1:I[411855,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"HTTPAccessFallbackBoundary"] 2:I[173709,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"NuqsAdapter"] 3:I[56913,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js"],"MantineThemeProvider"] 4:I[56913,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js"],"CSPostHogProvider"] 5:I[857342,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"ModalsProvider"] 6:I[647384,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"modals"] 7:I[56913,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js"],"GeneralUtils"] 8:I[187233,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"Notifications"] 17:I[253348,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/0etetzolq26a6.js","/_next/static/immutable/chunks/1y0yg88od_lid.js"],"default"] :HL["/_next/static/immutable/chunks/3qcgait30h-sj.css","style"] :HL["/_next/static/immutable/chunks/1kcvv4guurxwh.css","style"] :HL["/_next/static/immutable/chunks/2ojxyc8kui2ci.css","style"] :HL["/_next/static/immutable/chunks/16ecsvtuc9a9i.css","style"] :HL["/_next/static/immutable/chunks/3o9c7gvideo11.css","style"] :HL["/_next/static/immutable/chunks/1ezpev3s3dmvh.css","style"] :HL["/_next/static/immutable/chunks/32h2yv50mt___.css","style"] :HL["/_next/static/immutable/chunks/0xlmktq4kl70g.css","style"] :HL["/_next/static/immutable/chunks/33yvqtdwhy513.css","style"] :HL["/_next/static/immutable/media/03bda585a99c6450.p.0glcd8n2pdab0.woff2","font",{"crossOrigin":"","type":"font/woff2"}] :HL["/_next/static/immutable/media/dc6d2a64e9dbf3bc-s.p.3yrvj83qsyboh.woff2","font",{"crossOrigin":"","type":"font/woff2"}] :HL["/_next/static/immutable/media/dc6d2a64e9dbf3bc.p.3yrvj83qsyboh.woff2","font",{"crossOrigin":"","type":"font/woff2"}] :HL["/_next/static/immutable/media/e8f2fbee2754df70-s.p.1gavkj72q9u43.woff2","font",{"crossOrigin":"","type":"font/woff2"}] :HL["/_next/static/immutable/chunks/36vc5xdsnnv-k.css","style"] :HL["/_next/static/immutable/chunks/2ys4rianfzaw1.css","style"] 12:X 0:{"P":null,"c":["","course","AASL","learn"],"q":"","i":false,"f":[[["",{"children":["(course)",{"children":["course",{"children":[["subject","AASL","d",["studio"]],{"children":["(banks)",{"children":["learn",{"children":["__PAGE__",{},"$undefined","$undefined",4096]},"$undefined","$undefined",4096]},"$undefined","$undefined",4096]},"$undefined","$undefined",4096]},"$undefined","$undefined",4096]},"$undefined","$undefined",4096],"auth":["(__SLOT__)",{"children":[["catchAll","course/AASL/learn","c",["(.)login","(.)signup","about","admin","api","blog","bouncer","calc-keys-preview","calculator","calculator-booklet","checkout","contact","course","demo-login","diagrams","email-link","flow","forgot-password","join","kamino","live","login","master","modules","onboard","pdf","pilot","privacy","privacy-settings","problems","qr","reddit","screenshot","signup","snippets","start","subprocessors","teach","team","terms","upgrade","upload","worksheets"]],{"children":["__PAGE__",{},"$undefined","$undefined",4096]},"$undefined","$undefined",4096]},"$undefined","$undefined",4096]},"$undefined","$undefined",4112],[["$","$L1","c",{"notFound":[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/3qcgait30h-sj.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","1",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/1kcvv4guurxwh.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","2",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ojxyc8kui2ci.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","3",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/16ecsvtuc9a9i.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","4",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/3o9c7gvideo11.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","5",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/1ezpev3s3dmvh.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","script","script-0",{"src":"/_next/static/immutable/chunks/18z7hbezgakd8.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/3s1f7foqpdvup.js","async":true,"nonce":"$undefined"}],["$","script","script-2",{"src":"/_next/static/immutable/chunks/2mkazo296h-fw.js","async":true,"nonce":"$undefined"}],["$","script","script-3",{"src":"/_next/static/immutable/chunks/3kinzrgjz1nll.js","async":true,"nonce":"$undefined"}],["$","script","script-4",{"src":"/_next/static/immutable/chunks/266ti09r7o-li.js","async":true,"nonce":"$undefined"}],["$","script","script-5",{"src":"/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","async":true,"nonce":"$undefined"}],["$","script","script-6",{"src":"/_next/static/immutable/chunks/3av6zvu370icl.js","async":true,"nonce":"$undefined"}],["$","script","script-7",{"src":"/_next/static/immutable/chunks/3et9qdvbyi-6u.js","async":true,"nonce":"$undefined"}],["$","script","script-8",{"src":"/_next/static/immutable/chunks/1b62qxcrax48_.js","async":true,"nonce":"$undefined"}],["$","script","script-9",{"src":"/_next/static/immutable/chunks/1qgctqfwjj94j.js","async":true,"nonce":"$undefined"}],["$","script","script-10",{"src":"/_next/static/immutable/chunks/36omjr-s6xpax.js","async":true,"nonce":"$undefined"}],["$","script","script-11",{"src":"/_next/static/immutable/chunks/39ps9az44hvg-.js","async":true,"nonce":"$undefined"}],["$","script","script-12",{"src":"/_next/static/immutable/chunks/1dr-zgur0-w1_.js","async":true,"nonce":"$undefined"}],["$","script","script-13",{"src":"/_next/static/immutable/chunks/0knlg885uauhx.js","async":true,"nonce":"$undefined"}],["$","script","script-14",{"src":"/_next/static/immutable/chunks/1u8v__oamgp49.js","async":true,"nonce":"$undefined"}],["$","script","script-15",{"src":"/_next/static/immutable/chunks/1o6d8gkxacyr3.js","async":true,"nonce":"$undefined"}],["$","script","script-16",{"src":"/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","async":true,"nonce":"$undefined"}],["$","script","script-17",{"src":"/_next/static/immutable/chunks/3it7cbupuus2e.js","async":true,"nonce":"$undefined"}],["$","script","script-18",{"src":"/_next/static/immutable/chunks/2bo-0yc5izpx4.js","async":true,"nonce":"$undefined"}],["$","script","script-19",{"src":"/_next/static/immutable/chunks/27vysu0t21548.js","async":true,"nonce":"$undefined"}],["$","script","script-20",{"src":"/_next/static/immutable/chunks/17kj450zyrjx4.js","async":true,"nonce":"$undefined"}]],["$","html",null,{"lang":"en","suppressHydrationWarning":true,"data-mantine-color-scheme":"light","children":["$","$L2",null,{"children":["$","body",null,{"suppressHydrationWarning":true,"children":["$","$L3",null,{"children":[["$","$L4",null,{"children":["$","$L5",null,{"modals":"$6","children":[["$","$L7",null,{}],["$","$L8",null,{}],"$undefined",[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ys4rianfzaw1.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}]],"$L9"]]}]}],"$La"]}]}]}]}]],"children":["$0:f:0:1:0:props:notFound:0","$Lb"]}],{"children":["$Lc",{"children":["$Ld",{"children":["$Le",{"children":["$Lf",{"children":["$L10",{"children":["$L11",{},null,false,null]},null,false,"$12"]},null,false,null]},null,false,null]},null,false,null]},null,false,null],"auth":["$L13",{"children":["$L14",{"children":["$L15",{},null,false,null]},null,false,"$12"]},null,false,"$12"]},null,false,null],"$L16",false]],"m":"$undefined","G":["$17",["$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e"]],"S":false,"h":null,"r":"$undefined","s":"$undefined","a":"$undefined","l":"$undefined","p":"$undefined","d":"$undefined"} 1f:I[522350,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/357-ajrm069n8.js"],"Image"] 20:I[275371,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/357-ajrm069n8.js"],""] 21:I[579142,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"Analytics"] 22:I[765452,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"default"] 23:I[719959,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"default"] 24:"$Sreact.fragment" 26:I[571959,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"ClientSegmentRoot"] 27:I[302303,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js"],"default"] 28:I[574041,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/1z7j2ml9psnk1.js","/_next/static/immutable/chunks/1y0yg88od_lid.js"],"default"] 2c:I[849375,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"OutletBoundary"] 2d:"$Sreact.suspense" 2f:I[146586,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/3859vhi-lf5p1.js","/_next/static/immutable/chunks/1y0yg88od_lid.js"],"default"] 30:I[849375,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"ViewportBoundary"] 32:I[849375,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"MetadataBoundary"] 9:[["$","main",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__root","children":["$","section",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__card","children":["$","div",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__content","children":[["$","$L1f",null,{"src":"/dawnbridge-wordmark.svg","alt":"Dawnbridge","width":188,"height":46,"priority":true,"className":"DawnbridgeUtilityShell-module__JpDsgG__wordmark"}],["$","header",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__header","children":[["$","p",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__eyebrow","children":"404"}],["$","h1",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__title","children":"This page moved"}],["$","p",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__description","children":"The link may be old, or the page may no longer be available."}]]}],"$undefined",["$","div",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__actions","children":[["$","$L20",null,{"href":"/course","className":"DawnbridgeUtilityShell-module__JpDsgG__primaryAction","children":"Go to your course"}],["$","$L20",null,{"href":"/","className":"DawnbridgeUtilityShell-module__JpDsgG__secondaryAction","children":"Back to home"}]]}]]}]}]}],"$0:f:0:1:0:props:notFound:1:props:children:props:children:props:children:props:children:0:props:children:props:children:3:0"] a:["$","$L21",null,{}] b:["$","html",null,{"lang":"en","suppressHydrationWarning":true,"data-mantine-color-scheme":"light","children":["$","$L2",null,{"children":["$","body",null,{"suppressHydrationWarning":true,"children":["$","$L3",null,{"children":[["$","$L4",null,{"children":["$","$L5",null,{"modals":"$6","children":[["$","$L7",null,{}],["$","$L8",null,{}],["$","$L22",null,{"parallelRouterKey":"auth","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}],["$","$L22",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$9","forbidden":"$undefined","unauthorized":"$undefined"}]]}]}],["$","$L21",null,{}]]}]}]}]}] c:["$","$24","c",{"children":[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/32h2yv50mt___.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","1",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/0xlmktq4kl70g.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","link","2",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/33yvqtdwhy513.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","script","script-0",{"src":"/_next/static/immutable/chunks/2vyef9ikm5oed.js","async":true,"nonce":"$undefined"}]],"$L25"]}] d:["$","$24","c",{"children":[[["$","script","script-0",{"src":"/_next/static/immutable/chunks/1016kmk_0_xoh.js","async":true,"nonce":"$undefined"}]],["$","$L26",null,{"Component":"$27","slots":{"children":["$","$L22",null,{"parallelRouterKey":"children","error":"$28","errorStyles":[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ys4rianfzaw1.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}]],"errorScripts":[["$","script","script-0",{"src":"/_next/static/immutable/chunks/1z7j2ml9psnk1.js","async":true}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/1y0yg88od_lid.js","async":true}]],"template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]},"serverProvidedParams":{"params":{},"promises":null}}]]}] e:["$","$24","c",{"children":[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/36vc5xdsnnv-k.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}],["$","script","script-0",{"src":"/_next/static/immutable/chunks/18-so5b68b4zs.js","async":true,"nonce":"$undefined"}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/2r657mtk43wxk.js","async":true,"nonce":"$undefined"}],["$","script","script-2",{"src":"/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","async":true,"nonce":"$undefined"}],["$","script","script-3",{"src":"/_next/static/immutable/chunks/3sak_jksml9vb.js","async":true,"nonce":"$undefined"}],["$","script","script-4",{"src":"/_next/static/immutable/chunks/43qmiwrh0zjbg.js","async":true,"nonce":"$undefined"}],["$","script","script-5",{"src":"/_next/static/immutable/chunks/3s5tdxs448l-j.js","async":true,"nonce":"$undefined"}],["$","script","script-6",{"src":"/_next/static/immutable/chunks/0w_ec4pysgbll.js","async":true,"nonce":"$undefined"}],["$","script","script-7",{"src":"/_next/static/immutable/chunks/40chzmfllpiuo.js","async":true,"nonce":"$undefined"}],["$","script","script-8",{"src":"/_next/static/immutable/chunks/1p35tho0xv6f4.js","async":true,"nonce":"$undefined"}],["$","script","script-9",{"src":"/_next/static/immutable/chunks/1oqo8q_chzpnd.js","async":true,"nonce":"$undefined"}],["$","script","script-10",{"src":"/_next/static/immutable/chunks/32je84c6xizbv.js","async":true,"nonce":"$undefined"}],["$","script","script-11",{"src":"/_next/static/immutable/chunks/3n9qnonh_f3cr.js","async":true,"nonce":"$undefined"}]],"$L29"]}] f:["$","$24","c",{"children":[null,"$L2a"]}] 10:["$","$24","c",{"children":[null,["$","$L22",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 11:["$","$24","c",{"children":["$L2b",[["$","script","script-0",{"src":"/_next/static/immutable/chunks/3xzmqebvf8-bn.js","async":true,"nonce":"$undefined"}]],["$","$L2c",null,{"children":["$","$2d",null,{"name":"Next.MetadataOutlet","children":"$@2e"}]}]]}] 13:["$","$24","c",{"children":[null,["$","$L22",null,{"parallelRouterKey":"children","error":"$2f","errorStyles":[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ys4rianfzaw1.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}]],"errorScripts":[["$","script","script-0",{"src":"/_next/static/immutable/chunks/3859vhi-lf5p1.js","async":true}],["$","script","script-1",{"src":"/_next/static/immutable/chunks/1y0yg88od_lid.js","async":true}]],"template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 14:["$","$24","c",{"children":[null,["$","$L22",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]]}] 15:["$","$24","c",{"children":[null,null,null]}] 16:["$","$24","h",{"children":[null,["$","$L30",null,{"children":"$L31"}],["$","div",null,{"hidden":true,"children":["$","$L32",null,{"children":["$","$2d",null,{"name":"Next.Metadata","children":"$L33"}]}]}],["$","meta",null,{"name":"next-size-adjust","content":""}]]}] 18:["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/3qcgait30h-sj.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 19:["$","link","1",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/1kcvv4guurxwh.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 1a:["$","link","2",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ojxyc8kui2ci.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 1b:["$","link","3",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/16ecsvtuc9a9i.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 1c:["$","link","4",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/3o9c7gvideo11.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 1d:["$","link","5",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/1ezpev3s3dmvh.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 1e:["$","link","6",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ys4rianfzaw1.