Grade 8 / Quotient and product quantities 49 exercises (100% corrected)

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12345678910ABConversionsTempératuresenoC-50510152025TempératuresenoF23324150596877 1. Conversions of quantities E.871 1 Perform the following length conversions : k h da u d c m 3.2 kg g 34 dam km 24.63 ‘ d‘ 24 m‘ h‘ 8.9 m mm 2 Perform the following volume conversions : km 3 hm 3 dam 3 um 3 dm 3 cm 3 mm 3 17 m 3 dm 3 3.3 dam 3 hm 3 534.2 ‘ dm 3 92 mm 3 cm 3 0.023 m 3 cm 3 E.3990 1 Convert the following times to hours : a 75 min b 42 min c 140 min 2 Convert the following times to minutes : a 1.75 h b 2.25 h c 5 3 h 3 Perform conversions to minutes and then to hours of the following durations : Durée en minutes en heures 2 h 30 min 5 h 12 min 0 h 45 min 1 h 36 min 1 h 05 min E.7625 In Únited States, tempera-ture is measured in degrees Fahrenheit (in o F) . In France, it is measured in degrees Cel-sius (in o C) . To make the con-versions from one unit to an-other, we used a spreadsheet program. Here’s a copy of the resulting screen opposite. 1 What temperature in o F corresponds to a temperature of 20 o C? 2 What temperature in o C corresponds to a temperature of 41 o F? 3 To convert the temperature from o C to o F, multiply the temperature in o C by 1.8 then add 32 . We wrote a formula in B4 then copied it down. What formula could have been entered in cell B4 ? E.1124 For each of the durations be-low, convert them into hours and then into minutes : a 1 h 12 min b 3 h 27 min c 40 min 2. Speed: quotient size E.9102 Definition: for a mobile moving by uniform motion, we call velocity of the mobile, the quotient of distance by time: v = d t It is expressed in the same units as the two quantities d and t : if d is expressed in kilometers and t in hours then the unit of speed is the ˇ kilometer per heure ı noted km = h . On the freeway, a motorist connects the towns of Montpel- lier and Bayonne, which are 532 km apart, in five hours at constant speed. Determine his speed in km = h . E.879 On November 7, 1998, on the return from John Glenn’s historic second trip into space, the space shuttle Discovery had traveled 5.8 million kilometers. As this mission lasted 8 days and 22 hours, calculate the shut-tle’s average speed expressed in km = h to the nearest unit. We’ll also give the result in scientific writing. https://chingmath.fr chapExoCorrec/871 sacados/871 chapExoCorrec/3990 sacados/3990 chapExoCorrec/7625 sacados/7625 Asie Juin 2017 4 points 12345678910ABConversionsTempératuresenoC-50510152025TempératuresenoF23324150596877 chapExoCorrec/1124 sacados/1124 chapExoCorrec/9102 sacados/9102 chapExoCorrec/879 sacados/879 Rennes - Juin 1999 - 3 points
Durée (enh)Distance (enkm)4512×v E.1125 Note: The number 60 has 12 divisors, which allows for the following conversions : 12 min = 0 ; 2 h ; 15 min = 0 ; 25 h 30 min = 0 ; 5 h ; 45 min = 0 ; 75 h 1 At a normal, constant pace, a walker covers 1 km in 15 min . Give its speed in km = h . 2 A car traveling at a constant speed covers 56 km in 30 minutes. Give its speed in km = h . 3 An airliner flying at a constant speed covers 170 km in 12 minutes. Give its speed in km = h . E.1436 A man is walking and covers the 13.65 km of the city’s circumference in 3 h 15 min. Calculate the walking speed of this man in miles per hour. E.9101 The earth makes its revolution around the sun (the act of circling its orbit) in 1 year and travels 940 million kilometers. Express its speed in km = h rounded to the nearest unit. E.9088 Light travels 150 million kilometers in 8 minutes. Determine the speed of light in m = s . Note: The result should be given in scientific notation. E.9095 When hunting, a peregrine falcon (the fastest bird) travels 150 meters in 3 seconds. 