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Since $500 \\div 50 = 10$, the smaller amount has **one tenth** as many sheets.","highlights":[{"text":"500 sheets of paper weigh 2.5kg.","location":"specification"},{"text":"50 sheets of paper","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=start}{500\\text{ sheets}}=2.5\\text{ kg}"},{"latex":"\\htmlData{anchor=calculation}{50\\text{ sheets}}=\\color{@sky}{2.5\\div10}\\text{ kg}"},{"latex":"\\htmlData{anchor=result}{50\\text{ sheets}}=\\color{@green}{0.25\\text{ kg}}"}],"highlights":[{"color":"sky","style":"text-color","anchor":"calculation"},{"color":"green","style":"text-color-with-background","anchor":"result"}]},"order":1,"title":"Scale the weight","description":"Divide the weight by the same scale factor. Dividing 2.5 by 10 earns M1; giving 0.25 kg earns A1."}]}],"generatedAt":"2026-07-20T16:36:16.089Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":75},"walkthroughVideo":null},{"id":"0108ae63-c532-453b-8ede-33f10fc6a858","revisionId":"d8aab0c0-7ee3-4230-b91c-1114a7c04302","questionNumber":"5","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Direct and Inverse Proportion","calculatorUse":null,"isCalculation":true,"parts":[{"id":"4d76fb61-17c0-4bc7-8f7d-fbdd2752d0dd","label":"0","content":"It takes 2 painters 4 days to complete a job.\n\nWork out how many days it would take 1 painter to complete the same job.","markscheme":"- $2 \\times 4 = 8$ M1\n- Final answer 8 days A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates the total man-days required ($2 \\times 4$).","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 8.","code":"A"}],"finalAnswers":["8"],"generatedAt":"2026-05-07T01:55:05.308Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"unitary_method","label":"Find the time for one painter","steps":[{"type":"text","order":0,"title":"Notice the relationship","content":"The job stays the same. With fewer painters, it takes longer: one painter must do all the work that both painters were sharing.","highlights":[{"text":"1 painter","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$W=\\color{@sky}{\\htmlData{anchor=calculation}{2\\times4}}$"},{"latex":"$$W=\\color{@green}{\\htmlData{anchor=result}{8}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"calculation"},{"color":"green","style":"text-color","anchor":"result"}],"connections":[{"to":"result","from":"calculation","color":"green","label":"calculate","style":"solid"}]},"order":1,"title":"Find the total work","description":"Let the letter W represent the total work, measured in painter-days. Multiplying the number of painters by the number of days earns M1."},{"type":"text","order":2,"title":"State the answer","content":"So one painter would take $8$ days to complete the same job. Including the unit **days** gives the final answer and earns **A1**.","highlights":[{"text":"how many days","location":"specification"},{"text":"same job","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:44:37.782Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":84},"walkthroughVideo":null},{"id":"038d9f99-963c-4ef7-b30a-7982baba1983","revisionId":"4b55e351-312b-42b1-b892-98c8414acc9c","questionNumber":"6","questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Direct and Inverse Proportion","calculatorUse":null,"isCalculation":true,"parts":[{"id":"3336d89a-63ec-4444-a8bb-9e22985b513c","label":"0","content":"It takes 3 machines 2 days to produce a batch of products\n\nWork out how long it would take 1 machine to produce the same batch of products.","markscheme":"- $3 \\times 2 = 6$ M1\n- Final answer 6 days A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates total machine-days required ($3 \\times 2$).","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 6.","code":"A"}],"finalAnswers":["6"],"generatedAt":"2026-05-07T01:55:05.308Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"machine_days","label":"Machine-days method","steps":[{"type":"text","order":0,"title":"Identify the total work","content":"The whole batch needs the same total amount of work, whether it is made by three machines or by one machine.","highlights":[{"text":"It takes 3 machines 2 days to produce a batch of products","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\color{@sky}{3\\text{ machines}}\\times\\color{@amber}{2\\text{ days}}=\\htmlData{anchor=result}{\\color{@green}{6\\text{ machine-days}}}$"},{"text":"This complete multiplication earns the M1 mark."}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"result"}]},"order":1,"title":"Calculate the work","description":"Multiply the number of machines by the number of days."},{"type":"text","order":2,"title":"State the time","content":"With only $1$ machine, it completes $1$ machine-day of work each day. Therefore it needs all $6$ machine-days itself, so it would take **$6$ days**. This earns the **A1** mark."}]}],"generatedAt":"2026-07-21T04:04:26.988Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":75},"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 4

Direct and Inverse Proportion Questions

Direct and Inverse Proportion

Question 4

Direct and Inverse Proportion Questions