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}] 34:I[115668,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js"],"Box"] 12:C 2a:["$","$L34",null,{"className":"max-w-screen","children":["$","$L22",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}]}] 35:I[52998,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js"],"AuthProvider"] 36:I[430359,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js"],"SolveStoreProvider"] 37:I[611346,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js"],"FormulaBookletProvider"] 39:I[622472,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js"],"ReferralAnnouncementModal"] 25:["$","$L35",null,{"user":null,"myData":null,"course":null,"idToken":null,"consentRequired":false,"analyticsContext":{"account_segment":"signed_out","user_role":"signed_out","analytics_schema_version":1},"children":[["$","$L36",null,{"initState":{"energy":0},"children":["$","$L37",null,{"initialPinnedFormulas":[],"children":["$","$L22",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":[["$","main",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__root","children":["$","section",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__card","children":["$","div",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__content","children":[["$","$L1f",null,{"src":"/dawnbridge-wordmark.svg","alt":"Dawnbridge","width":188,"height":46,"priority":true,"className":"DawnbridgeUtilityShell-module__JpDsgG__wordmark"}],["$","header",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__header","children":[["$","p",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__eyebrow","children":"404"}],["$","h1",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__title","children":"This page moved"}],["$","p",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__description","children":"The link may be old, or the page may no longer be available."}]]}],"$undefined",["$","div",null,{"className":"DawnbridgeUtilityShell-module__JpDsgG__actions","children":[["$","$L20",null,{"href":"/course","className":"DawnbridgeUtilityShell-module__JpDsgG__primaryAction","children":"Go to your course"}],["$","$L20",null,{"href":"/","className":"DawnbridgeUtilityShell-module__JpDsgG__secondaryAction","children":"Back to home"}]]}]]}]}]}],[["$","link","0",{"rel":"stylesheet","href":"/_next/static/immutable/chunks/2ys4rianfzaw1.css","precedence":"next","crossOrigin":"$undefined","nonce":"$undefined"}]]],"forbidden":"$undefined","unauthorized":"$undefined"}]}]}],"$L38",["$","$L39",null,{}]]}] 38:null 31:[["$","meta","0",{"charSet":"utf-8"}],["$","meta","1",{"name":"viewport","content":"width=device-width, initial-scale=1"}]] 3a:I[905754,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js"],"IconMark"] 2e:null 33:[["$","title","0",{"children":"Lessons | IB Math AASL | Dawnbridge"}],["$","meta","1",{"name":"description","content":"Step-by-step lessons for every concept in your course."}],["$","link","2",{"rel":"manifest","href":"/manifest.webmanifest","crossOrigin":"$undefined"}],["$","meta","3",{"property":"og:title","content":"Dawnbridge | Interactive IB Math Practice"}],["$","meta","4",{"property":"og:description","content":"Dawnbridge is the next generation of resources for IB Math. Easily ace your exams with the help of our interactive problems and resources."}],["$","meta","5",{"property":"og:url","content":"https://www.dawnbridge.education"}],["$","meta","6",{"property":"og:site_name","content":"Dawnbridge"}],["$","meta","7",{"property":"og:type","content":"website"}],["$","meta","8",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","9",{"name":"twitter:title","content":"Dawnbridge | Interactive IB Math Practice"}],["$","meta","10",{"name":"twitter:description","content":"Dawnbridge is the next generation of resources for IB Math. Easily ace your exams with the help of our interactive problems and resources."}],["$","link","11",{"rel":"icon","href":"/favicon.ico?favicon.1io2l46hsrw7z.ico","sizes":"32x32","type":"image/x-icon"}],["$","link","12",{"rel":"icon","href":"/favicon.ico","sizes":"32x32","type":"image/x-icon"}],["$","link","13",{"rel":"icon","href":"/icon.svg","sizes":"any","type":"image/svg+xml"}],["$","link","14",{"rel":"icon","href":"/icon-96.png","sizes":"96x96","type":"image/png"}],["$","link","15",{"rel":"apple-touch-icon","href":"/apple-icon.png","sizes":"96x96","type":"image/png"}],["$","$L3a","16",{}]] 3b:I[56913,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js"],"DesmosProvider"] 3c:I[962899,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js"],"default"] 3d:Td80,{"version":11,"randomSeed":"f1189518f4cf6a6dabef5f52d51559a4","graph":{"viewport":{"xmin":-0.8183456824969637,"ymin":-0.019352588053772823,"xmax":1.7275820927338188,"ymax":1.0157776236938085},"showGrid":false,"showXAxis":false,"showYAxis":false,"degreeMode":true,"product":"geometry-calculator","__v12ViewportLatexStash":{"xmin":"-0.8183456824969637","xmax":"1.7275820927338188","ymin":"-0.019352588053772823","ymax":"1.0157776236938085"}},"expressions":{"list":[{"type":"folder","id":"**dcg_geo_folder**","title":"geometry","secret":true},{"type":"expression","id":"1","color":"#C72106","latex":"L=1"},{"type":"expression","id":"2","color":"#C72106","latex":"f_{square}\\left(X_{bl},l\\right)=\\operatorname{polygon}\\left(X_{bl},X_{bl}+\\left(l,0\\right),X_{bl}+\\left(l,l\\right),X_{bl}+\\left(0,l\\right)\\right)"},{"type":"expression","id":"32","color":"#7950F2","latex":"w\\left(n\\right)=L\\cdot\\left(\\frac{1}{2}\\right)^{\\operatorname{floor}\\left(\\frac{n}{2}\\right)}","hidden":true},{"type":"expression","id":"36","color":"#C72106","latex":"h\\left(n\\right)=L\\cdot\\left(\\frac{1}{2}\\right)^{\\operatorname{floor}\\left(\\frac{n+1}{2}\\right)}","hidden":true},{"type":"expression","id":"28","color":"#C72106","latex":"P\\left(1\\right)=\\left(0,0\\right)"},{"type":"expression","id":"39","color":"#7950F2","latex":"P\\left(n\\right)=P\\left(n-1\\right)+4^{-\\operatorname{floor}\\left(\\frac{n-2}{4}\\right)}\\left\\{\\operatorname{mod}\\left(n,4\\right)=2:\\left(0,0.5\\right),\\operatorname{mod}\\left(n,4\\right)=3:\\left(0.5,0.25\\right),\\operatorname{mod}\\left(n,4\\right)=0:\\left(0.25,-0.25\\right),\\operatorname{mod}\\left(n,4\\right)=1:\\left(-0.25,-0\\right)\\right\\}"},{"type":"expression","id":"52","color":"#7950F2","latex":"N=\\left[1...10\\right]"},{"type":"expression","id":"54","color":"#7950F2","latex":"o\\left(n\\right)=0.5s\\left(n,10\\right)","hidden":true},{"type":"expression","id":"60","color":"#7950F2","latex":"o\\left(1\\right)"},{"type":"expression","id":"57","color":"#7950F2","latex":"s\\left(t_{m},v\\right)=\\frac{1}{1+e^{-\\left(t-t_{m}\\right)v}}"},{"type":"expression","id":"53","color":"#7950F2","latex":"t=1.008","slider":{"hardMin":true,"hardMax":true,"animationPeriod":20000,"loopMode":"LOOP_FORWARD","isPlaying":true,"min":"0","max":"13"}},{"type":"expression","id":"50","color":"#7950F2","latex":"\\left[f_{rect}\\left(P\\left(k\\right),w\\left(k\\right),h\\left(k\\right)\\right)\\operatorname{for}k=N\\right]","fillOpacity":"o\\left(N\\right)","lineOpacity":"2o\\left(N\\right)"},{"type":"expression","id":"61","color":"#FFFFFF","latex":"\\left[P\\left(k\\right)+0.5\\left(w\\left(k\\right),h\\left(k\\right)\\right)\\operatorname{for}k=N\\right]","showLabel":true,"label":"${N}","hidden":true,"labelSize":"\\frac{2.3}{\\sqrt{N}}","suppressTextOutline":true,"pointOpacity":"2o\\left(N\\right)"},{"type":"expression","id":"12","color":"#7950F2","latex":"f_{rect}\\left(X_{bl},w,h\\right)=\\operatorname{polygon}\\left(X_{bl},X_{bl}+\\left(w,0\\right),X_{bl}+\\left(w,h\\right),X_{bl}+\\left(0,h\\right)\\right)"},{"type":"expression","id":"10","color":"#7950F2","latex":"\\operatorname{polygon}\\left(\\left(0,0\\right),\\left(0,1\\right),\\left(1,1\\right),\\left(1,0\\right)\\right)","fill":false,"lineStyle":"DASHED"},{"type":"expression","id":"74","color":"#C72106"}]},"geometryToolbar":{"toolbar":"none"},"includeFunctionParametersInRandomSeed":true,"doNotMigrateMovablePointStyle":true}3e:T1eaa,{"version":11,"randomSeed":"f1189518f4cf6a6dabef5f52d51559a4","graph":{"viewport":{"xmin":-1.220033498802791,"ymin":-1.4301720834491765,"xmax":9.68785295394013,"ymax":1.3295342003916761},"showGrid":false,"xAxisNumbers":false,"yAxisNumbers":false,"polarNumbers":false,"product":"geometry-calculator"},"expressions":{"list":[{"type":"folder","id":"**dcg_geo_folder**","title":"geometry","secret":true},{"type":"expression","id":"2","color":"#106BC7","latex":"x^{2}+y^{2}=1"},{"type":"expression","id":"21","color":"#106BC7","latex":"d=0.1"},{"type":"expression","id":"3","color":"#106BC7","latex":"\\alpha=2.987","slider":{"hardMin":true,"hardMax":true,"animationPeriod":11428.57142857143,"loopMode":"LOOP_FORWARD","isPlaying":true,"min":"0","max":"4\\pi"}},{"type":"expression","id":"20","color":"#106BC7","latex":"R=\\alpha\\to0,s\\to\\left[\\right],c\\to\\left[\\right]"},{"type":"expression","id":"18","color":"#106BC7","latex":"s=\\left[0,0.09983341664682815,0.19866933079506122,0.29552020666133955,0.3894183423086505,0.479425538604203,0.5646424733950354,0.644217687237691,0.7173560908995228,0.7833269096274834,0.8414709848078965,0.8912073600614354,0.9320390859672263,0.963558185417193,0.9854497299884601,0.9974949866040544,0.9995736030415051,0.9916648104524686,0.9738476308781951,0.9463000876874145,0.9092974268256817,0.8632093666488737,0.8084964038195901,0.7457052121767203,0.675463180551151,0.5984721441039565,0.5155013718214642,0.4273798802338298,0.3349881501559051,0.23924932921398243,0.1411200080598672,0.04158066243329049,-0.058374143427580086,-0.1577456941432482,-0.2555411020268312,-0.35078322768961984,-0.44252044329485246,-0.5298361409084934,-0.6118578909427189,-0.6877661591839738,-0.7568024953079282,-0.8182771110644103,-0.8715757724135882,-0.9161659367494549,-0.951602073889516,-0.977530117665097,-0.9936910036334644,-0.9999232575641008,-0.9961646088358407,-0.9824526126243325,-0.9589242746631385,-0.9258146823277325,-0.8834546557201531,-0.8322674422239013,-0.7727644875559871,-0.7055403255703919,-0.6312666378723216,-0.5506855425976376,-0.46460217941375737,-0.373876664830236,-0.27941549819892586,-0.18216250427209588,-0.0830894028174964,0.016813900484349713,0.11654920485049364,0.21511998808781552,0.31154136351337786,0.4048499206165983,0.49411335113860816,0.5784397643882001,0.6569865987187891,0.7289690401258759,0.7936678638491531,0.8504366206285644,0.8987080958116269,0.9379999767747389,0.9679196720314863,0.9881682338770004,0.998543345374605,0.998941341839772,0.9893582466233818,0.9698898108450863,0.9407305566797731,0.9021718337562933,0.8545989080882804,0.7984871126234903,0.7343970978741133,0.6629692300821833,0.5849171928917617,0.5010208564578846,0.4121184852417566,0.3190983623493521,0.22288991410024764,0.1244544235070617,0.024775425453357765,-0.0751511204618093,-0.17432678122297965,-0.27176062641094245,-0.3664791292519284,-0.45753589377532133,-0.5440211108893698,-0.6250706488928821,-0.6998746875935423,-0.7676858097635825,-0.8278264690856537,-0.87969575997167,-0.9227754216128066,-0.9566350162701879,-0.9809362300664916,-0.9954362533063774,-0.9999902065507035,-0.9945525882039892,-0.9791777291513174,-0.954019249902089,-0.9193285256646757,-0.8754521746884285,-0.8228285949687089,-0.7619835839190333,-0.6935250847771224,-0.6181371122370333,-0.5365729180004349,-0.44964746453460147,-0.3582292822368287,-0.26323179136580094,-0.1656041754483094,-0.06632189735120068,0.033623047221136695,0.13323204141994222,0.23150982510153895,0.32747443913769303,0.4201670368266409,0.5086614643723737\\right]"},{"type":"expression","id":"19","color":"#106BC7","latex":"c=\\left[1,0.9950041652780258,0.9800665778412416,0.955336489125606,0.9210609940028851,0.8775825618903728,0.8253356149096783,0.7648421872844885,0.6967067093471654,0.6216099682706644,0.5403023058681398,0.4535961214255773,0.3623577544766736,0.26749882862458735,0.16996714290024104,0.0707372016677029,-0.029199522301288815,-0.12884449429552464,-0.2272020946930871,-0.32328956686350335,-0.4161468365471424,-0.5048461045998576,-0.5885011172553458,-0.6662760212798241,-0.7373937155412454,-0.8011436155469337,-0.8568887533689473,-0.9040721420170612,-0.9422223406686581,-0.9709581651495905,-0.9899924966004454,-0.9991351502732795,-0.9982947757947531,-0.9874797699088649,-0.9667981925794611,-0.9364566872907963,-0.896758416334147,-0.848100031710408,-0.7909677119144168,-0.7259323042001402,-0.6536436208636119,-0.5748239465332692,-0.4902608213406994,-0.40079917207997545,-0.30733286997841935,-0.2107957994307797,-0.11215252693505487,-0.01238866346289056,0.0874989834394464,0.18651236942257576,0.28366218546322625,0.37797774271298024,0.4685166713003771,0.5543743361791608,0.6346928759426347,0.70866977429126,0.7755658785102496,0.8347127848391598,0.8855195169413189,0.9274784307440359,0.960170286650366,0.9832684384425845,0.9965420970232175,0.9998586363834151,0.9931849187581926,0.9765876257280235,0.9502325919585296,0.9143831482353194,0.8693974903498253,0.8157251001253568,0.7539022543433046,0.6845466664428066,0.6083513145322546,0.5260775173811053,0.43854732757439036,0.3466353178350258,0.2512598425822557,0.15337386203786435,0.05395542056264975,-0.04600212563953695,-0.14550003380861354,-0.2435441537357911,-0.3391548609838345,-0.4313768449706208,-0.5192886541166856,-0.6020119026848236,-0.6787200473200125,-0.7486466455973987,-0.811093014061656,-0.8654352092411123,-0.9111302618846769,-0.9477216021311119,-0.9748436214041636,-0.9922253254526034,-0.9996930420352065,-0.9971721561963784,-0.984687855794127,-0.9623648798313102,-0.9304262721047533,-0.8891911526253609,-0.8390715290764524,-0.7805681801691837,-0.7142656520272003,-0.6408264175949933,-0.5609842574272288,-0.4755369279959925,-0.3853381907718296,-0.2912892817213455,-0.1943299064553348,-0.09542885100095065,0.004425697988050785,0.10423602686569687,0.2030048638187504,0.2997453432770149,0.3934908663478909,0.4833047587530059,0.5682896297679736,0.6475963386538759,0.7204324789908387,0.7860702961410393,0.8438539587324921,0.8932061115093225,0.9336336440746373,0.9647326178866098,0.9861923022788637,0.9977982791785807,0.9994345855010047,0.9910848718142532,0.9728325656974354,0.9448600381598606,0.9074467814501962,0.8609666164623065\\right]"},{"type":"expression","id":"30","color":"#106BC7","latex":"y=\\sin\\alpha\\left\\{\\cos\\alpha0:0,\\sin\\alpha\\right\\}0:\\sin\\alpha,0\\right\\}\\right\\}","lineStyle":"DASHED"},{"type":"expression","id":"25","color":"#106BC7","latex":"\\left[\\left(kd,s\\left[k\\right]\\right)\\left\\{kd<\\alpha\\right\\}\\operatorname{for}k=\\left[1...\\operatorname{count}\\left(s\\right)\\right]\\right]"},{"type":"expression","id":"32","color":"#f76707","latex":"\\left[\\left(kd,c\\left[k\\right]\\right)\\left\\{kd<\\alpha\\right\\}\\operatorname{for}k=\\left[1...\\operatorname{count}\\left(s\\right)\\right]\\right]"},{"type":"expression","id":"22","color":"#106BC7","latex":"B=\\left\\{\\alpha>4\\pi:R,\\left\\{\\operatorname{mod}\\left(\\alpha,\\frac{d}{5}\\right)=0:\\left(S,C,T\\right),T\\right\\}\\right\\}"},{"type":"expression","id":"23","color":"#106BC7","latex":"S=s\\to\\operatorname{join}\\left(s,\\sin\\alpha\\right)"},{"type":"expression","id":"24","color":"#106BC7","latex":"C=c\\to\\operatorname{join}\\left(c,\\cos\\alpha\\right)"},{"type":"expression","id":"17","color":"#106BC7","latex":"T=\\alpha\\to\\alpha+d"},{"type":"expression","id":"4","color":"#106BC7","latex":"P=\\left(\\cos\\alpha,\\sin\\alpha\\right)","dragMode":"NONE"},{"type":"expression","id":"5","color":"#106BC7","latex":"\\operatorname{segment}\\left(P,\\left(0,0\\right)\\right)"}],"ticker":{"handlerLatex":"B","minStepLatex":"20","open":true}},"geometryToolbar":{"toolbar":"none"},"includeFunctionParametersInRandomSeed":true}29:["$","$L3b",null,{"children":["$","$L3c",null,{"subject":"AASL","urlSubject":"AASL","units":[{"id":358,"name":"Cartesian plane & lines","slug":"cartesian-plane-lines","topic":2,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"2PWB3y28WgU","concepts":[{"id":456,"name":"Coordinates, midpoint, and distance","slug":"coordinates-midpoint-and-distance","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029427801-Artboard%2031.png?alt=media&token=95ab7b9a-5982-46be-9e4e-9550a0c061b7","type":"image"},"skills":[1083,1084,748,749,750],"description":"Points \$\\left(x,y\\right)\$ in the Cartesian plane, the midpoint, and distances between points.","hasLesson":true},{"id":458,"name":"Gradient and line equations","slug":"gradient-and-line-equations","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029420274-Artboard%2032.png?alt=media&token=cdabe575-6e4b-43ce-9317-7e886d22c505","type":"image"},"skills":[366,365,367,751,752],"description":"

Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line

\n","hasLesson":true},{"id":369,"name":"Line intersections, parallel lines, and perpendicular lines","slug":"line-intersections-parallel-lines-and-perpendicular-lines","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029411556-Artboard%2033.png?alt=media&token=ca7518c8-6ff1-4743-aa59-ba4fc0c1a0d8","type":"image"},"skills":[799,753,754,755],"description":"

Parallel and perpendicular lines, intersection of 2 straight lines, solving a two-variable system of equations

","hasLesson":true}],"description":"

Coordinates in the Cartesian plane, gradients and the distance/midpoint formulas, equations of straight lines, parallel and perpendicular lines, and systems of linear equations.

\n"},{"id":106,"name":"Quadratics","slug":"quadratics","topic":2,"subjects":["AAHL","AASL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"-f2Vrii1MY8","concepts":[{"id":404,"name":"Quadratics and parabolas","slug":"quadratics-and-parabolas","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1770853908080-quadratics.png?alt=media&token=e4ba899b-9802-4e8e-9c73-a720fbeb521e","type":"image"},"skills":[806,805,406,407,800,411,408,405,845,801,802],"description":"Quadratic expressions \$ax^2+bx+c\$, their parabola graphs, the axis of symmetry, vertex, and intercetps.","hasLesson":true},{"id":223,"name":"Applications of Quadratics","slug":"applications-of-quadratics","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1770854104447-quadratic%20applications.png?alt=media&token=fe504cd1-e3c5-4205-9363-26479955bca3","type":"image"},"skills":[766,924],"description":"

Evaluating the discriminant, sum and product of roots, quadratic inequalities, quadratics of other forms.

