Grade 11 - STMG / Evolution 46 exercises (including 40 corrected)

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Valeur initialeAugmentationValeur ∏nale30050251215020%% Valeur initialeAugmentationValeur ∏nale200501204405512%−12% 1. Percentages E.7464 Using mental arithmetic, give the re-quested percentages of the values : a 20 % de 300 b 10 % de 156 c 25 % de 440 d 15 % de 250 e 70 % de 150 f 12 % de 110 2. Increases and reductions E.7453 Complete the table below : E.7454 Complete the table below : E.7455 Requested prices will be rounded to the nearest cent. 1 On a website, the price of a computer is 450 e hors tax. Since the VAT (value-added tax) is 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. 3. Multiplier coefficient E.7456 1 Find the multiplier coefficients associated with each of the percentage change rates shown below : a +10 % b − 12 % c +2 % d +112 % e − 10 % f − 25 % 2 For each multiplier, find the associated percentage change rate: a 1.05 b 1.2 c 0.8 d 0.95 e 1.4 f 0.6 , E.7457 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 , E.7545 1 When the price of an apartment changed, its price was multiplied by 1.055 . Give the nature of this change and the percentage change. 2 The demographic study of a city shows that the popula-tion has multiplied by 0.82 . Give the nature of this evolution and the percentage of this evolution. E.7427 A home parcel delivery company asks an accounting firm to carry out a study of its business. Part of the data concerns the profits (in thousands of euros) made each year since 2007 . This information is summarized in the table below : Année 2007 2008 2009 2010 2011 2012 Benefit en milliers of euros 10 ; 2 12.8 13.8 14.4 16.7 17.5 1 Determine the absolute change in profit between 2007 and 2012 . 2 Determine the rate of change, rounded to the nearest thousandth, in profit between 2007 and 2012 . 3 Determine the multiplier coefficient associated with the change in profit between 2007 and 2012 . https://chingmath.fr chapExoCorrec/7464 sacados/7464 chapExoCorrec/7453 sacados/7453 Valeur initialeAugmentationValeur ∏nale30050251215020%% chapExoCorrec/7454 sacados/7454 Valeur initialeAugmentationValeur ∏nale200501204405512%−12% chapExoCorrec/7455 sacados/7455 chapExoCorrec/7456 sacados/7456 chapExoCorrec/7457 sacados/7457 chapExoCorrec/7545 sacados/7545 chapExoCorrec/7427 sacados/7427
E.7481 An entrepreneur launches new high-end shells for cell phones onto the market. Noting x the number of products manufactured expressed in hundreds of units, we model : revenues, in thousands of euros, by the function R de-fined on 0 ; 7 by: R ( x )= − 2 · x 3 +4.5 · x 2 +62 · x costs, in thousands of euros, by the function C defined on 0 ; 7 by: C ( x )=20 · x +10 In December 2017 , the company produced 300 hulls, whereas in January 2018 , the company produced only 150 hulls. 1 Determine the profits made by the company for Decem-ber 2017 and January 2018 . 2 Determine the rate of change, rounded to the nearest thousandth, in profit over this period and the associated multiplier coefficient. E.11192 1 Below are the rates of change in percentage terms. For each of them, give the associated multiplier coefficient : a +12% b − 36% c +0 ; 5% 2 Below are the multiplier coefficients associated with changes. For each of them, give their rate in percent-age terms : a 1 ; 2 b 0 ; 76 c 0 ; 005 4. Determining the final value E.7449 The survival of African elephants is threatened by poaching (illegal hunting) . In the absence of poaching, the African elephant population growth rate is estimated at 1.5 % per year. The total population of African elephants was estimated at 470 000 individuals in 2013 . 1 Give the value of the multiplier coefficient associated with this annual evolution. 