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For example, miles per hour means the number of miles divided by the number of hours."},{"text":"Multiplied by.","correct":false,"explanation":"Multiplication combines quantities rather than forming a rate. In compound measures, “per” means divided by, as in distance divided by time for speed."},{"text":"Added to.","correct":false,"explanation":"Adding quantities does not produce a compound rate. The word “per” means divided by, such as pounds divided by kilogram in a price rate."},{"text":"Subtracted from.","correct":false,"explanation":"Subtraction finds a difference rather than a rate. In a compound measure, “per” means divided by, so one quantity is divided by another."}]},{"id":"e59f48f8-41cc-4493-986c-d71c6b4433b8","cardType":"basic","points":1,"front":"What calculation gives average speed?","back":"Distance ÷ time.","mcqOptions":[{"text":"Distance ÷ time.","correct":true,"explanation":"Average speed is found by dividing the total distance travelled by the total time taken, using compatible units for distance and time."},{"text":"Distance × time.","correct":false,"explanation":"Multiplying distance by time does not calculate a rate. Average speed is the total distance divided by the total time taken."},{"text":"Time ÷ distance.","correct":false,"explanation":"Reversing the division gives time per unit of distance, not distance per unit of time. Average speed is distance divided by time."},{"text":"Distance + time.","correct":false,"explanation":"Adding distance and time combines quantities with incompatible units and cannot produce speed. Average speed is calculated as distance divided by time."}]},{"id":"bef3029a-ba62-4312-991a-8683f986fbe8","cardType":"cloze","points":null,"front":"If speed is in mph, time must be in [ ]; if speed is in m/s, time must be in [ ].","back":"If speed is in mph, time must be in hours; if speed is in m/s, time must be in seconds.","mcqOptions":[{"text":"If speed is in mph, time must be in hours; if speed is in m/s, time must be in seconds.","correct":true,"explanation":"Miles per hour requires time measured in hours, while metres per second requires time measured in seconds, so the units match each speed."},{"text":"If speed is in mph, time must be in minutes; if speed is in m/s, time must be in seconds.","correct":false,"explanation":"Using minutes with miles per hour creates inconsistent units. Time must be in hours for mph and in seconds for m/s."},{"text":"If speed is in mph, time must be in hours; if speed is in m/s, time must be in minutes.","correct":false,"explanation":"Hours match mph, but minutes do not match metres per second. For m/s, the time must be converted into seconds."},{"text":"If speed is in mph, time must be in seconds; if speed is in m/s, time must be in hours.","correct":false,"explanation":"These time units are both mismatched with the stated speed units. Mph requires hours, whereas m/s requires seconds."}]},{"id":"438f827a-a4e1-4875-abe3-05613d722f90","cardType":"basic","points":1,"front":"Convert 4 hours 15 minutes into hours.","back":"4.25 hours.","mcqOptions":[{"text":"4.25 hours.","correct":true,"explanation":"Fifteen minutes is $15 \\div 60=0.25$ hours. Adding this to 4 hours gives a total of 4.25 hours."},{"text":"4.15 hours.","correct":false,"explanation":"Writing 15 minutes as 0.15 hours treats time as base 100. Since an hour has 60 minutes, 15 minutes is 0.25 hours, giving 4.25 hours."},{"text":"4.5 hours.","correct":false,"explanation":"This treats 15 minutes as half an hour. Fifteen minutes is one quarter of 60 minutes, so the correct total is 4.25 hours."},{"text":"4.75 hours.","correct":false,"explanation":"This converts 15 minutes into three quarters of an hour instead of one quarter. Dividing 15 by 60 gives 0.25, so the total is 4.25 hours."}]},{"id":"a79f22aa-fdc6-4bdd-96c4-88e7760f02d3","cardType":"cloze","points":null,"front":"3 hours 30 minutes is [ ], not [ ].","back":"3 hours 30 minutes is 3.5 hours, not 3.30 hours.","mcqOptions":[{"text":"3 hours 30 minutes is 3.5 hours, not 3.30 hours.","correct":true,"explanation":"Thirty minutes is half of 60 minutes, so it equals 0.5 hours. Decimal time is not written by simply placing the minutes after a decimal point."