{"id":15911,"date":"2024-12-25T16:47:15","date_gmt":"2024-12-25T16:47:15","guid":{"rendered":"https:\/\/ibmaths.com\/?page_id=15911"},"modified":"2025-02-19T12:39:58","modified_gmt":"2025-02-19T11:39:58","slug":"ibaahl","status":"publish","type":"page","link":"https:\/\/ibmaths.com\/ibaahl\/","title":{"rendered":"IBAAHL"},"content":{"rendered":"<div class=\"brz-root__container brz-reset-all brz brz-root__container-page\">\n<section id=\"020c9e6ce9ed902f3d1c_lMSTn56iuWMj\" class=\"brz-section brz-css-z2q6fd\">\n<div class=\"brz-section__content brz-section--boxed brz-css-sbbn76 brz-css-l4f545\" data-brz-custom-id=\"foDAXyppWH2I\">\n<div class=\"brz-bg\">\n<div class=\"brz-bg-color\"><\/div>\n<\/div>\n<div class=\"brz-container brz-css-9g5gjg\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"onu4XYSPVNZP\">\n<div data-brz-translate-text=\"1\">\n<h4 class=\"brz-tp-lg-heading4 brz-css-cDxzd\" data-generated-css=\"brz-css-d6IPT\" data-uniq-id=\"gtckN\"><strong class=\"brz-cp-color5\">IB Math Analysis and Approaches Higher Level (AA HL)<\/strong><span class=\"brz-cp-color5\"> <\/span><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"d60185c660c331df3b74_db6yoc1y2W2e\" class=\"brz-section brz-css-z2q6fd\">\n<div class=\"brz-section__content brz-section--boxed brz-css-sbbn76 brz-css-18xir0o\" data-brz-custom-id=\"nwwUxausigr5\">\n<div class=\"brz-bg\">\n<div class=\"brz-bg-color\"><\/div>\n<\/div>\n<div class=\"brz-container brz-css-9g5gjg\">\n<div class=\"brz-row__container brz-css-73ukg3\" data-brz-custom-id=\"cV4hyYApexIV\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-row brz-css-qrby90 brz-css-l30oc2\">\n<div class=\"brz-columns brz-css-tpgd33 brz-css-18jbsg1\" data-brz-custom-id=\"tYfeUEkbtULL\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1xep52d\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"wWYZoH_Y720P\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-wKK9A\" data-uniq-id=\"aRNie\" data-generated-css=\"brz-css-xs9xL\"><span class=\"brz-cp-color3\">00<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-1jiwlyj brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"lPV9qXLvx83j\">\n<div data-brz-translate-text=\"1\">\n<h5 data-uniq-id=\"sbMNo\" data-generated-css=\"brz-css-whs0i\" class=\"brz-tp-lg-heading5 brz-css-dj_3c\"><span class=\"brz-cp-color3\">Pre Course<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"vmPjBwJDjRSF\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-tMDxt\" data-uniq-id=\"iHimq\" data-generated-css=\"brz-css-lMY8q\"><span class=\"brz-cp-color3\">Straight lines<\/span><\/li>\n<li data-uniq-id=\"g_p1g\" data-generated-css=\"brz-css-dyUMv\" class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-uTe77\"><span class=\"brz-cp-color3\">Surds<\/span><\/li>\n<li data-uniq-id=\"ttLHf\" data-generated-css=\"brz-css-tCeWD\" class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-z7nWt\"><span class=\"brz-cp-color3\">Basic Quadratics<\/span><\/li>\n<li data-uniq-id=\"d_CMA\" data-generated-css=\"brz-css-vBOZO\" class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-kGHpd\"><span class=\"brz-cp-color3\">Completing the Square<\/span><\/li>\n<li data-uniq-id=\"ohTZT\" data-generated-css=\"brz-css-lapj6\" class=\"brz-tp-lg-z6fFstO9H4nb brz-css-bnmju\"><span class=\"brz-cp-color3\">Quadratic Discriminat<\/span> <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa0\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1yswa4e\" data-brz-custom-id=\"uBtNBOYfnpRd\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-meb6d3\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"q8zfYG9x0BrG\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-bzMZr\" data-uniq-id=\"z5Gb5\" data-generated-css=\"brz-css-btzxY\"><strong class=\"brz-cp-color3\">01<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-xrm8he brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"e0Ocw2bN27Lv\">\n<div data-brz-translate-text=\"1\">\n<h5 data-uniq-id=\"v7Y1n\" data-generated-css=\"brz-css-wgebf\" class=\"brz-tp-lg-heading5 brz-css-yYefe\"><span class=\"brz-cp-color3\">Algebra and Number<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"wkYNrqUvyjGl\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-fLFyt\" data-uniq-id=\"y2ncK\" data-generated-css=\"brz-css-qQgB6\"><strong class=\"brz-cp-color3\">Inequalities<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-kOfuy\" data-uniq-id=\"bbS3v\" data-generated-css=\"brz-css-p1xXs\"><strong class=\"brz-cp-color3\">Quadratic and Polynomial Roots<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-dJFHl\" data-uniq-id=\"rTrnr\" data-generated-css=\"brz-css-lbHh2\"><strong class=\"brz-cp-color3\">Partial Fractions<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-rmQcy\" data-uniq-id=\"oQMtm\" data-generated-css=\"brz-css-eVZTk\"><strong