2 Calculate the number of African elephants in 2014 in the absence of poaching. E.7495 The number of birds of a partic-ular species, shorebirds, staying on the Île de Ré during the years 2010 to 2014 was recorded. The results are shown in the table below, where the number of birds in 2014 has been deleted. Year 2010 2011 2012 2013 2014 Number 250 225 202 182 : : : Over the entire study period, the overall percentage change measured was − 52 % . Determine the number of birds in 2014 , rounded to the nearest whole number. 5. Determine initial value E.7458 1 An object has undergone an increase of 8 % . After this increase, its price is 264.60 e . What was its initial price? 2 The sale price of an item is 135 e . It is displayed with a discount of 40 % . What was the price of the item before the sale? E.7496 The table below shows the number of inhabitants in millions of the French population according to the year in which the data for that year was deleted. Year 2000 2002 2004 2006 2008 2010 Nombre Inhabitants in millions : : : 61.4 62.3 63.2 63.9 64.6 Given that the overall percentage change over the period 2000 to 2010 is 6.78 % , determine the number of inhabitants in the French population in 2000 , rounded to the nearest tenth of a million. E.7546 Below is an extract from a spread-sheet giving the number of road safety-related personal injury accidents in mainland France, from 2011 to 2013 . Année 2011 2012 2013 Nombre d’accidents corporels : : : 60 437 56 812 1 a Give the absolute change in the number of personal injury accidents between 2012 and 2013 . b Give the percentage change, in the number of injury accidents between 2012 and 2013 , rounded to the near-est tenth. 2 It is assumed that the change in the number of personal injury accidents was constant from 2011 to 2013 . De-termine the number of bodily injury accidents in 2011 rounded to the nearest unit. 6. Successive developments: determining the final value https://chingmath.fr chapExoCorrec/7481 sacados/7481 chapExoCorrec/11192 sacados/11192 chapExoCorrec/7449 sacados/7449 chapExoCorrec/7495 sacados/7495 chapExoCorrec/7458 sacados/7458 chapExoCorrec/7496 sacados/7496 chapExoCorrec/7546 sacados/7546
Valeur0Valeur1×:::5%Valeur2×:::5%×::::::% V0V1V2×...×...×... 123ABCDEFAnnée20112012201320142015SMIChorairebruteneuro99,319,439,539,61Tauxd’évolutionenpourcentage E.7459 1 a Donner le coefficient multiplicateur associé à une augmentation de 5 % ? b Complete the diagram below, indicating : the multiplying coefficient for going from ˇvaleur 0ı to ˇvaleur 1ı the multiplying coefficient from ˇvalue 1ı to ˇvaleur 2ı c Deduct the overall multiplier coefficient associated with the two successive increases in 5 % (allowing to go from ˇvalue 0ı to ˇvalue 2ı) . 2 a Give the overall rate of change associated with two successive increases and of respective rates 10 % and 5 % ? The diagram below can be completed to begin answer-ing the question : b Give the overall evolution rate associated with two suc-cessive evolutions and of respective rate +20 % and − 20 % ? E.7462 Note: This exercise is a multiple-choice quiz. For each question, there are four possible answers, only one of which is correct. 1 The value of a publicly traded stock fell by 37 ; 5 % . Its value has been multiplied by: a 0 ; 375 b 1 ; 375 c 1 ; 625 d 0 ; 625 2 The price of a food item increased by 2 % in the first month and then decreased by 10 % in the second month. Its value has been multiplied by: a 1 ; 122 b 1 ; 022 c 0 ; 918 d 1 ; 102 E.7647 Note: This exercise is a multiple-choice quiz. For each question, there are four possible answers, only one of which is correct. 