34:I[196793,["/_next/static/chunks/2jz5imjnk1dsn.js?dpl=nogit-1792077011","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1792077011","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1792077011","/_next/static/chunks/02eggfg7vwd9q.js?dpl=nogit-1792077011","/_next/static/chunks/1gm-hv-3-fp7_.js?dpl=nogit-1792077011","/_next/static/chunks/2xa0kylife8l8.js?dpl=nogit-1792077011","/_next/static/chunks/2lsi6eli88uwt.js?dpl=nogit-1792077011","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1792077011","/_next/static/chunks/0kyh6u8hfv06h.js?dpl=nogit-1792077011","/_next/static/chunks/1zirpvj720iz0.js?dpl=nogit-1792077011","/_next/static/chunks/0mt9yp27gb-6w.js?dpl=nogit-1792077011","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1792077011","/_next/static/chunks/0myxz4gywm9of.js?dpl=nogit-1792077011","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1792077011","/_next/static/chunks/1jo7uanvci4-r.js?dpl=nogit-1792077011","/_next/static/chunks/0papbjd-vx5q5.js?dpl=nogit-1792077011","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1792077011","/_next/static/chunks/11kq2otno6-oj.js?dpl=nogit-1792077011","/_next/static/chunks/23f2tb1apskc8.js?dpl=nogit-1792077011","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1792077011","/_next/static/chunks/3x5t_ry1ziv7r.js?dpl=nogit-1792077011","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1792077011","/_next/static/chunks/0iapw94rt37n4.js?dpl=nogit-1792077011","/_next/static/chunks/2rvalcou1gw7v.js?dpl=nogit-1792077011","/_next/static/chunks/05mo4k9k-ry1n.js?dpl=nogit-1792077011","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1792077011","/_next/static/chunks/04wg1hnm8knmc.js?dpl=nogit-1792077011","/_next/static/chunks/3_six85qevnm3.js?dpl=nogit-1792077011","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1792077011","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1792077011","/_next/static/chunks/1vovlfobo0rf7.js?dpl=nogit-1792077011","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1792077011","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1792077011","/_next/static/chunks/1jxfzuqocprar.js?dpl=nogit-1792077011","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1792077011","/_next/static/chunks/1h7qr4subpkxv.js?dpl=nogit-1792077011","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1792077011","/_next/static/chunks/0ltoscgl22itf.js?dpl=nogit-1792077011","/_next/static/chunks/0beaxlbowx15e.js?dpl=nogit-1792077011","/_next/static/chunks/376bkwrx00xp0.js?dpl=nogit-1792077011","/_next/static/chunks/26d_zs_7_ka17.js?dpl=nogit-1792077011","/_next/static/chunks/1w193fj-lcfgs.js?dpl=nogit-1792077011","/_next/static/chunks/2l63yczi1z2qz.js?dpl=nogit-1792077011","/_next/static/chunks/2yss1g0cimuwe.js?dpl=nogit-1792077011","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1792077011","/_next/static/chunks/1zo1304bjzjl_.js?dpl=nogit-1792077011","/_next/static/chunks/0wv8cpdr6cvhr.js?dpl=nogit-1792077011","/_next/static/chunks/1drwxxqzvnao9.js?dpl=nogit-1792077011","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1792077011","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1792077011","/_next/static/chunks/3f11o876enqgd.js?dpl=nogit-1792077011","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1792077011","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1792077011","/_next/static/chunks/33y-ad8441jub.js?dpl=nogit-1792077011","/_next/static/chunks/3qiv_uhu50h9w.js?dpl=nogit-1792077011","/_next/static/chunks/2mbz851h6l6ul.js?dpl=nogit-1792077011","/_next/static/chunks/1iyn56mfdoj9b.js?dpl=nogit-1792077011","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1792077011","/_next/static/chunks/3n19bhgn4l5zi.js?dpl=nogit-1792077011","/_next/static/chunks/1d4d88jx43_iw.js?dpl=nogit-1792077011","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1792077011"],"Gingerbread"] 