\n","hasLesson":true}],"description":"

Quadratic expressions and functions in standard, factored and vertex form, including graphing parabolas, roots, axis of symmetry and vertex, factoring, completing the square, quadratic formula, discriminant, inequalities, calculator methods and simple optimization.

\n"},{"id":99,"name":"Exponents & Logarithms","slug":"exponents-logarithms","topic":1,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"Y_x-KthdQmc","concepts":[{"id":168,"name":"Exponentiation and integer exponent laws","slug":"exponentiation-and-integer-exponent-laws","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030280792-Artboard%201.png?alt=media&token=6be9f1a7-c875-4ed1-bf66-e1be44cf57e4","type":"image"},"skills":[620,621,614,618,616,622,619,613,844],"description":"

Exponential notation and algebra, including laws for zero and negative exponents, multiplying and dividing powers with the same base, products and quotients with the same exponent, powers of powers, equating exponents in exponential equations, and rationalizing denominators when needed.

\n","hasLesson":true},{"id":879,"name":"Radicals and roots","slug":"radicals-and-roots","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030066026-Artboard%203.png?alt=media&token=8e47da95-01c8-40c1-8577-c825a8f16f5f","type":"image"},"skills":[1072,886,888,889,892,893,895,897],"description":"

Square roots and nth roots, including \\sqrt[n]{a}=a^{\\frac1n}, rational exponents a^{\\frac{m}{n}}, simplifying radicals, roots of negative numbers, and rationalizing denominators using roots or conjugates.

\n","hasLesson":true},{"id":171,"name":"Logarithm algebra","slug":"logarithm-algebra","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030072565-Artboard%202.png?alt=media&token=7a029ca5-f0a3-452e-8694-6ab671866da3","type":"image"},"skills":[624,625,360,626,361,1066,628,627,362],"description":"

Logarithm algebra including the definition \\log_a b=x \\Leftrightarrow a^x=b, base 10 and natural logs, evaluating logs exactly or with technology, and using the rules \\log_a x+\\log_a y=\\log_a(xy), \\log_a x-\\log_a y=\\log_a(x/y), \\log_a(x^m)=m\\log_a x, change of base, and logarithms to solve exponential equations.

\n","hasLesson":true},{"id":170,"name":"Exponential functions","slug":"exponential-functions","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030057079-Artboard%204.png?alt=media&token=eabb4444-acbe-474e-8671-d9c3c8b4b523","type":"image"},"skills":[493,494,797,904,901,902],"description":"

Exponential functions f(x)=a^x and logarithmic functions f(x)=\\log_a x, their domains and ranges, inverse relationship and symmetry in y=x, and graphing/making sense of exponential growth and decay models such as ca^x+k or Ab^t+c.

\n","hasLesson":true}],"description":"

Exponents, roots and rational powers, logarithm laws and change of base, and exponential and logarithmic functions and equations.

\n"},{"id":104,"name":"Function Theory","slug":"function-theory","topic":2,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"5-tzjROivOo","concepts":[{"id":252,"name":"Functions and their properties","slug":"functions-and-their-properties","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1770684953385-function%20machine.png?alt=media&token=c59ac711-975a-4c73-ae39-f10fda053427","type":"image"},"skills":[384,1073,1074,1075,1085],"description":"The concept of a function as a mathematical machine, the notation f\\left(x\\right)=\\ldots, and function tables / diagrams.","hasLesson":true},{"id":258,"name":"Function Graphs","slug":"function-graphs","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1770685518993-function%20graphs.png?alt=media&token=d16df97f-db93-49ec-a84f-bd64de28e3ec","type":"image"},"skills":[415,847,849,260,505,373,391,375,374,376,1035,907],"description":"

Graphing functions with a calculator, characteristics of a function, even and odd functions, x and y intercepts, horizontal and vertical asymptotes, maxima and minima

","hasLesson":true},{"id":253,"name":"Function Composition","slug":"function-composition","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1770854427967-function%20composition.png?alt=media&token=81948aeb-8bb9-4784-8de2-4a1944a38553","type":"image"},"skills":[763],"description":"

Composing functions like f\\circ g

","hasLesson":true},{"id":970,"name":"Inverse Functions","slug":"inverse-functions","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1770854455145-inverse%20functions.png?alt=media&token=539c397b-5ca2-4e26-9810-ce37225be884","type":"image"},"skills":[386,378,379,416,377,380],"description":"The concept of an inverse function, its graph as a reflection in the line y=x, finding the inverse of a specific value, and domain and range of inverse functions. When inverse functions exist, and how to find them when they do.","hasLesson":true}],"description":"

Function notation and representations, including evaluating, graphing and modeling functions, domain and range, composition and inverse functions, and using technology to analyze graphs, intercepts, extrema and asymptotes.

\n"},{"id":865,"name":"Rounding & Error","slug":"rounding-error","topic":1,"subjects":["AISL","AASL","AIHL","AAHL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":866,"name":"Rounding and estimation","slug":"rounding-and-estimation","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030041198-Artboard%205.png?alt=media&token=25922b18-0ebb-4291-af0d-e8584c14c0e9","type":"image"},"skills":[869,877],"description":"

Rounding, significant figures, decimal places

","hasLesson":true},{"id":868,"name":"Scientific Notation","slug":"scientific-notation","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1773515918578-Artboard%206.png?alt=media&token=69a03129-81d4-4eeb-a181-bef451d1b1cd","type":"image"},"skills":[882,885,887],"description":"

Converting numbers to and from scientific notation \\left(a\\times10^{k}\\right)

","hasLesson":true}],"description":"

Rounding, significant figures, and scientific notation.

"},{"id":30,"name":"Sequences & Series","slug":"sequences-series","topic":1,"subjects":["AAHL","AIHL","AISL","AASL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"DI2cudLIWEk","concepts":[{"id":27,"name":"Arithmetic Sequences","slug":"arithmetic-sequences","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029981178-Artboard%207.png?alt=media&token=8a340859-acc8-458a-a5be-e962cb927b61","type":"image"},"skills":[602,603],"description":"

Introduction to the definition, properties, and general term of an arithmetic sequence

","hasLesson":true},{"id":28,"name":"Geometric Sequences","slug":"geometric-sequences","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030011943-Artboard%208.png?alt=media&token=96b137e1-fd1c-43b5-9749-9222bc9e9393","type":"image"},"skills":[604,40],"description":"

Introduction to definition, identification, and general term of geometric sequences

","hasLesson":true},{"id":31,"name":"Arithmetic Series","slug":"arithmetic-series","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757030004817-Artboard%209.png?alt=media&token=4f2e2c52-6ec5-4ca1-b258-67a93d257f07","type":"image"},"skills":[607,46],"description":"

Definition of series, formula for arithmetic series

","hasLesson":true},{"id":860,"name":"Summation notation","slug":"summation-notation","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029991958-Artboard%2010.png?alt=media&token=dcfdc9b6-9e57-47bc-b6bc-9b4088d76eb5","type":"image"},"skills":[47,837,861,862,863,905],"description":"

Summation notation, properties of sums

","hasLesson":true},{"id":859,"name":"Geometric Series","slug":"geometric-series","isPaywalled":true,"isPublic":true,"thumbnail":{"type":"graph","graph":{"data":"$3d","mode":"geometry"}},"skills":[606,608,51],"description":"

Finite geometric series with sum S_{n}=\\frac{u_1(1-r^n)}{1-r}, and infinite geometric series convergence when |r|<1 so that S_\\infty=\\frac{u_1}{1-r}.

\n","hasLesson":true},{"id":906,"name":"Sequence Mode (Calculator)","slug":"sequence-mode-calculator","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029904498-Artboard%2011.png?alt=media&token=542aa577-0f10-43f9-b206-99a890877c96","type":"image"},"skills":[],"description":"

Working with sequences on a calculator, computations and applications of a calculator

","hasLesson":true},{"id":870,"name":"Compound interest, depreciation and inflation","slug":"compound-interest-depreciation-and-inflation","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029508658-Artboard%2012.png?alt=media&token=fb6f46c3-0587-4c9c-83b6-2dd08aad7ca4","type":"image"},"skills":[872,871,883,896,873],"description":"

Compound growth, depreciation, interest, inflation, real value

","hasLesson":true}],"description":"Arithmetic sequences u_{n}=u_1+\\left(n-1\\right)d and geometric sequences v_{n}=v_1r^{n-1}, as well as their series and the \\Sigma notation for summation."},{"id":100,"name":"Counting & Binomials","slug":"counting-binomials","topic":1,"subjects":["AAHL","AASL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"w08O6aqQegU","concepts":[{"id":246,"name":"Pascal's Triangle and nCr","slug":"pascals-triangle-and-ncr","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029889677-Artboard%2013.png?alt=media&token=8abbdcf6-30e5-4df2-a898-50033c4a5db7","type":"image"},"skills":[631,630,629,1025],"description":"

Pascal's triangle and binomial coefficients, using factorials and ^{n}C_{r}=\\frac{n!}{r!(n-r)!} to find combinations and the coefficients in binomial expansions.

\n","hasLesson":true},{"id":248,"name":"Binomial Theorem","slug":"binomial-theorem","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029881955-Artboard%2014.png?alt=media&token=1442315c-0b38-4a37-a959-022b43646b65","type":"image"},"skills":[249,632],"description":"

Expansion of \\left(a+b\\right)^n using binomial coefficients, including the general term \\binom{n}{r}a^{n-r}b^r and finding the coefficient of a specified term.

\n","hasLesson":true}],"description":"

Factorials, combinations and Pascal's triangle, and using the binomial theorem to expand \\left(a+b\\right)^n and find specific coefficients.

\n"},{"id":102,"name":"Proof and Reasoning","slug":"proof-and-reasoning","topic":1,"subjects":["AAHL","AASL"],"isVideoReady":true,"videoId":"syZ6AKBabRA","concepts":[{"id":240,"name":"Proof by deduction","slug":"proof-by-deduction","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029849287-Artboard%2017.png?alt=media&token=312ca3d8-5599-4f64-8439-464901c0de57","type":"image"},"skills":[652,650],"description":"

Strict logical proofs by deduction, including parity arguments with even and odd integers written as n=2k and n=2k+1, and direct proofs that two expressions are equivalent by showing \\text{LHS}\\equiv\\text{RHS} for all variables.

\n","hasLesson":true}],"description":"

Simple deductive proofs to show LHS\\equiv RHS.

"},{"id":108,"name":"Transformations & asymptotes","slug":"transformations-asymptotes","topic":2,"subjects":["AAHL","AASL","AIHL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"xr5EGY1f9Ps","concepts":[{"id":263,"name":"Linear Transformations","slug":"linear-transformations","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029188684-Artboard%2038.png?alt=media&token=eab72306-0d65-4d6a-882d-85b179795b8d","type":"image"},"skills":[11,769,770,771,772,773,774],"description":"

Linear transformations of graphs and points: translations by a vector \\begin{pmatrix}a\\\\ b\\end{pmatrix}, vertical and horizontal stretches y=af(x) and y=f(qx), vertical and horizontal translations y=f(x)+b and y=f(x-a), and reflections in the x- and y-axes.

\n","hasLesson":true},{"id":255,"name":"Rational functions","slug":"rational-functions","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029160193-Artboard%2039.png?alt=media&token=cced4769-0d16-429a-8ae4-bd3a62d893ca","type":"image"},"skills":[808,364],"description":"

The reciprocal function f\\left(x\\right)=\\frac{1}{x}, its undefined value at x=0, self-inverse property, and the vertical and horizontal asymptotes of linear rational functions f\\left(x\\right)=\\frac{ax+b}{cx+d}.

