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of hours."},{"text":"Multiply: miles × hours.","correct":false,"explanation":"Multiplication combines the two quantities rather than forming a rate. “Per” signals division, so miles must be divided by hours."},{"text":"Subtract: miles − hours.","correct":false,"explanation":"Subtracting unlike quantities does not produce a meaningful rate. “Per” means divide, so miles per hour is miles divided by hours."},{"text":"Add: miles + hours.","correct":false,"explanation":"Adding distance and time cannot give a rate because they have different units. “Per” signals division, giving miles divided by hours."}]},{"id":"a770b050-4470-17dd-b6fe-ca897305a6ec","cardType":"basic","points":1,"front":"Which calculation gives average speed from distance and time?","back":"Average speed = distance ÷ time.","mcqOptions":[{"text":"Average speed = distance ÷ time.","correct":true,"explanation":"Average speed measures the distance covered per unit of time, so total distance is divided by the total time taken."},{"text":"Average speed = distance × time.","correct":false,"explanation":"Multiplying distance by time does not calculate speed and gives the wrong units. Average speed is total distance divided by total time."},{"text":"Average speed = time ÷ distance.","correct":false,"explanation":"This reverses the division and calculates time per unit distance. Average speed is distance per unit time, so use distance divided by time."},{"text":"Average speed = distance − time.","correct":false,"explanation":"Subtracting time from distance mixes different types of quantity and cannot produce speed. Average speed is calculated as distance divided by time."}]},{"id":"c42fe990-62f9-831d-425b-d3b27d229cc0","cardType":"cloze","points":null,"front":"Density is found by [ ].","back":"Density is found by mass ÷ volume.","mcqOptions":[{"text":"mass ÷ volume","correct":true,"explanation":"Density describes the amount of mass contained in each unit of volume, so it is calculated by dividing mass by volume."},{"text":"volume ÷ mass","correct":false,"explanation":"This reverses the density formula and gives volume per unit mass. Density is mass per unit volume, so the correct calculation is mass divided by volume."},{"text":"mass × volume","correct":false,"explanation":"Multiplying mass and volume does not measure how concentrated the mass is. Density is calculated by dividing the mass by the volume."},{"text":"mass − volume","correct":false,"explanation":"Mass and volume are different types of quantity, so subtracting them is not meaningful. Density is found by dividing mass by volume."}]},{"id":"911165aa-9d2c-e445-8ab9-ca5e429a7670","cardType":"basic","points":1,"front":"Which calculation gives pressure from force and area?","back":"Pressure = force ÷ area.","mcqOptions":[{"text":"Pressure = force ÷ area.","correct":true,"explanation":"Pressure measures how much force acts on each unit of area, so the applied force is divided by the contact area."},{"text":"Pressure = force × area.","correct":false,"explanation":"Multiplying force by area gives incorrect units and makes pressure increase with contact area. Pressure is force divided by area."},{"text":"Pressure = area ÷ force.","correct":false,"explanation":"This reverses the required ratio and gives area per unit force. Pressure is force per unit area, calculated as force divided by area."},{"text":"Pressure = force − area.","correct":false,"explanation":"Force and area are different types of quantity, so subtracting them cannot produce pressure. Pressure is calculated by dividing force by area."}]},{"id":"9e373e58-3602-a8aa-972a-6ee52234ada8","cardType":"cloze","points":null,"front":"To substitute into a formula, replace the words with [ ].","back":"To substitute into a formula, replace the words with the numbers from the question.","mcqOptions":[{"text":"the numbers from the question","correct":true,"explanation":"Substitution means replacing each variable or named quantity in a formula with the corresponding numerical value provided in the question."},{"text":"the units from the question","correct":false,"explanation":"Units identify how quantities are measured but do not replace variables during calculation. Substitution uses the numerical values given in the question."},{"text":"the formula from the question","correct":false,"explanation":"The formula provides the mathematical relationship and is not inserted into itself. Substitution replaces its words or symbols with the numbers from the question."