},{"text":"3 hours 30 minutes is 3.3 hours, not 3.30 hours.","correct":false,"explanation":"Dividing 30 by 100 instead of 60 produces 0.3 hours. Thirty minutes is $30 \\div 60=0.5$ hours, so the total is 3.5 hours."},{"text":"3 hours 30 minutes is 3.30 hours, not 3.5 hours.","correct":false,"explanation":"This reverses the correct and incorrect conversions. Thirty minutes is half an hour, so the time is 3.5 hours rather than 3.30 hours."},{"text":"3 hours 30 minutes is 3.5 hours, not 3.03 hours.","correct":false,"explanation":"The first conversion is correct, but 3.03 hours is not the tempting place-value error. Writing the minutes directly gives 3.30 hours, which is still incorrect."}]},{"id":"75cd679c-ae73-4e57-91a5-5408d6dab575","cardType":"basic","points":2,"front":"A car travels 250 miles in 4 hours 30 minutes. What is its average speed to 1 d.p.?","back":"55.6 mph.","mcqOptions":[{"text":"55.6 mph.","correct":true,"explanation":"Four hours 30 minutes is 4.5 hours, so the average speed is $250 \\div 4.5=55.555\\ldots$ mph, which rounds to 55.6 mph."},{"text":"58.8 mph.","correct":false,"explanation":"This result comes from treating 4 hours 30 minutes as 4.25 hours. Thirty minutes is 0.5 hours, so $250 \\div 4.5$ rounds to 55.6 mph."},{"text":"58.1 mph.","correct":false,"explanation":"This result treats 4 hours 30 minutes as 4.3 hours by using decimal place value incorrectly. The journey lasts 4.5 hours, giving 55.6 mph."},{"text":"62.5 mph.","correct":false,"explanation":"This ignores the additional 30 minutes and divides 250 miles by only 4 hours. Using the full 4.5 hours gives an average speed of 55.6 mph."}]},{"id":"a518de7f-d86f-4b00-b7b9-11bc349b119a","cardType":"basic","points":1,"front":"What formula gives time from distance and speed?","back":"Time = distance ÷ speed.","mcqOptions":[{"text":"Time = distance ÷ speed.","correct":true,"explanation":"Rearranging $\\text{speed}=\\text{distance}\\div\\text{time}$ gives time as distance divided by speed. Compatible units then determine the time unit."},{"text":"Time = distance × speed.","correct":false,"explanation":"Multiplying distance by speed gives incorrect compound units and does not calculate duration. Time is found by dividing distance by speed."},{"text":"Time = speed ÷ distance.","correct":false,"explanation":"This reverses the required division and gives the reciprocal-type quantity. To calculate journey time, divide the distance by the speed."},{"text":"Time = distance + speed.","correct":false,"explanation":"Adding distance and speed combines incompatible units, so it cannot give a duration. The correct relationship is time equals distance divided by speed."}]},{"id":"3313ef0f-1639-477f-896b-1436f13d5d93","cardType":"basic","points":3,"front":"Nadia leaves at 08:10 and drives 63 miles at 28 mph. What is her arrival time?","back":"10:25.","mcqOptions":[{"text":"10:25.","correct":true,"explanation":"The journey takes $63 \\div 28=2.25$ hours, and 0.25 hours is 15 minutes. Adding 2 hours 15 minutes to 08:10 gives 10:25."},{"text":"10:35.","correct":false,"explanation":"This treats 0.25 hours as 25 minutes rather than converting it using 60 minutes per hour. The journey lasts 2 hours 15 minutes, giving 10:25."},{"text":"10:10.","correct":false,"explanation":"This omits the extra 15 minutes represented by 0.25 hours. The travel time is 2 hours 15 minutes, so 08:10 becomes 10:25."},{"text":"09:55.","correct":false,"explanation":"This subtracts the 15-minute part instead of adding it to the two full hours. Adding the complete 2 hours 15 minutes gives 10:25."}]},{"id":"5be652e5-8a63-46ac-bf03-b7ef660ec8cc","cardType":"cloze","points":null,"front":"Whole-journey average speed = [ ] ÷ [ ].","back":"Whole-journey average speed = total distance ÷ total time.","mcqOptions":[{"text":"Whole-journey average speed = total distance ÷ total time.","correct":true,"explanation":"Average speed measures the total distance covered per unit of time across the entire journey, so all distances and all corresponding times must be combined."},{"text":"Whole-journey average speed = sum of speeds ÷ number of stages.","correct":false,"explanation":"This calculates the arithmetic mean of the stage speeds, which is only valid in special cases such as equal times. Average speed uses total distance divided by total time."