Grade 10 / Proportion and evolution 102 exercises (100% corrected)

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1234567ABCDAnnéeNombred’abonnésQuotientPourcentaged’augmentation1995341996561,6471651997921,64296419981451,57615819992431,67596820004141,703770 1234567ABCDEFNordSudEstOuestTOTALFootball15012575250600Handball50753085240Tennis35301550130Judo705020100240TOTAL3052801404851210Fréquenceen%25,223,111,640,1100 12345678910111213ABCDETableau2:enpourcentageparrapportàl’e∑ectiftotalTableau1:e∑ectifMasse(eng)\Diamètre(mm)717579Total700215731231803708372030034122231094357452124298219237029Total728410227603623547Masse(eng)\Diamètre(mm)717579Total7009,213,37,730,172012,817,59,840,1745912,78,229,9Total30,943,425,6100% ChingQuizz : 11 exercises available for Quizz assessment : 1. Use of a spreadsheet E.6027 A gym manager wants to know how his clientele is progressing. He creates the following spread-sheet : 1 Which of the following formulas was entered in cell C3 and copied to range C3:C7 ? a =B3/B2 b =arrondi(B3/B2;4) c =B2/B3 d =arrondi(B2/B3;4) 2 Which of the following formulas was entered in the cell D3 and copied to the range D3:D7 ? a =arrondi((C3-1)*100;0) b =arrondi((C3-1)/100;0) c =arrondi((1-C3)*100;0) d =arrondi((1-C3)/100;0) E.5687 A study looks at the number of sports licensees in a département. To facilitate this study, the department has been divided into four parts (North, South, East, West) . Here is the table summarizing this study : The data in the range B2:E5 were entered, and then three formulas were used : A formula in F2 , then copied over the range F2:F5 ; A formula in B6 , then recopied on the range B6:F6 ; A formula in B7 , then recopied on the range B7:F7 ; 1 Which of the following formulas is used in F2 ? a =SOMME(B2:E2) b =SOMME(B$2:E$2) 2 Which of the following formulas is used in B6 ? a =SOMME(B2:B5) b =SOMME($B2:$B5) 3 Which of the following formulas is used in B7 ? a =ARRONDI(B6/F6;2) b =ARRONDI(B6/F$6;2) c =ARRONDI(B6/$F6;2) d =ARRONDI(B$6/F6;2) E.6028 A pétanque boules factory tested these production lines by recording the weights and diame-ters of the boules produced on a single day. The results were entered in the spreadsheet below : 1 a Which formula has been entered in the cell E3 then recopy on the range E3:E6 ? b What formula was entered in cell B6 then recopy on range B6:D6 ? 2 What formula has been entered in cell B10 , then recopy to range B10:E13 ? (without forgetting the rounding performed by the spread-sheet) 2. Proportion https://chingmath.fr chapExoCorrec/6027 sacados/6027 1234567ABCDAnnéeNombred’abonnésQuotientPourcentaged’augmentation1995341996561,6471651997921,64296419981451,57615819992431,67596820004141,703770 chapExoCorrec/5687 sacados/5687 1234567ABCDEFNordSudEstOuestTOTALFootball15012575250600Handball50753085240Tennis35301550130Judo705020100240TOTAL3052801404851210Fréquenceen%25,223,111,640,1100 chapExoCorrec/6028 sacados/6028 12345678910111213ABCDETableau2:enpourcentageparrapportàl’e∑ectiftotalTableau1:e∑ectifMasse(eng)\Diamètre(mm)717579Total700215731231803708372030034122231094357452124298219237029Total728410227603623547Masse(eng)\Diamètre(mm)717579Total7009,213,37,730,172012,817,59,840,1745912,78,229,9Total30,943,425,6100%
RougeVertBleuJaune E.7074 Consider the four figures below : 1 For the first three figures, determine the value of the quotient : nombre of squares noires nombre of squares 2 In the fourth figure, there is the same proportion of black squares as in the first three figures. Knowing that this figure contains 100 squares, how many squares are black? E.151 In one high school, 51 of the 85 stu-dents in the Première class take part in extra-curricular ac-tivities. 1 Calculate the share of students performing an activity. Give this value in fractional form, then its decimal value. 2 Deduct the percentage of pupils taking part in an ex-tracurricular activity. E.4364 The total number of first-year STMG students in one school is 94 . Five of these students were absent at the start of the school year Give the proportion, rounded to the nearest 0.001 , of students present at the start of the school year. E.7079 In a village of 658 people registered to vote, only 271 people voted in the first round of the presi-dential elections. Give the proportion, rounded to the nearest 0.001 , of people who abstained. E.9759 Cameroon’s independence was pro-claimed in January 1960. Cameroon is currently divided into 10 provinces and 58 departments. The Littoral province has 4 departments. What is the Littoral’s share of the total number of departments? Hint: this proportion will first be expressed as an irre-ducible fraction, then with a decimal number rounded to the nearest hundredth. 3. Reminders: percentage E.4352 A cake weighs 300 g . The packaging states that this cake contains 75 g of chocolate. What percentage of chocolate, rounded to the nearest tenth, is contained in this cake? E.9776 In a school with 452 pupils, 35 pupils play volleyball. What percentage of students, rounded to the nearest tenth, play this sport in the school? E.223 Paul, Marie and Laurent get together to buy the PlagaStation3. Here’s the summary table of the sums paid by each of them : Paul Marie Laurent 172 135 251 1 For each person, determine the percentage of the sum paid relative to the total price. Round to the nearest tenth. 2 If they had shared the purchase of this games console equally, how much would each of them have paid? E.157 1 What quantity represents 30 % of 120 e .? 