{"id":6955,"date":"2026-04-05T08:07:07","date_gmt":"2026-04-05T08:07:07","guid":{"rendered":"https:\/\/okmathscenter.com\/?page_id=6955"},"modified":"2026-04-05T08:08:04","modified_gmt":"2026-04-05T08:08:04","slug":"programi-i-matematikes-ne-mature-shteterore","status":"publish","type":"page","link":"https:\/\/okmathscenter.com\/sq\/programi-i-matematikes-ne-mature-shteterore\/","title":{"rendered":"Programi i Matematik\u00ebs n\u00eb Matur\u00eb Shtet\u00ebrore"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"6955\" class=\"elementor elementor-6955\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f9f97da e-flex e-con-boxed e-con e-parent\" data-id=\"f9f97da\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5285e6a elementor-widget elementor-widget-text-editor\" data-id=\"5285e6a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><strong>Programi i Matematik\u00ebs n\u00eb Matur\u00eb Shtet\u00ebrore. \u00a0<\/strong><\/p><p>Njohurit\u00eb p\u00ebr realizimin e kompetencave matematikore jan\u00eb t\u00eb renditura sipas 6 tematikave kryesore, me n\u00ebntematika specifike p\u00ebr secil\u00ebn.<\/p><p>K\u00ebto njohuri lidhen drejtp\u00ebrdrejt me rezultatet e nx\u00ebn\u00ebsit dhe kompetencat (lidhje konceptuale, zgjidhje problemore, arsyetim, modelim).<\/p><p>M\u00eb posht\u00eb renditen t\u00eb gjitha n\u00ebntematikat me njohurit\u00eb kryesore, t\u00eb nxjerr\u00eb nga faqja zyrtare e Ministris\u00eb s\u00eb Arsimit.<\/p><p><strong><u>Numri (17%)<\/u><\/strong><\/p><p><strong>Bashk\u00ebsit\u00eb:<\/strong><\/p><ul><li>Bashk\u00ebsit\u00eb dhe marr\u00ebdh\u00ebnia nd\u00ebr tyre.<\/li><li>Bashk\u00ebsit\u00eb numerike.<\/li><li>Prerja dhe bashkimi i dy bashk\u00ebsive.<\/li><\/ul><p><strong>Veprimet me numra:<\/strong><\/p><ul><li>Rrjedha e veprimeve (kllapat, fuqit\u00eb, rr\u00ebnj\u00ebt).<\/li><li>Numrat e thjesht\u00eb, faktor\u00ebt pjestues\/shumfisha (shvp, pmp), fuqit\u00eb rr\u00ebnj\u00ebt, numra iracional\u00eb.<\/li><li>Thyesat dhe numrat dhjetor: Kthimi i numrave dhjetor t\u00eb fund\u00ebm n\u00eb thyes\u00eb dhe anasjelltas.<\/li><\/ul><p><strong>Raporti, p\u00ebrpjestimi dhe p\u00ebrqindja:<\/strong><\/p><ul><li>Raporti si thyes\u00eb.<\/li><li>P\u00ebrpjes\u00ebtimi si raporte t\u00eb barabarta.<\/li><li>\u00a0Lidhja e raportit me funksionet lineare.<\/li><li>P\u00ebrqindja si thyes\u00eb ose num\u00ebr dhjetor.<\/li><li>Sasia si p\u00ebrqindje t\u00eb nj\u00eb sasie tjet\u00ebr.<\/li><li>Interesi i thjesht\u00eb n\u00eb matematik\u00ebn financiare.<\/li><li>Interesi i p\u00ebrb\u00ebr\u00eb.<\/li><li>Fuqit\u00eb dhe rr\u00ebnj\u00ebt.<\/li><li>Vetit\u00eb e logaritmeve<\/li><\/ul><p><strong><u>Matjet (15%)<\/u><\/strong><\/p><p><strong>Matjet dhe sakt\u00ebsia e tyre:<\/strong><\/p><ul><li>K\u00ebmbimi i nj\u00ebsimve standarde p\u00ebrfshir\u00eb nj\u00ebsit\u00eb e p\u00ebrbra.<\/li><li>Shkalla e zmadhimit\/zvog\u00eblimit dhe hartat.<\/li><li>Nj\u00ebsimet e matjes (gjat\u00ebsi, sip\u00ebrfaqe, v\u00ebllim, mas\u00eb, koh\u00eb, para),<\/li><li>Perimet\u00ebr\/sip\u00ebrfaqe\/v\u00ebllim figurash.<\/li><li>Kongruenca\/ngjashm\u00ebria e figurave.