36:I[647935,["/_next/static/chunks/2jz5imjnk1dsn.js?dpl=nogit-1792077011","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1792077011","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1792077011","/_next/static/chunks/02eggfg7vwd9q.js?dpl=nogit-1792077011","/_next/static/chunks/1gm-hv-3-fp7_.js?dpl=nogit-1792077011","/_next/static/chunks/2xa0kylife8l8.js?dpl=nogit-1792077011","/_next/static/chunks/2lsi6eli88uwt.js?dpl=nogit-1792077011","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1792077011","/_next/static/chunks/0kyh6u8hfv06h.js?dpl=nogit-1792077011","/_next/static/chunks/1zirpvj720iz0.js?dpl=nogit-1792077011","/_next/static/chunks/0mt9yp27gb-6w.js?dpl=nogit-1792077011","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1792077011","/_next/static/chunks/0myxz4gywm9of.js?dpl=nogit-1792077011","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1792077011","/_next/static/chunks/1jo7uanvci4-r.js?dpl=nogit-1792077011","/_next/static/chunks/0papbjd-vx5q5.js?dpl=nogit-1792077011","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1792077011","/_next/static/chunks/11kq2otno6-oj.js?dpl=nogit-1792077011","/_next/static/chunks/23f2tb1apskc8.js?dpl=nogit-1792077011","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1792077011","/_next/static/chunks/3x5t_ry1ziv7r.js?dpl=nogit-1792077011","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1792077011","/_next/static/chunks/0iapw94rt37n4.js?dpl=nogit-1792077011","/_next/static/chunks/2rvalcou1gw7v.js?dpl=nogit-1792077011","/_next/static/chunks/05mo4k9k-ry1n.js?dpl=nogit-1792077011","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1792077011","/_next/static/chunks/04wg1hnm8knmc.js?dpl=nogit-1792077011","/_next/static/chunks/3_six85qevnm3.js?dpl=nogit-1792077011","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1792077011","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1792077011","/_next/static/chunks/1vovlfobo0rf7.js?dpl=nogit-1792077011","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1792077011","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1792077011","/_next/static/chunks/1jxfzuqocprar.js?dpl=nogit-1792077011","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1792077011","/_next/static/chunks/1h7qr4subpkxv.js?dpl=nogit-1792077011","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1792077011","/_next/static/chunks/0ltoscgl22itf.js?dpl=nogit-1792077011","/_next/static/chunks/0beaxlbowx15e.js?dpl=nogit-1792077011","/_next/static/chunks/376bkwrx00xp0.js?dpl=nogit-1792077011","/_next/static/chunks/26d_zs_7_ka17.js?dpl=nogit-1792077011","/_next/static/chunks/1w193fj-lcfgs.js?dpl=nogit-1792077011","/_next/static/chunks/2l63yczi1z2qz.js?dpl=nogit-1792077011","/_next/static/chunks/2yss1g0cimuwe.js?dpl=nogit-1792077011","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1792077011","/_next/static/chunks/1zo1304bjzjl_.js?dpl=nogit-1792077011","/_next/static/chunks/0wv8cpdr6cvhr.js?dpl=nogit-1792077011","/_next/static/chunks/1drwxxqzvnao9.js?dpl=nogit-1792077011","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1792077011","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1792077011","/_next/static/chunks/3f11o876enqgd.js?dpl=nogit-1792077011","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1792077011","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1792077011","/_next/static/chunks/33y-ad8441jub.js?dpl=nogit-1792077011","/_next/static/chunks/3qiv_uhu50h9w.js?dpl=nogit-1792077011","/_next/static/chunks/2mbz851h6l6ul.js?dpl=nogit-1792077011","/_next/static/chunks/1iyn56mfdoj9b.js?dpl=nogit-1792077011","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1792077011","/_next/static/chunks/3n19bhgn4l5zi.js?dpl=nogit-1792077011","/_next/static/chunks/1d4d88jx43_iw.js?dpl=nogit-1792077011","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1792077011"],"RecordResourceResume"] 