2 How many hours and minutes does 10 % represent in a day? E.9762 Students were asked to indicate their favorite color among red, green, blue and yellow. The results of this study are shown in the diagram below : Unfortunately, the graduation on the y-axis has been erased. What percentage of people chose the color ˇredı. E.3077 In a mineral water bottling plant, a statistical study was carried out to measure bottle filling at the end of the production line. Here is a table summarizing the data collected: Volume d’eau (en ‘ ) 1.35 1.40 1.45 1.50 1.55 1.60 Nombre de bouteilles 23 79 378 562 35 4 Bottle filling machines are considered to be ˇ well adjusted ı if they meet the following two conditions : Bottles strictly exceeding a water volume of 1.5 ‘ should account for no more than 5 % of the bottles tested. The frequency of cylinders not contained in the interval 1.45 ; 1.55 must not exceed 10 % . Determine whether the machines in this factory are ˇ properly adjusted ı. Justify all your statements. 4. Proportion: search for numbers https://chingmath.fr chapExoCorrec/7074 sacados/7074 chapExoCorrec/151 sacados/151 chapExoCorrec/4364 sacados/4364 chapExoCorrec/7079 sacados/7079 chapExoCorrec/9759 sacados/9759 chapExoCorrec/4352 sacados/4352 chapExoCorrec/9776 sacados/9776 chapExoCorrec/223 sacados/223 chapExoCorrec/157 sacados/157 chapExoCorrec/9762 sacados/9762 RougeVertBleuJaune chapExoCorrec/3077 sacados/3077
E.9461 According to a study by 2011 , 713 thousands of students finished or stopped their studies during the years 2008 , 2009 and 2010 . Of these people, 9 % have no educational qualifications. How many people are in this group? (Source education.gouv.fr) E.7080 A chocolate spread offers pots of 950 g . The packaging states that it consists of 31 % fat. How much fat is included in these pots? E.7128 Consider a study population E and a subpopulation A of the population E . We note : n A and n E the respective numbers of the populations A and E . p the proportion of the A subpopulation to E . Each row in the table below represents a different situation où one of the values has been deleted. n E n A p a 512 346 b 3451 0.78 c 375 0.21 Copy and complete the table. No justification is required. Numbers should be rounded to the nearest whole number and proportions to the nearest hundredth. E.4432 Information on electricity produc-tion in Germany and France is given below : In Germany, 20.34 GW of electrical energy was of nuclear origin. It accounted for 28.4 % of its total electricity pro-duction. In France, 63.13 GW of electrical energy was generated by its nuclear power plants. This represented 74.1 % of its total electricity production. Determine the total electricity production of these two coun-tries rounded to the nearest GW hundredth. E.4428 The table below shows the number of companies in France according to the number of employees employed by each of them at 1 er January 2009. Number de salariés 0 1 to 49 50 to 499 Au moins 500 Nombre d’entreprises 1 911 485 1 162 654 ? 2 557 1 Knowing that companies with between 1 and 49 employ-ees represent 37.41 % of the number of French companies, determine the total number of companies in France at 1 er January 2009 rounded to the nearest unit. 2 What percentage do companies with no employees rep-resent of all French companies? Round to the nearest tenth. 5. Proportion: subpopulation with two characteristics E.7066 A school has 1 200 students. The following information is available: Half of the students are girls. One-third of the students participate in a sport within the UNSS. Only 10 % of the girls are registered with the UNSS. Answer the following questions : 1 How many girls are there in this school? 2 How many students are registered with the UNSS? 3 How many girls are enrolled in the UNSS? 4 Deduce the number of boys enrolled in the UNSS. Additional question: Which presentation is most appro-priate for solving this exercise? E.7069 A company closes in July and August. All the company’s 50 employees take their vacations during this period. We have the following information : July August Total Femmes en vacances 10 7 17 Hommes en vacances 12 21 33 Total en vacances 22 28 50 Results should be rounded to the nearest thousandth. 1 Among the ˇ women on holiday ı, what is the proportion of the sub-population of women gone in July? 2 Among all employees, what is the proportion of the sub-population of employees gone on vacation in July? 3 Among employees who went on vacation in August, what is the proportion of the subpopulation of ˇ men on vaca-tion ı? https://chingmath.fr chapExoCorrec/9461 sacados/9461 chapExoCorrec/7080 sacados/7080 chapExoCorrec/7128 sacados/7128 chapExoCorrec/4432 sacados/4432 chapExoCorrec/4428 sacados/4428 chapExoCorrec/7066 sacados/7066 chapExoCorrec/7069 sacados/7069
12345678910ABCDEFG0à10fois11à20fois21à30fois31à40fois40foisouplusTotal14ans15ans16ans17ans18ans19ans20ansTotal10222750381471536478678262225849809029920587212080350225570110803371758761109435513496268582501193364036245182000NombredeconnexionsAge 121314151617181920ABCDEFG0à10fois11à20fois21à30fois31à40fois40foisouplusTotal14ans15ans16ans17ans18ans19ans20ans6,80%14,97%18,37%34,01%25,85%100,00%5,73%13,74%17,94%32,82%29,77%100,00%7,36%19,40%16,39%26,76%30,10%100,00%5,71%16,57%20,57%34,29%22,86%100,00%6,53%16,32%20,77%34,64%23,74%100,00%4,79%30,99%26,48%100,00%5,20%19,60%24,80%27,20%23,20%100,00%NombredeconnexionsAge E.1826 In India, a population census is taken every ten years. The last census was carried out in 2001. It revealed the dis-tribution of India’s population according to various criteria including age, gender, place of residence, and took stock of India’s literacy. (source: Census of india 2001) A literate person being one who can read and write, children aged 0-6 have been excluded from the statistics. Here is an extract from the data collected on the population aged 7 and over (in millions of inhabitants) . Population aged 7 and plus (in millions of inhabitants) Hommes Femmes Total Rural 318 301 619 Urban environment 131 119 250 Total 449 420 869 Population aged 7 and over non alphabetic (in million inhabitants) Hommes Femmes Total Rural 91 161 252 Urban environment 18 32 50 Total 109 193 302 The following statements concern the population of India aged 7 and over in 2001. For each of these statements, say whether it is true or false, justifying the answer. 