1 Determine its speed in m = s 2 Determine his speed in km = h E.9090 Looking at the mile markers at the side of the road, a child counts 14 kilometers in 7 minutes when the car is traveling at constant speed. What was its speed expressed in km = h ? E.881 We’ll assume that the earth’s orbit around the sun is circular and that the earth-sun distance is 150 million kilometers (We’ll ignore the fact that this orbit is actually elliptical) . Assuming that the earth completes its orbit in 365 days, cal-culate the earth’s speed of rotation around the sun, expressed in km = h and rounded to the nearest unit. . Note: the circumference of a circle of radius r is given by the formula : 2 × ı × r where ı ≈ 3.14 . One liter is equal to one cubic decimeter. 3. Speed: distance and time E.9098 Proposition: Average speed connects distance and dura-tion of uniform motion through three equivalent identities: v = d t d = v × t t = d v A commercial airliner flew from Paris to Mexico City in 11 h 50 min . We assume that its cruising speed of 238 m = s was maintained throughout the journey. Determine the distance traveled by this aircraft in km . E.9099 A friend of his walks along the beach-front at a speed of 1.2 m = s for 35 minutes. How far did he walk? E.890 Sound propagates at a speed of 330 m = s and light propagates at a speed of 299 792 458 m = s in air. Thus, when the thunder is triggered, it is assumed that the observer instantly sees the light and hears the thunder afterwards. After the lightning strikes, an observer hears thunder 9 sec-onds after seeing the lightning. Determine the distance separating the observer from the light-ning strike. E.1128 On 18 May 1990 , the T.G.V. (High Speed Train) reached a speed of 515 km = h . How many miles did it travel in 5 minutes? We will round the distance to the nearest meter. E.488 The speed of light is 300 000 km = s . 1 Light takes 1.3 seconds to travel from a satellite to Earth. Calculate the distance from the satellite to the Earth. 2 Light takes about 8 minutes and 30 seconds to reach us from the sun. Calculate the distance separating us from the Sun. Give the result in scientific writing. E.9092 The European probe ˇ Mars Express ı was launched on 2 June 2003 and has traveled 56 mil-lion kilometers to reach the planet Mars at an average speed of 3 131 m = s . Determine, in number of days, the travel time of this probe (rounded to the unit) . 4. Speed and proportionality E.9100 For uniform motion, velocity is the coefficient of proportion-ality that allows us to pass from duration to distance : https://chingmath.fr chapExoCorrec/1125 sacados/1125 chapExoCorrec/1436 sacados/1436 chapExoCorrec/9101 sacados/9101 chapExoCorrec/9088 sacados/9088 chapExoCorrec/9095 sacados/9095 chapExoCorrec/9090 sacados/9090 chapExoCorrec/881 sacados/881 chapExoCorrec/9098 sacados/9098 chapExoCorrec/9099 sacados/9099 chapExoCorrec/890 sacados/890 chapExoCorrec/1128 sacados/1128 chapExoCorrec/488 sacados/488 Amerique du Nord Juin 2011 chapExoCorrec/9092 sacados/9092 chapExoCorrec/9100 sacados/9100 Durée (enh)Distance (enkm)4512×v
500014000 18300 The cheetah, at maximum speed, can cover 275 meters in 9 seconds. Express its speed in km = h . E.9091 The marathon is a sporting event in which participants must run 42 195 m . The world record was set in 2003 at the Berlin Marathon in 2 h 05 min . Give its average speed expressed in km = h rounded to the near-est unit. E.1437 On May 26, 2001, the TGV (Train à Grande Vitesse) performed the record of traveling the 1067 km of track separating Calais from Marseille in 3 h 29 min . Calculate the average speed of the train in km = h rounding to the nearest unit. E.9097 At the beginning of its liftoff, Ariane 5 climbs vertically until its first stage separates in 9 min 35 s and it has reached an altitude of 147 km , . Calculate her average speed in km = h rounding to the nearest unit? E.1434 Marie-José Perec ran the 400 m in 48.26 s during the Atlanta Olympics of 1996 . How long will it take him to run a marathon (42.195km) at the same speed? Hint: we express the result as : : : : h : : : min : : : s 5. Speed: unit conversion E.2630 Perform the following speed conver-sions, rounded to the nearest tenth : a 35 km = h en m = s b 2.4 m = s en km = h c 3 × 10 5 km = an en m = s d 274 dm = min en m = s e 289 m = min en km = h E.9096 A snail has an average speed of 12 cm = min . Determine the average speed of the snail at m = h . E.880 An ant is observed for 15 seconds, moving uniformly over a distance of 48 centimetres. Determine the ant’s speed expressed in : a centimeters per second ( cm = s ) ; b kilometers per hour ( km = h ) . 