37:I[830476,["/_next/static/chunks/2jz5imjnk1dsn.js?dpl=nogit-1792077011","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1792077011","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1792077011","/_next/static/chunks/02eggfg7vwd9q.js?dpl=nogit-1792077011","/_next/static/chunks/1gm-hv-3-fp7_.js?dpl=nogit-1792077011","/_next/static/chunks/2xa0kylife8l8.js?dpl=nogit-1792077011","/_next/static/chunks/2lsi6eli88uwt.js?dpl=nogit-1792077011","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1792077011","/_next/static/chunks/0kyh6u8hfv06h.js?dpl=nogit-1792077011","/_next/static/chunks/1zirpvj720iz0.js?dpl=nogit-1792077011","/_next/static/chunks/0mt9yp27gb-6w.js?dpl=nogit-1792077011","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1792077011","/_next/static/chunks/0myxz4gywm9of.js?dpl=nogit-1792077011","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1792077011","/_next/static/chunks/1jo7uanvci4-r.js?dpl=nogit-1792077011","/_next/static/chunks/0papbjd-vx5q5.js?dpl=nogit-1792077011","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1792077011","/_next/static/chunks/11kq2otno6-oj.js?dpl=nogit-1792077011","/_next/static/chunks/23f2tb1apskc8.js?dpl=nogit-1792077011","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1792077011","/_next/static/chunks/3x5t_ry1ziv7r.js?dpl=nogit-1792077011","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1792077011","/_next/static/chunks/0iapw94rt37n4.js?dpl=nogit-1792077011","/_next/static/chunks/2rvalcou1gw7v.js?dpl=nogit-1792077011","/_next/static/chunks/05mo4k9k-ry1n.js?dpl=nogit-1792077011","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1792077011","/_next/static/chunks/04wg1hnm8knmc.js?dpl=nogit-1792077011","/_next/static/chunks/3_six85qevnm3.js?dpl=nogit-1792077011","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1792077011","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1792077011","/_next/static/chunks/1vovlfobo0rf7.js?dpl=nogit-1792077011","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1792077011","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1792077011","/_next/static/chunks/1jxfzuqocprar.js?dpl=nogit-1792077011","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1792077011","/_next/static/chunks/1h7qr4subpkxv.js?dpl=nogit-1792077011","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1792077011","/_next/static/chunks/0ltoscgl22itf.js?dpl=nogit-1792077011","/_next/static/chunks/0beaxlbowx15e.js?dpl=nogit-1792077011","/_next/static/chunks/376bkwrx00xp0.js?dpl=nogit-1792077011","/_next/static/chunks/26d_zs_7_ka17.js?dpl=nogit-1792077011","/_next/static/chunks/1w193fj-lcfgs.js?dpl=nogit-1792077011","/_next/static/chunks/2l63yczi1z2qz.js?dpl=nogit-1792077011","/_next/static/chunks/2yss1g0cimuwe.js?dpl=nogit-1792077011","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1792077011","/_next/static/chunks/1zo1304bjzjl_.js?dpl=nogit-1792077011","/_next/static/chunks/0wv8cpdr6cvhr.js?dpl=nogit-1792077011","/_next/static/chunks/1drwxxqzvnao9.js?dpl=nogit-1792077011","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1