1 Less than one in four men is non-literate. 2 At least two-thirds of non-literates are women. 3 In urban areas, one in five people is non-literate. 4 More than 80 % of non-literate women live in rural areas. E.1808 We asked 2 000 young people to count the number of times they went online during a given week. The results are grouped by the students’ ages in the table below, which was created using a table the table was split in two for easier reading 1 a Explain in one sentence the value listed in cell C4 of the table above. b What formula was entered in cell B10 to obtain the number 119 ? 2 Among these young people, what percentage are 18 years old and went online between 31 and 40 times during the week? 3 Among the young people who logged in between 31 and 40 times, what percentage are 18 years old? 4 Another part of the same spreadsheet is shown below. The cells in rows 14 à 20 and columns B et G are format-ted as ˇPercentage, displayed to two decimal placesı : a Explain in one sentence the meaning of the value en-tered in cell B14 of the previous table. b Which of the following formulas should be entered in cell B14 so that, when automatically copied into cells C14 à G14 of the table in Question 4, it yields the per-centages shown? =B3/G10 ; =B3/G3 ; =B3/$G$3 ; =B3/$G$10 c Calculate the missing percentage in cell C19 . 6. Proportion: two-character subpopulation to be completed E.7151 new Caledonia ffl March 2006 ffl 10 points We want to tile a rectangular room 6 m long and 4 m wide using tiles in 2 colors: red and gray. What’s more, there are two types of tile in each color: patterned tiles and plain tiles. So there are a total of 4 tile patterns. For installation purposes, it is necessary to buy at least 672 tiles, of which 25 % in red, the rest in grey. It is also planned to lay for each each color 1 = 3 of patterned tiles, the rest being plain. Copy and complete the table below, leaving traces of your research. https://chingmath.fr chapExoCorrec/1826 sacados/1826 chapExoCorrec/1808 sacados/1808 12345678910ABCDEFG0à10fois11à20fois21à30fois31à40fois40foisouplusTotal14ans15ans16ans17ans18ans19ans20ansTotal10222750381471536478678262225849809029920587212080350225570110803371758761109435513496268582501193364036245182000NombredeconnexionsAge 121314151617181920ABCDEFG0à10fois11à20fois21à30fois31à40fois40foisouplusTotal14ans15ans16ans17ans18ans19ans20ans6,80%14,97%18,37%34,01%25,85%100,00%5,73%13,74%17,94%32,82%29,77%100,00%7,36%19,40%16,39%26,76%30,10%100,00%5,71%16,57%20,57%34,29%22,86%100,00%6,53%16,32%20,77%34,64%23,74%100,00%4,79%30,99%26,48%100,00%5,20%19,60%24,80%27,20%23,20%100,00%NombredeconnexionsAge chapExoCorrec/7151 sacados/7151
EAB EAB×...×...×... Rouges Gris Total Motifs Unis Total E.7072 In the French rail network, trains ˇGrandes lignesı are of two types : Corail or TGV (Train à Grande Vitesse) and customers are offered second-or first-class travel. A survey is carried out in a provincial station during the first week of July 2006. Of the 2 450 tickets sold, 82 % are second-class tickets. Of the 850 TGV tickets sold, 14 % are first-class tickets. 1 Copy and complete the following table : Corail tickets TGV tickets Total Billets Seconde classe Billets Première classe Total 850 2 450 2 Verify that the percentage of first-class tickets among Corail tickets sold during the first week of July month of July 2006 is 20 % (rounded to the nearest whole number) . 3 Can the station manager deduce from this survey that approximately 34 % of the tickets sold in his station dur-ing the first week of July 2006 were first-class tickets? Justify. E.7065 Using a machine, a supermar-ket checks the authenticity of 2 000 banknotes. Furthermore, we know that : Of all banknotes, forged banknotes account for 1.2 % and genuine 20 e banknotes account for 44.5 % Forged bills from 10 e represent 37.5 % of forged bills. The table below, despite missing data, summarizes the result of the banknote control: Coupure de 10 e Coupure de 20 e Total Billets falsifiés Tickets authentiques Total 2 000 7. Introduction to successive proportions E.7098 In one high school, of the 375 stu-dents in the Première class, 19.2 % of the students take part in extra-curricular activities. We know that 4.8 % of this school’s students are enrolled in the ˇ Théatre ı activity. 1 a Determine the number of students performing an ac-tivity and students enrolled in the activity ˇ Théatre ı. b What is the percentage of students enrolled in ˇ Théa-tre ı among all students participating in an activity? 2 Determine the value of p 1 × p 2 where : p 1 : the proportion of pupils enrolled in an extracurric-ular activity among the school’s pupils. p 2 : the proportion of students enrolled at ˇ Théatre ı among students enrolled in an extracurricular activity. What does this value represent? E.7100 In a population E , consider the two subpopulations A and B verifying B ⊂ A . 1 Suppose A represents 62.5 % of E and B represents 72 % of A . a Complete the diagram below with the data from the statement : b Deduct the percentage represented by B elements among E . 2 Suppose A represents 32 % of E and B represents 12 % of E . a Complete the diagram below with the data from the statement : b Deduct the percentage represented by B elements among A . https://chingmath.fr chapExoCorrec/7072 sacados/7072 chapExoCorrec/7065 sacados/7065 chapExoCorrec/7098 sacados/7098 chapExoCorrec/7100 sacados/7100 EAB EAB×...×...×... EAB×...×...×...