1 The value of a publicly traded stock fell by 17 ; 5 % . Its value has been multiplied by: a 0 ; 175 b 1 ; 175 c 1 ; 825 d 0 ; 825 2 The price of a food item fell by 4 % in the first month and then rose by 4 % in the second month. Its value has been multiplied by: a 1 b 1 ; 016 c 0 ; 9984 d 0 ; 9216 E.7445 Type 1 diabetes is a disease that most often appears during childhood or adoles-cence. Individuals with this disease produce very lit-tle or no insulin, a hormone essential for the body’s absorption of blood glucose. In 2016 , 542 000 children worldwide had type 1 diabetes. Re-cent studies suggest that the number of children with diabetes will increase by 3 % per year starting in 2016 . Determine the number of children with type 1 diabetes during the first four years of the study : Year 2016 Number of children with diabetes E.7452 Note: This exercise is a multiple-choice questionnaire. (QCM) . For each question, only one of the four answers provided is correct. For each question, indicate the question number and copy the chosen answer onto your answer sheet. No justification is required. Each correct answer is worth 1 points. Incorrect answers and unanswered questions do not add or subtract points. The table below, taken from a spreadsheet, shows the evo-lution of the gross hourly minimum wage (SMIC) in euros between 2011 and 2015. It also shows the annual rates of change rounded to 0 ; 1 % . 1 The overall rate of change in the gross hourly SMIC be-tween 2011 and 2015 , rounded to 0 ; 1 % , is : a 6 ; 0 % b 6 ; 8 % c 7 ; 0 % d − 6 ; 3 % 2 The average annual rate of change in the gross hourly minimum wage between 2011 and 2013 , rounded to 0 ; 1 % , is : a 1 ; 7 % b 1 ; 9 % c 2 ; 1 % d 2 ; 3 % 3 What formula can be entered in cell C3 to obtain, by copying to the right, the rates of change from one year to the next? The cell range C3:F3 is in percentage for-mat rounded to 0 ; 1 % a (C2-B2)/C2 b (C2-B$2)/C2 c (C2-B2)/B2 d (C2-$B$2)/B2 https://chingmath.fr chapExoCorrec/7459 sacados/7459 Valeur0Valeur1×:::5%Valeur2×:::5%×::::::% V0V1V2×...×...×... chapExoCorrec/7462 sacados/7462 chapExoCorrec/7647 sacados/7647 chapExoCorrec/7445 sacados/7445 chapExoCorrec/7452 sacados/7452 123ABCDEFAnnée20112012201320142015SMIChorairebruteneuro99,319,439,539,61Tauxd’évolutionenpourcentage
V0V1V2×...×...×... E.11726 Une imprimante 3D coûtait 200 euros. Quatre années successives, son prix subit une augmentation de 4 % . Déterminer son prix final (arrondi au dixième près) . Indication : on pourra se servir des tableaux de valeurs : n 1 2 3 4 4 n 4 16 64 256 0 ; 4 n 0 ; 4 0 ; 16 0 ; 064 0 ; 0256 0 ; 04 n 0 ; 04 0 ; 0016 0 ; 000064 0 ; 00000256 1 ; 4 n 1 ; 4 1 ; 96 2 ; 744 3 ; 8416 1 ; 04 n 1 ; 04 1 ; 0816 1 ; 124864 1 ; 16985856 0 ; 6 n 0 ; 6 0 ; 36 0 ; 216 0 ; 1296 0 ; 96 n 0 ; 96 0 ; 9216 0 ; 884736 0 ; 84934656 7. Successive trends: overall rate of change E.7460 We counted the number of homes con-nected 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.7548 1 The price of a cell phone has undergone a first reduction of 10 % , then a second reduction of 50 % . a Determine the overall multiplier coefficient associated with each of these two reductions rounded to 10 − 4 . b Give the percentage of the overall change associated with these two changes rounded to the nearest tenth. 2 A company’s sales undergo a constant monthly increase of 4 % over the course of a year. Determine the percentage of overall change over the year rounded to the nearest hundredth. E.11368 1 An object undergoes two successive increases of +28 % and +25 % . a Complete the following diagram representing the over-all change undergone by this object : b Give the percentage rate of the overall change under-gone by this object. 2 An object undergoes a reduction of − 16 % , then an in-crease of +15 % . Determine the percentage change undergone by this ob-ject. Hint: indicate the method used. E.11389 1 An object undergoes two successive increases of +15 % and +18 % . Determine the rate, as a percentage, of the overall change undergone by this object. 