},{"text":"the answer from the question","correct":false,"explanation":"The answer is obtained only after substitution and calculation, so it cannot be inserted beforehand. Use the numbers supplied in the question."}]},{"id":"3e2d0fe9-defe-843d-be24-96ed770b9d83","cardType":"basic","points":2,"front":"A runner covers 240 m in 30 s. What is the average speed?","back":"8 m/s.","mcqOptions":[{"text":"8 m/s.","correct":true,"explanation":"Average speed is distance divided by time. Calculating 240 ÷ 30 gives 8, so the runner’s average speed is 8 m/s."},{"text":"7 m/s.","correct":false,"explanation":"This results from an arithmetic error when dividing 240 by 30. Average speed is distance ÷ time, and 240 ÷ 30 equals 8 m/s."},{"text":"9 m/s.","correct":false,"explanation":"This overestimates the quotient when dividing the distance by the time. The correct calculation is 240 ÷ 30, which gives 8 m/s."},{"text":"80 m/s.","correct":false,"explanation":"This is a place-value error that effectively treats 30 as 3. Dividing 240 by 30 correctly gives an average speed of 8 m/s."}]},{"id":"8657a534-4bb8-6724-e8ca-4c319c530c4a","cardType":"basic","points":2,"front":"An object has mass 630 g and volume 35 cm³. What is its density?","back":"18 g/cm³.","mcqOptions":[{"text":"18 g/cm³.","correct":true,"explanation":"Density is mass divided by volume. Calculating 630 ÷ 35 gives 18, so the object’s density is 18 g/cm³."},{"text":"22 g/cm³.","correct":false,"explanation":"This comes from an incorrect division of 630 by 35. Using density = mass ÷ volume gives 630 ÷ 35 = 18 g/cm³."},{"text":"595 g/cm³.","correct":false,"explanation":"This subtracts the volume from the mass, although quantities with different units cannot be subtracted meaningfully. Dividing 630 by 35 gives 18 g/cm³."},{"text":"0.056 g/cm³.","correct":false,"explanation":"This reverses the density calculation by dividing volume by mass. Density is mass ÷ volume, so 630 ÷ 35 gives 18 g/cm³."}]},{"id":"78848f7c-85ac-a3af-9731-f24cbaf9db59","cardType":"basic","points":2,"front":"A crate exerts 150 N over 6 m². What is the pressure?","back":"25 N/m².","mcqOptions":[{"text":"25 N/m².","correct":true,"explanation":"Pressure is force divided by area. Calculating 150 ÷ 6 gives 25, so the pressure is 25 N/m²."},{"text":"900 N/m².","correct":false,"explanation":"This multiplies force by area instead of dividing. Pressure is force ÷ area, so 150 ÷ 6 gives 25 N/m²."},{"text":"144 N/m².","correct":false,"explanation":"This subtracts the area from the force, which does not calculate force per unit area. Dividing 150 by 6 gives 25 N/m²."},{"text":"0.04 N/m².","correct":false,"explanation":"This reverses the formula by dividing area by force. Pressure requires force ÷ area, so 150 ÷ 6 gives 25 N/m²."}]},{"id":"27047371-3731-7678-aaea-d7f738be15e0","cardType":"cloze","points":null,"front":"For $a=\\frac{b}{c}$, the top quantity is $b=$ [ ].","back":"For $a=\\frac{b}{c}$, the top quantity is $b=$ a × c.","mcqOptions":[{"text":"a × c","correct":true,"explanation":"Multiplying both sides of $a=\\frac{b}{c}$ by $c$ cancels the denominator, giving $a × c=b$. Therefore the top quantity is found using $a × c$."},{"text":"a ÷ c","correct":false,"explanation":"Dividing $a$ by $c$ does not reverse the original division. Multiplying both sides by $c$ gives $b=a × c$, so the top quantity is $a × c$."},{"text":"c ÷ a","correct":false,"explanation":"Dividing $c$ by $a$ reverses the quantities without correctly rearranging the equation. Since $ac=b$, the required expression for the top quantity is $a × c$."},{"text":"a + c","correct":false,"explanation":"Adding the two quantities is not a valid way to undo division by $c$. Multiply both sides by $c$, which gives the correct expression $a × c$."}]},{"id":"072c5405-76ca-dbfb-2b6f-cf36773d8935","cardType":"basic","points":1,"front":"For $a=\\frac{b}{c}$, how do you find the bottom quantity $c$?","back":"$c=\\frac{b}{a}$.","mcqOptions":[{"text":"$c=\\frac{b}{a}$.","correct":true,"explanation":"Multiplying $a=\\frac{b}{c}$ by $c$ gives $ac=b$. Dividing by $a$ then isolates the bottom quantity, so $c=\\frac{b}{a}$."},{"text":"$c=\\frac{a}{b}$.","correct":false,"explanation":"Reversing the fraction without following algebraic steps swaps the required numerator and denominator. From $ac=b$, dividing by $a$ gives $c=\\frac{b}{a}$."