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number of significant figures.","markscheme":"- Calculates the mean value of $t$, showing a correct method or obtaining $0.523...\\text{ s}$ M1\n- States the final answer to 2 significant figures as $0.52\\text{ s}$ A1","marks":2,"order":0,"markingRubric":null,"tableImages":[],"explanation":{"methods":[{"id":"calculate_mean","label":"Calculate the mean","steps":[{"type":"text","order":0,"title":"Use the mean rule","content":"The **mean** is found by adding all the readings, then dividing by how many readings there are. Here there are three time readings.","highlights":[{"text":"They record three values for time $t$:","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"t_{\\mathrm{mean}}=\\frac{\\htmlData{anchor=readings}{0.53+0.48+0.56}}{3}"},{"latex":"t_{\\mathrm{mean}}=\\frac{\\htmlData{anchor=total}{1.57}}{3}"},{"latex":"t_{\\mathrm{mean}}=\\htmlData{anchor=mean}{0.523333\\ldots\\ \\mathrm{s}}"}],"highlights":[{"color":"amber","style":"box","anchor":"mean"}],"connections":[{"to":"total","from":"readings","color":"sky","label":"add the readings"}]},"order":1,"title":"Calculate the mean","description":"Add the three measured times and divide by 3. Setting up this calculation earns the M1 mark."},{"type":"text","order":2,"title":"Round the answer","content":"Give the result to **2 significant figures**, matching the precision of the time readings. The first two significant digits are $5$ and $2$, and the next digit is $3$, so it rounds down.\n\n$$\\boxed{t=0.52\\ \\text{s}}$$\n\nThis is the A1 mark.","highlights":[{"text":"Calculate the mean value of time $t$ to an appropriate number of significant figures.","location":"specification"}]}]}],"generatedAt":"2026-07-22T09:14:10.292Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"e3c7820b-c73c-4ac5-afd3-af8fe4e059f3:calculate_mean","label":"Calculate the mean","steps":[{"type":"text","order":0,"title":"Use the mean rule","content":"The **mean** is found by adding all the readings, then dividing by how many readings there are. Here there are three time readings.","highlights":[{"text":"They record three values for time $t$:","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"t_{\\mathrm{mean}}=\\frac{\\htmlData{anchor=readings}{0.53+0.48+0.56}}{3}"},{"latex":"t_{\\mathrm{mean}}=\\frac{\\htmlData{anchor=total}{1.57}}{3}"},{"latex":"t_{\\mathrm{mean}}=\\htmlData{anchor=mean}{0.523333\\ldots\\ \\mathrm{s}}"}],"highlights":[{"color":"amber","style":"box","anchor":"mean"}],"connections":[{"to":"total","from":"readings","color":"sky","label":"add the readings"}]},"order":1,"title":"Calculate the mean","description":"Add the three measured times and divide by 3. Setting up this calculation earns the M1 mark."},{"type":"text","order":2,"title":"Round the answer","content":"Give the result to **2 significant figures**, matching the precision of the time readings. The first two significant digits are $5$ and $2$, and the next digit is $3$, so it rounds down.\n\n$$\\boxed{t=0.52\\ \\text{s}}$$\n\nThis is the A1 mark.","highlights":[{"text":"Calculate the mean value of time $t$ to an appropriate number of significant figures.","location":"specification"}]}]}],"generatedAt":"2026-08-24T02:42:11.822Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":61},"walkthroughVideo":null},{"id":"232092f9-1364-4646-a0a5-ff7cd217baab","revisionId":"c9857afd-7bdb-4b72-9b26-34371810d145","questionNumber":null,"questionType":"LA","specification":"","difficulty":5,"difficultyBand":"easy","tier":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"3cde7af4-4a82-453a-908f-ed220fdb4344","label":null,"content":"An industrial nozzle spray has a flow rate of $7.2\\text{ g s}^{-1}$. Show that this rate of flow is greater than a rate of $25.5\\text{ kg h}^{-1}$.","markscheme":"- Converts $7.2\\text{ g s}^{-1}$ to $\\text{kg h}^{-1}$ by multiplying by $3600$ and dividing by $1000$ (or converts $25.5\\text{ kg h}^{-1}$ to $\\text{g s}^{-1}$ by multiplying by $1000$ and dividing by $3600$) M1\n- Obtains $25.92\\text{ kg h}^{-1}$ (or $25.9\\text{ kg h}^{-1}$), or conversely $7.08\\text{ g s}^{-1}$ (or $7.1\\text{ g s}^{-1}$), and states that $25.92\\text{ kg h}^{-1} > 25.5\\text{ kg h}^{-1}$ (or $7.2\\text{ g s}^{-1} > 7.08\\text{ g s}^{-1}$) A1","marks":2,"order":0,"markingRubric":null,"tableImages":[],"explanation":{"methods":[{"id":"convert_to_kg_per_hour","label":"Convert to kg per hour","steps":[{"type":"text","order":0,"title":"Match the units","content":"To compare the two flow rates, express both in the same units. Convert $7.2\\text{ g s}^{-1}$ into $\\text{kg h}^{-1}$, because the other rate is already in those units.