and development of heritage sites within the country. Now one can easily guess why Max Mueller has said these lines about India"If we were to look over the whole world to find out the country most richly endowed with all the wealth, power and beauty that nature can bestow in some parts, a very paradise on earth, I should point to India." Such is our India. It is undoubtedly a paradise for the tourists.

SOME PROBABLE QUESTIONS 1. Prepare a histogram on the percentage distribution of Foreign Tourists Arrival in India according to age groups during 1996 – 2012 for class size 10 (using Table 3). (3 marks) 2. On the basis of the given bar graph on month – wise percentage share of FTAs in India, answer the following: (3 marks) (a) Which season has the maximum number of FTAs in India? (b) Which month has the minimum number of FTAs in India? What according to you could be the reason for less visitors in this particular month? (c) Find the mean percentage of foreign visitors in the months April to September? 3. On the basis of the given bar graph on month – wise percentage share of FTAs in India, answer the following: (3 marks) (a) Which season has the minimum number of FTAs in India? (b) Which month has the maximum number of FTAs in India? What according to you could be the reason for more visitors in this particular month? (c) Find the mean percentage of foreign visitors in the months January to June? 4. Government proposes to sanction Rs. 1000 crores for development of tourism industry in India. Which five areas could be taken into consideration and in what percentages? Justify the distribution and represent through a bar graph. (4 marks) Prepared by: M. S. KumarSwamy, TGT(Maths)

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5. Find the median of month-wise percentage share of FTAs in India, 2012. 6. Find the mean of month-wise percentage share of FTAs in India, 2012. 7. Find the mean of percentage change of FTAs over previous year from 2000 to 2008. 8. Prepare a pie chart to represent the data given in Table 2 for year 2011. 9. Prepare a pie chart to represent the data given in Table 2 for year 2012. 10. Find the median of percentage change of foreign exchange earnings (Millions US$) over previous year 2000 to 2011. 11. Find the median of percentage change of foreign exchange earnings (Rs. Crore) over previous year 2000 to 2011. 12. Find the median of percentage change of FTAs over previous year from 2000 to 2011. 13. Find the mean of percentage change of foreign exchange earnings (Millions US$) over previous year 2000 to 2011. 14. Find the mean of percentage change of foreign exchange earnings (Rs. Crore) over previous year 2000 to 2011. 15. Find the mean of percentage change of FTAs over previous year from 2000 to 2011. 16. Find the mean number of FTAs from different regions of the world for the year 2011. 17. Find the mean number of FTAs from different regions of the world for the year 2012. 18. Prepare the frequency distribution table for the modes of Travel of FTAs in India using Figure 2. Which is the most preferred mode of travel and which is the least preferred mode of travel? 19. Prepare the frequency distribution table for the modes of Travel of FTAs in India using Figure 1. Which is the most preferred month and which is the least preferred month? 20. Which states of India are the most popular states for foreign tourists in 2012? Which four most visited of India by foreign tourists during the year 2012? 21. What is the rank of Chennai, Delhi, Mumbai, Agra and Kolkata in the world in terms of foreign tourist arrivals? 22. What is the rank of India in the world in terms of foreign tourist arrivals? 23. If FTA is selected at random from the Table 2. for the year 2011, find the probability that the Foreign Tourist selected at random arrived from (i) Eastern Europe Prepared by: M. S. KumarSwamy, TGT(Maths)

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(ii) Africa (iii) East Asia (iv) Australia (v) Central and South America (vi) neither from Africa not from Australia (vii) neither from East Asia nor from Eastern Europe. 24. The table 3 shows the percentage distribution of FTAs in India according to the agegroups during 1996-2012. One of the foreign tourist is selected at random. Find the probability that his/her age is (i) less than 15 years (ii) 15 years or more but less than 25 years. (iii) 25 years or more but less than 35 years. (iv) 35 years or more but less than 45 years. (v) 45 years or more. (vi) 45 years or more but less than 55 years. (vii) 55 years or more but less than 65 years. (viii) 15 years or more but less than 45 years. (ix) 25 years or more but less than 65 years. (x) 45 years or more but less than 65 years. (xi) 15 years or more. (xii) 25 years or more. 25. A Foreign Tourist is selected at random (see Figure 2.). Find the probability that the Foreign Tourist selected at random arrived in India through the modes of travel by (i) Land (ii) Sea (iii) Air 26. If FTA is selected at random from the Table 2. for the year 2012, find the probability that the Foreign Tourist selected at random arrived from (i) Eastern Europe (ii) Africa (iii) East Asia (iv) Australia (v) Central and South America (vi) neither from Africa not from Australia (vii) neither from East Asia nor from Eastern Europe. 27. Draw a double bar graph for number of FTAs from different regions of the world for the years 2011 and 2012 using Table 2.