},{"text":"Whole-journey average speed = total time ÷ total distance.","correct":false,"explanation":"This reverses the speed formula and gives time per unit distance instead. Whole-journey average speed is total distance divided by total time."},{"text":"Whole-journey average speed = total distance ÷ average time.","correct":false,"explanation":"Using an average of the stage times fails to represent the duration of the whole journey. The denominator must be total time, not average time."}]},{"id":"04e90b64-0eda-4e23-9aed-77dba3e3e8a3","cardType":"basic","points":2,"front":"Why is a journey at 60 mph then 40 mph not automatically 50 mph on average?","back":"Use total distance ÷ total time.","mcqOptions":[{"text":"Use total distance ÷ total time.","correct":true,"explanation":"The runner or vehicle may spend unequal times at the two speeds, so average speed must be calculated from the journey’s total distance and total time."},{"text":"Use total time ÷ total distance.","correct":false,"explanation":"This reverses the speed formula, producing time per unit distance rather than speed. The average speed is found using total distance divided by total time."},{"text":"Use the most frequent speed.","correct":false,"explanation":"The speed maintained most often is the mode, not the average speed for a journey. Average speed requires total distance divided by total time."},{"text":"Use the two speeds’ midpoint.","correct":false,"explanation":"Taking the midpoint assumes the two speeds apply for equal times. That is not automatic, so the reliable calculation is total distance divided by total time."}]},{"id":"6876adad-721a-4bfa-9cc1-4c339e828384","cardType":"basic","points":2,"front":"If speed stays constant, how do time and distance change?","back":"They increase in the same ratio.","mcqOptions":[{"text":"They increase in the same ratio.","correct":true,"explanation":"Since distance equals speed multiplied by time, a constant speed makes distance directly proportional to time. Multiplying time by any factor multiplies distance by the same factor."},{"text":"They increase in an inverse ratio.","correct":false,"explanation":"An inverse relationship would mean distance decreases as time increases. At constant speed, doubling the travel time doubles the distance, so they increase in the same ratio."},{"text":"They increase by the same amount.","correct":false,"explanation":"Equal numerical increases are not required because time and distance have different units. At constant speed, their proportional changes are equal, so they increase in the same ratio."},{"text":"They increase in different ratios.","correct":false,"explanation":"Different ratios would imply that the speed is changing. When speed remains constant, time and distance are directly proportional and therefore increase in the same ratio."}]},{"id":"b47c8fad-d932-453b-9a3f-38fe7dbd7507","cardType":"basic","points":2,"front":"If a runner slows down over a longer distance, what happens to a same-speed time estimate?","back":"It is too small; real time is longer.","mcqOptions":[{"text":"It is too small; real time is longer.","correct":true,"explanation":"A same-speed estimate assumes the runner maintains the earlier, faster pace. Slowing down means later sections take longer, so the estimate understates the real time."},{"text":"It is too large; real time is shorter.","correct":false,"explanation":"This reverses the effect of slowing down. Covering part of the route at a lower speed increases the real time, making a same-speed estimate too small."},{"text":"It is accurate; real time is unchanged.","correct":false,"explanation":"The estimate would only remain accurate if the assumed speed were maintained. Slowing down increases the time needed, so the same-speed estimate is too small."},{"text":"It is too large; real time is unchanged.","correct":false,"explanation":"This treats the reduction in speed as having no effect on journey time. A lower speed over part of the distance makes real time longer than the estimate."