Grade 11 - STMG / Worksheet 10 exercises (including 1 corrected)

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123456789ABCnunvn12345678 01234567891011001300150017001900 12345678ABCDEFGHIJn123456789Devis1coûttotaldenmètresforés190340Devis2coûtdunemètre135139,05coûttotaldenmètresforés135274,05 1. suite E.7412 A company offers a prospective employee two types of contracts : Option 1 : The initial salary will be 1200 e per month, with an increase of 50 e applied each year. Option 2 : The initial salary will be 1100 e per month and an increase of 5 % (multiplication factor of 1.05 ) will be applied each year. Note u n your salary for the first type n year after you start, u n your salary with formula 1 and v n with formula 2. 1 Complete the table below : 2 a Using the previous table, place the coordinate points in the grid below : ( n ; u n ) ; ( n ; v n ) b Connect these points. E.7413 In the summer of 2003, an exceptional heatwave hit France. Mr. Dupont wants to dig a well at the bottom of his garden. A natural underground water reserve is located 9 meters below the surface. He requests quotes for the drilling. Quote n 1 Flat-rate fee, site visit: 40 e Including tax. Flat rate per meter drilled: 150 e TTC Quote n 2 No flat rate, but the price per meter depends on the depth reached : the first meter costs 135 e including tax, each sub-sequent meter costs 3% more than the previous one. We will examine these two quotes to assess the cost of drilling a 9-meter well. 1 Examination of quote 1 : What formula should be entered in cell D6 to obtain, in each cell, after automatic copying to J6 , , the cost of the n th meter drilled? 2 Study of estimate 2 : a What formula should be entered in cell D6 to obtain, after automatic copying to J6 , , the cost of the n th meter drilled in each cell? b What formula should be entered in cell D7 to obtain, after automatic copying to J7 , , the total cost of n meters drilled in each cell? 3 a Complete this table. Amounts will be rounded to the nearest cent. b What is the best quote for drilling 9 meters? https://chingmath.fr sacados/7412 123456789ABCnunvn12345678 01234567891011001300150017001900 sacados/7413 12345678ABCDEFGHIJn123456789Devis1coûttotaldenmètresforés190340Devis2coûtdunemètre135139,05coûttotaldenmètresforés135274,05
1234567ABCDAnnéePopulationdePau1janvierPopulationdeVau1janvierPopulationdeIau1janvier2002200000300000 1234567ABCDAnnéeNombred’utilisateursQuotientPourcentaged’augmentation1995341996561,64711997921,642919981451,576119992431,675920004141,7037 123456789ABCnun501234567q2 E.7414 In an imaginary country noted I , there is a capital P and a collection of villages V . At 1 er January 2002, P and V had 200 000 and 300 000 inhab-itants respectively. Each year, the population of P increases by 10 % , while that of V decreases by 20 000 inhabitants. A spreadsheet gives in the column A the years from 2002 to 2007, in the column B the population of the capital P , in the column C the population of all villages V and in the column D the total population of the country I as at 1 er January of the corresponding year. 1 a Indicate the formulas that should be written in the cells D2 , A3 , B3 and C3 in order to obtain automati-cally, by copying down the years in the column A and the populations in the columns B , C and D . Recall that an increase of 10 % is associated with a multiplier coefficient of 1.1 . b Fill in the table provided below and return it with the copy 2 Using the features of your spreadsheet program, plot the population curves of P and V . 2. function E.7411 The following table shows the number of Internet users worldwide (in millions) for the years 1995 to 2000. Year 1995 1996 1997 1998 1999 2000 Number of users (in millions) 34 56 92 145 243 414 We want to use a spreadsheet to analyze this data. We have created the table provided in Appendix (to be submitted with the copy) . 1 Explain how it is possible to fill in column A without having to enter all the values contained in the cells. 2 In cell C3 , we calculated the quotient of the number of Internet users in 1996 divided by the number of Internet users in 1995. What does this quotient represent? What is the formula to enter in cell C3 to perform this calculation and obtain the numbers in column C ? 3 a What is the percentage increase in the number of Internet users between 1995 and 1996? Between 1996 and 1997? (Give percentages rounded to the nearest whole num-ber.) b What formula should be entered in cell D3 to obtain, by copying down, the percentage changes in the number of Internet users over the years? c Complete column D of the table in the appendix (to be submitted with the copy) 3. absolute E.7407 Consider the sequence u n defined for any natural number n positive or zero ( n N ) which is geo-metric of first term 5 and reason 2 . 1 Enter the table below into your spreadsheet. https://chingmath.fr sacados/7414 1234567ABCDAnnéePopulationdePau1janvierPopulationdeVau1janvierPopulationdeIau1janvier2002200000300000 sacados/7411 1234567ABCDAnnéeNombred’utilisateursQuotientPourcentaged’augmentation1995341996561,64711997921,642919981451,576119992431,675920004141,7037 sacados/7407 123456789ABCnun501234567q2