792077011","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1792077011","/_next/static/chunks/3f11o876enqgd.js?dpl=nogit-1792077011","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1792077011","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1792077011","/_next/static/chunks/33y-ad8441jub.js?dpl=nogit-1792077011","/_next/static/chunks/3qiv_uhu50h9w.js?dpl=nogit-1792077011","/_next/static/chunks/2mbz851h6l6ul.js?dpl=nogit-1792077011","/_next/static/chunks/1iyn56mfdoj9b.js?dpl=nogit-1792077011","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1792077011","/_next/static/chunks/3n19bhgn4l5zi.js?dpl=nogit-1792077011","/_next/static/chunks/1d4d88jx43_iw.js?dpl=nogit-1792077011","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1792077011"],"FlashcardAccessBranch"] 38:I[315438,["/_next/static/chunks/2jz5imjnk1dsn.js?dpl=nogit-1792077011","/_next/static/chunks/2_6olli-sutu3.js?dpl=nogit-1792077011","/_next/static/chunks/0z347qy8pf1j3.js?dpl=nogit-1792077011","/_next/static/chunks/02eggfg7vwd9q.js?dpl=nogit-1792077011","/_next/static/chunks/1gm-hv-3-fp7_.js?dpl=nogit-1792077011","/_next/static/chunks/2xa0kylife8l8.js?dpl=nogit-1792077011","/_next/static/chunks/2lsi6eli88uwt.js?dpl=nogit-1792077011","/_next/static/chunks/0zkcxwtbsqliz.js?dpl=nogit-1792077011","/_next/static/chunks/0kyh6u8hfv06h.js?dpl=nogit-1792077011","/_next/static/chunks/1zirpvj720iz0.js?dpl=nogit-1792077011","/_next/static/chunks/0mt9yp27gb-6w.js?dpl=nogit-1792077011","/_next/static/chunks/38w1x0vrld4-w.js?dpl=nogit-1792077011","/_next/static/chunks/0myxz4gywm9of.js?dpl=nogit-1792077011","/_next/static/chunks/40lyu17d590zu.js?dpl=nogit-1792077011","/_next/static/chunks/1jo7uanvci4-r.js?dpl=nogit-1792077011","/_next/static/chunks/0papbjd-vx5q5.js?dpl=nogit-1792077011","/_next/static/chunks/3ml3vooxhiupb.js?dpl=nogit-1792077011","/_next/static/chunks/11kq2otno6-oj.js?dpl=nogit-1792077011","/_next/static/chunks/23f2tb1apskc8.js?dpl=nogit-1792077011","/_next/static/chunks/04zr-wqafvwoa.js?dpl=nogit-1792077011","/_next/static/chunks/3x5t_ry1ziv7r.js?dpl=nogit-1792077011","/_next/static/chunks/2mv9l1xl_aa4j.js?dpl=nogit-1792077011","/_next/static/chunks/0iapw94rt37n4.js?dpl=nogit-1792077011","/_next/static/chunks/2rvalcou1gw7v.js?dpl=nogit-1792077011","/_next/static/chunks/05mo4k9k-ry1n.js?dpl=nogit-1792077011","/_next/static/chunks/0v4byuex1x38h.js?dpl=nogit-1792077011","/_next/static/chunks/04wg1hnm8knmc.js?dpl=nogit-1792077011","/_next/static/chunks/3_six85qevnm3.js?dpl=nogit-1792077011","/_next/static/chunks/2dx-vzwyw9a3g.js?dpl=nogit-1792077011","/_next/static/chunks/1ku-vdy4ggo41.js?dpl=nogit-1792077011","/_next/static/chunks/1vovlfobo0rf7.js?dpl=nogit-1792077011","/_next/static/chunks/0llqhg6-bxn_b.js?dpl=nogit-1792077011","/_next/static/chunks/1coblm1-go81_.js?dpl=nogit-1792077011","/_next/static/chunks/1jxfzuqocprar.js?dpl=nogit-1792077011","/_next/static/chunks/0k-y_4mcfub-p.js?dpl=nogit-1792077011","/_next/static/chunks/1h7qr4subpkxv.js?dpl=nogit-1792077011","/_next/static/chunks/3it1o0ex-l5qz.js?dpl=nogit-1792077011","/_next/static/chunks/0ltoscgl22itf.js?dpl=nogit-1792077011","/_next/static/chunks/0beaxlbowx15e.js?dpl=nogit-1792077011","/_next/static/chunks/376bkwrx00xp0.js?dpl=nogit-1792077011","/_next/static/chunks/26d_zs_7_ka17.js?dpl=nogit-1792077011","/_next/static/chunks/1w193fj-lcfgs.js?dpl=nogit-1792077011","/_next/static/chunks/2l63yczi1z2qz.js?dpl=nogit-1792077011","/_next/static/chunks/2yss1g0cimuwe.js?dpl=nogit-1792077011","/_next/static/chunks/13gj59kzq50t_.js?dpl=nogit-1792077011","/_next/static/chunks/1zo1304bjzjl_.js?dpl=nogit-1