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28. Prepare a pie chart on the percentage distribution of Foreign Tourists Arrival in India according to age groups during 1996 – 2012 (using Table 3). Which age-group is the most common and which age-group is rarer? 29. What message have you got from the verse “Atithidevo Bhavah”? 30. Is “Atithidevo Bhavah” an appropriate slogan for the tourism industry? 31. According to you, what measures India should take in order to improve its world ranking in terms of foreign tourist arrival? 32. Do you like Aamir Khan’s “Atithidevo Bhavah” advertisement? Why? 33. What is the main aim of the government in the nationwide campaigning of “Atithidevo Bhavah”? 34. Does the “Swachh Bharat” campaign of our government help to promote foreign tourism? How? 35. A Foreign Tourist is selected at random. Find the probability that the Foreign Tourist selected at random arrived in India is (i) male (ii) female


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THEME – 2 : EMPOWER TO LEARN OPEN TEXT MATERIAL ABSTRACT : Harshit heard of the social networking sites and started exploring them on the internet. To his surprise he came across various educational as well as social networking sites that give innovative and improved ways of learning. He gradually got prone to the facilities these platforms offer which broadened his perspectives. He realised that this advancement in social networking platform is providing him with much better options to engage with his contemporaries, enhance his skills and access a wide variety of academic tools and resources which most definitely add up to his convenience. Harshit learnt about LEARNOUT, a free social learning network for university and school students. It offers a platform for its users where they can engage in activities like sharing study related materials, counselling or simply connecting through a vast network of existing users from around the world. Within a small time span of two years, more than 80,00,000 students registered for the website and they use the website on daily basis. The distribution of the students in different age groups was graphically presented and he got inspired as he thought to himself that maximum number of children of his age is gaining from this site. Figure 1: Histogram showing the number of students using learnout in different age groups

The website offers user generated contents in 7 different languages including Italian, English, Spanish, Polish, Russian, Serbian and Portuguese. The website is directly operated from its respective regional head offices thereby providing a direct approach to the users. LEARNOUT also has its free application available for all android devices. The website also has a dedicated 24/7 support team to assist the students in their matters. He surveyed a number of people and recorded his findings on the percentage of users using this site in different languages: Prepared by: M. S. KumarSwamy, TGT(Maths)

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Table 1: The percentage of users in different languages of LEARNOUT is given in the table below: Language

Italian

English

Spanish

Polish

Russian

Serbian

Portuguese

Percentage of users

11

57

6

4

10

9

3

He also discovered a site named TWOWAY which provides its students with a different approach towards studies. It offers an interactive way of studying where students get to create and animate flashcards. The website currently has about 1 million study content authored by the students. The website also conducts different quizzical campaigns for the students and tracks the progress of its users. The issues on which the campaigns were conducted are presented in the form of pie chart. Harshit also got a platform to spread awareness of the issues which he has to record in his project work given by his teacher. He could collect the data globally and interpret it from different perspectives. Figure 2: The pie chart shows the campaigns conducted on TWOWAY in different subjects.

Mathematics was troubling him and he needed a special assistance in various concepts. He received many resource materials to gain more knowledge and achieved higher level of learning. The site named TROUBLE BUBBLE was the answer to his queries. TROUBLE BUBBLE offers a very interactive way to the students looking for answers to the distressing questions. They can ask questions directly from the academic experts through their vast network. The following data shows the number of questions asked by students between 2:00pm to 9:00pm.


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Table 2: The table below shows the average number of questions asked at different hours of the day on TROUBLE BUBBLE. Time

2 to 3pm

3 to 4pm

4 to 5pm

5 to 6pm

6 to 7pm

7 to 8pm

8 to 9pm

Number of questions

180

270

360

440

520

300

190

Harshit was pleased to know that he has the facility to get immediate answers to his queries through this site. SUPERB, another educational networking site, offers its users with a unique way to have interaction. It builds a strong connection between students and renowned teachers from around the world. SUPERB offers a number of free tools and services to the teachers, which literally transforms the way of teaching and helps in the provision of superior quality of services to its users. The website is suitable for students of all ages, whether be a student of middle school or an undergraduate, SUPERB has stored a lot more for its users to achieve their educational goals. The advancements in technology proved to be beneficial for Harshit. With social networking platforms advancing, they are playing their role to facilitate the students with their needs and benefit them to achieve their goals. The given frequency polygon displayed maximum benefit taken by the students from this site. It was an eye opener for Harshit as he wanted extended learning in all the subjects. Being a smart boy, he always used to check data before taking any decision. Figure 3: Frequency Polygon showing the percentage of campaigns conducted in different subjects