EAB×a×b×a×b Location280Utilitaires175Avechayon EtablissementFrançaisGarçonsfrançais Valeur initialeRéductionValeur ∏nale200501204405512%−12% 8. Successive proportions E.7099 Proposition: Let E be a set, A a subset of E , and B a subset of A . Let us denote : a the proportion of elements of A belonging to E ; b the proportion of elements of B belonging to A . The proportion of elements of B belonging to E has a value of a × b , as shown in the diagram below : A car rental agency rents out passenger cars and commercial vehicles. The graph below shows some of the data for this company: In addition, we know that 28 % of the commercial vehicles are hatchbacks. 1 Determine the proportion of commercial vehicles among all rentals. 2 Deduce the proportion of hatchbacks among all rental vehicles. E.7095 In 2006 at the Lycée Français de Mexico, 80 % of students are French and that 37.5 % of French students are French boys. Determine the percentage proportion of French boys in the school. E.150 At the Lycée Français in Mexico City, a fifth-grade class has 24 students, including 14 Mexicans, 8 French and 2 students of other nationalities. 1 Determine the share of Mexican students in this class. 2 Knowing that 75 % of Mexicans are girls. Give the per-centage of Mexican girls relative to the whole class. E.153 At the Estates-General meeting in 1789, the assembly consisted of 1,320 members representing three social groups : the clergy, the nobility, and the Third Estate. The Third Estate had 660 members, of whom 16 % repre-sented merchants, farmers, and industrialists, while the rest represented law enforcement and the liberal professions. 1 Determine the proportion of the Third Estate in this gen-eral assembly. Calculate the percentage of this represen-tation. 2 Determine the proportion represented by merchants, farmers, and industrialists relative to the entire assem-bly, rounded to the nearest thousandth. (From the Universalis Encyclopedia 10) E.7096 At the Lycée Français in Mexico City, 40 % of the students are hispanophones and 4 5 of them are Mexican. Give the proportion of Mexican students in the school’s stu-dent body. E.7150 A factory produces computer screens. To do this, it has two C 1 and C 2 production lines. We are interested in the production of this factory during the last month. Numbers should be rounded to the nearest whole number and percentage proportions to the nearest tenth. 1 We know that 67 % of the screens produced by the fac-tory come off the assembly line C 1 . Of these screens, 4 % have defects. Determine the percentage of screens exiting the produc-tion line C 1 with a defect among all the screens produced by the factory. 2 Knowing that the factory produced 1 200 screens this month and that 30 screens left the C 2 chain with a de-fect, determine the percentage proportion of screens with a defect among the screens exiting the chain C 2 . Indication : the number of screens will be rounded to the unit and the proportions in percentages to the nearest tenth. 9. Changes: rate of change and multiplying factor E.4351 Complete the table below : https://chingmath.fr chapExoCorrec/7099 sacados/7099 EAB×a×b×a×b Location280Utilitaires175Avechayon chapExoCorrec/7095 sacados/7095 EtablissementFrançaisGarçonsfrançais chapExoCorrec/150 sacados/150 chapExoCorrec/153 sacados/153 chapExoCorrec/7096 sacados/7096 chapExoCorrec/7150 sacados/7150 chapExoCorrec/4351 sacados/4351 Valeur initialeRéductionValeur ∏nale200501204405512%−12%
Valeur initialeAugmentationValeur ∏nale30050251215020%% E.4350 Complete the table below : E.145 Proposal: Applying a change to a value is equivalent to using a multiplier coefficient whose value is : 1+ a 100 if this change is an increase of a % ; 1 − a 100 if this change is a decrease of a % ; 1 Find the multiplier coefficients representing each of the following changes : a 10 % b 12 % c 0 ; 1 % d 112 % e 90 % f 3 ; 2 % 2 For each multiplier coefficient, find the associated change and the corresponding percentage: a 0 ; 15 b 1 ; 12 c 5 ; 1 d 0 ; 99 e 0 ; 905 f 1 ; 009 E.1830 1 Determine the type of evolution and the percentage asso-ciated with each of the following multiplier coefficients : a 1.35 b 0.84 c 2.07 2 Determine the multiplier coefficient associated with each of the following changes : a 2.5 % b 82.4 % c 212 % E.4361 1 Find the multiplier coefficients associated with each of the percentage change rates shown below : a +10 % b − 12 % c +0.1 % d +112 % e − 90 % f − 3.2 % 2 For each multiplier, find the percentage change rate pre-sented below : a 0.15 b 1.12 c 5.1 d 0.99 e 0.905 f 1.009 10. Changes: variations and rates of change E.7446 Definition: Consider a quantity changing from the value v 1 to the value v 2 . The absolute variation of this evolution is defined by the difference : v 2 − v 1 The relative variation of this evolution is defined by the quotient : v 2 − v 1 v 1 We are interested in the number of blood donations at blood drives organized within the Etablissement Français du Sang (EFS) since 2010 . Année 2010 2011 2012 2013 2014 Nombres de dons de sang (en milliers) 2 473 2 586 2 612 2 589 2 547 Source : EFS website 1 Determine the absolute change in this evolution between 2010 and 2014 . 2 Determine the relative change in this evolution between 2010 and 2014 rounded to the nearest ten-thousandth. E.7463 Definition: Relative change is also called rate of change of the trend. Le Percentage change is the rate of change multi-plied by 100 . Thus, the percentage change has the following value : v 2 − v 1 v 1 × 100 The table below shows the change, in five-year increments, in the world population (in billions) between 1980 and 2010 . Year 1980 1985 1990 1995 2000 2005 2010 Nombre Population (in billions) 4 ; 4 4 ; 8 5 ; 3 5 ; 7 6 ; 1 6 ; 5 6 ; 8 1 Determine the absolute change between 1980 and 2010 . 2 a Determine the relative change in the trend between 1980 and 2010 rounded to three decimal places. b Determine the characteristics of the change in the num-ber of inhabitants of the world population between 1980 and 2010 , where the percentage change will be given rounded to 10 − 2 . https://chingmath.fr chapExoCorrec/4350 sacados/4350 Valeur initialeAugmentationValeur ∏nale30050251215020%% chapExoCorrec/145 sacados/145 chapExoCorrec/1830 sacados/1830 chapExoCorrec/4361 sacados/4361 chapExoCorrec/7446 sacados/7446 chapExoCorrec/7463 sacados/7463
