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This gives the number of days they need."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$18\\div \\color{@sky}{2}=\\color{@green}{9}\\text{ days}$"},{"text":"A1: 18 ÷ 2 = 9 days."}]},"order":3,"title":"Calculate the time","description":"Share the total painter-days between the two painters."}]}],"generatedAt":"2026-07-21T04:03:51.923Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"9605641e-203d-4029-a823-1c3ccff3f1f7","revisionId":"2ba24c69-c7fd-472e-a1e7-44d6d7262cfb","questionNumber":"8","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Direct and Inverse Proportion","calculatorUse":null,"isCalculation":true,"parts":[{"id":"e435908b-23ec-4b3c-948a-d601c5fadb7b","label":"0","content":"It takes 5 machines 6 hours to produce 1000 DVDs\n\nWork out how long it would take 4 machines to produce 1000 DVDs.","markscheme":"- $5 \\times 6 = 30$ machine hours M1\n- $30 \\div 4 = 7.5$ hours A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates total machine-hours required ($5 \\times 6$).","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 7.5.","code":"A"}],"finalAnswers":["7.5"],"generatedAt":"2026-05-07T01:55:05.308Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"machine_hours","label":"Use machine-hours","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$5\\text{ machines}\\times6\\text{ hours}=30\\text{ machine-hours}$"},{"text":"The units are machine-hours."}]},"order":0,"title":"Calculate total work","description":"Five machines working for six hours gives 30 machine-hours. Calculating 5 × 6 = 30 machine-hours earns the M1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$30\\text{ machine-hours}\\div4\\text{ machines}=7.5\\text{ hours}$"},{"text":"The units simplify to hours, the unit required for the answer."}]},"order":1,"title":"Find the time","description":"Sharing the 30 machine-hours between four machines gives the time needed for the job. Calculating 30 ÷ 4 = 7.5 hours earns the A1 mark."}]}],"generatedAt":"2026-07-21T04:22:43.919Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"9e94d0ab-75c0-4238-890e-ce2bdba4d447","revisionId":"3537f6cd-8c69-4b34-a5be-36e7a3ba3ca1","questionNumber":"9","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Direct and Inverse Proportion","calculatorUse":null,"isCalculation":true,"parts":[{"id":"cd46b2ff-722a-4a06-a1d1-a93dabf10258","label":"0","content":"$$x$ is inversely proportional to $y$.\n\n$x$ is given by the formula: $x = \\frac{1000}{y}$\n\nFind the value of $x$ when $y = 50$","markscheme":"- $x = \\frac{1000}{50}$ M1\n- $x = 20$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Substitute $y = 50$ into the formula.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 20.","code":"A"}],"finalAnswers":["20"],"generatedAt":"2026-05-07T01:55:05.308Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"substitution","label":"Substitution","steps":[{"type":"text","order":0,"title":"Substitute the value","content":"Use $y=50$ in the given formula:\n\n$$x=\\frac{1000}{50}$$\n\nThis substitution earns the **M1** mark, even if the division is then incorrect.","highlights":[{"text":"when $y = 50$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"x=\\htmlData{anchor=quotient}{\\frac{1000}{50}}"},{"latex":"x=\\htmlData{anchor=answer}{\\color{@green}{20}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"quotient","color":"sky","label":"divide","style":"solid"}]},"order":1,"title":"Calculate the quotient","description":"Divide the full fraction. This earns the A1 mark."}]}],"generatedAt":"2026-07-21T03:19:59.527Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths","summaries":[{"id":"8286ab57-5f99-40c5-893b-799bc2a05cd9","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c7ee7497-43ea-4dbf-b587-30c5720537f9","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"141f8f3c-efaa-4a0b-b184-a152070e0ab4","difficultyBand":"medium","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"901a3643-3e7a-4442-911a-f774c439b453","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"0108ae63-c532-453b-8ede-33f10fc6a858","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"038d9f99-963c-4ef7-b30a-7982baba1983","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"0cc81215-f670-41ed-888d-67d91df12b4b","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"9605641e-203d-4029-a823-1c3ccff3f1f7","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"9e94d0ab-75c0-4238-890e-ce2bdba4d447","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"0e06aefd-a803-4159-ba49-6ca68eeac850","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"125424f0-b7d7-43fc-8b49-75b9dad7003c","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"d6e20bbb-0f8f-4247-b514-8890ed31b776","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true}],"title":"Direct and Inverse Proportion","topicId":"43e15371-e0da-4def-ad81-6a08e34e76b1","topicSidebar":"$L3c","topicSlug":"grade-6-6-3-direct-and-inverse-proportion","topicTitle":"Direct and Inverse Proportion"}]}],"$L3d","$L3e"]}]

Direct and Inverse Proportion

Question 7

Direct and Inverse Proportion Questions

Direct and Inverse Proportion

Question 7

Direct and Inverse Proportion Questions