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PISA LIKE TEST ITEMSMATHEMATICAL LITERACY- QUESTIONS

INDEXS. NO.TITLE OF THE QUESTIONPAGE NUMBER1.Old Woman’s Will012.Badminton Tournament013.Bike Puzzle01-024.Car Jack02-035.Closed Circuit Cameras6.Digital Versatile Compact (DVD)04-057.Day and Night06-088.Decision Making089.Do Biga Jameen0910.Drilling a sphere10-1111.Fractions12.Golden Ratio13-1413.Guessing the Day14-1614.How many rounds?15.Great Mathematicians16-1716.Internet Relay Chat17-1817.Investments18.Juicy Watermelons18-1919.Kutty’s tiling problem19-2020.Largest Equilateral Triangle from a square20-2121.Maximum Area22.Sphere and Cylinder21-2223.Plotting Area22-2324.Rate of Foreign Exchange2425.Rectangle and square2526.Revolving Door25-2627.Scout Camp26-2728.Speed of racing car27-2829.Traveller’s puzzle30.War Plane03121618212930-31

01. OLD WOMAN’S WILLAn old woman wants to divide her 19 camels among her 3 daughter. According to old woman the oldest1daughter should get half of the camels, the middle daughter should get 4 of the camels and the youngest1daughter should get 5 of the camels. After her death her daughters were not able to divide the camels asthe result was coming in fractions. Just then their aunt arrived. She proposed a solution with which allthe daughter got their share in the property. Their aunt added 1 camel to the group of camels.1.2.3.4.5.6.What was the advice given?What is the share of 3 daughters after division?Calculate the ratio of share of three daughters before and after division?Can you justify the above division of camels by LCM1 1 1191 Student added 4 5 2 and got 20 and which is less than 1. How will you justify this?If one camel occupies area of 3m2 , find what will be area of shed of three daughters if each shedalso include one hay stack bundled in cuboids of length 200cm and breadth 100 cm and height50cm ?02. BADMINTON TOURNAMENTQuestion 1: Rajesh, Meena, Nisha and Yash have formed a practice group in Badminton club. Eachplayer wishes to play against each other player once. They have reserved two practice tables for thesematches.Complete the following match schedule by writing the names of player in each match.RoundPractice Table-11Rajesh - NishaPractice Table-22303. BIKE PUZZLERIDDLE 1Vikram was riding his bicycle with his friend Sekhar when he found that his bicycle pedal gotentangled with a rope lying on the floor. He got down removing the rope.Situation 1

At first he went down and tried to remove the rope by pulling it as illustrated in situation 1.1. What could have been the effective outcome of the event?2. Was the outcome as per expected lines?3. If ‘no’ then what could have been the reason.Situation 21. What could be the possible outcome now?2. If the outcome was different from situation then why is it so?04. Car JackA car jack is a mechanical device which is used to raise a car or a heavy load with the help of a smalleffort applied at its handle.The figure shows a car jack which consists of a nut, a screw and a handle fitted to the head of the screw.

The load or car to be lifted is placed on the head of the screw. At the end of the handle fitted to thescrew head, an effort P is applied in the horizontal direction to lift the car (or Load).When the handle is rotated through one complete turn, the screw is also rotated through one turn. TheLoad (or car) is lifted by a height (called pitch of screw).A Jack is also useful to lower a heavy weight.Questions:Q.1. What is the use of Car Jack?Q.2. What is the pitch of a screw?Q.3. Why does the less effort is required to lift a heavy Load (or a car)by using a jack than the effortrequired in direct lifting by hand without using jack ?Q.4. If the length of the handle is decreased then what change will required on the applied effort onthe handle?Q.5. If the pitch of the screw is reduced then what change will to do on the applied effort on thehandle?Q.6. If the diameter of the screw is increased then what change will be required in the effort on thehandle?05. CLOSED CIRCUIT CAMERASA CC Camera can cover a distance of 20 meters and can rotate upto 900. If a room is circular in shapewith radius 10 m how many cameras do you need to cover entire room.Does this set up with cover entire room?A school has 8 rooms out of which there are 2 are circular 2 are hexagonal 2 are square and 2 arerectangular. If there are total of 3 types of cameras available with following specifications.TypeDistance rangeRotation rangeCostMaintenance cost per yearA20 M900100 ZED50 ZEDB20 M600100 ZED10 ZEDC20 M45030 ZED10 ZED