\n","hasLesson":true}],"description":"

Translations, reflections and stretches of graphs, including reciprocal and linear rational functions with vertical and horizontal asymptotes.

\n"},{"id":356,"name":"2D & 3D Geometry","slug":"2d-geometry","topic":3,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"GnG2jU8VpUg","concepts":[{"id":82,"name":"Right-angled triangles","slug":"right-angled-triangles","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029099320-Artboard%2046.png?alt=media&token=803487ed-7a2d-4c58-88e5-31cba1785454","type":"image"},"skills":[87,36,56,716,83,717],"description":"

Pythagoras's theorem, SOHCAHTOA, finding side length from angles

","hasLesson":true},{"id":37,"name":"Non-right-angled triangles","slug":"non-right-angled-triangles","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757029088911-Artboard%2047.png?alt=media&token=80493296-567f-4f51-b0b3-4c328ab90285","type":"image"},"skills":[88,73,74,718],"description":"

Area of non-right-angled triangles using A=\\frac12ab\\sin C, the sine rule \\frac{a}{\\sin A}=\\frac{b}{\\sin B}=\\frac{c}{\\sin C}, the cosine rule c^2=a^2+b^2-2ab\\cos C, and the ambiguous case when solving triangles.

\n","hasLesson":true},{"id":65,"name":"Radians, arcs and sectors","slug":"radians-arcs-and-sectors","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028966537-Artboard%2049.png?alt=media&token=21e1f320-b306-4587-8651-9991150cbd34","type":"image"},"skills":[492,66,720,4,68,14],"description":"

Radian measure, converting between radians and degrees, and calculating arc length and sector area using l=r\\theta, A=\\frac12\\theta r^2, C=2\\pi r, and A=\\pi r^2.

\n","hasLesson":true},{"id":722,"name":"3D volume and surface area","slug":"3d-volume-and-surface-area","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028955870-Artboard%2050.png?alt=media&token=3f2ceb70-0712-4f69-81cc-c257607a3013","type":"image"},"skills":[1080,1094,723,724,725,834,835],"description":"

Spheres, cylinders, prisms, right cones, right pyramids, and combinations of solids

","hasLesson":true},{"id":89,"name":"Angles of elevation and depression","slug":"angles-of-elevation-and-depression","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028981407-Artboard%2048.png?alt=media&token=5b9c00d8-8c4e-40c8-afef-26030c38db55","type":"image"},"skills":[90],"description":"Angles measured between a horizontal line and some elevated or depressed object.","hasLesson":true}],"description":"

2D and 3D geometry including circle measures and sectors, right-triangle and non-right-triangle trigonometry, bearings and angles of elevation/depression, 3D coordinates and angles in space, and surface area and volume of common solids.

\n"},{"id":58,"name":"Trig equations & identities","slug":"trig-equations-identities","topic":3,"subjects":["AAHL","AASL","AIHL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"M87nP0Y-Pds","concepts":[{"id":65,"name":"Radians, arcs and sectors","slug":"radians-arcs-and-sectors","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028966537-Artboard%2049.png?alt=media&token=21e1f320-b306-4587-8651-9991150cbd34","type":"image"},"skills":[492,66,720,4,68,14],"description":"

Radian measure, converting between radians and degrees, and calculating arc length and sector area using l=r\\theta, A=\\frac12\\theta r^2, C=2\\pi r, and A=\\pi r^2.

\n","hasLesson":true},{"id":166,"name":"The Unit Circle","slug":"the-unit-circle","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028896524-Artboard%2053.png?alt=media&token=6f0c6598-c2ab-4090-99f1-8e7ccf54e5df","type":"image"},"skills":[69,70,729,730,728,732,731,734,389,61],"description":"

The unit circle: using \\cos\\theta and \\sin\\theta as the x- and y-coordinates of a point on the circle, key exact values and quadrants, symmetry rules, periodicity, tangent as \\tan\\theta=\\frac{\\sin\\theta}{\\cos\\theta}, and \\sin^2\\theta+\\cos^2\\theta=1.

\n","hasLesson":true},{"id":735,"name":"Sinusoidal functions","slug":"sinusoidal-functions","isPaywalled":false,"isPublic":true,"thumbnail":{"type":"graph","graph":{"data":"$3e","mode":"geometry"}},"skills":[736,76,14,75],"description":"

Radian measure, the sine and cosine functions with domain x\\in\\R and range (-1,1), the tangent function \\tan x=\\frac{\\sin x}{\\cos x} with its asymptotes and roots, and sinusoidal functions of the form a\\sin\\left(b\\left(x+c\\right)\\right)+d or a\\cos\\left(b\\left(x+c\\right)\\right)+d.

\n","hasLesson":true},{"id":949,"name":"Tangent and reciprocal trig functions","slug":"tangent-and-reciprocal-trig-functions","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028852382-Artboard%2054.png?alt=media&token=c153b834-4d14-48e7-b00c-ce7ed61b764b","type":"image"},"skills":[],"description":"

Reciprocal trigonometric functions: secant \\sec x = \\frac{1}{\\cos x}, cosecant \\cosec x = \\frac{1}{\\sin x}, and cotangent \\cot x = \\frac{1}{\\tan x}, including their basic values and graph behaviour where defined.

\n","hasLesson":true},{"id":396,"name":"Trigonometric equations","slug":"trigonometric-equations","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028815933-Artboard%2055.png?alt=media&token=283b491c-074b-4773-bc66-4c839b2c8cb5","type":"image"},"skills":[746,1021,744,745,747],"description":"

Solving trigonometric equations algebraically in a specified domain, including \\sin\\theta=a, \\cos\\theta=a, \\tan\\theta=a, equations with arguments of the form ax+b, and trigonometric quadratics using identities such as \\sin^2\\theta+\\cos^2\\theta=1.

\n","hasLesson":true},{"id":393,"name":"Pythagorean and double-angle identities","slug":"pythagorean-and-double-angle-identities","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028794001-Artboard%2057.png?alt=media&token=6c43949e-408e-48a5-aa5d-2ee8a9e57c20","type":"image"},"skills":[61,739,740],"description":"

Trigonometric identities including \\sin^2\\theta+\\cos^2\\theta=1, \\sin2\\theta=2\\sin\\theta\\cos\\theta, and the equivalent forms of \\cos2\\theta: \\cos^2\\theta-\\sin^2\\theta, 2\\cos^2\\theta-1, and 1-2\\sin^2\\theta.

\n","hasLesson":true}],"description":"

Unit circle trigonometry, key values, quadrant/sign rules, symmetry and periodicity, double angle and Pythagorean identities, and solving basic trigonometric equations and trigonometric quadratics in a given domain.

\n"},{"id":346,"name":"Differentiation","slug":"differentiation","topic":5,"subjects":["AAHL","AASL","AIHL","AISL"],"isVideoReady":true,"videoId":"7GKpUTrLk_o","concepts":[{"id":111,"name":"Limits and Derivatives","slug":"limits-and-derivatives","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027621748-Artboard%2086.png?alt=media&token=f862e464-90a6-482b-9b52-1be5899b056c","type":"image"},"skills":[565,566,567,570,569,571,535,534,19],"description":"

The basic idea of a limit \\lim_{x\\to a}f(x) from tables and graphs, slope as a limit, rate of change and gradient, derivatives of x^n, and linearity for sums and scalar multiples.

\n","hasLesson":true},{"id":112,"name":"Differentiation rules","slug":"differentiation-rules","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027576694-Artboard%2088.png?alt=media&token=b370fb29-0b88-471e-867c-06e32f483988","type":"image"},"skills":[541,539,538,336,533,335,535,534],"description":"

Derivatives of x^{r},e^{x},\\ln x,\\sin x and \\cos x. The chain, product and quotient rules.

","hasLesson":true},{"id":326,"name":"Tangents and normals","slug":"tangents-and-normals","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027557648-Artboard%2088_1.png?alt=media&token=ba008df4-2d3c-426c-bf8f-0809dadd8f51","type":"image"},"skills":[575,576],"description":"

Definitions of tangent and normal, finding tangent and normal lines to a function

","hasLesson":true},{"id":331,"name":"Applications of the First Derivative","slug":"applications-of-the-first-derivative","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027540062-Artboard%2089.png?alt=media&token=8765b377-ec1c-498c-8770-e7f8904405d4","type":"image"},"skills":[573,16,531],"description":"

Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation

","hasLesson":true},{"id":7,"name":"Second Derivatives and Applications","slug":"second-derivatives-and-applications","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027522497-Artboard%2090.png?alt=media&token=08f7442f-e526-4cd9-af09-980e1d6aa69c","type":"image"},"skills":[348,330,574,18,532],"description":"

Second derivatives f'', using the sign of f'' to determine concavity, locate inflexion points where f''(x)=0 and changes sign, and classify stationary points with the second derivative test.

\n","hasLesson":true}],"description":"

Limits and rates of change, differentiation rules for polynomial, exponential, logarithmic and trigonometric functions, and applications to tangents, normals, stationary points, concavity and optimisation.

\n"},{"id":114,"name":"Integration","slug":"integration","topic":5,"subjects":["AAHL","AASL","AIHL","AISL"],"isVideoReady":true,"videoId":"Ex7Qii1AXn8","concepts":[{"id":450,"name":"Definite Integrals and Basic Anti-Derivatives","slug":"definite-integrals-and-basic-anti-derivatives","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027038579-Artboard%2093.png?alt=media&token=bb418ca4-71b9-42ce-b97d-090a1379edea","type":"image"},"skills":[418,293,294,295,587,581,583,545,584,585,41],"description":"

Concept of an integral, areas with definite integrals, and basic anti-derivative solving skills

\n","hasLesson":true},{"id":425,"name":"Anti-Derivative Rules","slug":"anti-derivative-rules","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027022392-Artboard%2094.png?alt=media&token=67fe5d1c-0469-4131-b445-d19e642ef49d","type":"image"},"skills":[546,422,426,420,1118],"description":"

Antiderivatives of polynomials, trigonometric, inverse trigonometric, exponential, and logarithmic functions

\n","hasLesson":true},{"id":542,"name":"Techniques of Integration","slug":"techniques-of-integration","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027007339-Artboard%2094%20copy.png?alt=media&token=a987c620-4834-46ff-afb4-3aab9c0b265e","type":"image"},"skills":[316,317,588],"description":"

Integration of composite functions using substitution, including integrals of the form f(ax+b), and handling definite integrals by changing the bounds or substituting back.

\n","hasLesson":true},{"id":231,"name":"Kinematics","slug":"kinematics","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757026968679-Artboard%2095.png?alt=media&token=8619b033-cbb4-41e2-b0f2-f691121bf19f","type":"image"},"skills":[311,592,591,500,313,1026],"description":"

Displacement and distance, velocity and acceleration, speed as |v|, average velocity and acceleration as \\Delta s/\\Delta t and \\Delta v/\\Delta t, and the relations v=\\mathrm{d}s/\\mathrm{d}t, a=\\mathrm{d}v/\\mathrm{d}t=\\mathrm{d}^2s/\\mathrm{d}t^2, \\int_{t_1}^{t_2} v(t)\\,\\mathrm{d}t for change in displacement, and \\int_{t_1}^{t_2} |v(t)|\\,\\mathrm{d}t for distance.

\n","hasLesson":true}],"description":"

Integration as reverse differentiation, including basic anti-derivatives, definite integrals, area under and between curves, substitution, and applications to displacement and distance.