12345678910111213141516171819202122232425ABCDEFTempsdeClémentTempsenheure/minutes/secondesTempsdeThéoTempsenheure/minutes/secondestempsensecondestempsenheuresheuresminutessecondes1erentraînement2255787572,432≥èmeentraînement2232686062,393≥èmeentraînement2203984392,344≥èmeentraînement227788272,455≥èmeentraînement2241986592,416≥èmeentraînement2213784972,367≥èmeentraînement2252187212,428≥èmeentraînement2195683962,33Tempsmoyen:2233386132,39tempsensecondestempsenheuresheuresminutessecondes1erentraînement2503102032,832≥èmeentraînement24918101582,833≥èmeentraînement24827101072,814≥èmeentraînement24759100792,805≥èmeentraînement24939101792,836≥èmeentraînement24826101062,817≥èmeentraînement2503102032,838≥èmeentraînement24847101272,81Tempsmoyen:24912101452,82 1234567ABCDEFNordSudEstOuestTOTALFootball15012575250600Handball50753085240Tennis35301550130Judo705020100240TOTAL3052801404851210Fréquenceen% 2 a Enter the formula ˇ =B2*C2 ı in cell B3 and copy it down to the cell range B3:B9 . b Do the values obtained in the column B correspond to the terms of the sequence u n ? Justify. 3 a Enter the formula ˇ =B2*$C$2 ı in the cell B3 and copy it down to the cell range B3:B9 . b Do the values obtained in the column B correspond to the terms of the sequence u n ? 4. Unclassified financial years E.7405 To study their performance in ski races, two friends Théo and Clément recorded in a table their times over 8 training sessions in this typical race. The table was created using a spreadsheet program. The table cells are in the format : num-ber, 2 decimal places. We read that Clément put in for his 1 er training : 2 hours 25 minutes 57 seconds, or 2.43 hours. 1 a Which formula has been entered in cell E4 , then copied down to E11 ? b What formula was entered in cell F4 , then copied down into formula F11 ? c What formula was entered in cell E12 to calculate Clé-ment’s average time? 2 The two friends want to join one of the two clubs next year. They compare their average times with those of skiers in both clubs. They would like to be in the same club and be in the top quarter of skiers. Is their wish achievable? Explain your answer. E.7406 In 2004, a census was taken in a medium-sized town, young people aged 10 to 15 regularly practicing a team sport (soccer, handball) or individual (tennis, judo) . It is assumed that each young person surveyed in this way plays just one sport. The city has been divided into four sec-tors : north, south, east and west. The results are shown in the table below : 1 We want to calculate the totals per row. What formula should we write in cell F2 to obtain by copying it down to F6 the total number of young people per line? 2 We want to calculate, by sector, the frequencies of young people practicing an individual or team sport, relative to the census population. What formula should we write in cell B7 to obtain, by copying it to the right to F7 , these frequencies? https://chingmath.fr chapExoCorrec/7405 sacados/7405 12345678910111213141516171819202122232425ABCDEFTempsdeClémentTempsenheure/minutes/secondesTempsdeThéoTempsenheure/minutes/secondestempsensecondestempsenheuresheuresminutessecondes1erentraînement2255787572,432≥èmeentraînement2232686062,393≥èmeentraînement2203984392,344≥èmeentraînement227788272,455≥èmeentraînement2241986592,416≥èmeentraînement2213784972,367≥èmeentraînement2252187212,428≥èmeentraînement2195683962,33Tempsmoyen:2233386132,39tempsensecondestempsenheuresheuresminutessecondes1erentraînement2503102032,832≥èmeentraînement24918101582,833≥èmeentraînement24827101072,814≥èmeentraînement24759100792,805≥èmeentraînement24939101792,836≥èmeentraînement24826101062,817≥èmeentraînement2503102032,838≥èmeentraînement24847101272,81Tempsmoyen:24912101452,82 sacados/7406 1234567ABCDEFNordSudEstOuestTOTALFootball15012575250600Handball50753085240Tennis35301550130Judo705020100240TOTAL3052801404851210Fréquenceen%
