{"id":1311,"date":"2016-06-15T14:30:02","date_gmt":"2016-06-15T14:30:02","guid":{"rendered":"http:\/\/timss2015.org\/advanced\/?page_id=1311"},"modified":"2019-07-08T18:24:43","modified_gmt":"2019-07-08T18:24:43","slug":"portugal-description-of-advanced-mathematics-programs-and-curricula","status":"publish","type":"page","link":"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/portugal-description-of-advanced-mathematics-programs-and-curricula\/","title":{"rendered":"Portugal: Description of Advanced Mathematics Programs and Curricula"},"content":{"rendered":"<div class=\"carouselwrap\"><div id=\"menu-programs-and-curriculum-advanced-mathematics\" class=\"carouselmenu\"><a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/france-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>France<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/italy-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Italy<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/lebanon-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Lebanon<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/norway-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Norway<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/portugal-description-of-advanced-mathematics-programs-and-curricula\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Portugal<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/russian-federation-description-of-advanced-mathematics-programs-and-curricula\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Russian Federation<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/slovenia-description-of-advanced-mathematics-programs-and-curricula\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Slovenia<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/sweden-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Sweden<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/united-states-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>United States<\/span><\/a><\/li>\n<\/div><\/div>\t<style>\n\t\t.carouselwrap{\n\t\t\tbackground: #e5eaef;\n\t\t}\t\t\n\t\t.owl-item a{\n\t\t\tbackground: #ffffff;\n\t\t\tborder: 4px #1FA67A solid;\n\t\t\tcolor: #000000;\n\t\t}\t\t\n\t\t.owl-item a:hover,\n\t\t.owl-item a:focus,\n\t\t.owl-item a.current-menu-item{\n\t\t\tbackground: #006544;\n\t\t\tborder: 4px #1FA67A solid;\n\t\t\t\n\t\t\tcolor: #ffffff;\n\t\t}\n\t<\/style>\n\t\n<div><a class=\"aboutTIMSS-download\" href=\"http:\/\/timss2015.org\/wp-content\/uploads\/filebase\/advanced\/advanced-mathematics\/M11.-programs-and-curriculum\/M11_1_adv-math-description-of-advanced-math-programs-and-curriculum.pdf\" target=\"_blank\">Download Description of the Advanced Mathematics Programs and Curriculum<\/a><\/div>\n<h2>Portugal: Description of the Advanced Mathematics Programs and Curriculum<\/h2>\n<p>Advanced Mathematics is a mandatory course for students in the upper-secondary Science and Technology and Socioeconomic Sciences academic tracks. The curriculum is divided into three main subjects: Probability and Combinatorics, Introduction to Differential Calculus II, and Trigonometry and Complex Numbers. The topics included in each main subject are listed below.<\/p>\n<table width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\" class=\"CurrTable\">\n<tbody>\n<tr>\n<th width=\"25%\">Main Subject<\/th>\n<th>Topics<\/th>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Probability and Combinatorics\n     <\/td>\n<td>\n      Introduction to probability: random experiments; outcome spaces; events and operations with events; classical, frequency and axiomatic definitions of probability; conditional probability and independence of events <\/p>\n<p>Relative frequency and probability distributions: random variables and density functions for discrete variables; sample versus population means and standard-deviations; binomial probability distributions; normal distributions; histograms versus continuous probability density functions <\/p>\n<p>Combinatorics: enumerative combinatorics; permutations and combinations; Pascal\u2019s Triangle and Newton\u2019s Binomial expansion; the Binomial Theorem; applications of probability calculations\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Introduction to Differential Calculus II <\/td>\n<td>\n     Exponential and logarithmic functions: analytical and graphical properties of exponential and logarithmic functions; rules for exponents and logarithms; modeling with exponential and logarithmic functions<\/p>\n<p>Limits theory: Heine\u2019s definition of the limit of a function and its properties; notable special limits; indeterminate forms of limits; asymptotes; continuity of functions, Bolzano-Cauchy\u2019s Theorem; numerical applications<\/p>\n<p>Differential calculus: Derivatives rules and applications; concavity and second derivatives; composite functions and their derivatives; properties of simple functions that can be determined by studying derivatives; optimization problems\n     <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Trigonometry and Complex Numbers <\/td>\n<td>\n<p>Trigonometry: intuitive study of the sine, cosine and tangent functions and their derivatives based on the unit circle; special limits of the sine function; use of trigonometry functions in modeling<\/p>\n<p>Complex numbers: introduction to complex numbers; the imaginary unit; algebraic form of and operations with complex numbers in this form; trigonometric form of complex numbers and operations with complex numbers in this form; geometric interpretation of operations with complex numbers; complex variables in the geometric plane\n      <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Download Description of the Advanced Mathematics Programs and Curriculum Portugal: Description of the Advanced Mathematics Programs and Curriculum Advanced Mathematics is a mandatory course for students in the upper-secondary Science and Technology and Socioeconomic Sciences academic tracks. The curriculum is &hellip; <a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/portugal-description-of-advanced-mathematics-programs-and-curricula\/\">Continued<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":1278,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1311","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1311","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/comments?post=1311"}],"version-history":[{"count":10,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1311\/revisions"}],"predecessor-version":[{"id":3051,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1311\/revisions\/3051"}],"up":[{"embeddable":true,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1278"}],"wp:attachment":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/media?parent=1311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}