\n"},{"id":96,"name":"Probability","slug":"probability","topic":4,"subjects":["AAHL","AASL","AIHL","AISL"],"isVideoReady":true,"videoId":"nTKI6Ze6SxE","concepts":[{"id":145,"name":"Foundations of probability","slug":"foundations-of-probability","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028648442-Artboard%2065.png?alt=media&token=5706f4de-134c-4cf9-b2be-c3b79211ab31","type":"image"},"skills":[701,702,699,700,32,703],"description":"

Theoretical and experimental probability, complementary events, expected number of outcomes, sample space

","hasLesson":true},{"id":154,"name":"Combined Events","slug":"combined-events","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028633410-Artboard%2066.png?alt=media&token=875764d4-1b49-4d32-9717-25ae5901b2f5","type":"image"},"skills":[156,155,157,163,34,33,1117,704],"description":"

Venn diagrams, intersection and union of events, conditional probability, independent events

","hasLesson":true},{"id":707,"name":"Tree Diagrams","slug":"tree-diagrams","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028620712-Artboard%2067.png?alt=media&token=62bf0ee2-5ee0-4524-9d9f-97eea0a4d381","type":"image"},"skills":[708,705],"description":"

Tree diagrams, selection with/without replacement, dependence

","hasLesson":true}],"description":"

Theoretical vs experimental probability, combined events, independence vs dependence.

"},{"id":94,"name":"Descriptive Statistics","slug":"descriptive-statistics","topic":4,"subjects":["AAHL","AASL","AIHL","AISL","ecolint-y11-hl"],"isVideoReady":true,"videoId":"Q6pTmvyBjtY","concepts":[{"id":461,"name":"Population, samples and data","slug":"population-samples-and-data","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028594946-Artboard%2069.png?alt=media&token=c647fb49-123f-411f-96bd-84222ced9a3c","type":"image"},"skills":[663,664,141,668,666,667,468,470,469,471,472,23],"description":"

Understand the basics of population, data collection, and sampling.

","hasLesson":true},{"id":683,"name":"Measures of center","slug":"measures-of-center","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028579941-Artboard%2070.png?alt=media&token=1bf0b1f0-af9c-495e-bcb5-7e57ec2ae2c4","type":"image"},"skills":[121,120,119],"description":"

Learn different ways to measure the \"center,\" or typical values, of a set of data: mean, median, and mode.

","hasLesson":true},{"id":682,"name":"Quartiles, outliers and box plots","slug":"quartiles-outliers-and-box-plots","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028567591-Artboard%2071.png?alt=media&token=289941af-343d-4b68-8b4b-0b2a5f0267f2","type":"image"},"skills":[669,670,733,1037],"description":"

Learn the concept of dispersion, range, IQR, outliers, and box and whisker plots.

","hasLesson":true},{"id":118,"name":"Standard Deviation and Variance","slug":"standard-deviation-and-variance","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028551868-SDVar.png?alt=media&token=91c80f18-8855-40d2-a00b-62b578ab007a","type":"image"},"skills":[672,671],"description":"

Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.

\n","hasLesson":true},{"id":126,"name":"Frequency tables and histograms","slug":"frequency-tables-and-histograms","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028166495-Artboard%2072.png?alt=media&token=2d41e78e-b5a6-4558-849d-c5ba24514aef","type":"image"},"skills":[127,673,674],"description":"Visualizing frequency data using tables and histograms.","hasLesson":true},{"id":1004,"name":"Cumulative frequency","slug":"cumulative-frequency","isPaywalled":false,"isPublic":true,"thumbnail":null,"skills":[675,676],"description":"Completing tables of cumulative frequency, and reading cumulative frequency diagrams.","hasLesson":true}],"description":"

Summarizing and interpreting data using measures of centre and spread, frequency tables and graphs, sampling methods, quartiles, IQR, box plots, cumulative frequency, and outlier analysis.

\n"},{"id":3,"name":"Bivariate Statistics","slug":"bivariate-statistics","topic":4,"subjects":["AISL","AIHL","AASL","AAHL"],"isVideoReady":false,"videoId":null,"concepts":[{"id":268,"name":"Linear regression and Pearson's coefficient","slug":"linear-regression-and-pearsons-coefficient","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028135613-Artboard%2074.png?alt=media&token=10413a3d-f49a-4178-a780-37cbede60ac6","type":"image"},"skills":[475,711,712,714,713,476,715],"description":"

Scatter diagrams and lines of best fit y=ax+b, by eye or with GDC, the Pearson correlation coefficient r, and making predictions with awareness of limitations.

\n","hasLesson":true}],"description":"

Correlation and linear regression for paired data, including best fit lines, Pearson's r, predictions from regression models, and the limits of extrapolation.

\n"},{"id":98,"name":"Distributions & Random Variables","slug":"distributions-random-variables","topic":4,"subjects":["AAHL","AIHL","AISL","AASL"],"isVideoReady":true,"videoId":"kFLHW61tj9o","concepts":[{"id":274,"name":"Binomial Distribution","slug":"binomial-distribution","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028018137-Artboard%2075.png?alt=media&token=cb09bf58-c604-4a22-b0a2-acd0f6653970","type":"image"},"skills":[690,691,693,1018,857],"description":"

Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution

","hasLesson":true},{"id":275,"name":"Normal Distribution","slug":"normal-distribution","isPaywalled":true,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757027990196-Artboard%2076.png?alt=media&token=06211191-fa11-4675-a226-3437a57fad92","type":"image"},"skills":[686,685,1024,1046,687,688,689],"description":"

The normal (bell-shaped) distribution X\\sim\\mathrm{N}(\\mu,\\sigma^2), its symmetry about \\mu, z-values z=\\frac{x-\\mu}{\\sigma} and standardization to Z\\sim\\mathrm{N}(0,1), the empirical rule, and calculator-based normal and inverse normal probability calculations.

\n","hasLesson":true},{"id":284,"name":"Discrete random variables","slug":"discrete-random-variables","isPaywalled":false,"isPublic":true,"thumbnail":{"url":"https://firebasestorage.googleapis.com/v0/b/perplex-learning.appspot.com/o/thumbnails%2F1757028049217-Artboard%2074_1.png?alt=media&token=aab272d8-f276-4926-8652-aa1cfc76c0ac","type":"image"},"skills":[678,677,679,279,287,956,957],"description":"Discrete random variables taking a finite set of values, with probability distributions in tables or as expressions where probabilities sum to 1, finding \$E(X)\$ and fair games.","hasLesson":true}],"description":"

Discrete random variables and probability distributions, including expected value and fair games, binomial models and calculator probabilities, and the normal distribution with z-values and standardization.