Harshit was empowered by these educational networking sites as they transformed him into a global citizen. He received input from across the world from different teachers who had shared the best of the ways to share their learning through innovative ideas of Prepared by: M. S. KumarSwamy, TGT(Maths)

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constructing knowledge with he students accessing their sites. Thus, technology supported Harshit to make the best use of time and energy to equip him to learn at his own pace but with global input in his learning process. SOME PROBABLE QUESTIONS 1. Justify giving examples, why Harshit is a smart boy in using technology for learning. (3 marks) 2. Prepare a pie chart to represent the data given in table 1. (3 marks) 3. Represent the frequency polygon as a histogram for figure 3. (4 marks) 4. Draw a frequency polygon for number of students (in millions) using Figure 1. 5. Draw a bar graph for the data represented in Table 1. 6. Draw a histogram to represent the data given in Table 2. 7. Draw a pie chart to represent the data given in Figure 3. 8. Prepare frequency distribution table from Figure 3 which is a Frequency Polygon showing the percentage of campaigns conducted in different subjects. Which subject show maximum percentage of students benefited and which subject show least percentage of students benefited. 9. Find the mean percentage of campaigns conducted in different subjects from Figure 3. 10. Find the median percentage of campaigns conducted in different subjects from Figure 3. 11. Find the mean of average number of questions asked per hour from 3pm to 9 pm on TROUBLE BUBBLE. 12. Find the mean of average number of questions asked per hour from 2pm to 8 pm on TROUBLE BUBBLE. 13. Find the median of average number of questions asked per hour from 3pm to 9 pm on TROUBLE BUBBLE. 14. Find the median of average number of questions asked per hour from 2pm to 8 pm on TROUBLE BUBBLE. 15. What message have you got from the theme “Empower to Learn”? 16. If you could give one educational tool to every child in the world, what would it be? Why? 17. What specific strategy we should follow in order to empower a student? 18. For a student, what is the optimal usage of a solution manual? Prepared by: M. S. KumarSwamy, TGT(Maths)

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19. What does empowerment mean to us? 20. Harshit heard about social networking websites and started to explore them on the Internet. He came across various educational social networking sites. How many such sites did he work upon? Name and describe them. 21. Find the mean percentage of users in different languages of LEARNOUT from Table 1. 22. Find the median percentage of users in different languages of LEARNOUT from Table 1. 23. The table 2 shows the average number of questions asked at different hours of the day on TROUBLE BUBBLE. A question is selected at random. Find the probability that the questions selected at random is asked at (i) 2 to 3pm (ii) 3 to 4pm (iii) 4 to 5pm (iv) 5 to 6pm (v) 6 to 7pm (vi) 7 to 8 pm (vii) 8 to 9pm (viii) 2 to 4pm (ix) 3 to 7pm (x) 4 to 9pm (xi) 5 to 9pm (xii) 6 to 9pm (xiii) 7 to 9pm (xiv) 2 to 7pm (xv) 3 to 8pm 24. A user is selected at random from LEARNOUT. Find the probability that the user selected at random is from language (i) Italian (ii) English (iii) Spanish (iv) Polish (v) Russian (vi) Serbian (vii) Portuguese (viii) not English (ix) not Spanish (x) not Russian (xi) neither English nor Serbian (xii) neither Polish nor Portuguese (xiii) neither Italian nor English (xiv) neither Spanish nor Serbian (xv) neither Russian nor Italian 25. Draw a bar graph to represent the data given in Figure 3.


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26. Figure 2 pie chart shows the campaigns conducted on TWOWAY in different subjects. One subject is selected at random. Find the probability that the subject is Environmental issue. 27. Explain how the site named TROUBLE BUBBLE is helpful to the students. 28. Explain how the site named TWOWAY is helpful to the students. 29. Explain how the site named SUPERB is helpful to the students. 30. Figure 1 Histogram showing the number of students using learnout in different age groups. A student is selected at random. Find the probability that the age group of student selected at random is (i) 5 to 8 (ii) 8 to 11 (iii) 11 to 14 (iv) 14 to 17 (v) 17 to 20 (vi) 20 to 23 (vii) 23 to 26 (viii) 5 to 20 (ix) 8 to 23 (x) 11 to 26 (xi) 14 to 26 (xii) 17 to 26 (xiii) 20 to 26 (xiv) 8 to 26 (xv) 5 to 26


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