123456789101112ABCDxRecetteCoûtBéné∏ce0020-2010299018528052030405060708090100 E.231 The table below shows the price per liter of petrol in three separate years : Year 1973 1980 1998 Prix (en centimes) 121 327 638 We will give the results to the following questions rounded to the nearest tenth. 1 Determine the characteristics of the price change between 1973 and 1980 , then for that between 1980 and 1998 . 2 Calculate the percentage increase from 1973 to 1998 . E.7447 An INSEE study has listed the evolution in France of average annual net salaries from 1990 to 2010 . Some values are shown in the table below : Année 1990 2000 2010 Salaire net annuel moyen for les hommes ( e ) 17 643 21 498 26 831 Salaire net annuel moyen for les femmes ( e ) 13 258 17 259 22 112 1 Determine the absolute change in this evolution between 1990 and 2000 for men, then for women. 2 Calculate the rate of change in the average wage for men, then for women, between 1990 and 2000 . Rates will be rounded to the nearest thousandth . 11. Evolutions: problem and search for the percentage of evolution E.4356 A traveler going to France every summer, observes that the price of his favorite cake has risen from 1.25 e à 1.75 e . Determine the percentage change. E.4355 In a travel agency, a flight to the West Indies is on sale : its price has risen from 634 e to 558 e . Determine the percentage change rounded to the nearest tenth. E.4430 According to an INSEE survey, the number of people not wishing to have home Internet access fell from 4.37 million to 1.1 million between the years 2008 and 2010 . Determine the percentage change rounded to the nearest tenth. E.4365 The rent for an apartment being 340 e , the lessor decides to increase this rent by 17 e . What is the percentage change in this increase? E.7497 A company manufactures a model of wooden furniture. It can produce a maximum of 100 furniture per day. For x furniture manufactured and sold, the daily production cost (expressed in euros) , noted C ( x ) , is given by: C ( x ) = 2.25 · x 2 − 6 · x + 20 Each piece of furniture is sold 299 e . The company is open five days a week. The company manager has created the following spreadsheet : 1 a Give a formula which, entered in cell B2 , gives, by copying down, the revenue as a function of the number of pieces of furniture made and sold each day. b Give a formula which, entered in cell C3 , obtains, by copying down, the cost as a function of the number of pieces of furniture made and sold each day. c Calculate the values associated with the cells B7 , C7 and D7 . 2 Knowing that one day the company delivered 10 furni-ture and that the next day it delivered 50 furniture, de-termine the percentage change in profit between these two days, rounded to the nearest tenth. E.7549 A company can produce daily between 1 and 20 tons of paint. The production cost, in thousands of euros, of x tons of paint is modeled by the function C defined on the interval 1 ; 20 by: C ( x ) = 0.05 · x 2 − 0.1 · x + 2.45 In September, the company produced 14 tons of paint, whereas in October, the company produced only 10 tons of paint. Determine the percentage change in production cost between September and October rounded to the nearest unit. E.4367 Consider a square whose sides mea-sure x . We decide to increase the dimensions of the square by 10 % . 1 Determine the percentage change in the perimeter of the square during this increase. 2 Determine the percentage change in the area of the square. E.7145 Consider a rectangle whose length and width have changed by +20 % . Determine the characteristics of the evolution of the area of this rectangle. https://chingmath.fr chapExoCorrec/231 sacados/231 chapExoCorrec/7447 sacados/7447 chapExoCorrec/4356 sacados/4356 chapExoCorrec/4355 sacados/4355 chapExoCorrec/4430 sacados/4430 chapExoCorrec/4365 sacados/4365 chapExoCorrec/7497 sacados/7497 123456789101112ABCDxRecetteCoûtBéné∏ce0020-2010299018528052030405060708090100 chapExoCorrec/7549 sacados/7549 chapExoCorrec/4367 sacados/4367 chapExoCorrec/7145 sacados/7145
12. Evolutions: search for the final value E.4357 A pair of shoes was worth 52 e . On sale, this same item has been discounted by 30 % . Determine its sale price rounded to the nearest euro. E.4353 Prices are rounded to the nearest cent. 1 On a website, the price of a computer is 450 e hors tax. The VAT (value-added tax) being 19.6 % , determine the purchase price of this computer. 2 In 2011, the VAT allocated to catering is 5.5 % , knowing that an invoice was 79 e HT , determine the price paid by customers. E.7144 The production of Tahitian cultured pearls is an important activity for French Polynesia. The amounts realized from the export of pearl products from 2008 to 2011 were given in the table below : Années 2008 2009 2010 2011 Gross values of produits perliers (in thousands of euros) 66 052 63 181 Source :ISPF (Institut des Statistiques de Polynésie Française) Results are rounded to the nearest thousand euros . 1 Knowing that the amounts of exports suffered a de-cline between 2009 and 2010 whose rate of evolution was − 2.07 % , determine the amount of exports in 2010 . 2 Between 2008 and 2011 , the fall in export amounts resulted in a reduction whose rate of evolution was − 22.29 % . Determine the amount of exports realized in 2008 . E.9766 To keep up with the country’s infla-tion, one employer raises his employees every year by 4 % . In 2009, Alexandre had a salary of 1240 e . What will his salary be in 2010? 2011? Hint: results will be rounded to the nearest euro. 13. Evolutions: search for the initial value E.4359 An item has undergone an increase of 8 % . After this increase its price is 264.60 e . What was its original price? E.7097 A store raises all its prices by 5 % and cans of soda are now worth 420 FCFA . What was the price of a can before the increase? E.1720 In January 2002, a retailer increases the prices of all its products at 12 % . 1 A DVD player costs, before increase, 372 euros. How much will it cost afterwards? 2 A television costs, after increase, 476 euros. How much did it cost before? E.7203 The main greenhouse gas (GHG) is carbon dioxide, noted CO 2 . In 2011 , France emitted 486 megatons of GHG in CO 2 equiv-alent, compared with 559 megatons in 1990 . 1 In the Kyoto agreement, France committed to reducing its GHGs by 8 % between 1990 and 2012 . Can we say that in 2011 France was already meeting this commitment? Justify the answer. 