class=\"brz-cp-color3\">Expansions<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-rRntJ\" data-uniq-id=\"kH8wM\" data-generated-css=\"brz-css-jFc6C\"><span class=\"brz-cp-color3\">Sequences and Series<\/span><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-tUN1D\" data-uniq-id=\"zEPwr\" data-generated-css=\"brz-css-qzneq\"><span class=\"brz-cp-color3\"> Exponents<\/span><\/li>\n<li data-uniq-id=\"zEPwr\" data-generated-css=\"brz-css-qzneq\" class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-e6AOU\"><span class=\"brz-cp-color3\">Logarithms<\/span><\/li>\n<li data-uniq-id=\"zEPwr\" data-generated-css=\"brz-css-qzneq\" class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-iS4T1\"><span class=\"brz-cp-color3\">Counting<\/span><\/li>\n<li data-uniq-id=\"zEPwr\" data-generated-css=\"brz-css-qzneq\" class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-hRbS2\"><span class=\"brz-cp-color3\">Row (Gaussian Reduction) <\/span><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa1\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1p9fgo7\" data-brz-custom-id=\"a4somTJJm_gu\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1s99dpv\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"bM7hN9fL5P01\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-dliJD\" data-uniq-id=\"eTBgD\" data-generated-css=\"brz-css-cckBq\"><strong class=\"brz-cp-color3\">02<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-1cnnzi1 brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"hoUvTOHSREJw\">\n<div data-brz-translate-text=\"1\">\n<h5 data-uniq-id=\"zCzEg\" data-generated-css=\"brz-css-s7Ya8\" class=\"brz-tp-lg-heading5 brz-css-bRg0G\"><span class=\"brz-cp-color3\">Functions<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"uKSnm63ndcp9\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-zrFMo\" data-uniq-id=\"zO4ie\" data-generated-css=\"brz-css-dVlgx\"><strong class=\"brz-cp-color3\">Notation<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-zX1Zg\" data-uniq-id=\"lCGPR\" data-generated-css=\"brz-css-vGcUD\">Odd and Even Functions<\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-w_5TF\" data-uniq-id=\"mqd4D\" data-generated-css=\"brz-css-x9Fd3\">Algebra of Functions<\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-fQfQb\" data-uniq-id=\"pEKY7\" data-generated-css=\"brz-css-c4Dk7\"><strong class=\"brz-cp-color3\">Graphing and Functions<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-kOp0Q\" data-uniq-id=\"pEKY7\" data-generated-css=\"brz-css-c4Dk7\"><strong class=\"brz-cp-color3\">Factor and Remainder Theorems <\/strong><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa2\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"8d96fb2f633eb5f50f2c_r3f7WK7jNvOY\" class=\"brz-section brz-css-z2q6fd\">\n<div class=\"brz-section__content brz-section--boxed brz-css-sbbn76 brz-css-eojigu\" data-brz-custom-id=\"fNW2Ugt3o6QO\">\n<div class=\"brz-bg\">\n<div class=\"brz-bg-color\"><\/div>\n<\/div>\n<div class=\"brz-container brz-css-9g5gjg\">\n<div class=\"brz-row__container brz-css-73ukg3\" data-brz-custom-id=\"b0OsKICIcNJl\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-row brz-css-qrby90 brz-css-l30oc2\">\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1oc5oxy\" data-brz-custom-id=\"p1f92lzQLp1i\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-k9mma0\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"wpDv05xbhFWO\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-tVqVM\" data-generated-css=\"brz-css-yQpHk\" data-uniq-id=\"qbvLu\"><span class=\"brz-cp-color5\">03<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-z2mbvx brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"dPPDoNqcAWC6\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-dO2lP\" data-generated-css=\"brz-css-lIvUm\" data-uniq-id=\"u3qYo\"><span class=\"brz-cp-color5\">Trigonometry<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"ny9fn2CqkAJB\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-og56W\" data-uniq-id=\"lVrOg\" data-generated-css=\"brz-css-uAoVW\"><span class=\"brz-cp-color5\">Non right angled trig.<\/span><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-cr9HO\" data-uniq-id=\"qEKwe\" data-generated-css=\"brz-css-y8ce2\">Radian and basic ratios<\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-nijBQ\" data-uniq-id=\"rTSlB\" data-generated-css=\"brz-css-sbtt9\">Trig. graphs and transformations<\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-v_D7c\" data-uniq-id=\"cHSeH\" data-generated-css=\"brz-css-yigZr\"><span class=\"brz-cp-color5\">Trig formulae &#8211; Pythagorean<\/span><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-iB4lG\" data-uniq-id=\"mLTT2\" data-generated-css=\"brz-css-zx94a\"><span class=\"brz-cp-color5\">Trig formulae &#8211; Double and Compound<\/span><\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-evLP5\" data-uniq-id=\"mLTT2\" data-generated-css=\"brz-css-zx94a\"><span