\n"}],"studySets":[],"assignments":[],"modules":[],"practiceTests":[],"courseSubject":"AASL","nowMs":1789916796707,"isCourseMember":false,"requiresSubjectChoice":false,"showRebrandBanner":false,"chrome":null,"children":"$L3f"}]}] 3f:["$","$L22",null,{"parallelRouterKey":"children","error":"$undefined","errorStyles":"$undefined","errorScripts":"$undefined","template":["$","$L23",null,{}],"templateStyles":"$undefined","templateScripts":"$undefined","notFound":"$undefined","forbidden":"$undefined","unauthorized":"$undefined"}] 40:I[629828,["/_next/static/immutable/chunks/18z7hbezgakd8.js","/_next/static/immutable/chunks/3s1f7foqpdvup.js","/_next/static/immutable/chunks/2mkazo296h-fw.js","/_next/static/immutable/chunks/3kinzrgjz1nll.js","/_next/static/immutable/chunks/266ti09r7o-li.js","/_next/static/immutable/chunks/3e0dg2cn3u5-1.js","/_next/static/immutable/chunks/3av6zvu370icl.js","/_next/static/immutable/chunks/3et9qdvbyi-6u.js","/_next/static/immutable/chunks/1b62qxcrax48_.js","/_next/static/immutable/chunks/1qgctqfwjj94j.js","/_next/static/immutable/chunks/36omjr-s6xpax.js","/_next/static/immutable/chunks/39ps9az44hvg-.js","/_next/static/immutable/chunks/1dr-zgur0-w1_.js","/_next/static/immutable/chunks/0knlg885uauhx.js","/_next/static/immutable/chunks/1u8v__oamgp49.js","/_next/static/immutable/chunks/1o6d8gkxacyr3.js","/_next/static/immutable/chunks/2l5zwdmfvhs7d.js","/_next/static/immutable/chunks/3it7cbupuus2e.js","/_next/static/immutable/chunks/2bo-0yc5izpx4.js","/_next/static/immutable/chunks/27vysu0t21548.js","/_next/static/immutable/chunks/17kj450zyrjx4.js","/_next/static/immutable/chunks/2vyef9ikm5oed.js","/_next/static/immutable/chunks/1016kmk_0_xoh.js","/_next/static/immutable/chunks/18-so5b68b4zs.js","/_next/static/immutable/chunks/2r657mtk43wxk.js","/_next/static/immutable/chunks/2wz3oi8jnzj1m.js","/_next/static/immutable/chunks/3sak_jksml9vb.js","/_next/static/immutable/chunks/43qmiwrh0zjbg.js","/_next/static/immutable/chunks/3s5tdxs448l-j.js","/_next/static/immutable/chunks/0w_ec4pysgbll.js","/_next/static/immutable/chunks/40chzmfllpiuo.js","/_next/static/immutable/chunks/1p35tho0xv6f4.js","/_next/static/immutable/chunks/1oqo8q_chzpnd.js","/_next/static/immutable/chunks/32je84c6xizbv.js","/_next/static/immutable/chunks/3n9qnonh_f3cr.js","/_next/static/immutable/chunks/3xzmqebvf8-bn.js"],"LearnView"] 2b:["$","$L40",null,{"topics":[{"topic":1,"units":[{"id":99,"name":"Exponents & Logarithms","slug":"exponents-logarithms","topic":1,"concepts":[{"id":168,"name":"Exponentiation and integer exponent laws","slug":"exponentiation-and-integer-exponent-laws","thumbnail":"$29:props:children:props:units:2:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Exponential notation and algebra, including laws for zero and negative exponents, multiplying and dividing powers with the same base, products and quotients with the same exponent, powers of powers, equating exponents in exponential equations, and rationalizing denominators when needed.","skillNames":["Exponential Notation","Exponent with zero","Multiplying powers with the same base","Negative exponents","Exponents of products & quotients","Dividing exponents with the same base","Exponential of exponential","Exponential Equations (Equating Indices)","Rationalizing the denominator"]},{"id":879,"name":"Radicals and roots","slug":"radicals-and-roots","thumbnail":"$29:props:children:props:units:2:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started"],"description":"Square roots and nth roots, including , rational exponents , simplifying radicals, roots of negative numbers, and rationalizing denominators using roots or conjugates.","skillNames":["Square roots","nth Roots","Converting nth roots to fractional exponents","Rational exponents","Simplest form radicals","Roots of negative numbers","Simplest form fractions with radicals (multiplying by roots)","Rationalizing Denominators with Conjugates"]},{"id":171,"name":"Logarithm algebra","slug":"logarithm-algebra","thumbnail":"$29:props:children:props:units:2:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started","not-started","not-started","not-started"],"description":"Logarithm algebra including the definition , base 10 and natural logs, evaluating logs exactly or with technology, and using the rules , , , change of base, and logarithms to solve exponential equations.","skillNames":["Definition of the logarithm","Log base 10","Sum and difference of logs","Natural logarithm","Log power rule","Evaluating logs algebraically","Evaluating logs using technology","Using logs to solve exponential equations","Log change of base"]},{"id":170,"name":"Exponential functions","slug":"exponential-functions","thumbnail":"$29:props:children:props:units:2:concepts:3:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Exponential functions and logarithmic functions , their domains and ranges, inverse relationship and symmetry in , and graphing/making sense of exponential growth and decay models such as or .","skillNames":["Exponential functions","Logarithmic functions","Log and exponent functions are inverse functions","Graphing Exponential Functions","Exponential growth","Exponential decay"]}]},{"id":865,"name":"Rounding & Error","slug":"rounding-error","topic":1,"concepts":[{"id":866,"name":"Rounding and estimation","slug":"rounding-and-estimation","thumbnail":"$29:props:children:props:units:4:concepts:0:thumbnail","exerciseStatuses":[],"description":"Rounding, significant figures, decimal places","skillNames":["Rounding rules","Significant figures"]},{"id":868,"name":"Scientific Notation","slug":"scientific-notation","thumbnail":"$29:props:children:props:units:4:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Converting numbers to and from scientific notation","skillNames":["Writing numbers in standard form","Adding & subtracting numbers in scientific notation","Multiplying & dividing numbers in scientific notation"]}]},{"id":30,"name":"Sequences & Series","slug":"sequences-series","topic":1,"concepts":[{"id":27,"name":"Arithmetic Sequences","slug":"arithmetic-sequences","thumbnail":"$29:props:children:props:units:5:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Introduction to the definition, properties, and general term of an arithmetic sequence","skillNames":["Identifying arithmetic sequences","General term"]},{"id":28,"name":"Geometric Sequences","slug":"geometric-sequences","thumbnail":"$29:props:children:props:units:5:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Introduction to definition, identification, and general term of geometric sequences","skillNames":["Identifying Geometric Sequences","General Term of a Geometric Sequence"]},{"id":31,"name":"Arithmetic Series","slug":"arithmetic-series","thumbnail":"$29:props:children:props:units:5:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Definition of series, formula for arithmetic series","skillNames":["A series is the sum of a sequence","Calculating arithmetic series"]},{"id":860,"name":"Summation notation","slug":"summation-notation","thumbnail":"$29:props:children:props:units:5:concepts:3:thumbnail","exerciseStatuses":["not-started"],"description":"Summation notation, properties of sums","skillNames":["Understanding summation notation","Properties of Σ","Sums with scalar multiples","Sum of a constant","Splitting a sum in Σ form","Sum of a sum"]},{"id":859,"name":"Geometric Series","slug":"geometric-series","thumbnail":"$29:props:children:props:units:5:concepts:4:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Finite geometric series with sum , and infinite geometric series convergence when so that .","skillNames":["Finite Geometric Series","Convergence","Infinite Geometric Series"]},{"id":906,"name":"Sequence Mode (Calculator)","slug":"sequence-mode-calculator","thumbnail":"$29:props:children:props:units:5:concepts:5:thumbnail","exerciseStatuses":["not-started"],"description":"Working with sequences on a calculator, computations and applications of a calculator","skillNames":[]},{"id":870,"name":"Compound interest, depreciation and inflation","slug":"compound-interest-depreciation-and-inflation","thumbnail":"$29:props:children:props:units:5:concepts:6:thumbnail","exerciseStatuses":["not-started"],"description":"Compound growth, depreciation, interest, inflation, real value","skillNames":["Depreciation","Compound Interest Formula","Inflation & Real Value","Positive & Negative Cash Flows (TVM)","Using TVM Solver (Calculator) - Compound Interest"]}]},{"id":100,"name":"Counting & Binomials","slug":"counting-binomials","topic":1,"concepts":[{"id":246,"name":"Pascal's Triangle and nCr","slug":"pascals-triangle-and-ncr","thumbnail":"$29:props:children:props:units:6:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Pascal's triangle and binomial coefficients, using factorials and to find combinations and the coefficients in binomial expansions.","skillNames":["Factorials","Binomial Coefficient nCr","Pascal's Triangle","Fractions of factorials as partial products"]},{"id":248,"name":"Binomial Theorem","slug":"binomial-theorem","thumbnail":"$29:props:children:props:units:6:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Expansion of using binomial coefficients, including the general term and finding the coefficient of a specified term.","skillNames":["The expansion of (a+b)ⁿ","Finding the coefficient of a specific term"]}]},{"id":102,"name":"Proof and Reasoning","slug":"proof-and-reasoning","topic":1,"concepts":[{"id":240,"name":"Proof by deduction","slug":"proof-by-deduction","thumbnail":"$29:props:children:props:units:7:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Strict logical proofs by deduction, including parity arguments with even and odd integers written as and , and direct proofs that two expressions are equivalent by showing for all variables.","skillNames":["Even and Odd Numbers","Deductive Proof"]}]}]},{"topic":2,"units":[{"id":358,"name":"Cartesian plane & lines","slug":"cartesian-plane-lines","topic":2,"concepts":[{"id":456,"name":"Coordinates, midpoint, and distance","slug":"coordinates-midpoint-and-distance","thumbnail":"$29:props:children:props:units:0:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Points \$\\left(x,y\\right)\$ in the Cartesian plane, the midpoint, and distances between points.","skillNames":["Cartesian Plane","Cartesian quadrants","Distance between 2 points","Midpoint of 2 points","Slope as rise over run"]},{"id":458,"name":"Gradient and line equations","slug":"gradient-and-line-equations","thumbnail":"$29:props:children:props:units:0:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line","skillNames":["Gradient-intercept form","Point-gradient form","Standard form of a line","Horizontal lines","Vertical lines"]},{"id":369,"name":"Line intersections, parallel lines, and perpendicular lines","slug":"line-intersections-parallel-lines-and-perpendicular-lines","thumbnail":"$29:props:children:props:units:0:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Parallel and perpendicular lines, intersection of straight lines, solving a two-variable system of equations","skillNames":["Systems of equations with 2 unknowns","Parallel lines","Perpendicular Lines","Intersections of straight lines"]}]},{"id":106,"name":"Quadratics","slug":"quadratics","topic":2,"concepts":[{"id":404,"name":"Quadratics and parabolas","slug":"quadratics-and-parabolas","thumbnail":"$29:props:children:props:units:1:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started","not-started"],"description":"Quadratic expressions \$ax^2+bx+c\$, their parabola graphs, the axis of symmetry, vertex, and intercetps.","skillNames":["Vertex Form & Coordinates","Equation of the axis of symmetry","Concavity of a parabola is the sign of a","Factoring by Inspection","General form of a quadratic","Factored form of quadratic","Quadratic formula","Completing the square","Solving Quadratics with a Calculator","Vertex and Axis of Symmetry","Quadratic x-intercepts"]},{"id":223,"name":"Applications of Quadratics","slug":"applications-of-quadratics","thumbnail":"$29:props:children:props:units:1:concepts:1:thumbnail","exerciseStatuses":["not-started"],"description":"Evaluating the discriminant, sum and product of roots, quadratic inequalities, quadratics of other forms.","skillNames":["The discriminant and solution count","Optimization With Quadratics"]}]},{"id":104,"name":"Function Theory","slug":"function-theory","topic":2,"concepts":[{"id":252,"name":"Functions and their properties","slug":"functions-and-their-properties","thumbnail":"$29:props:children:props:units:3:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"The concept of a function as a mathematical machine, the notation , and function tables / diagrams.","skillNames":["Evaluating functions","Function as a mathematical machine","Function diagram","Table of function values","Expression of a function f(x)"]},{"id":258,"name":"Function Graphs","slug":"function-graphs","thumbnail":"$29:props:children:props:units:3:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started","not-started","not-started","not-started","not-started"],"description":"Graphing functions with a calculator, characteristics of a function, even and odd functions, and intercepts, horizontal and vertical asymptotes, maxima and minima","skillNames":["Graph of a function","Vertical line test","Finding function values from graph","Graphing with technology","Intersections with GDC","x-intercepts","y-intercepts","Vertical asymptotes","Horizontal asymptotes","Maxima and Minima","Finding maxima & minima with technology","Calculator: finding value of a function"]},{"id":253,"name":"Function Composition","slug":"function-composition","thumbnail":"$29:props:children:props:units:3:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Composing functions like","skillNames":["Composite functions"]},{"id":970,"name":"Inverse Functions","slug":"inverse-functions","thumbnail":"$29:props:children:props:units:3:concepts:3:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started"],"description":"The concept of an inverse function, its graph as a reflection in the line , finding the inverse of a specific value, and domain and range of inverse functions. When inverse functions exist, and how to find them when they do.","skillNames":["Finding inverse of specific value","Graphs of inverse functions","Domain & range of inverse functions","Inverse applied to function is identity x","Finding inverse functions","Existence of inverse function"]}]},{"id":108,"name":"Transformations & asymptotes","slug":"transformations-asymptotes","topic":2,"concepts":[{"id":263,"name":"Linear Transformations","slug":"linear-transformations","thumbnail":"$29:props:children:props:units:8:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Linear transformations of graphs and points: translations by a vector , vertical and horizontal stretches and , vertical and horizontal translations and , and reflections in the - and -axes.","skillNames":["Translation by a vector","Vertical scaling of graphs y=af(x)","Vertical translation of graphs y=f(x)+b","Horizontal translation","Horizontal scaling","Reflection in the y-axis","Reflection in the x-axis"]},{"id":255,"name":"Rational functions","slug":"rational-functions","thumbnail":"$29:props:children:props:units:8:concepts:1:thumbnail","exerciseStatuses":["not-started"],"description":"The reciprocal function , its undefined value at , self-inverse property, and the vertical and horizontal asymptotes of linear rational functions .","skillNames":["The reciprocal function 