6. Speed and problems E.7630 In this exercise, we’ll be looking at the speed of a TGV passing through a station without stop-ping. Information 1: The whole train passed me in 13 sec-onds and 53 hundredths. Information 2: Diagram of the power cars and car-riages making up a TGV trainset : Length measurements are expressed in millimeters. Information 3: Composition of TGV passing station : The TGV consists of two trainsets. Each trainset is made up of two type A power cars framing ten type B cars At what speed (in km = h ) did the TGV pass, without stopping, in front of me? The result will be rounded to the nearest whole number. https://chingmath.fr chapExoCorrec/9091 sacados/9091 chapExoCorrec/1437 sacados/1437 chapExoCorrec/9097 sacados/9097 chapExoCorrec/1434 sacados/1434 chapExoCorrec/2630 sacados/2630 chapExoCorrec/9096 sacados/9096 chapExoCorrec/880 sacados/880 chapExoCorrec/7630 sacados/7630 500014000 18300
TessalitKidalGaoTombouctouKayesMoptiSegouBamakoSikasso Groupe1Groupe21000km E.6286 Mathilde and Eva are in the Baie des Citrons. They watch a cruise ship leave the port of Nouméa. Mathilde thinks it is sailing at a speed of 20 knots. Eva estimates that he is sailing at more like 10 knots. They then decide to determine this speed mathematically. On her phone, Mathilde first uses the stopwatch function. She starts the stopwatch when the bow of the ship passes a coconut tree and stops it when the stern of the ship passes the same coconut tree ; it elapses 40 seconds. Next, Eva searches the Internet for the characteristics of the boat. Here’s what she found : Specifications : Longueur : 246 m Largeur : 32 m Calming: 6 m Commissioning : 1990 Maximum number of passengers : 1 596 Members of équipages : 677 Questions: 1 How far did the ship travel in 40 seconds? 2 Who is closer to the truth, Mathilde or Eva? Justify the answer. Reminder : The ˇ knot ı is a unit of speed. Sailing at 1 knot means traveling 0.5 meter in 1 second. In this exercise, any trace of research, even if incomplete or unsuccessful, will be considered in the assessment. E.6386 Below is a map of Mali: All distances considered are distances ˇ as the crow flies ı. 1 The distance from Bamako to Timbuktu is 705 kilome-ters. a Determine the distance from Bamako to Kidal. b Determine the scale of this map. 2 For this question, show on the copy the approach used. Any trace of research will be taken into account during the evaluation even if the work is not completely completed. Ignoring the takeoff and landing phases, an airplane trav-els at the speed of 730 km = h . It makes the trip : Bamako Kayes Gao Bamako How long is his journey? E.7973 Whales emit sounds, with fre-quencies between 10 Hz and 10 kHz , that travel through the water at a speed of approximately 1 500 m = s . The study of whale songs aims to elucidate their possible sig-nificance ; sexual partner selection and social communication are hypotheses under consideration. 1 Convert the propagation speed of these sounds to km = h . 2 Two groups of whales located off Alaska communicate with each other. a Calculate the distance between the two groups of whales. You will give the result rounded to the nearest 50 km . b How long does it take a sound wave emitted by a whale in group 1 to reach the whales in group 2? You will give the result rounded to the minute. 3 The drawing below gives an idea of the size of a blue whale compared to a human. Assuming that the diver in the picture is 1.75 m , calcu-late the approximate size of the whale shown below. You will give the result rounded to the nearest meter. The process and traces of research will be valued and taken into account in scoring. https://chingmath.fr chapExoCorrec/6286 sacados/6286 chapExoCorrec/6386 sacados/6386 TessalitKidalGaoTombouctouKayesMoptiSegouBamakoSikasso chapExoCorrec/7973 sacados/7973 Groupe1Groupe21000km