2 An object undergoes a reduction of − 15 % , then an in-crease of +6 % . Determine the rate, as a percentage, of the overall change undergone by this object. Hint: indicate the method used. E.11390 1 An object undergoes two successive increases of +12 % and +15 % . Determine the rate, as a percentage, of the overall change undergone by this object. 2 An object undergoes a reduction of − 5 % , then an in-crease of +4 % . Determine the rate, as a percentage, of the overall change undergone by this object. Hint: indicate the method used. E.11391 1 An object undergoes two successive increases of +5 % and +14 % . Determine the rate, as a percentage, of the overall change undergone by this object. 2 An object undergoes a reduction of − 8 % , then an in-crease of +15 % . Determine the rate, as a percentage, of the overall change undergone by this object. Hint: indicate the method used. 8. Successive evolution: determine initial value https://chingmath.fr sacados/11726 chapExoCorrec/7460 sacados/7460 chapExoCorrec/7548 sacados/7548 chapExoCorrec/11368 sacados/11368 V0V1V2×...×...×... chapExoCorrec/11389 sacados/11389 chapExoCorrec/11390 sacados/11390 chapExoCorrec/11391 sacados/11391
E.7448 Note: This exercise is a multiple-choice questionnaire. (QCM) . For each question, only one of the four answers provided is correct. A beekeeper observes that between March 1 and March 2, the adult bee population in his hive has decreased by 4 per year. On March 1 er , 2016, the beekeeper counted 55 200 adult bees in his hive. How many adult bees can be estimated to have populated the hive on March 1 er , 2014, rounded to the nearest hundred? a 73 000 b 107 100 c 76 400 d 71 800 E.7502 The table below shows the net monthly minimum wage as of September 1 er of each year: Year 2010 2011 2012 2013 Amount in euros : : : : : : 1118.29 1120.43 1 Determine the rate of change in the minimum wage be-tween years 2012 and 2013 . (The value will be rounded to the nearest 10 − 5 ) . 2 Assume that the annual rate of change between years 2010 and 2013 is constant. Determine the amount of the minimum wage on Septem-ber 1 er 2010 . 9. Average change (2 changes) E.11710 1 Un objet subit deux augmentations successives de +12 % et de +15 % . Déterminer l’évolution moyenne subie par cet objet lors de ces deux augmentations. 2 Un objet subit une réduction de − 5 % , puis une augmen-tation de +4 % . Déterminer l’évolution moyenne subie par cet objet lors de ces deux augmentations. Indication : on indiquera la démarche utilisée. E.11711 1 Un objet subit deux augmentations successives de +22 % et de − 10 % . Déterminer l’évolution moyenne subie par cet objet lors de ces deux augmentations. 2 Un objet subit une réduction de − 30 % , puis une augmen-tation de +10 % . Déterminer l’évolution moyenne subie par cet objet lors de ces deux augmentations. Indication : on indiquera la démarche utilisée. E.7461 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 from one year to the next. E.7450 The following table shows the evo-lution of the daily circulation (number of copies printed per day) of the daily general and political press in France. Year 2010 2011 2012 Daily circulation in millions of copies 1.80 1.72 1.60 1 Determine the overall rate of change, rounded to 0.01 % , in daily circulation between 2010 and 2012 . 2 Calculate the average annual growth rate over this pe-riod, rounded to 0.01 % , of the daily circulation. E.7537 The table below shows the con-sumption of healthcare and medical goods (CSBM) in France, in billions of euros : Year 2006 2007 2008 Consumption (CSBM) in billions of euros 153.7 : : : 165.7 We assume that CSBM consumption remained constant over the two years between 2006 and 2008 . Determine the annual percentage change over the period between 2006 and 2008 , rounded to two decimal places. E.7538 In recent years, tourism distribu-tion channels have changed in favor of online tourism. More than 30 