}]},{"id":"b9c8fb0f-1cee-49d3-8c4f-35b132aca197","cardType":"basic","points":1,"front":"What calculation gives density?","back":"Mass ÷ volume.","mcqOptions":[{"text":"Mass ÷ volume.","correct":true,"explanation":"Density measures how much mass is contained in each unit of volume. Dividing the object’s mass by its volume therefore gives its density."},{"text":"Volume ÷ density.","correct":false,"explanation":"This is not a valid rearrangement of the density relationship and has unsuitable units. Density is calculated by dividing an object’s mass by its volume."},{"text":"Mass × volume.","correct":false,"explanation":"Multiplying confuses the operation in the density formula and gives incorrect units. Density measures mass per unit volume, so mass must be divided by volume."},{"text":"Volume ÷ mass.","correct":false,"explanation":"This gives volume per unit mass, which is the reciprocal of density. Density is mass per unit volume, calculated as mass divided by volume."}]},{"id":"99583a84-6332-4413-8167-de8a09783676","cardType":"basic","points":1,"front":"What formula gives volume from mass and density?","back":"Volume = mass ÷ density.","mcqOptions":[{"text":"Volume = mass ÷ density.","correct":true,"explanation":"Starting from density equals mass divided by volume, multiply by volume and divide by density. This leaves volume equal to mass divided by density."},{"text":"Volume = density ÷ mass.","correct":false,"explanation":"This reverses the required division and does not follow from density equals mass divided by volume. Rearranging correctly gives volume equals mass divided by density."},{"text":"Volume = mass × density.","correct":false,"explanation":"Multiplication is a common rearrangement error. Since mass equals density multiplied by volume, isolating volume requires dividing mass by density."},{"text":"Volume = density × mass.","correct":false,"explanation":"Changing the multiplication order does not fix the incorrect operation. To isolate volume from mass equals density times volume, divide mass by density."}]},{"id":"c4d4c1b2-6be3-42f9-bd23-bfefe198803e","cardType":"cloze","points":null,"front":"Mass = [ ] × [ ].","back":"Mass = density × volume.","mcqOptions":[{"text":"Mass = density × volume.","correct":true,"explanation":"Density is mass divided by volume. Multiplying both sides by volume gives mass equal to density multiplied by volume."},{"text":"Mass = density × area.","correct":false,"explanation":"Area does not account for an object’s third dimension, so it cannot determine mass from density. Mass equals density multiplied by the object’s volume."},{"text":"Mass = volume × mass.","correct":false,"explanation":"This incorrectly includes mass on both sides and omits density, so it cannot calculate an unknown mass. The required product is density multiplied by volume."},{"text":"Mass = pressure × volume.","correct":false,"explanation":"Pressure describes force per unit area and is not used to calculate mass from volume. The relevant material property is density, so mass equals density times volume."}]},{"id":"f1a3df35-ca2c-48c0-8acc-34b86b75944e","cardType":"cloze","points":null,"front":"Pressure = [ ] ÷ [ ].","back":"Pressure = force ÷ area.","mcqOptions":[{"text":"Pressure = force ÷ area.","correct":true,"explanation":"Pressure measures how concentrated a force is over a surface. Dividing the perpendicular force by the area over which it acts gives the pressure."},{"text":"Pressure = area ÷ force.","correct":false,"explanation":"This reverses the pressure formula and produces the reciprocal units. Pressure measures force distributed over each unit of area, so it is force divided by area."},{"text":"Pressure = force ÷ volume.","correct":false,"explanation":"Dividing force by volume describes force per cubic unit rather than force acting on a surface. Pressure is force divided by the contact area."},{"text":"Pressure = mass ÷ area.","correct":false,"explanation":"Mass is not itself a force, although weight can be calculated from mass and gravitational field strength. Pressure requires force divided by area."}]},{"id":"0e7d6cac-3b79-47c0-80ce-ad2d63de6199","cardType":"basic","points":2,"front":"In a liquid mixture question, what should you track separately?","back":"Masses and volumes.","mcqOptions":[{"text":"Masses and volumes.","correct":true,"explanation":"Each liquid’s mass and volume must be tracked separately before the totals are combined, because mixture density is total mass divided by total volume."