1234567891011121314ABCDEDépenseTotaleAppareilTéléviseurOrdinateurParaboleFourDémo-dulateursatelliteLecteurDVDMachineàlaverConsoledejeuFouràmicro-ondesTéléphonesans∏lLave-vaiselleChargeurbatterieNombred’appareils312132111114Consom-mationenveilleparanpourunappareil(enkWh)77209131865958514225251713Prixdukilowatt-heure(eneuro)0,130,130,130,130,130,130,130,130,130,130,130,13Dépense(eneuro)30,0327,1734,0611,1823,0115,086,635,463,253,252,216,76168,09Données extraites du site de l’ADEME 7. Density E.876 At a temperature of 0 o C , the air density is 1.29 kg = m 3 . We’re interested in a classroom whose volume measures 250 m 3 . Give the mass of air, rounded to the nearest kilogram, con-tained in this room at this temperature. E.9089 At the sea surface, air has a density of 1.2 kg = m 3 . Calculate the mass of air, rounded to the nearest gram, contained in a 1.5 l bottle. E.883 Gold has a density of 19 300 kg = m 3 . Knowing that a gold bar weighs 1 kg , determine the volume occupied by a gold bar rounded to the nearest cm 3 . E.882 At a temperature of 20 o C , the den-sity of air is 1.2 kg = m 3 . A room has dimensions 9 m in length, 6 m in width and 4 m in height. Give the weight of air contained in this room rounded to the nearest kilogram. E.9103 Knowing that air has a density of 0.909 kg = m 3 at an altitude of 3000 m , calculate the volume, rounded to the nearest deciliter, occupied by 1.8 g of air. E.9093 Gold has a density of 19300 kg = m 3 , a gold ring weighs 6.5 g . 1 Give the density expressed in g = cm 3 2 Give the volume of this ring rounded to the nearest tenth of cm 3 . 8. Product sizes E.895 An electric iron has a power of 1 200 watts. It is used for 20 minutes. What is the energy used in kWh ? E.9105 Determine the energy, in Wh , used by a computer of 300 W if it is used nine minutes a day for one year (counting 365 days for one year) . E.6308 Appliances in the home con-sume energy even when they are on standby. The spreadsheet below gives the consumption in kilowatt-hours (kWh) of a family’s standby appliances for a year and the corresponding expenditure in euros : 1 a What calculation verifies the result 34.06 displayed in cell E4 ? b What formula was entered in cell E2 before copying it down? c One of the four formulas below was entered in cell E14 to obtain the total amount of expenses due to vigils. Copy this formula onto the copy. =SOMME(E2:E13) =E2:E13 =E2+E13 =SOMME(E2:E14) 2 In one room of this house, the following devices are on standby are: a television set a game console a computer a DVD player Does the computer’s power consumption account for more than half of the total power consumption of the appliances in this room? E.2629 1 A 40 Watt bulb remains lit for 4 h 24 min . Give the energy consumed in Wh 2 Determine the time, expressed in minutes, needed for the 300 W computer to use the same energy as the bulb. https://chingmath.fr chapExoCorrec/876 sacados/876 chapExoCorrec/9089 sacados/9089 chapExoCorrec/883 sacados/883 chapExoCorrec/882 sacados/882 chapExoCorrec/9103 sacados/9103 chapExoCorrec/9093 sacados/9093 chapExoCorrec/895 sacados/895 chapExoCorrec/9105 sacados/9105 chapExoCorrec/6308 sacados/6308 1234567891011121314ABCDEDépenseTotaleAppareilTéléviseurOrdinateurParaboleFourDémo-dulateursatelliteLecteurDVDMachineàlaverConsoledejeuFouràmicro-ondesTéléphonesans∏lLave-vaiselleChargeurbatterieNombred’appareils312132111114Consom-mationenveilleparanpourunappareil(enkWh)77209131865958514225251713Prixdukilowatt-heure(eneuro)0,130,130,130,130,130,130,130,130,130,130,130,13Dépense(eneuro)30,0327,1734,0611,1823,0115,086,635,463,253,252,216,76168,09Données extraites du site de l’ADEME chapExoCorrec/2629 sacados/2629