1. How many cameras do you need for entire school if you choosea. Type Ab. Type Bc. Type C2. If you ignore maintenance costs which type would you prefer?3. If you are planning for a period of 10 years which model should be preferred?06. DIGITAL VERSATILE COMPACT (DVD)DVD (an abbreviation of digital versatile disc)is a digital optical disc storage format invented anddeveloped in 1995. The medium can store any kind of digital data and is widely used for software andother computer files as well as video programs watched using DVD players. DVDs offer higher storagecapacity than compact discs while having the same dimensions.DVDs have differing capacities: One of the most common DVDs is the single-sided, single-layer disc, capable of holding 4.7 GB.The single-sided, double-layer disc is capable of holding between 8.5-8.7 GB.The double-sided, single-layer disc is capable of holding 9.4 GB.Although rare, the double-sided, double-layer disc is capable of holding up to 17.08 GB.Kumar has a DVD that storage musics, videos and photos. His DVD has a capacity of 4.7 GB (4700 MB).The graph below shows the current status of his pen drive.MusicsVideosPhotosFree SpaceTotalQ 1.Space7001000200010004700During the following weeks. Kumar deletes some photos but also adds some music’s. The newstatus is shown below:His brother gives him a new DVD of capacity 9.4 GB (9400 MB) which istotally empty. Kumar transfers the content of his old DVD to the new DVD.MusicsVideosPhotosFree SpaceTotalSpace12001000150010004700

Which one of the following graphs represents the new DVD status?Circle A, B, C or D.(A)(B)(C)(D)Q 2.The details of the film songs status in the 9.4 GB DVD is given below:Film (Music)SpaceFilm 1100Film 2150Film 3125Film 4275Film 5150Film 6225Film 7100Film 875

07. DAYS AND NIGHTSLook at the following.Which part of the following picture shows day light.Which part of the picture depicts night?What is the duration of a day and what is the duration of a night.Look at the following picturesSun rise at KanyakumariSun set at KanyakumariWhat do you see in these pictures?At any place the time duration between sun rise and sun set is known as the day time while the periodfrom sun set to sun rise is called night.Sun rise at Gandhinagar on 27 June 2019: 05:55 hoursSun set at Gandhinagar on 27 June 2019: 19:29 hoursSun rise at Gandhinagar on 28 June 2019: 05:56 hoursSun rise at Gandhinagar on 1 January 2019: 7:20 hoursSun set at Gandhinagar on 1January 2019: 18:05 hours

Sun rise at Gandhinagar on 2 January 2019 7:20 hoursCCL IIT GandhinagarQuestion:1.2.3.4.5.How long was the day at IIT Gandhinagar on 27 June 2019.How long was the night at IIT Gandhinagar on 27 June 2019?How long was the day at IIT Gandhinagar on 1 January 2019?How long was the night at IIT Gandhinagar on 1 January 2019?When is the day and when is the night longer?Effect of tilt of the earth’s axis

The axis of the earth is tilted in the same direction throughout the year, however as the earth orbits thesun the hemisphere tilted away from the sun will gradually come to be tilted towards the sun and viceversa. You observed that whichever hemisphere currently tilted towards the sun experiences the morehours of sunlight each day. Due to which sun never sets for several days on this polar region. Similarly onthe other polar region nights will be for several days.Questions:1.2.3.4.5.6.7.At what angle axis of earth is tilted?What is the difference between the solar day and sidereal day?How does the tilt of axis of earth affect the day length?What is the effect of revolution of earth around the sun on its time of one rotation about its axis?What are the four reasons which affect the length of the day on earth?What will happen if earth stops revolving around the sun?If earth stops spinning how will it affect day and night?08. DECISION MAKINGIn zed country, the government was worried about the health of its citizens. So it conducted a study, theresults of which were as follows. The prime focus is on major 3 diseases out of which two are genetic.The diseases are found to be ignorable due to their short term effects and non-fatality.Disease A is wide spread with around 62% of population getting affected by it every year. It is a nonrecurring disease. The survival rate (number of people surviving the disease) of the effected is almost99.99%. The disease was found to be disturbing productivity of people by confining them home forweeks together.Disease B is known to cause around 55 % of deaths annually caused by illness in the country. Only 5 % ofpopulation are getting affected by this disease. The onset of disease cannot be easily recognised and thepatient doesn’t know that he has this disease until a few hours before his death so the fatality is 100%.The disease can be identified using advance medical technology interventions by doing medical checkup.Disease C is caused by unclean surroundings and unhealthy eating habits. The disease is a known toaffect every 1 out of 5 people of the country. With 1 lac deaths last year, the fatality rate of this diseaseis calculated as 10%. The disease is known to confine people affected to hospital forever.1.2.3.4.5.Which among the above do you think is affecting most percent of population and how much?Which disease is most dangerous and why?Which disease effecting productivity of the country the most?As per the survey, which among the above can be easily avoided?If the government has limited resources and it can spend on only one disease which one do youthink the government would focus on?6. In general a country can be called a healthy nation if less than 40 % of people have diseases thenbased on that, what do you think the health condition of the country?a.Healthyb.unhealthyc.average7. What is the population of the country?8. What is number of people who died because of diseases?