2 Knowing that 2011 emissions marked a decrease of 5.6 % compared to 2010 , calculate the number of megatons in CO 2 equivalent emitted by France in 2010 . Round the result to 0.1 . E.4366 The price of an item was displayed at 50 e including VAT at 19.6 % . The government has decided to reduce VAT on this type of product to 5 % . What is the advertised price of this item? 14. Subgroup developments E.7141 In a commune, a sports association had 440 members in the first half of the year, including 182 girls. In the second half of the year, the number of male mem-bers fell by 14 % , while the number of female members rose by 5 % . How many members does the association have in the second half of the year? https://chingmath.fr chapExoCorrec/4357 sacados/4357 chapExoCorrec/4353 sacados/4353 chapExoCorrec/7144 sacados/7144 chapExoCorrec/9766 sacados/9766 chapExoCorrec/4359 sacados/4359 chapExoCorrec/7097 sacados/7097 chapExoCorrec/1720 sacados/1720 chapExoCorrec/7203 sacados/7203 Extrait Liban Juin 2017 chapExoCorrec/4366 sacados/4366 chapExoCorrec/7141 sacados/7141
n:::n:::n:::Fig.1Fig.2Fig.3:::%:::%:::% Valeur0Valeur1×:::5%Valeur2×:::5%×::::::% E.163 A precious metal is obtained by mix-ing 60% copper and 40% silver. We know that : 100 g of copper costs 2 euros ; 100 g of silver costs 25 euros. 1 A jeweler makes a ring worth 120 g with this precious metal. Determine the price of one of these rings. 2 The jeweler wants to make a profit of 15% . Determine the selling price of this ring displayed by the jeweler. 3 The jeweler is updating the prices in his catalog because, over the course of the year, gold has increased by 25% and the price of diamonds has remained stable. In particular, the price of a necklace is broken down as follows : 80% for the gold used and 20 % for its diamond composition. Determine the percentage increase in the price of this necklace. 15. Reciprocal developments E.4398 During a stock market session, the price of a share fell by 45 % . 1 What multiplier coefficient corresponds to this evolution? 2 a Determine the multiplier coefficient, rounded to the hundredth, associated with the evolution allowing, starting from the new price, to recover the initial price? b Give the characteristics of this reciprocal evolution. E.4373 The price of a product increases by 25 % . What percentage reduction is needed to bring the product back to its original price? E.4397 The price of an item has been mul-tiplied by 1.13 . 1 Specify the characteristics of the price evolution of this object. 2 Determine the percentage of reciprocal evolution? Round the percentage to the unit. E.4434 The price of a barrel of oil rose +55.2 % between February 2009 and May 2009. What is the percentage change, rounded to the nearest tenth, that will bring the price back to the February 2009 level? E.9769 The number of recruits for school teacher posts fell by − 55.6% between the years 2010 and 2011 . Determine the percentage change, rounded to the nearest tenth, that will bring back for 2012 the same number of re-cruits as in 2010 . 16. Successive evolutions: search for the global percentage E.4372 A figure undergoes two successive evolutions : 1 Determine the three rates of change expressed as percent-ages shown in the figure. 2 Is the overall rate of evolution (passage from Fig.1 to Fig.3) equal to the sum of the rates of the two interme-diate evolutions? E.4348 1 Give the multiplier coefficient associated with an increase of 5 % ? 2 Complete the diagram below, indicating : the multiplying coefficient to go from ˇvalue 0ı to ˇvaleur 1ı the multiplying coefficient to go from ˇvalue 1ı to ˇvaleur 2ı 3 Deduce the overall multiplicataur coefficient associated with the two successive increases in 5 % (allowing to go from ˇvalue 0ı to ˇvalue 2ı) . https://chingmath.fr chapExoCorrec/163 sacados/163 chapExoCorrec/4398 sacados/4398 chapExoCorrec/4373 sacados/4373 chapExoCorrec/4397 sacados/4397 chapExoCorrec/4434 sacados/4434 chapExoCorrec/9769 sacados/9769 chapExoCorrec/4372 sacados/4372 n:::n:::n:::Fig.1Fig.2Fig.3:::%:::%:::% chapExoCorrec/4348 sacados/4348 Valeur0Valeur1×:::5%Valeur2×:::5%×::::::%
V0V1V2×...×...×... V1V2V3×1,3×...×1,43 E.9770 Give the overall rate of change as-sociated with two successive augmentations and of respective rates 10 % and 5 % ? The diagram below can be completed to begin answering the question : E.9771 Give the overall rate of change asso-ciated with two successive changes of respective rates +20 % and − 20 % ? E.4371 Determine the percentage change corresponding to : 1 an increase of 15 % , then a reduction of 20 % ; 2 an increase in 50 % , then an increase in 60 % ; 3 a reduction of 5 % , then an increase of 10 % , then a re-duction of 5 % . E.5153 The following three changes are suc-cessively applied to a store’s price : 5 % ; 24 % ; 2.5 % Characterize the overall price evolution on this store following these three evolutions. E.4368 We counted the number of house- holds connected to the Internet in a city: from 2000 to 2002 , this number increased by 90 % ; from 2002 to 2004 , this number increased by 75 % Determine the overall percentage change from 2000 to 2004 . E.4369 The table below (source INSEE) represents the evolution of the French population and the percentage of people owning a cell phone : Année 1998 2001 2004 Population française (en millions) 60.05 61.04 62.18 Proportion de personnes possédant un téléphone mobile 18.7 % 60.6 % 71.6 % Nombre de personnes possédant un téléphone mobile (en millions) 1 Determine the number of people owning a cell phone for each of these three years rounded to the tenth of a million people. 2 Determine the percentage change in the number of French people owning a cell phone : a 1998 to 2001 b 2001 to 2004 3 Determine the overall percentage change between years 1998 and 2004 in the number of people with cell phones. 17. Successive evolutions: search for the intermediate percentage E.8548 We consider two evolutions evolving the value V 1 to the value V 3 : 1 On these two evolutions, we built the diagram below with two of the three multiplying coefficients : Determine the multiplying coefficient to go from the value V 2 to the value V 3 . 