Téléchargé:9;7sur115;2Mo(1,3Mo=s) OUNTYB234m155m90m25m Format4=3Format16=964cm64cm48cm 9. Other sizes E.3380 The mass of a carbon atom is equal to 1.99 × 10 − 26 kg . Chemists consider packets containing 6.022 × 10 23 atoms. Calculate the mass in grams of such a packet of carbon atoms. E.7963 We consider the download window below : If the download speed remains constant, will it take more than one minute and twenty-five seconds for the download to finish? E.5928 In this exercise, if the work is not completed, still leave a record of the research, it will be considered in the assessment. The Amazon River has the largest average flow in the world. It is approximately 190 00 m 3 = s . In France, a household of 3 people consumes on average 10 000 L of water per month. Give an order of magnitude of how many of these households this river could supply in one year. Recall: 1 L =1 dm 3 ; 1 m 3 =1 000 L 10. Open problems E.5926 Here is the route of the cross-country race at La Bounty College shown in the figure below : 1 Show that the length NT is equal to 194 m . 2 The start and finish of each cross-country race are at point B . Calculate the length of one lap of the course. 3 3 th students must complete 4 laps of the course. Calcu-late the total length of their run. 4 Terii, the winner of the 3 th boys’ race completed his race in 10 minutes and 42 seconds. Calculate his average speed and express it in m = s . Round to the nearest hundredth. 5 If Terii maintained his average speed, do you think he could beat champion George Richmond, who recently won the 15 km Foulées du Front de mer race in 55 min-utes and 11 seconds? For this question, any trace of research, no matter how incomplete, will be considered in the evaluation. E.5769 A farmer wants to buy a piece of land : he retrieves the satellite photograph from a geo-location site. Here is the land hatched in the photograph below : Knowing that, on average, a hectare of farmland costs 5430 e , give the purchase price of this land. E.5767 A television is at ˇ format 4 = 3 ı when the quotient of the screen length by its width equals the frac-tion 4 3 . The same definition applies for a screen at ˇ format 16 = 9 ı. An industrialist used to produce only televisions, whose screen format 4 = 3 , had for dimensions 64 cm × 48 cm . Now he decides to produce televisions in the 16 = 9 format with the same length. How much screen area is saved on each TV by choosing this new TV format? https://chingmath.fr chapExoCorrec/3380 sacados/3380 A refaire pas de sens chapExoCorrec/7963 sacados/7963 Téléchargé:9;7sur115;2Mo(1,3Mo=s) chapExoCorrec/5928 sacados/5928 chapExoCorrec/5926 sacados/5926 OUNTYB234m155m90m25m chapExoCorrec/5769 sacados/5769 chapExoCorrec/5767 sacados/5767 Format4=3Format16=964cm64cm48cm
S1S2S3S4S8S5S6S74cm 6m4m2m E.5768 Consider a square with side 10 cm , the representation of which is given below. This square is cut into several pieces : a square defines the surface S 1 ; two right-angled triangles de-fine surfaces S 3 and S 4 ; a rhombus defines the surface S 2 ; any two triangles define the surfaces S 5 and S 6 ; a trapezoid defines the surface S 7 o where the small base measures 4 cm . Determine the area of the surface S 8 . E.5770 A goat is in a rectangular-shaped pasture of dimensions 6 m × 4 m where a square-shaped shed, measuring 2 m square, is located in a corner of the pasture. The goat is attached by a 4 m -long rope to the shed as shown in the sketch below : Determine, rounded to the nearest dm 2 , the area of pasture accessible by the goat. Hint: we’ll use : ı ≈ 3.1416 https://chingmath.fr chapExoCorrec/5768 sacados/5768 S1S2S3S4S8S5S6S74cm chapExoCorrec/5770 sacados/5770 6m4m2m