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1076.66","code":"B"}],"finalAnswers":["1076.66"],"generatedAt":"2026-05-06T15:40:37.681Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"square_and_add","label":"Square then add","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=firstsquare}{\\color{@sky}{30.5^2}}=930.25"},{"latex":"\\htmlData{anchor=secondsquare}{\\color{@green}{12.1^2}}=146.41"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"firstsquare"},{"color":"green","style":"text-color-with-background","anchor":"secondsquare"}]},"order":1,"title":"Work out the squares","description":"Square each number, then add the results."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=total}{\\color{@orange}{930.25+146.41=1076.66}}"},{"text":" "}]},"order":2,"title":"Add the results","description":"Now add the two squared values. Giving the correct final value earns the B1 mark."}]}],"generatedAt":"2026-07-21T04:09:51.056Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"b342ade0-8d6b-4361-a6f8-f3bd68e53493","label":"b","content":"Find the value of $\\sqrt{5.13 + 10.28} - 0.97$","markscheme":"- Award method mark for evaluating the square root $\\sqrt{15.41}$ or $3.9255...$ M1\n- Final answer 2.955557285 A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evaluates the square root part as $\\sqrt{15.41}$ or approx $3.9255$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer 2.955557285","code":"A"}],"finalAnswers":["2.955557285"],"generatedAt":"2026-05-06T15:40:37.681Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null},{"id":"8f11d194-6371-48a0-b11d-a5f6fa362456","revisionId":"4f5fdab4-edaf-4979-ba5f-564656f4d029","questionNumber":"11","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Using a Calculator","calculatorUse":null,"isCalculation":true,"parts":[{"id":"77358e41-fc4a-4ea4-96f9-6fa839b517da","label":"0","content":"Work out $\\sqrt{12^2 + 15^2 - 54 \\cos(80)}$\n\nWrite down all the figures on your calculator display.","markscheme":"- Award method mark for evaluating the expression inside the root $359.622...$ M1\n- Final answer 18.96372849 A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evaluates the expression inside the square root as approx $359.62$.","code":"M"},{"id":"p2","marks":1,"description":"Final answer 18.96372849","code":"A"}],"finalAnswers":["18.96372849"],"generatedAt":"2026-05-06T15:40:37.681Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"calculator_evaluation","label":"Evaluate with a calculator","steps":[{"type":"text","order":0,"title":"Use degree mode","content":"Because the angle is written as $80$ (in degrees), first check that your calculator is in **degree** mode. Then enter the whole expression under one square-root sign.","highlights":[{"text":"Work out $\\sqrt{12^2 + 15^2 - 54 \\cos(80)}$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\htmlData{anchor=expression}{12^2+15^2-54\\cos(80)}"},{"latex":"\\htmlData{anchor=radicand}{359.62299840598575\\ldots}"}],"connections":[{"to":"radicand","from":"expression","color":"sky","label":"evaluate in degree mode","style":"solid"}]},"order":1,"title":"Evaluate inside the root","description":"Evaluate the expression inside the square root first. Examiner annotation: 359.622... earns M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\sqrt{\\htmlData{anchor=radicand}{359.62299840598575\\ldots}}"},{"latex":"\\htmlData{anchor=answer}{18.96372849}"}],"connections":[{"to":"answer","from":"radicand","color":"green","label":"square root","style":"solid"}]},"order":2,"title":"Take the square root","description":"Now take the square root, keeping every digit your calculator displays. Examiner annotation: 18.96372849 earns A1."}]}],"generatedAt":"2026-07-21T04:08:32.309Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths__cie","summaries":[{"id":"c62eab09-52f9-47ce-82a5-e99d1591306d","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"a3e754f6-ec5b-4da1-91f6-f2b7c5f67260","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"b00371ac-7a40-4a2e-8427-8cf5c1fff218","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"7fbf0ace-de59-4dfe-b9b4-d66fdc1cf738","difficultyBand":"easy","calculatorUse":null,"totalMarks":1,"questionType":"LA","isCalculation":false},{"id":"f035fada-f39d-4bd2-afe1-107e0527bade","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"cae2cc84-4985-4add-90c5-3480e98b0b3c","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"c3553241-8240-4c30-a8d7-358076b5a559","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"e4480a23-5472-4fc6-9a08-2e1295ed1c95","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"16e2be3a-0d6a-4ce6-9651-e9148b68483d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"827386ad-2dfc-4cb5-a43c-a165d7fb1447","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8f11d194-6371-48a0-b11d-a5f6fa362456","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"215c6732-da5f-4f90-8675-8076c050b6e8","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"3f641c1c-731d-4110-8c8a-360650587b74","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"e096bdcc-64cd-4f92-9aac-11f274b1c654","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true}],"title":"Using a Calculator","topicId":"2b972b56-5b53-421b-a771-e9ad3f18f36c","topicSidebar":"$L3a","topicSlug":"grade-2-2-2-using-a-calculator","topicTitle":"Using a Calculator"}]}],"$L3b","$L3c"]}]