class=\"brz-cp-color5\">Reciprocal and inverse trig. <\/span><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa3\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1nq3l7c\" data-brz-custom-id=\"nh7GG343TjdJ\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-sq3uux\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"te9wil5LdLCc\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-rltvS\" data-generated-css=\"brz-css-egBZZ\" data-uniq-id=\"fRAqC\"><strong class=\"brz-cp-color5\">04<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-1sr1hk3 brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"y_LMbK_HXlKf\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-qlt43\" data-generated-css=\"brz-css-glvMV\" data-uniq-id=\"zeaKF\"><span class=\"brz-cp-color5\">Proof<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"mgceTBrrxjLr\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-axtLW\" data-generated-css=\"brz-css-yol00\" data-uniq-id=\"qDAlg\"><strong class=\"brz-cp-color5\">Direct proof<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-rVKB6\" data-generated-css=\"brz-css-ra1p8\" data-uniq-id=\"nn6bt\">Proof by contrapositive<\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-zPPxf\" data-generated-css=\"brz-css-wJxNl\" data-uniq-id=\"zLtCH\"><strong class=\"brz-cp-color5\">Proof by contradiction<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-qfg5D\" data-generated-css=\"brz-css-aU_NQ\" data-uniq-id=\"r14Eo\"><strong class=\"brz-cp-color5\">Induction &#8211; series<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-jgGOA\" data-generated-css=\"brz-css-c3RmX\" data-uniq-id=\"dxf46\"><strong class=\"brz-cp-color5\">Induction &#8211; division<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-vZ3ln\" data-generated-css=\"brz-css-u6IfI\" data-uniq-id=\"vry1o\"><strong class=\"brz-cp-color5\">Induction &#8211; other<\/strong><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa4\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-n8yl6h\" data-brz-custom-id=\"fkM_FjaaB3n0\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-ow0of3\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"eEtHWaqfb2Vr\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-vo8gw\" data-generated-css=\"brz-css-zK6UX\" data-uniq-id=\"xOE90\"><strong class=\"brz-cp-color5\">05<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-1nfpmck brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"clQ15kh4dhE0\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-p34SH\" data-generated-css=\"brz-css-e79sE\" data-uniq-id=\"uDxTA\"><span class=\"brz-cp-color5\">Complex Numbers<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"zJINnPmpgJDK\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-qD_4l\" data-generated-css=\"brz-css-qPFXU\" data-uniq-id=\"vnqHu\"><strong class=\"brz-cp-color5\">The number i<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-p3LaL\" data-generated-css=\"brz-css-jj0NI\" data-uniq-id=\"voefC\"><strong class=\"brz-cp-color5\">Complex number algebra<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-dTUoO\" data-generated-css=\"brz-css-pJL5O\" data-uniq-id=\"eRawg\"><strong class=\"brz-cp-color5\">The Argand plane and polar form<\/strong><\/li>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-kfPDF\" data-generated-css=\"brz-css-bjn2z\" data-uniq-id=\"azsIb\">De Moivre&#8217;s Theorem and roots.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa5\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"83318d3b23b6ec423609_av_zoeDW_xl1\" class=\"brz-section brz-css-z2q6fd\">\n<div class=\"brz-section__content brz-section--boxed brz-css-sbbn76 brz-css-17jknq9\" data-brz-custom-id=\"uNgpKhXNGj6o\">\n<div class=\"brz-bg\">\n<div class=\"brz-bg-color\"><\/div>\n<\/div>\n<div class=\"brz-container brz-css-9g5gjg\">\n<div class=\"brz-row__container brz-css-73ukg3\" data-brz-custom-id=\"hX452i6698FZ\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-row brz-css-qrby90 brz-css-l30oc2\">\n<div class=\"brz-columns brz-css-tpgd33 brz-css-odif42\" data-brz-custom-id=\"cveGk6o1UWzY\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1b8d4g2\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"uNTlYHwMgoJf\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-gM3NI\" data-generated-css=\"brz-css-b6Z73\" data-uniq-id=\"iKP0c\"><span class=\"brz-cp-color3\">06<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-19zyv2a brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"l9HBOZX94yRU\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-fNSDJ\" data-generated-css=\"brz-css-mrb5L\" data-uniq-id=\"s83Rh\"><span class=\"brz-cp-color3\">Differentiation<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"mS5SvAqyes9b\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-nDe3U\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">First