1234567ABCDEAnnéeNombredepaysdel’UE(enmillionsd’habitants)Populationdel’UE(enmillionsd’habitants)Augmentationdelapopulationdel’UE(en%)Super∏ciedel’UE(enkm2)19576210,7123510319739279,715888291981102901720455198612341,92317515199515364,131501742004254393888717 12345678ABCDEFGDésignationdel’articlePrixunitaire(HT)TVAà5;5%TVAà19;6%PrixunitaireTTCQuantitésPrixTotalTTCradiateur1;20m49,004radiateur0;80m37,002thermostat17,343chaudière66,751maind’oeuvre25,5065Total 12345678ABCDEFG0à10fois11à20fois21à30fois31à40fois40foisouplusTotal14ans15ans1022275038147153647867826214ans15ans6,80%14,97%18,37%34,01%25,85%100,00%5,73%13,74%17,94%32,82%29,77%100,00%NombredeconnexionsAge E.7408 The European Union, rated UE , grew from 15 to 25 member countries on 1 er May 2004. Table 2 provides information on the European Union each time the number of member countries changes. It was ob-tained using a table. 1 In this question, we are interested in the increase in the EU population. a What formula can be written in cell D3 to automat-ically copy down the percentage increase in the EU population on each date of change in the number of member countries, compared to the previous date of change? b Complete column D (the results will be rounded to two decimal places) c Calculate the percentage increase in the EU popula-tion from 1957 to 2004. 2 In this question, we are interested in the population den-sity of EU countries, i.e. the number of inhabitants per km 2 (the results will be rounded to the nearest whole num-ber) . The table below shows the population densities of EU countries in 2004. Country Finland Sweden Estonia Latvia Density 15 22 30 37 Country Ireland Lithuania Greece Spain Density 55 57 78 81 Country Cyprus Austria Slovenia Hungary Density 91 97 98 107 Country Slovakia France Portugal Denmark Density 110 118 123 Country Poland Czech Rep. Czech Republic Luxembourg Italy Density 123 129 155 187 Country Germany Royaume Uni Belgium Netherlands Malta Density 231 248 338 388 1 266 a Given that France had a population of 61.2 million in 2004 and an area of 543 965 km 2 , calculate the popula-tion density of France in 2004 b Determine the median and quartiles of this series of densities, then make a box plot (the maximum will not be included) c Calculate the average population density of EU coun-tries. Note that the average is higher than the median. Explain why. 3 This question focuses on France’s position within the EU in 2004. (The results will be rounded to the nearest whole number.) . a What percentage of the EU population did France rep-resent in 2004? b What percentage of the EU’s total area did France rep-resent in 2004? 4 Answer the following three statements with true or false : a The EU population increased by 108 % (to the nearest whole number) between 1957 and 2004 b The EU’s land area doubled between 1957 and 2004. c At least 75 % EU countries had a population density greater than or equal to 150 in 2004. E.7409 A private individual is fitting out the house he has just bought : he is having a new gas heater in-stalled. He makes a model of the future bill on the basis of the information provided by his installer; the latter gives him the prices HT (excluding tax) . To obtain the prices TTC (all taxes included) , he must add to the price HT the amount of the TV A (value-added tax) ; this TV A is expressed as a per-centage of the price HT : it is 5.5 % for supplies (radiators, thermostat, boiler) and 19.6 % for labor. The unit price for labor is counted by the hour. The table, provided below represents elements of a spread-sheet on which the individual has made his invoice template. Throughout the exercise will be rounded to the hundredth Complete the table below : E.7410 2 000 young people were asked to count the number of their Internet connections for a given week. The results are grouped according to the age of the students in the table below made with a table. Which of the following formulas is entered in cell B6 and which, by automatic copy in the cells B6 to G7 of the table allows to obtain the indicated percentages? =B3/G10 ; =B3/G3 ; =B3/$G$3 ; =B3/$G$10 https://chingmath.fr sacados/7408 1234567ABCDEAnnéeNombredepaysdel’UE(enmillionsd’habitants)Populationdel’UE(enmillionsd’habitants)Augmentationdelapopulationdel’UE(en%)Super∏ciedel’UE(enkm2)19576210,7123510319739279,715888291981102901720455198612341,92317515199515364,131501742004254393888717 sacados/7409 12345678ABCDEFGDésignationdel’articlePrixunitaire(HT)TVAà5;5%TVAà19;6%PrixunitaireTTCQuantitésPrixTotalTTCradiateur1;20m49,004radiateur0;80m37,002thermostat17,343chaudière66,751maind’oeuvre25,5065Total sacados/7410 12345678ABCDEFG0à10fois11à20fois21à30fois31à40fois40foisouplusTotal14ans15ans1022275038147153647867826214ans15ans6,80%14,97%18,37%34,01%25,85%100,00%5,73%13,74%17,94%32,82%29,77%100,00%NombredeconnexionsAge