},{"text":"$c=a × b$.","correct":false,"explanation":"Multiplying $a$ and $b$ does not isolate the denominator in the original fraction. Rearranging $ac=b$ requires division by $a$, giving $c=\\frac{b}{a}$."},{"text":"$c=b-a$.","correct":false,"explanation":"Subtracting $a$ from $b$ treats the fractional relationship as an additive one. The equation rearranges through multiplication and division, giving $c=\\frac{b}{a}$."}]},{"id":"13a376cc-b633-dec0-a459-9014c0a4c071","cardType":"basic","points":1,"front":"How do you find volume if mass and density are known?","back":"Volume = mass ÷ density.","mcqOptions":[{"text":"Volume = mass ÷ density.","correct":true,"explanation":"Density is mass divided by volume. Rearranging this relationship makes volume equal to mass divided by density, with compatible units used throughout the calculation."},{"text":"Volume = mass × density.","correct":false,"explanation":"Multiplying mass by density applies the relationship in the wrong direction. Since density equals mass divided by volume, volume must equal mass divided by density."},{"text":"Volume = density ÷ mass.","correct":false,"explanation":"Dividing density by mass reverses the required quotient. Rearranging density = mass ÷ volume gives volume = mass ÷ density, not density ÷ mass."},{"text":"Volume = mass + density.","correct":false,"explanation":"Adding mass and density is invalid because they are different physical quantities with incompatible units. Volume is calculated by dividing mass by density."}]},{"id":"0aa33a20-06a2-68b8-37d8-c77d88f0c1a2","cardType":"basic","points":1,"front":"How do you find area if force and pressure are known?","back":"Area = force ÷ pressure.","mcqOptions":[{"text":"Area = force ÷ pressure.","correct":true,"explanation":"Pressure equals force divided by area. Rearranging this formula gives area equal to force divided by pressure, provided the force and pressure units are compatible."},{"text":"Area = force × pressure.","correct":false,"explanation":"Multiplying force by pressure does not correctly rearrange the pressure formula. From pressure = force ÷ area, the area is found using force ÷ pressure."},{"text":"Area = pressure ÷ force.","correct":false,"explanation":"Dividing pressure by force reverses the required quotient. Rearranging pressure = force ÷ area gives area = force ÷ pressure."},{"text":"Area = force - pressure.","correct":false,"explanation":"Subtracting pressure from force combines quantities with incompatible units and does not follow the formula. Area is calculated by dividing force by pressure."}]},{"id":"6e12d4dd-f1bb-cf14-ae53-0f72cb799007","cardType":"cloze","points":null,"front":"For speed in mph, time must be in [ ]; for m/s, time must be in [ ].","back":"For speed in mph, time must be in hours; for m/s, time must be in seconds.","mcqOptions":[{"text":"For speed in mph, time must be in hours; for m/s, time must be in seconds.","correct":true,"explanation":"Miles per hour uses hours as its time unit, while metres per second uses seconds. Matching the time units prevents a factor-of-60 or factor-of-3600 error."},{"text":"For speed in mph, time must be in minutes; for m/s, time must be in seconds.","correct":false,"explanation":"Minutes do not match the “per hour” unit in mph, although seconds are correct for m/s. Convert the mph time to hours before calculating speed."},{"text":"For speed in mph, time must be in hours; for m/s, time must be in minutes.","correct":false,"explanation":"Hours are correct for mph, but minutes do not match the “per second” unit in m/s. Time must be measured in seconds for an m/s calculation."},{"text":"For speed in mph, time must be in seconds; for m/s, time must be in hours.","correct":false,"explanation":"The time units have been reversed. Mph requires time in hours because it means miles per hour, while m/s requires time in seconds."}]},{"id":"37d6ed6d-f810-827e-8042-110585552b27","cardType":"basic","points":1,"front":"How do you convert minutes to hours?","back":"Divide by 60.","mcqOptions":[{"text":"Divide by 60.","correct":true,"explanation":"There are 60 minutes in one hour, so dividing a number of minutes by 60 converts it into the equivalent number of hours."},{"text":"Multiply by 60.","correct":false,"explanation":"Multiplying by 60 converts hours to minutes, which is the opposite direction. To convert minutes to hours, divide the number of minutes by 60."