792077011","/_next/static/chunks/0wv8cpdr6cvhr.js?dpl=nogit-1792077011","/_next/static/chunks/1drwxxqzvnao9.js?dpl=nogit-1792077011","/_next/static/chunks/36nndwkz7iik3.js?dpl=nogit-1792077011","/_next/static/chunks/1lsxkfxy262n-.js?dpl=nogit-1792077011","/_next/static/chunks/3f11o876enqgd.js?dpl=nogit-1792077011","/_next/static/chunks/3q5gc8lbwr4b4.js?dpl=nogit-1792077011","/_next/static/chunks/1ksyn9m68446d.js?dpl=nogit-1792077011","/_next/static/chunks/33y-ad8441jub.js?dpl=nogit-1792077011","/_next/static/chunks/3qiv_uhu50h9w.js?dpl=nogit-1792077011","/_next/static/chunks/2mbz851h6l6ul.js?dpl=nogit-1792077011","/_next/static/chunks/1iyn56mfdoj9b.js?dpl=nogit-1792077011","/_next/static/chunks/24srd-xd1m5z8.js?dpl=nogit-1792077011","/_next/static/chunks/3n19bhgn4l5zi.js?dpl=nogit-1792077011","/_next/static/chunks/1d4d88jx43_iw.js?dpl=nogit-1792077011","/_next/static/chunks/0zg1om_k0m5zv.js?dpl=nogit-1792077011"],"TopicFlashcardRunner"] 25:[["$","$L34",null,{"feature":"flashcards"}],"$L35",["$","$L36",null,{"href":"/a-level/maths/ocr/mei/numerical-methods-to-solve-problems/flashcards","label":"1.10.8 Numerical methods to solve problems (A-level only)","subjectCode":"a_level_maths__ocr_mei","surface":"flashcards"}],["$","$L37",null,{"runner":["$","div",null,{"className":"min-h-0 flex-1 overflow-hidden bg-background","children":["$","$L38",null,{"decks":[{"id":"6a079b54-7ac9-48eb-8cec-6e677eff3b7c","title":"1.10.8 Numerical methods to solve problems (A-level only) Flashcards","topicId":"9e718bca-686b-4d64-990b-9365f173c1fe","topicSlug":"numerical-methods-to-solve-problems","cards":[{"id":"33ae3a8c-5845-4ac1-8240-7ce34fb99ff1","cardType":"basic","points":1,"front":"How should a contextual condition be prepared for root-finding?","back":"Rearrange it into the form $f(x)=0$.","mcqOptions":null},{"id":"7bf99a8e-db9a-4938-bfb2-37891da507a7","cardType":"basic","points":1,"front":"What equation must a root $x=\\alpha$ satisfy?","back":"$f(\\alpha)=0$.","mcqOptions":null},{"id":"62bc40a3-b0d2-4d92-9b66-1294f28e3588","cardType":"cloze","points":null,"front":"A numerical method produces an [ ] using repeated calculations.","back":"A numerical method produces an approximate solution using repeated calculations.","mcqOptions":null},{"id":"c006f456-10d7-45c2-b355-0b8054a6c532","cardType":"cloze","points":null,"front":"For continuous $f$ on $[a,b]$, opposite endpoint signs give $\\text{[...]}$.","back":"For continuous $f$ on $[a,b]$, opposite endpoint signs give $\\boxed{f(a)f(b)<0}$.","mcqOptions":null},{"id":"9c6232c5-7093-4ece-98b6-c2ac8f0b3b22","cardType":"basic","points":2,"front":"Why is continuity required when using a sign change to locate a root?","back":"It ensures the graph cannot jump across the axis.","mcqOptions":null},{"id":"2ae74eaf-db9b-4cf3-95cc-a0a28a044988","cardType":"basic","points":1,"front":"What does $f(a)f(b)<0$ prove when $f$ is continuous on $[a,b]$?","back":"There is at least one root in $(a,b)$.","mcqOptions":null},{"id":"2c1fd7fe-dce5-4f5d-9d22-6a8081211c3e","cardType":"basic","points":1,"front":"What extra property can establish that a bracketed root is unique?","back":"$$f$ is strictly increasing or strictly decreasing.","mcqOptions":null},{"id":"9364dcd4-b2d7-45e0-b8c5-ac2c439b29c5","cardType":"basic","points":2,"front":"Why can a sign-change test miss a repeated root?","back":"The graph may touch the axis and turn without changing sign.","mcqOptions":null},{"id":"59caba90-f825-4451-8915-8d8b98adc134","cardType":"cloze","points":null,"front":"In bisection, the midpoint of $[a,b]$ is $\\text{[...]