principles<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-x_tjU\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">Simple differentiation<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-fr5nJ\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">Tangents and normals<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-nI3FO\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">The chain rule<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-iOtNB\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">Product and Quotient rules<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-nF9C1\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">Functions and differentiation rules<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-e1EsB\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">Turning porints<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-hWKsl\" data-generated-css=\"brz-css-geSEV\" data-uniq-id=\"w7c9N\">Implicit differentiation <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa6\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-pxwq8c\" data-brz-custom-id=\"eBBju893k93v\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1ez7ohn\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"sELA4SZ4qVw0\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-dlDGC\" data-generated-css=\"brz-css-zSzDE\" data-uniq-id=\"v8ySI\"><strong class=\"brz-cp-color3\">07<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-f9l9je brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"bQNDFOV1acA4\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-v2lND\" data-generated-css=\"brz-css-nzMrV\" data-uniq-id=\"a8zdE\"><span class=\"brz-cp-color3\">Integration <\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"tuf1UDUeAl7G\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-kJtVL\" data-uniq-id=\"qk19v\" data-generated-css=\"brz-css-gzSIT\">Anti differentiation<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-nglo4\" data-uniq-id=\"a_ZHB\" data-generated-css=\"brz-css-hmpN5\">Definite integrals<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-oLQCn\" data-uniq-id=\"r35w8\" data-generated-css=\"brz-css-mZ4Gx\">Integration by substitution<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-nL6vc\" data-uniq-id=\"miCr4\" data-generated-css=\"brz-css-qDKwj\"><strong>Integration by<\/strong> parts<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-hC5t5\" data-uniq-id=\"nMh9K\" data-generated-css=\"brz-css-yIQlu\"><strong>Integration by<\/strong> partial fractions<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-e6hvd\" data-uniq-id=\"nMh9K\" data-generated-css=\"brz-css-yIQlu\">Volumes of revolution<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-awgWs\" data-uniq-id=\"nMh9K\" data-generated-css=\"brz-css-yIQlu\">Kinetics <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa7\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1sapcao\" data-brz-custom-id=\"c7eBYnGBcqnA\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1k19v68\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"sJmkAUfCyWXq\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-vdXz3\" data-generated-css=\"brz-css-ytTrZ\" data-uniq-id=\"xgBvA\"><strong class=\"brz-cp-color3\">08<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-n3kjeq brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"zSPwva99RyPd\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-hj9JG\" data-generated-css=\"brz-css-t5NDt\" data-uniq-id=\"gvr0g\"><span class=\"brz-cp-color3\">Statistics and Probability<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"ztmAEGyNe0YE\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color3 brz-css-aNu18\" data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\">Cumulative frequency and box-plots<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-h36To\" data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\">Basic probability and formulae<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-ginCT\" data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\">Discrete tables<\/li>\n<li class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-rdiSu\" data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\">Binomial distribution<\/li>\n<li data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\" class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-wPhnv\">Normal distribution<\/li>\n<li data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\" class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-nReNd\">Continuos distributions<\/li>\n<li data-uniq-id=\"ugnGL\" data-generated-css=\"brz-css-oqsrp\" class=\"brz-bcp-color3 brz-tp-lg-z6fFstO9H4nb brz-css-iSArp\">Bayes Theorem <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa8\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section id=\"f4a10fca048e6e7e30b9_fgLtIymh0bkr\" class=\"brz-section brz-css-z2q6fd\">\n<div