},{"text":"Divide by 100.","correct":false,"explanation":"Dividing by 100 incorrectly treats time as a base-10 measurement. An hour contains 60 minutes, so the correct conversion is to divide by 60."},{"text":"Multiply by 100.","correct":false,"explanation":"Multiplying increases the value and also uses an incorrect base-10 conversion. Because 60 minutes make one hour, minutes must be divided by 60."}]},{"id":"9853267c-1a1c-8cd5-88f5-27b1b07decd7","cardType":"basic","points":1,"front":"What decimal hours is 4 hours 15 minutes?","back":"4.25 hours.","mcqOptions":[{"text":"4.25 hours.","correct":true,"explanation":"Fifteen minutes is $\\frac{15}{60}=0.25$ hours. Adding this to 4 hours gives a total time of 4.25 hours."},{"text":"4.15 hours.","correct":false,"explanation":"Writing 15 minutes as 0.15 hours treats time as base 100. Dividing by 60 gives $15÷60=0.25$, so the total is 4.25 hours."},{"text":"4.5 hours.","correct":false,"explanation":"This treats 15 minutes as half an hour rather than a quarter. Since $15÷60=0.25$, the correct decimal time is 4.25 hours."},{"text":"4.75 hours.","correct":false,"explanation":"A decimal part of 0.75 represents 45 minutes, not 15 minutes. Fifteen minutes is 0.25 hours, making the total 4.25 hours."}]},{"id":"74cf6e54-0c18-9b32-2cd1-9d4680c172c1","cardType":"basic","points":1,"front":"What decimal hours is 5 hours 40 minutes?","back":"5.666... hours.","mcqOptions":[{"text":"5.666... hours.","correct":true,"explanation":"Forty minutes is $\\frac{40}{60}=\\frac{2}{3}=0.666...$ hours. Adding this fraction to 5 hours gives 5.666... hours."},{"text":"5.4 hours.","correct":false,"explanation":"Writing 40 minutes as 0.4 hours treats the minutes as decimal digits. Since $40÷60=0.666...$, the correct total is 5.666... hours."},{"text":"5.75 hours.","correct":false,"explanation":"A decimal part of 0.75 represents 45 minutes, not 40 minutes. Converting correctly gives $40÷60=0.666...$, so the total is 5.666... hours."},{"text":"6.666... hours.","correct":false,"explanation":"This adds an unnecessary extra hour after converting the minutes. Forty minutes contributes only 0.666... hours, so the total is 5.666... hours."}]},{"id":"3ac74a74-3c0c-7e4c-269b-f5b17345725a","cardType":"basic","points":2,"front":"A driver travels 81 miles at 36 mph. What is the time?","back":"2.25 hours.","mcqOptions":[{"text":"2.25 hours.","correct":true,"explanation":"Time is calculated using distance ÷ speed, so $81 \\div 36 = 2.25$ hours. This is equivalent to 2 hours and 15 minutes."},{"text":"1.25 hours.","correct":false,"explanation":"This results from incorrectly treating the remaining 45 miles as 0.25 hours. Using time = distance ÷ speed gives $81 \\div 36 = 2.25$ hours."},{"text":"2.5 hours.","correct":false,"explanation":"This comes from an inaccurate division or rounding slip. The exact calculation is $81 \\div 36 = 2.25$ hours, equivalent to 2 hours and 15 minutes."},{"text":"3.24 hours.","correct":false,"explanation":"This reverses or misuses the figures rather than applying the speed formula correctly. Time is distance ÷ speed, so $81 \\div 36 = 2.25$ hours."}]},{"id":"3f9c8954-76cd-8215-e48e-b609205cacb0","cardType":"cloze","points":null,"front":"For a whole journey, average speed = [ ].","back":"For a whole journey, average speed = total distance ÷ total time.","mcqOptions":[{"text":"total distance ÷ total time","correct":true,"explanation":"Average speed for an entire journey is found by dividing the total distance travelled by the total time taken, including all stages of the journey."},{"text":"total time ÷ total distance","correct":false,"explanation":"This reverses the required division and gives time per unit distance. Average speed is total distance ÷ total time, producing units such as mph or km/h."},{"text":"total distance × total time","correct":false,"explanation":"Multiplying distance by time does not produce a speed. Average speed is calculated by dividing the total distance travelled by the total time taken."},{"text":"total distance ÷ number of stages","correct":false,"explanation":"Dividing by the number of stages gives an average distance per stage, not a speed. Average speed requires total distance ÷ total time."