}$.","back":"In bisection, the midpoint of $[a,b]$ is $\\boxed{m=\\frac{a+b}{2}}$.","mcqOptions":null},{"id":"79fd4746-0e20-4759-8547-805da23716da","cardType":"basic","points":1,"front":"After evaluating the midpoint in bisection, which half-interval is retained?","back":"The half containing the sign change.","mcqOptions":null},{"id":"2cd7329e-a18a-4f3f-8963-78bbf954992a","cardType":"basic","points":1,"front":"Which boundaries test whether a positive root rounds to $r$ to 2 decimal places?","back":"$r-0.005$ and $r+0.005$.","mcqOptions":null},{"id":"99a3dfbd-3612-4ae0-8711-3310d7577988","cardType":"basic","points":2,"front":"How does a narrow bracket justify a rounded answer?","back":"Every value in the bracket rounds to the stated answer.","mcqOptions":null},{"id":"b34746e3-c787-4888-8f84-737f6fbb1ef5","cardType":"cloze","points":null,"front":"Fixed-point iteration uses $\\text{[...]}$ from an initial estimate $x_0$.","back":"Fixed-point iteration uses $\\boxed{x_{n+1}=g(x_n)}$ from an initial estimate $x_0$.","mcqOptions":null},{"id":"9a144218-28f5-4a32-a653-7fe31304eb2f","cardType":"basic","points":1,"front":"If fixed-point iteration converges to $\\alpha$, what equation must $\\alpha$ satisfy?","back":"$\\alpha=g(\\alpha)$.","mcqOptions":null},{"id":"9e106a80-a300-43dc-8cd8-1663fdb7e45f","cardType":"cloze","points":null,"front":"Convergence near a fixed point $\\alpha$ is likely when $\\text{[...]}$.","back":"Convergence near a fixed point $\\alpha$ is likely when $\\boxed{\\left|g'(\\alpha)\\right|<1}$.","mcqOptions":null},{"id":"75cb6d1b-eef6-450d-ad47-4731507d94cd","cardType":"basic","points":2,"front":"Why can two rearrangements of the same equation behave differently under fixed-point iteration?","back":"Their functions $g$ can have different convergence behaviour.","mcqOptions":null},{"id":"2076ca01-342e-4e1f-95aa-70f87e5031ab","cardType":"cloze","points":null,"front":"Newton-Raphson iteration uses $\\text{[...]}$.","back":"Newton-Raphson iteration uses $\\boxed{x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}}$.","mcqOptions":null},{"id":"5a2a0218-5e11-4410-86f0-b4ed39a73285","cardType":"basic","points":2,"front":"Why does Newton-Raphson fail when $f'(x_n)=0$?","back":"The iteration requires division by zero.","mcqOptions":null},{"id":"1f08fb89-e4ca-4cf1-bd16-2155810659bc","cardType":"basic","points":2,"front":"Why do identical displayed iterates not prove a root's stated accuracy?","back":"Calculator rounding can hide differences beyond the displayed digits.","mcqOptions":null},{"id":"c4174967-daf2-4606-9c1d-5aa6658bd583","cardType":"basic","points":2,"front":"A model gives a minimum requirement of 7.2 buses. What should be reported?","back":"8 buses, since rounding down fails the requirement.","mcqOptions":null},{"id":"46fdf0b7-acda-4a26-9fd3-68cdfadddb30","cardType":"basic","points":2,"front":"Why should extra figures be retained during a numerical method?","back":"To avoid premature rounding error in the final result.","mcqOptions":null},{"id":"c729d276-c7b8-4cc1-a3e6-9b9a5756a32c","cardType":"basic","points":3,"front":"What must be attached to a numerical root when reporting it in context?","back":"Its meaning, units and valid-domain check.","mcqOptions":null}]}],"examCountdown":{"examDate":"2027-05-26","paperLabel":"Paper 1"},"heading":"1.10.8 Numerical methods to solve problems (A-level only)","title":"1.10.8 Numerical methods to solve problems (A-level only) Flashcards","topbar":{"backHref":"/a-level/maths/ocr/mei/flashcards"},"topicSidebar":"$L39"}]}],"topicId":"9e718bca-686b-4d64-990b-9365f173c1fe","walled":"$L3a"}],"$L3b","$L3c"]