class=\"brz-section__content brz-section--boxed brz-css-sbbn76 brz-css-uj1glm\" data-brz-custom-id=\"b_z11kzIfDeN\">\n<div class=\"brz-bg\">\n<div class=\"brz-bg-color\"><\/div>\n<\/div>\n<div class=\"brz-container brz-css-9g5gjg\">\n<div class=\"brz-row__container brz-css-73ukg3\" data-brz-custom-id=\"xEv72rz6Qa07\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-row brz-css-qrby90 brz-css-l30oc2\">\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1g1i2c4\" data-brz-custom-id=\"ykzw98XS8_9L\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1jrfmd6\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"qx5zZliY7Br6\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-hJGCM\" data-uniq-id=\"fWVes\" data-generated-css=\"brz-css-g8RAz\"><span class=\"brz-cp-color5\">09<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-dno7ve brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"yiylwaMX05X6\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-wzNTr\" data-uniq-id=\"h0TUT\" data-generated-css=\"brz-css-yXoU0\"><span class=\"brz-cp-color5\">Vectors<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"s60PoULSm7B2\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-sFRWF\" data-uniq-id=\"e18Hl\" data-generated-css=\"brz-css-nabQg\">Vector geometry and basics<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-pS2gS\" data-uniq-id=\"e18Hl\" data-generated-css=\"brz-css-nabQg\">2d and 3d Vectors line equations<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-kasLB\" data-uniq-id=\"e18Hl\" data-generated-css=\"brz-css-nabQg\">The Cross product<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-jE5cG\" data-uniq-id=\"e18Hl\" data-generated-css=\"brz-css-nabQg\">Vector planes<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-esOPh\" data-uniq-id=\"e18Hl\" data-generated-css=\"brz-css-nabQg\">Shortest distance problems <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa9\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1mz747y\" data-brz-custom-id=\"bo5hYkNbMyd4\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-1gp25yb\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"iHBpeUW3TEEj\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-mvHac\" data-uniq-id=\"stkoM\" data-generated-css=\"brz-css-nYvMv\"><strong class=\"brz-cp-color5\">10<\/strong><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-5wg89w brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"zkb8stjZM3a_\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-tWPap\" data-uniq-id=\"wbqV8\" data-generated-css=\"brz-css-lUryo\"><span class=\"brz-cp-color5\">Further Calculus<\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"rpIpUJAQIcGG\">\n<div data-brz-translate-text=\"1\">\n<ul>\n<li class=\"brz-tp-lg-z6fFstO9H4nb brz-bcp-color5 brz-css-opxrh\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">Maclaurin&#8217;s Series<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-rszos\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">L&#8217;Hopitals<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-srJ9h\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">Differential equations<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-zQjh9\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">Euler&#8217;s Method<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-f5o_F\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">Homogeneous equations<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-j3YEm\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">Integrating factor<\/li>\n<li class=\"brz-bcp-color5 brz-tp-lg-z6fFstO9H4nb brz-css-qi30L\" data-generated-css=\"brz-css-xBngD\" data-uniq-id=\"a9Oo3\">Maclaurin&#8217;s Series and differential equations <\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><a class=\"brz-a brz-container-link\" href=\"https:\/\/ibmaths.com\/ibaahl\/hlaa10\/\" target=\"_self\" rel=\"noopener\" data-brz-link-type=\"page\"><\/a><\/div>\n<div class=\"brz-columns brz-css-tpgd33 brz-css-1gcv33n\" data-brz-custom-id=\"jfTM2iszeZjn\">\n<div class=\"brz-bg\"><\/div>\n<div class=\"brz-column__items brz-css-1sv7dma brz-css-avjxze\">\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"qbyyGxTIhg2b\">\n<div data-brz-translate-text=\"1\">\n<p class=\"brz-tp-lg-heading3 brz-css-lOS9W\" data-uniq-id=\"xKRs4\" data-generated-css=\"brz-css-e8JHg\"><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-css-l3018y brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"pVhD7JDzhtRV\">\n<div data-brz-translate-text=\"1\">\n<h5 class=\"brz-tp-lg-heading5 brz-css-aCkuM\" data-uniq-id=\"s7Dq9\" data-generated-css=\"brz-css-a_CT3\"><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"\" class=\"brz-css-69hdiv brz-wrapper\">\n<div class=\"brz-rich-text brz-rich-text__custom brz-css-dwph6s\" data-brz-custom-id=\"mL3NA2dICaQK\">\n<div 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