\n\nThere are $3600\\text{ s}$ in $1\\text{ h}$, and $1000\\text{ g}$ in $1\\text{ kg}$.","highlights":[{"text":"$$7.2\\text{ g s}^{-1}$","location":"specification"},{"text":"$$25.5\\text{ kg h}^{-1}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"7.2\\ \\mathrm{g\\ s^{-1}}\\times\\htmlData{anchor=seconds}{3600\\ \\mathrm{s\\ h^{-1}}}"},{"latex":"\\htmlData{anchor=grams}{25920\\ \\mathrm{g\\ h^{-1}}}\\times\\frac{1\\ \\mathrm{kg}}{1000\\ \\mathrm{g}}"},{"latex":"\\htmlData{anchor=converted}{25.92\\ \\mathrm{kg\\ h^{-1}}}"}],"highlights":[{"color":"green","style":"box","anchor":"converted"}],"connections":[{"to":"grams","from":"seconds","color":"sky","label":"seconds to hours"},{"to":"converted","from":"grams","color":"green","label":"grams to kg"}]},"order":1,"title":"Convert the flow rate","description":"First change seconds to hours by multiplying by 3600. Then change grams to kilograms by dividing by 1000; this conversion method earns the M1 mark."},{"type":"text","order":2,"title":"Compare the rates","content":"Now both rates are in $\\text{kg h}^{-1}$:\n\n$$25.92\\text{ kg h}^{-1} > 25.5\\text{ kg h}^{-1}$$\n\nTherefore, the industrial nozzle spray flow rate is greater. This correct converted value and comparison earn the A1 mark.","highlights":[{"text":"Show that this rate of flow is greater than a rate of $25.5\\text{ kg h}^{-1}$","location":"specification"}]}]}],"generatedAt":"2026-07-22T09:40:33.595Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"3cde7af4-4a82-453a-908f-ed220fdb4344:convert_to_kg_per_hour","label":"Convert to kg per hour","steps":[{"type":"text","order":0,"title":"Match the units","content":"To compare the two flow rates, express both in the same units. Convert $7.2\\text{ g s}^{-1}$ into $\\text{kg h}^{-1}$, because the other rate is already in those units.\n\nThere are $3600\\text{ s}$ in $1\\text{ h}$, and $1000\\text{ g}$ in $1\\text{ kg}$.","highlights":[{"text":"$$7.2\\text{ g s}^{-1}$","location":"specification"},{"text":"$$25.5\\text{ kg h}^{-1}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"7.2\\ \\mathrm{g\\ s^{-1}}\\times\\htmlData{anchor=seconds}{3600\\ \\mathrm{s\\ h^{-1}}}"},{"latex":"\\htmlData{anchor=grams}{25920\\ \\mathrm{g\\ h^{-1}}}\\times\\frac{1\\ \\mathrm{kg}}{1000\\ \\mathrm{g}}"},{"latex":"\\htmlData{anchor=converted}{25.92\\ \\mathrm{kg\\ h^{-1}}}"}],"highlights":[{"color":"green","style":"box","anchor":"converted"}],"connections":[{"to":"grams","from":"seconds","color":"sky","label":"seconds to hours"},{"to":"converted","from":"grams","color":"green","label":"grams to kg"}]},"order":1,"title":"Convert the flow rate","description":"First change seconds to hours by multiplying by 3600. Then change grams to kilograms by dividing by 1000; this conversion method earns the M1 mark."},{"type":"text","order":2,"title":"Compare the rates","content":"Now both rates are in $\\text{kg h}^{-1}$:\n\n$$25.92\\text{ kg h}^{-1} > 25.5\\text{ kg h}^{-1}$$\n\nTherefore, the industrial nozzle spray flow rate is greater. This correct converted value and comparison earn the A1 mark.","highlights":[{"text":"Show that this rate of flow is greater than a rate of $25.5\\text{ kg h}^{-1}$","location":"specification"}]}]}],"generatedAt":"2026-08-24T02:43:59.821Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"41bef5f6-acfb-4b3d-80c0-fb589453d8a1","revisionId":"cf210c70-c40e-4b86-ae5b-b178debbbe6d","questionNumber":null,"questionType":"LA","specification":"","difficulty":5,"difficultyBand":"easy","tier":null,"totalMarks":2,"sourceTitle":null,"calculatorUse":null,"isCalculation":true,"parts":[{"id":"2370bdae-431a-49ee-bd04-41bddcacab06","label":null,"content":"Show that a speed of $45\\text{ m s}^{-1}$ is greater than a speed of $160\\text{ km h}^{-1}$.","markscheme":"- Converts $45\\text{ m s}^{-1}$ to $\\text{km h}^{-1}$ by multiplying by $3.6$ to get $162\\text{ km h}^{-1}$ (or converts $160\\text{ km h}^{-1}$ to $\\text{m s}^{-1}$ by dividing by $3.6$ to get $44.4\\text{ m s}^{-1}$) M1\n- Compares the two values ($162 > 160$ or $45 > 44.4$) to show that $45\\text{ m s}^{-1}$ is greater than $160\\text{ km h}^{-1}$ A1","marks":2,"order":0,"markingRubric":null,"tableImages":[],"explanation":{"methods":[{"id":"convert_to_kmh","label":"Convert to km/h","steps":[{"type":"text","order":0,"title":"Use matching units","content":"To compare speeds fairly, first express both speeds in the same units. Convert $45\\text{ m s}^{-1}$ into $\\text{km h}^{-1}$; the conversion factor is $3.6$.","highlights":[{"text":"Show that a speed of $45\\text{ m s}^{-1}$ is greater than a speed of $160\\text{ km h}^{-1}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"v=45\\,\\mathrm{m\\,s^{-1}}"},{"latex":"v=45\\,\\mathrm{m\\,s^{-1}}\\times\\htmlData{anchor=conversion}{3.6\\,\\frac{\\mathrm{km\\,h^{-1}}}{\\mathrm{m\\,s^{-1}}}}"},{"latex":"v=\\htmlData{anchor=converted}{162\\,\\mathrm{km\\,h^{-1}}}"}],"highlights":[{"color":"green","style":"box","anchor":"converted"}],"connections":[{"to":"converted","from":"conversion","color":"sky","label":"calculate"}]},"order":1,"title":"Convert the speed","description":"Multiplying by 3.6 converts metres per second to kilometres per hour. Writing this conversion earns the method mark."},{"type":"text","order":2,"title":"Compare the values","content":"Now both speeds are in $\\text{km h}^{-1}$, so compare them directly: $162\\text{ km h}^{-1}>160\\text{ km h}^{-1}$. Therefore, $45\\text{ m s}^{-1}$ is greater than $160\\text{ km h}^{-1}$. This comparison earns the accuracy mark.","highlights":[{"text":"greater than","location":"specification"}]}]}],"generatedAt":"2026-07-22T11:11:40.802Z","modelVersion":"gpt-5.6-terra+diagrams-1","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"gcse_physics","summaries":[{"id":"0c2b5f55-5bda-4b25-b50c-f5bbffdcc285","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"0e7344ce-4446-4d42-8565-258d3b4ff5c9","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"134e14e6-856b-4b64-93e1-a1db4146eb27","difficultyBand":"medium","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"232092f9-1364-4646-a0a5-ff7cd217baab","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"3872f655-f3c7-4b72-8998-24184826739e","difficultyBand":"hard","calculatorUse":null,"totalMarks":1,"questionType":"MC","isCalculation":true},{"id":"41bef5f6-acfb-4b3d-80c0-fb589453d8a1","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"559ca8df-aa6f-4665-8271-e04c71e8621c","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"72befa53-b658-4c1c-928f-97b710bf980d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"85e92d82-43b5-4ccb-8d7c-a1deaa622d33","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"MC","isCalculation":true},{"id":"93ce2533-fdfd-4c6c-abae-e130b2213df3","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"95e36ad9-5929-48fd-827a-55c81be9f1c4","difficultyBand":"medium","calculatorUse":null,"totalMarks":1,"questionType":"MC","isCalculation":true},{"id":"b54ecb40-5403-4131-9f80-846d3023623d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"b8b17718-bc00-4baa-99d4-3cac55f94659","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"bea8a367-0604-4942-98c7-c6e61bd6b060","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c00c78a9-bb1b-4d0b-ad2c-0a72ceaebe43","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"MC","isCalculation":false},{"id":"cc5ee04c-f2b7-404d-81c8-37e43f7d2a4b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"ee5e85df-448d-4893-b4db-3191306832b2","difficultyBand":"medium","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"fdc940f5-f194-43e7-8aa7-74be063529a0","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true}],"title":"1.1 Units and quantities","topicId":"e07bd01c-5a0c-5242-bebe-d6392b801fd8","topicSidebar":"$L3b","topicSlug":"units-and-prefixes","topicTitle":"1.1 Units and quantities"}]}],"$L3c","$L3d"]}]

1.1 Units and quantities

Question 3

1.1 Units and quantities Questions

1.1 Units and quantities

Question 3

1.1 Units and quantities Questions