1/x","Graphs of linear rational functions"]}]}]},{"topic":3,"units":[{"id":356,"name":"2D & 3D Geometry","slug":"2d-geometry","topic":3,"concepts":[{"id":82,"name":"Right-angled triangles","slug":"right-angled-triangles","thumbnail":"$29:props:children:props:units:9:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Pythagoras's theorem, SOHCAHTOA, finding side length from angles","skillNames":["Area of triangle equals ½bh","Pythagoras' Theorem","Trigonometric Ratios","Triangle Angles Sum to 180°","Finding angles in right angled triangles","Finding side lengths from an angle in right triangle"]},{"id":37,"name":"Non-right-angled triangles","slug":"non-right-angled-triangles","thumbnail":"$29:props:children:props:units:9:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started"],"description":"Area of non-right-angled triangles using , the sine rule , the cosine rule , and the ambiguous case when solving triangles.","skillNames":["Area of non-right-angled triangles","Sine rule","Cosine rule","Ambiguous Case of the Sine rule"]},{"id":65,"name":"Radians, arcs and sectors","slug":"radians-arcs-and-sectors","thumbnail":"$29:props:children:props:units:9:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Radian measure, converting between radians and degrees, and calculating arc length and sector area using , , , and .","skillNames":["Circumference & Area of a circle","Arc length (radians)","Converting Between Radians & Degrees","Sector (degrees)","Sector area (radians)","Radian measure"]},{"id":722,"name":"3D volume and surface area","slug":"3d-volume-and-surface-area","thumbnail":"$29:props:children:props:units:9:concepts:3:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started"],"description":"Spheres, cylinders, prisms, right cones, right pyramids, and combinations of solids","skillNames":["3D coordinates","Angles in 3D","Spheres","Cylinders","Volume of a prism","Right cones","Right Pyramid"]},{"id":89,"name":"Angles of elevation and depression","slug":"angles-of-elevation-and-depression","thumbnail":"$29:props:children:props:units:9:concepts:4:thumbnail","exerciseStatuses":["not-started"],"description":"Angles measured between a horizontal line and some elevated or depressed object.","skillNames":["Angles of elevation & depression"]}]},{"id":58,"name":"Trig equations & identities","slug":"trig-equations-identities","topic":3,"concepts":[{"id":166,"name":"The Unit Circle","slug":"the-unit-circle","thumbnail":"$29:props:children:props:units:10:concepts:1:thumbnail","exerciseStatuses":["not-started"],"description":"The unit circle: using and as the - and -coordinates of a point on the circle, key exact values and quadrants, symmetry rules, periodicity, tangent as , and .","skillNames":["Sine and Cosine on the Unit Circle","Key values of Sin, Cos & Tan","Relating Angles Between Quadrants","Symmetry About the Y-axis","Quadrants","Symmetry About the Origin","Symmetry About the X-axis","Periodicity","Tan as Slope in the Unit Circle","sin²θ+cos²θ=1"]},{"id":735,"name":"Sinusoidal functions","slug":"sinusoidal-functions","thumbnail":"$29:props:children:props:units:10:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Radian measure, the sine and cosine functions with domain and range , the tangent function with its asymptotes and roots, and sinusoidal functions of the form or .","skillNames":["Sinusoidal Functions","Tan function","Radian measure","Sine and Cosine functions"]},{"id":949,"name":"Tangent and reciprocal trig functions","slug":"tangent-and-reciprocal-trig-functions","thumbnail":"$29:props:children:props:units:10:concepts:3:thumbnail","exerciseStatuses":[],"description":"Reciprocal trigonometric functions: secant , cosecant , and cotangent , including their basic values and graph behaviour where defined.","skillNames":[]},{"id":396,"name":"Trigonometric equations","slug":"trigonometric-equations","thumbnail":"$29:props:children:props:units:10:concepts:4:thumbnail","exerciseStatuses":["not-started"],"description":"Solving trigonometric equations algebraically in a specified domain, including , , , equations with arguments of the form , and trigonometric quadratics using identities such as .","skillNames":["Solving trig equations algebraically in specific domain","Solving tan(x)=a","Solving sinθ=a","Solving cosθ=a","Trigonometric Quadratics"]},{"id":393,"name":"Pythagorean and double-angle identities","slug":"pythagorean-and-double-angle-identities","thumbnail":"$29:props:children:props:units:10:concepts:5:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Trigonometric identities including , , and the equivalent forms of : , , and .","skillNames":["sin²θ+cos²θ=1","Sine Double Angle Identity","Cosine Double Angle Identity"]}]}]},{"topic":4,"units":[{"id":96,"name":"Probability","slug":"probability","topic":4,"concepts":[{"id":145,"name":"Foundations of probability","slug":"foundations-of-probability","thumbnail":"$29:props:children:props:units:13:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Theoretical and experimental probability, complementary events, expected number of outcomes, sample space","skillNames":["Trial, Outcome and Event","Sample Space","Theoretical Probability","Experimental Probability","Expected number of occurrences","Complementary Event"]},{"id":154,"name":"Combined Events","slug":"combined-events","thumbnail":"$29:props:children:props:units:13:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Venn diagrams, intersection and union of events, conditional probability, independent events","skillNames":["Intersection of probabilities","Union of probabilities","Mutually exclusive events","Conditional Probability","Independent events","Sample space diagrams","Calculating probabilities from Venn diagrams","Venn Diagrams "]},{"id":707,"name":"Tree Diagrams","slug":"tree-diagrams","thumbnail":"$29:props:children:props:units:13:concepts:2:thumbnail","exerciseStatuses":["not-started"],"description":"Tree diagrams, selection with/without replacement, dependence","skillNames":["Selection with & without replacement","Tree Diagram"]}]},{"id":94,"name":"Descriptive Statistics","slug":"descriptive-statistics","topic":4,"concepts":[{"id":461,"name":"Population, samples and data","slug":"population-samples-and-data","thumbnail":"$29:props:children:props:units:14:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Understand the basics of population, data collection, and sampling.","skillNames":["Population","Types of Variables","Sampling Error","Measurement Error","Coverage Error","Non-response error","Random sampling","Convenience sampling","Systematic sampling","Stratified random sampling","Quota sampling","Identifying and Removing Outliers"]},{"id":683,"name":"Measures of center","slug":"measures-of-center","thumbnail":"$29:props:children:props:units:14:concepts:1:thumbnail","exerciseStatuses":["not-started"],"description":"Learn different ways to measure the \"center,\" or typical values, of a set of data: mean, median, and mode.","skillNames":["Mean","Mode","Median"]},{"id":682,"name":"Quartiles, outliers and box plots","slug":"quartiles-outliers-and-box-plots","thumbnail":"$29:props:children:props:units:14:concepts:2:thumbnail","exerciseStatuses":["not-started"],"description":"Learn the concept of dispersion, range, IQR, outliers, and box and whisker plots.","skillNames":["Quartiles","Interquartile Range & Outliers","Box & Whisker Plots","Range"]},{"id":118,"name":"Standard Deviation and Variance","slug":"standard-deviation-and-variance","thumbnail":"$29:props:children:props:units:14:concepts:3:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.","skillNames":["Constant changes to data","Variance & SD on Calculator (Sx vs σ)"]},{"id":126,"name":"Frequency tables and histograms","slug":"frequency-tables-and-histograms","thumbnail":"$29:props:children:props:units:14:concepts:4:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Visualizing frequency data using tables and histograms.","skillNames":["Discrete Frequency Tables","Grouped Frequency Tables","Histograms"]},{"id":1004,"name":"Cumulative frequency","slug":"cumulative-frequency","thumbnail":null,"exerciseStatuses":["not-started"],"description":"Completing tables of cumulative frequency, and reading cumulative frequency diagrams.","skillNames":["Cumulative frequency graphs and tables","Median, quartiles & percentiles on CF Graphs"]}]},{"id":3,"name":"Bivariate Statistics","slug":"bivariate-statistics","topic":4,"concepts":[{"id":268,"name":"Linear regression and Pearson's coefficient","slug":"linear-regression-and-pearsons-coefficient","thumbnail":"$29:props:children:props:units:15:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Scatter diagrams and lines of best fit , by eye or with GDC, the Pearson correlation coefficient , and making predictions with awareness of limitations.","skillNames":["Regression line y on x","Pearson's Product-Moment Correlation Coefficient","Predicting y from x","Limitations of predicting x from y","Danger of extrapolation","Plotting approximate best fit line","Regression line x on y"]}]},{"id":98,"name":"Distributions & Random Variables","slug":"distributions-random-variables","topic":4,"concepts":[{"id":274,"name":"Binomial Distribution","slug":"binomial-distribution","thumbnail":"$29:props:children:props:units:16:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started"],"description":"Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution","skillNames":["The Concept of a Binomial Distribution","Binomial PDF with calculator","Binomial CDF with Calculator","Using the binomial distribution","Expectation and Variance of Binomial Distribution"]},{"id":275,"name":"Normal Distribution","slug":"normal-distribution","thumbnail":"$29:props:children:props:units:16:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started"],"description":"The normal (bell-shaped) distribution , its symmetry about , z-values and standardization to , the empirical rule, and calculator-based normal and inverse normal probability calculations.","skillNames":["The Normal Distribution","The Bell Curve properties","Z-values","The Empirical Rule","Normal calculations","Inverse Normal Calculations","Normal Standardization (z-values)"]},{"id":284,"name":"Discrete random variables","slug":"discrete-random-variables","thumbnail":"$29:props:children:props:units:16:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Discrete random variables taking a finite set of values, with probability distributions in tables or as expressions where probabilities sum to 1, finding \$E(X)\$ and fair games.","skillNames":["Concept of a random variable","Concept of a discrete random variable","Discrete probability distributions in a table","Expected Value","Fair Games","Discrete probabilities sum to 1","Discrete probability distributions as an expression"]}]}]},{"topic":5,"units":[{"id":346,"name":"Differentiation","slug":"differentiation","topic":5,"concepts":[{"id":111,"name":"Limits and Derivatives","slug":"limits-and-derivatives","thumbnail":"$29:props:children:props:units:11:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started","not-started"],"description":"The basic idea of a limit from tables and graphs, slope as a limit, rate of change and gradient, derivatives of , and linearity for sums and scalar multiples.","skillNames":["Basic concept of a limit","Limit from a table","Limit from a graph","Slope as a Limit","Rate of Change","Gradient","Derivative of xⁿ where n is an integer","Derivatives of sums and scalar multiples","Graphing a derivative with a GDC"]},{"id":112,"name":"Differentiation rules","slug":"differentiation-rules","thumbnail":"$29:props:children:props:units:11:concepts:1:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Derivatives of and . The chain, product and quotient rules.","skillNames":["Derivative of xⁿ where n is rational","Derivative of e^x","Derivatives of sin and cos","Product and Quotient rule","Derivative of ln","Chain rule","Derivative of xⁿ where n is an integer","Derivatives of sums and scalar multiples"]},{"id":326,"name":"Tangents and normals","slug":"tangents-and-normals","thumbnail":"$29:props:children:props:units:11:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Definitions of tangent and normal, finding tangent and normal lines to a function","skillNames":["Tangent to f(x)","Normal to f(x)"]},{"id":331,"name":"Applications of the First Derivative","slug":"applications-of-the-first-derivative","thumbnail":"$29:props:children:props:units:11:concepts:3:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation","skillNames":["Maxima & Minima","Optimisation","Stationary points & Increasing/Decreasing Regions"]},{"id":7,"name":"Second Derivatives and Applications","slug":"second-derivatives-and-applications","thumbnail":"$29:props:children:props:units:11:concepts:4:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Second derivatives , using the sign of to determine concavity, locate inflexion points where and changes sign, and classify stationary points with the second derivative test.","skillNames":["Second Derivative","Inflexion Points","Concavity","Classifying stationary points using the second derivative","Graphs of f, f' and f''"]}]},{"id":114,"name":"Integration","slug":"integration","topic":5,"concepts":[{"id":450,"name":"Definite Integrals and Basic Anti-Derivatives","slug":"definite-integrals-and-basic-anti-derivatives","thumbnail":"$29:props:children:props:units:12:concepts:0:thumbnail","exerciseStatuses":["not-started","not-started","not-started","not-started"],"description":"Concept of an integral, areas with definite integrals, and basic anti-derivative solving skills","skillNames":["Definite Integrals","Area under a curve","Area between curve and x-axis","Area between curves","Definite Integral Rules","Integration as reverse differentiation","The Integration Constant","Anti-Derivative of xⁿ, n∈ℤ","Integrals of sums and scalar products","Boundary Conditions","Calculating Definite Integral with GDC"]},{"id":425,"name":"Anti-Derivative Rules","slug":"anti-derivative-rules","thumbnail":"$29:props:children:props:units:12:concepts:1:thumbnail","exerciseStatuses":["not-started"],"description":"Antiderivatives of polynomials, trigonometric, inverse trigonometric, exponential, and logarithmic functions","skillNames":["Anti-Derivative of xⁿ, n∈ℚ","Anti-Derivative of sin and cos","Anti-Derivative of e^x","Anti-Derivative of 1/x","Anti-derivatives of sums and scalar multiples"]},{"id":542,"name":"Techniques of Integration","slug":"techniques-of-integration","thumbnail":"$29:props:children:props:units:12:concepts:2:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Integration of composite functions using substitution, including integrals of the form , and handling definite integrals by changing the bounds or substituting back.","skillNames":["Integrating f(ax+b)","Integration by substitution","Substitution and Integral Bounds"]},{"id":231,"name":"Kinematics","slug":"kinematics","thumbnail":"$29:props:children:props:units:12:concepts:3:thumbnail","exerciseStatuses":["not-started","not-started","not-started"],"description":"Displacement and distance, velocity and acceleration, speed as , average velocity and acceleration as and , and the relations , , for change in displacement, and for distance.","skillNames":["Displacement, velocity and acceleration","Displacement vs Distance","Change in Displacement from Velocity","Distance from Velocity","Speed","Average Velocity and Acceleration"]}]}]}],"recentConcepts":[],"baseUrl":"/course/AASL","signedIn":false}]