},{"text":"Densities and volumes.","correct":false,"explanation":"Densities cannot be combined as though they were additive quantities. Track the masses and volumes separately, then divide the total mass by the total volume."},{"text":"Masses and densities.","correct":false,"explanation":"Tracking density instead of volume leaves no denominator for the final calculation. The masses and volumes must be totalled separately to calculate mixture density."},{"text":"Temperatures and volumes.","correct":false,"explanation":"Temperature is not one of the quantities needed in this mixture calculation. Track each liquid’s mass and volume, then combine their respective totals."}]},{"id":"eb57c9d9-4e7f-4c09-a461-f9830edd3868","cardType":"cloze","points":null,"front":"Final mixture density = [ ] ÷ [ ].","back":"Final mixture density = total mass ÷ total volume.","mcqOptions":[{"text":"Final mixture density = total mass ÷ total volume.","correct":true,"explanation":"Density is mass per unit volume, so the combined mass of all the liquids must be divided by their combined volume."},{"text":"Final mixture density = total volume ÷ total mass.","correct":false,"explanation":"This reverses the density formula and would give volume per unit mass. Mixture density is found by dividing total mass by total volume."},{"text":"Final mixture density = total density ÷ total volume.","correct":false,"explanation":"Densities are not added to form a meaningful total density. First find total mass, then divide it by the total volume of the mixture."},{"text":"Final mixture density = total mass ÷ total density.","correct":false,"explanation":"Density cannot be used as the denominator when it is the quantity being calculated. Divide the mixture’s total mass by its total volume."}]},{"id":"73b43978-0fd5-4d9c-b203-d99b59482436","cardType":"basic","points":2,"front":"Why can’t you add liquid densities directly to find mixture density?","back":"Density depends on mass and volume.","mcqOptions":[{"text":"Density depends on mass and volume.","correct":true,"explanation":"Density is the ratio of mass to volume. Different liquid volumes contribute different masses, so both quantities must be totalled before calculating the mixture density."},{"text":"Density depends on distance and time.","correct":false,"explanation":"Distance and time determine speed, not density. Density depends on mass and volume, which must be combined separately before finding their ratio."},{"text":"Density depends on force and area.","correct":false,"explanation":"Force divided by area defines pressure, not density. Density depends on mass and volume, so adding densities directly ignores how much of each liquid is present."},{"text":"Density depends on mass and acceleration.","correct":false,"explanation":"Mass multiplied by acceleration determines force, not density. Density depends on mass and volume, and the mixture uses the totals of both quantities."}]},{"id":"63a2f082-efbf-459e-aa50-0916c2e54ced","cardType":"basic","points":3,"front":"150 ml at 0.8 g/ml is mixed with 250 ml at 1.2 g/ml. What is the mixture density?","back":"1.05 g/ml.","mcqOptions":[{"text":"1.05 g/ml.","correct":true,"explanation":"The masses are 150 × 0.8 = 120 g and 250 × 1.2 = 300 g. Therefore, the density is 420 ÷ 400 = 1.05 g/ml."},{"text":"1.00 g/ml.","correct":false,"explanation":"This is the simple mean of the two densities, which wrongly assumes equal volumes. Using the actual masses and total volume gives 420 ÷ 400 = 1.05 g/ml."},{"text":"0.95 g/ml.","correct":false,"explanation":"This results from pairing each density with the other liquid’s volume. Using 150 ml at 0.8 g/ml and 250 ml at 1.2 g/ml gives 1.05 g/ml."},{"text":"1.20 g/ml.","correct":false,"explanation":"This keeps the density of the larger portion and ignores the less dense liquid. The combined mass is 420 g over 400 ml, giving 1.05 g/ml."}]}]}],"examCountdown":{"examDate":"2027-05-14","paperLabel":"Paper 1"},"heading":"Speed and Density","title":"Speed and Density Flashcards","topbar":{"backHref":"/igcse/maths/edexcel/flashcards"},"topicSidebar":"$L38"}]}],"topicId":"a1a226f3-5b6b-47bd-84dd-2c2e671748a7","walled":"$L39"}],"$L3a","$L3b"]