million French people have visited websites to plan their vacations in 2013 . The table below gives the evolution of sales, noted CA , of the online tourism market from 2011 to 2013 in France. Année 2011 2012 2013 CA in milliard d’euros 10 ; 9 : : : 12.4 It is assumed that the change in online tourism market sales from 2011 to 2013 in France was constant over this period. Determine the annual percentage change corresponding to this period. E.7547 The table below shows the amount of greenhouse gases emitted annually in France between 2009 and 2012 . This amount is expressed in millions of tons and rounded to two decimal places. Year 2009 2010 2011 2012 Amount emitted 509.25 : : : 490.01 : : : Assuming that the annual change was constant over the pe-riod from 2009 to 2012 , the aim of the exercise is to predict the amount of greenhouse gases emitted in 2012 . 1 Determine the annual rate of change in the amount of greenhouse gas emissions rounded to the nearest thou-sandth. 2 Determine the amount of greenhouse gases emitted in 2012 rounded to the nearest hundredth. https://chingmath.fr chapExoCorrec/7448 sacados/7448 chapExoCorrec/7502 sacados/7502 sacados/11710 sacados/11711 chapExoCorrec/7461 sacados/7461 chapExoCorrec/7450 sacados/7450 Extrait Antilles-Guyane Juin 2017 chapExoCorrec/7537 sacados/7537 chapExoCorrec/7538 sacados/7538 chapExoCorrec/7547 sacados/7547
12345ABCDEEtéPrixdumenu(eneuro)NombrehebdomadairemoyendecouvertsTauxd’évolutionannueldunombrehebdomadairemoyendecouversTauxd’évolutionannuelduprix21029,8420210311,00395-5,95%12,24%210412,30370210513,80345 E.7451 In 2012 , the manager of a beach-front brasserie offers a lunch menu for 9.80 e . At this price, he serves an average of 420 covers per week. This formula is so successful that he decides to increase the price in subsequent summers. He observes a slight decrease in the number of meals served, but his formula remains profitable. The following table shows the change in the number of meals served when the price of the menu varies. Été 2012 2013 2014 2015 Menu price (in euros) 9.80 11.00 12.30 13.80 Weekly number of covers 420 395 370 345 The manager created the table below from a spreadsheet : The range of cells D3:E5 is formatted as a percentage rounded to 0.01 % . 1 Propose a formula to be entered in cell D3 , that can be copied down to complete the cells D4 et D5 . 2 Similarly, suggest a formula to enter in cell E3 , that can be copied down to complete cells E4 et E5 . 3 In this question, we assume that the change in menu prices between 2012 and 2014 has been constant : a Calculate the multiplier coefficient, rounded to 0.000 1 % , associated with the annual change in the menu price between summer 2012 and summer 2014 . b Deduce the annual rate of change in the menu price between 2012 and 2014 . E.7482 The table below shows the change in the world population (in billions) between 1980 and 2010 , in five-year increments. 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 Give the rate of change in population between 1980 and 2010 . 2 Establish that this change corresponds to a constant change of 7.52 % per 5 years. 10. Average Change E.11709 Voici un aperçu d’une feuille de cal-cul regroupant le nombre de naissances dans un département français de 2009 à 2016. Année 2009 2010 2011 2012 2013 2014 2015 2016 Nombre de naissances 8304 8111 8041 7833 7644 7466 7199 6927 Source : INSEE - 2017 Déterminer le taux d’évolution annuel moyen sur cette péri-ode. E.11727 Un objet a subit 5 augmentations succes-sives et identiques. Son prix a été multiplié par 1 ; 4 . Décrire chacune de ces augmentations. Indication : on arrondira le pourcentage au dixième près, on utilisera le tableau de valeurs ci-dessous : n 2 3 4 5 6 n 1 ; 4 1 ; 1832 1 ; 1187 1 ; 0878 1 ; 0696 1 ; 0577 E.11728 Un objet a subit 6 réductions succes-sives et identiques. Son