2 The two evolutions applied to the value V 1 are +30 % and a % respectively. It is known that the value V 1 has undergone an evolution of +43 % to obtain the value V 3 . Determine the percentage associated with the second evo-lution. 18. Successive evolutions: search for a value E.4370 A bank offers investments with a fixed interest of 1.75 % per year. 1 John deposits the sum of 2 500 e . How much capital will she have three years later? 2 Emilie has 5 788 e in her account on her investment. What was the sum originally contributed four years ago? E.4431 The table below shows changes in the investissement of Eurozone countries in energy renouvela-bles : Année 2004 2007 2009 Investissement +396.9 % -10.1 % 1 Determine the overall percentage change in these invest-ments between the years 2004 and 2009 . (round percentage to the nearest tenth) 2 Knowing that investment by Eurozone countries in 2004 was 9.9 billion dollars, determine the amount of this in-vestment for the year 2009 . (round investment to the tenth of a billion dollars) E.7143 The price of a share has risen each month by 5 % for 3 consecutive months ; Knowing that at the end of the three months its price was 52 e , determine its ini-tial price. Round the initial price to the nearest cent. https://chingmath.fr chapExoCorrec/9770 sacados/9770 V0V1V2×...×...×... chapExoCorrec/9771 sacados/9771 chapExoCorrec/4371 sacados/4371 chapExoCorrec/5153 sacados/5153 chapExoCorrec/4368 sacados/4368 chapExoCorrec/4369 sacados/4369 chapExoCorrec/8548 sacados/8548 V1V2V3×1,3×...×1,43 chapExoCorrec/4370 sacados/4370 chapExoCorrec/4431 sacados/4431 chapExoCorrec/7143 sacados/7143
19. Successive evolutions and use of power E.7140 In order to combat air pollu-tion, as early as the year 2013 certain companies were obliged to reduce the quantity of pollutants they released into the air each year. These companies discharged 410 tonnes of these pollutants in 2013 and 332 tonnes in 2015 . The annual rate of decrease in the mass of pollutants dis-charged is assumed to be constant. 1 Justify that the year-on-year change can be considered to correspond to a decrease of 10 % . 2 Assuming that this rate of 10 % remains constant for the coming years, determine the quantity of pollutants dis-charged in 2020 Round the result to the nearest tenth of a ton. E.9772 In 2010 , the population of the United Kingdom was 61.0 million and the percentage change in its population was +0.2 % . . Assuming this constant evolution, give the number of inhabi-tants of the United Kingdom in 2000 , rounded to the nearest tenth of a million. E.4391 The French population was 56.6 mil-lion in 2000 . On average, the percentage change per year in this population is 0.4 % . Assuming this evolution constant : 1 Determine the characteristics of the overall evolution. 2 Give the number of inhabitants of France in 2010 to the nearest tenth of a million. E.4435 The price of an item has risen by 44 % in two years. Assuming that the change has been constant over the two years, determine the percentage change for each year. 20. Successive developments: average E.106 1 Three brothers put in 152 e , 213 e and 178 e respectively to buy a computer. How much should they have put in fairly to get the same amount? 2 An object undergoes a first increase of 10 % and 20 % . Can we say that this is equivalent to undergoing two suc-cessive increases in 15 % ? Give an example. E.9774 Show that if a value x undergoes an increase of 47 % and then 8 % , this is equivalent to undergoing two successive increases 26 % E.9775 Two forms of averages are defined : The arithmetic mean of two numbers a and b is a + b 2 . the geometric mean of two numbers a and b is √ a × b Which average is best suited to talking about percentage av-erages? 21. Indexes E.4396 From 1994 to 2001 , a company has compiled its annual production statistics. We choose the base 100 in 1994 to establish the production indices. Année 1994 1995 1996 1997 1998 1999 2000 2001 Production 17 525 18 927 21 731 28 741 32 947 45 565 Indice 100 124 140 164 188 224 260 Fill in the missing values in this table (values will be rounded to the unit) . E.4374 Here are the admissions recorded in July by a museum in different years : Année 2006 2007 2008 2009 Nombre d’entrées 754 921 1041 1204 Indice 1 Taking the base index 100 into 2006 , complete the index line in the table below (to the nearest hundredth) . 2 Determine, to the nearest tenth, the percentage change between the years 2007 and 2009 . https://chingmath.fr chapExoCorrec/7140 sacados/7140 chapExoCorrec/9772 sacados/9772 chapExoCorrec/4391 sacados/4391 chapExoCorrec/4435 sacados/4435 chapExoCorrec/106 sacados/106 chapExoCorrec/9774 sacados/9774 chapExoCorrec/9775 sacados/9775 chapExoCorrec/4396 sacados/4396 chapExoCorrec/4374 sacados/4374
123ABCDEFGDate1/7/001/7/011/7/021/7/031/7/041/7/05Smichorairebrut6,416,676,837,197,618,03Indices100125,3 12345678ABCDEFGDésignationdel’articlePrixunitaire(HT)TVAà5;5%TVAà19;6%PrixunitaireTTCQuantitésPrixTotalTTCRadiateur1;20m49,004Radiateur0;80m37,002Chaudière66,751Maind’oeuvre25,5065Thermostat17,343Total E.4395 An internet service provider, wishes to make a forecast of the number of its subscribers for the year 2005 ; it draws up a statement of the number of subscribers for the years 2000 and 2004 . It assigns the index 100 to the year 2000 to establish sub-scriber statistics and records the data on the table and graph below : Année 2000 2001 2002 2003 2004 Indice 100 112 130 160 200 1 The number of subscribers was 2040 for the year 2000 , how many is it for the year 2004 ? 2 What is the percentage increase in subscribers between 2003 and 2004 ? E.4429 The table below shows the num-ber of companies created between the years 2004 and 2010 in France. We define the base 100 index for the year 2004 . Année 2004 2005 2006 2007 2008 2009 2010 Nombre d’entreprises crées (en milliers) × 282 290 313 × 589 612 Indice 100 102.9 × 114.2 116.4 215.0 223.4 Complete the table above, leaving a trace of your approach. (the good number of businesses created in 2009 comes from the creation of the auto-entreprise status) E.519 The table belowbelow shows the change in the gross hourly amount of the SMIC (Salaire minimum interprofessionnel de croissance) in France from 1 er July 2000 to 1 er July 2005 . Gross hourly wage in euros 1 er July 2000 6.41 1 er july 2001 6.67 1 er july 2002 6.83 1 er july 2003 7.19 1 er july 2004 7.61 1 er july 2005 8.03 1 What was the gross hourly Smic at 1 er July 1999 know-ing that it increased between 1 er July 1999 and the 1 er July 2000 of 3.2 % ? 