}]},{"id":"2f17d886-5eac-357e-2fa4-b8869f26122b","cardType":"basic","points":2,"front":"Why is simply averaging two journey speeds usually wrong?","back":"Average speed uses total distance ÷ total time.","mcqOptions":[{"text":"Average speed uses total distance ÷ total time.","correct":true,"explanation":"Different speeds may be maintained for different lengths of time or distance, so the whole journey’s average must use total distance divided by total time."},{"text":"Average speed uses total time ÷ total distance.","correct":false,"explanation":"This reverses the speed formula and calculates time per unit distance. Average speed uses total distance ÷ total time because speed measures distance travelled per unit time."},{"text":"Average speed uses total distance ÷ number of speeds.","correct":false,"explanation":"Dividing total distance by the number of speeds does not account for journey time. Average speed is total distance ÷ total time across the whole journey."},{"text":"Average speed uses total time ÷ number of speeds.","correct":false,"explanation":"This calculates an average time per journey section rather than a speed. The correct whole-journey calculation is total distance ÷ total time."}]},{"id":"c313406e-727c-e206-d73c-fd3846223cb4","cardType":"cloze","points":null,"front":"In liquid mixture problems, do not add [ ] directly.","back":"In liquid mixture problems, do not add densities directly.","mcqOptions":[{"text":"densities","correct":true,"explanation":"Densities cannot generally be added because density is a ratio of mass to volume. Add the masses and volumes separately, then divide total mass by total volume."},{"text":"masses","correct":false,"explanation":"Masses should be added directly when liquids are combined, assuming none is lost. It is the densities that must not be added; calculate density from total mass ÷ total volume."},{"text":"volumes","correct":false,"explanation":"Volumes are normally added directly in GCSE mixture problems unless stated otherwise. Densities are not added; first find total mass and total volume, then divide."},{"text":"quantities","correct":false,"explanation":"The quantities of liquid may be combined when calculating totals. The specific values that must not be added directly are densities, because density is mass ÷ volume."}]},{"id":"35468abb-08ea-39dd-ddd6-4cddd64171fc","cardType":"basic","points":1,"front":"After finding total mass and total volume of a liquid mixture, how do you find density?","back":"Density = total mass ÷ total volume.","mcqOptions":[{"text":"Density = total mass ÷ total volume.","correct":true,"explanation":"Density is mass per unit volume. For a mixture, add all masses and all volumes separately, then divide the total mass by the total volume."},{"text":"Density = total volume ÷ total mass.","correct":false,"explanation":"This reverses the density formula and produces volume per unit mass. Density is mass per unit volume, so use total mass ÷ total volume."},{"text":"Density = total mass × total volume.","correct":false,"explanation":"Multiplying mass and volume gives the wrong dimensions and does not calculate density. The mixture’s density is found using total mass ÷ total volume."},{"text":"Density = total mass ÷ number of liquids.","correct":false,"explanation":"This gives average mass per liquid rather than mass per unit volume. Density must be calculated by dividing the total mass by the total volume."}]},{"id":"b324ffe4-6889-cc2a-42a1-0a3fc6d765f2","cardType":"basic","points":2,"front":"Liquid B has mass 90 g and volume 80 cm³. What is its density?","back":"1.125 g/cm³.","mcqOptions":[{"text":"1.125 g/cm³.","correct":true,"explanation":"Density equals mass ÷ volume, so $90 \\div 80 = 1.125$. Therefore, the liquid’s density is $1.125$ g/cm³."},{"text":"0.889 g/cm³.","correct":false,"explanation":"This comes from reversing the division and calculating $80 \\div 90$. Density is mass ÷ volume, so the correct calculation is $90 \\div 80 = 1.125$ g/cm³."},{"text":"1.25 g/cm³.","correct":false,"explanation":"This value would result from using 100 g instead of the stated 90 g. Using the actual mass gives $90 \\div 80 = 1.125$ g/cm³."},{"text":"1.0125 g/cm³.","correct":false,"explanation":"This introduces an extra zero during the decimal calculation. Dividing the stated mass by volume correctly gives $90 \\div 80 = 1.125$ g/cm³."}]}]}],"examCountdown":null,"heading":"Speed and Density","title":"Speed and Density Flashcards","topbar":{"backHref":"/gcse/maths/ccea/flashcards"},"topicSidebar":"$L39"}]}],"topicId":"92ce6af0-7f4c-a20a-49b0-0bbb1ee1fdbd","walled":"$L3a"}],"$L3b","$L3c"]