prix a été multiplié par 0 ; 9 . Décrire chacune de ces réductions. Indication : on arrondira le pourcentage au dixième près, on utilisera le tableau de valeurs ci-dessous : n 2 3 4 5 6 7 0 ; 9 1 n 0 ; 9487 0 ; 9655 0 ; 974 0 ; 9791 0 ; 9826 0 ; 9851 11. Evolution and follow-up E.7483 In one city, it is estimated that from 2013 , the number of electric cars on the road increases by 12 % per year. At 1 er January 2013 , this town offers 148 dedicated parking spaces with charging stations. The municipality plans to cre-ate 13 additional spaces each year. The spreadsheet below should account for this data. Cells are in the format ˇ number with zero decimal places ı. https://chingmath.fr chapExoCorrec/7451 sacados/7451 12345ABCDEEtéPrixdumenu(eneuro)NombrehebdomadairemoyendecouvertsTauxd’évolutionannueldunombrehebdomadairemoyendecouversTauxd’évolutionannuelduprix21029,8420210311,00395-5,95%12,24%210412,30370210513,80345 chapExoCorrec/7482 sacados/7482 sacados/11709 sacados/11727 sacados/11728 chapExoCorrec/7483 sacados/7483
123ABCDEFGHDate1erjanvier20131erjanvier20141erjanvier20151erjanvier20161erjanvier20171erjanvier20181erjanvier2019Nombredevoituresélectriques100112Nombredeplacesspéci∏ques148161 1 Specify a formula which, entered in cell C2 , allows, by copying to the right, to obtain the contents of the cells in the range C2:H2 . 2 Determine the overall percentage change in the num-ber of electric cars on the road between 2013 and 2016 , rounded to 0.1 % . 3 Let n be a natural number. The number of electric cars in circulation on 1 er January of the year (2013+ n ) is mod-eled by the term V n of a geometric sequence. Thus, V 0 =100 . a Determine the reason for the sequence V n . b Specify the expression of V n as a function of n . c Calculate V 8 and V 9 rounded to unity. 12. Mutual evolution E.7755 Reminders: A change can be characterized by: its rate of change ( t ) ; its percentage change ( p ) ; its multiplier coefficient ( k ) . Here are the relationships between these values : p = t × 100 ; t = p 100 ; k =1+ t ; t =1 − k If a quantity has changed from value v 0 to v 1 , then its rate of change is : t = v 1 − v 0 v 0 1 a A jacket costs 50 e and undergoes an increase of 28 % . What is its new price? b A pair of shoes costs 64 e and undergoes a reduction of 21 ; 875 % . What is its new price? 2 Characterize the reciprocal change of an increase of 28 % . E.7722 A company’s stock is listed at 124 e on 1 er September. 1 On 17 September, the stock has a value of 150.04 e . De-termine the percentage of this change. 2 On 15 October, the share price has returned to 124 e . Determine the percentage change, rounded to the near-est tenth, over the period between 17 September and 15 October. E.7723 Each line of the table below represents an evolution and its reciprocal evolution. Complete the table by indicating the percentage of the recip-rocal evolution to the nearest hundredth. Evolution Reciprocal evolution Increase in 25 % Increase in 60 % Increase in 10 % Reduction in 28 % Reduction of 50 % Reduction of 7 % E.7743 As a result of inflation, the price of a ton of rice rose 402 e in 2017 to 421 e in 2018 . 1 Determine the percentage of this inflation, rounded to the nearest tenth. 2 If this inflation became constant over the period from 2017 to 2022 , what would be the price of a ton of rice in 2022 rounded to the nearest euro? 3 What must be the percentage, rounded to the nearest tenth, of deflation between 2018 and 2019 for the price of a ton of rice to return to 402 e ? https://chingmath.fr 123ABCDEFGHDate1erjanvier20131erjanvier20141erjanvier20151erjanvier20161erjanvier20171erjanvier20181erjanvier2019Nombredevoituresélectriques100112Nombredeplacesspéci∏ques148161 chapExoCorrec/7755 sacados/7755 chapExoCorrec/7722 sacados/7722 chapExoCorrec/7723 sacados/7723 chapExoCorrec/7743 sacados/7743