09. DO BIGHA JAMEENTwo friends Satyam and Shivam wanted to buy plots of land so they decided to meet a property dealerBabu Rao in Ahmedabad. The dealer was really an interesting person. He told them the rate of the landis Rs.1 Crore per minute. Both the friends were stunned and again asked that they wanted to purchasethe land. But the dealer repeated the same and explained, “whatever the land covered by you in oneminute will be yours”. They agreed and next day both the friends started running to cover maximumarea and they covered the land as shown below:-Answer the following questions:a)b)c)d)e)f)What is the shape of each plot?Who covered the more area?Find the perimeter of Satyam’s plot.Which plot has more dimensions in North-South direction?Find the rate of Shivam’s plot per sq. meter.Had you been there, in which geometrical shape would you have run to cover maximum area ifyou have the same speed as of Shivam?g) What is the area covered by you?h) Which shape 150 km X 50 km or 50 km X 150 km of land and where would you like to buy on theearth? Justify your answer?

10. DRILLING A SPHEREAnand’s father offers him an ice cream ball which is spherical. After having fun time with the deliciousice cream when Anand goes for littering the ball to the bin, the father asks him not to throw the ball andsays that he has a question for him. The question is : “if you drill a cylindrical hole six inches long straightthrough the centre of the ball in your hand, What is the volume remaining in the ball?SOLUTION FOR THE ACTIVITYCASE 1—IF THE DIAMETER OF THE BALL IS LESS THAN 6 INCHES.It is not possible to drill a 6 inches hole through a sphere whose diameter is less than 6 inches.CASE 2 – IF THE DIAMETER OF THE BALL IS GREATER THAN OR EQUAL TO 6 INCHES.R Radius of the sphereH height of the cylinderTherefore radius of the cylindrical hole 𝑅 2 9Required volume Volume of sphere – {Volume of the cylinder 2(Volume of spherical cap)}𝜋 6 63 36 𝜋 cubic units.PISA QUESTIONS BASED ON THIS ACTIVITY

Question 1: Can this conclusion be drawn from the figures? Circle Yes or No.Conclusion1.Can you compare the shape of the objectin picture to the shape of earth?2.Do you think that the surface of ball is flat?3.Does the ball have a base?4.Does the ball have a face?Can the conclusion be drawn? Yes/NoYes/NoYes/NoYes/NoYes/NoQuestion2: What is the shape of the ball?Question 3: How many curved surfaces does the ball have?Question 4: What is the surface area of the ball?Question 5: A customer wants to buy water melon for making juice, for which the skin of the watermelon has to be peeled off, and therefore is a waste. Which shape should the customer calQuestion 6: When can the ball be taken as two concentric circles as shown in the figure?Question 7: The . of the outer circle is the . to the inner circle.Question 8: What is the volume of the ball if the diameter is 6 inches?Question 9: When the ball is of diameter 3 inches, can a hole of length 4 inches be drilled along thecentre of the ball? Why, justify your answer.Question 10: As shown in the figure, if a hole of length 6 inches is drilled through the centre of the ball,what will be the remaining volume?Question 11:If the ball is the size of the Earth, and if a hole of 6 inches long is drilled through the centreof the Earth, then will the volume remain same ?.

11. FRACTIONSPICTURES CAN MAKE THE FRACTIONS EASIER!Anushka and Madhusmita were on a survey to mark the rate of literacy in two neighbouri

DAYS AND NIGHTS Look at the following. Which part of the following picture shows day light. Which part of the picture depicts night? What is the duration of a day and what is the duration of a night. Look at the following pictures Sun rise at Kanyakumari Sun set at Kanyakumari What do you see in these pictures? At any place the time duration between sun rise and sun set is known as the day .