2 An index table is constructed taking 100 July 1 er 2000 as a base. a Copy, then complete the spreadsheet extract below. Give decimal values rounded to the tenth. b What formula, to be copied over the range D3:G3 , can be entered in cell C3 ? c Determine the rate of change in the gross hourly Smic between 1 er July 2000 and 1 er July 2005 . The result will be rounded to the nearest thousandth. 22. Unclassified exercises E.6026 The spreadsheet below allows an indi-vidual to determine the cost of installing a heating system in his home : 1 Which formula should be entered in the cell C2 and copied to the range C2:C3 ? 2 What formula should be entered in cell B4 ? 3 What formula should be entered in cell D5 ? 4 What formulas should be entered in cells B6 and C6 ? 5 Which formula should be entered in the cell E2 and copied to the range E2:E5 ? 6 What formula should be entered in cell G2 in order to copy it over the range G2:G6 ? 7 What formula should be entered in cell G8 ? E.228 A precious metal is obtained by a mixture whose weight consists of 60 % copper and 40 % silver. 100 g of copper costs 2 euros and 100 g of silver costs 25 euros. 1 a A jeweler makes a 120 g ring from this alloy. Calcu-late the cost price of this ring. b Wishing to make a profit of 15 % on the sale of the ring, what should be the selling price of this ring? 2 Over one year, precious metal prices have moved : copper has risen by 30 % and silver by 7 % . a Determine the new price for making this ring. b Give the percentage increase in the price of making this ring over one year. https://chingmath.fr chapExoCorrec/4395 sacados/4395 chapExoCorrec/4429 sacados/4429 chapExoCorrec/519 sacados/519 123ABCDEFGDate1/7/001/7/011/7/021/7/031/7/041/7/05Smichorairebrut6,416,676,837,197,618,03Indices100125,3 chapExoCorrec/6026 sacados/6026 12345678ABCDEFGDésignationdel’articlePrixunitaire(HT)TVAà5;5%TVAà19;6%PrixunitaireTTCQuantitésPrixTotalTTCRadiateur1;20m49,004Radiateur0;80m37,002Chaudière66,751Maind’oeuvre25,5065Thermostat17,343Total chapExoCorrec/228 sacados/228
1234567ABCDAnnéeNombred’utilisateursQuotientPourcentaged’augmentation1995341996561,64711997921,642919981451,576119992431,675920004141,7037 Valeur0Valeur1×?5%Valeur2×?5%×??% E.143 Complete the following table : Initial value (in e ) Évolution (en % ) CM : coefficient multiplier Value finale in e 520 +20 242 -12 15 +5 203 -82 753 0.92 416 1.62 E.1827 The following table gives the number of Internet users worldwide (in millions) for the years 1995 to 2000. Year 1995 1996 1997 1998 1999 2000 Nombre d’utilisateurs (en millions) 34 56 92 145 243 414 We want to use a spreadsheet to analyze this data. The fol-lowing table has been drawn up : 1 Explain how it is possible to complete the column A with-out having to enter all the values contained in the cells. 2 In cell C3 , we have calculated the quotient of the number of Internet users in 1996 by the number of Internet users in 1995. a What does this quotient represent? b What is the formula to enter in cell C3 to perform this calculation and obtain the numbers in column C ? 3 a What was the percentage increase in the number of Internet users between 1995 and 1996? Between 1996 and 1997? (Percentages rounded to the nearest whole number will be given.) b What formula must be entered in cell D3 to obtain, by copying down, the percentages of variation in the number of Internet users over the years? c Complete the column D of the table in appendix (to be returned with copy) E.888 1 a What is the multiplier associated with an increase of 5 % ? b Complete the diagram below, in which the value 0 un-dergoes two successive increases of 5 % . c Determine the percentage increase that takes the value 0 to the value 2 . 2 a What is the percentage of the total increase when a value undergoes two percentage increases of 10 % and then 5 % , respectively? b What can be said about the change in a value that un-dergoes, in succession, an increase of 20 % followed by a decrease of 20 % ? Specify the percentage associated with this overall change. E.875 A stock on the stock exchange underwent an increase of 15% at the beginning of the month, then a fur-ther rise of 5% in the middle of the month. What was the increase over the month? E.870 We successively increase the price of a security at 20 % , then reduce it at 10 % . Give the nature of the overall change undergone by this value and its associated percentage. E.897 In 2004, a company increased its sales by 30 % In 2005, sales increased again, this time by 20 % . Calculate the overall percentage increase over these two years. E.873 1 Pinocchio, in front of his mathematics teacher, pretended to have forgotten a book, his nose lengthened from 4 cm to 15 cm . . . Calculate the percentage increase associated with this rise. 2 Arriving at his parents’ house, he told them the day had gone well and lengthened his nose by 12 % . How long is his nose at bedtime? 3 What percentage increase did the length of his nose un-dergo over the course of the day? https://chingmath.fr chapExoCorrec/143 sacados/143 chapExoCorrec/1827 sacados/1827 1234567ABCDAnnéeNombred’utilisateursQuotientPourcentaged’augmentation1995341996561,64711997921,642919981451,576119992431,675920004141,7037 chapExoCorrec/888 sacados/888 Valeur0Valeur1×?5%Valeur2×?5%×??% chapExoCorrec/875 sacados/875 chapExoCorrec/870 sacados/870 chapExoCorrec/897 sacados/897 Afrique - 2006 chapExoCorrec/873 sacados/873
E.4392 A town council subsidizes a sports club to the tune of 15 000 e for the year 2008 to supervise school outings. The table below represents the percentage change from one year to the next in the subsidy from the town hall: Year 2008 2009 2010 2011 2012 2013 Pourcentage d’évolution +7 % +12 % +3 % − 4 % +8 % Coefficient multiplicateur 1 a Compléter the table above. b Determine the percentage, rounded to the tenth, of overall change in this subsidy between the year 2008 and 2013 . 2 Give the amount of town hall subsidy received by the sports club in 2013 . E.11784 Un article qui valait 100 e il y a deux mois, a subi une hausse de 10 % puis une baisse de 10 % . Quel est son prix actuel? https://chingmath.fr chapExoCorrec/4392 sacados/4392 chapExoCorrec/11784 sacados/11784 Extrait Juin 2002 - Groupe Est - 8 points