<\/li><li>Teorema\/t e Pitagor\u00ebs\/Euklidit.<\/li><\/ul><p><strong>Vektor\u00ebt:<\/strong><\/p><ul><li>Mbledhja dhe zbritja e vektor\u00ebve.<\/li><li>Shum\u00ebzimi i vektor\u00ebve me nj\u00eb num\u00ebr.<\/li><li>Paraqitja e vektorit gjeometrikisht dhe n\u00eb shtyll\u00eb me an\u00eb t\u00eb koordinatave.<\/li><li>Vektor\u00ebt me dy koordinata.<\/li><li>Gjat\u00ebsia e nj\u00eb vektori.<\/li><li>Rregulla e paralelogramit dhe e trek\u00ebnd\u00ebshit p\u00ebr mbledhjen e vektor\u00ebve.<\/li><li>Paraqitja algjebrike e mbledhjes s\u00eb vektor\u00ebve si dhe e shum\u00ebzimit t\u00eb vektorit me nj\u00eb num\u00ebr.<\/li><li>Largesa nd\u00ebrmjet dy pikave.<\/li><\/ul><p><strong>Trigonometria:<\/strong><\/p><ul><li>Koncepti i sinusit, kosinusit, tangjentit dhe kotangjentit.<\/li><li>Formulat trigonometrike baz\u00eb n\u00eb trek\u00ebnd\u00ebshin k\u00ebnddrejt\u00eb (sinus, kosinus dhe tangjent).<\/li><li>Teorema e sinusit dhe teorema e kosinusit n\u00eb trek\u00ebnd\u00ebsh.<\/li><li>Formula S = \u00bd ab sinA p\u00ebr t\u00eb njehsuar syprin\u00ebn, brinj\u00ebt ose k\u00ebndet n\u00eb nj\u00eb trek\u00ebnd\u00ebsh.<\/li><li>Formula e tangentit t\u00eb k\u00ebndit.<\/li><li>Formula themelore e trigonometris\u00eb.<\/li><\/ul><p><strong><u>Gjeometria (13%)<\/u><\/strong><\/p><ul><li>Kuptimi i larges\u00ebs s\u00eb pik\u00ebs nga nj\u00eb drejt\u00ebz.<\/li><li>Vetit\u00eb e k\u00ebndeve me kulm t\u00eb p\u00ebrbashk\u00ebt: shtuese, plot\u00ebsuese, k\u00ebnde t\u00eb kund\u00ebrt n\u00eb kulm etj.<\/li><li>\u00a0K\u00ebndet korresponduese q\u00eb formohen nga drejt\u00ebza paralele.<\/li><li>Kongruenca e trek\u00ebnd\u00ebshave t\u00eb \u00e7far\u00ebdosh\u00ebm (BKB, KBK, BBB) dhe trek\u00ebnd\u00ebshave k\u00ebnddrejt\u00eb.<\/li><li>Teoremat e rrethit q\u00eb I referohen k\u00ebndeve, rrezes, tangjentes, kordave.<\/li><li>Ekuacioni i rrethit n\u00eb trajt\u00ebn (x-a)<sup>2<\/sup> + (y-b)<sup>2<\/sup> = r<sup>2<\/sup> .<\/li><li>Ekuacioni i drejt\u00ebz\u00ebs n\u00eb plan.<\/li><li>Kushti i paralelizmit dhe i pingultis\u00eb s\u00eb dy drejt\u00ebzave.<\/li><\/ul><p><strong>Shnd\u00ebrrime gjeometrike:<\/strong><\/p><ul><li>Simetria, zhvendosja paralele dhe zmadhimi (p\u00ebrfshir\u00eb edhe koeficient\u00eb thyesor\u00eb apo negativ\u00eb).<\/li><li>\u00a0Ndryshimet dhe elementet e pandryshuesh\u00ebm gjat\u00eb shnd\u00ebrrimeve gjeometrike: simetris\u00eb, zhvendosjes paralele dhe zmadhimit.<\/li><\/ul><p><strong>Gjeometria n\u00eb hap\u00ebsir\u00eb:<\/strong><\/p><ul><li>Vetit\u00eb e faqeve, brinj\u00ebve, kulmeve, sip\u00ebrfaqeve t\u00eb kuboidit, prizmit, cilindrit, piramid\u00ebs, konit, sfer\u00ebs.<\/li><\/ul><p><strong><u>Algjebra dhe funksioni (Derivati dhe Integrali) (38%)<\/u><\/strong><\/p><p><strong>Simbolet, veprimet algjebrike dhe funksioni:<\/strong><\/p><ul><li>Z\u00ebvend\u00ebsimi i vlerave numerike n\u00eb formula dhe shprehje algjebrike.<\/li><li>Paraqitja n\u00eb m\u00ebnyr\u00eb m\u00eb t\u00eb thjesht\u00eb e shprehjeve algjebrike.<\/li><li>Shnd\u00ebrrime t\u00eb nj\u00ebvlershme n\u00eb shprehjet algjebrike.<\/li><li>Funksione me t\u00eb dh\u00ebna (bashk\u00ebsia e p\u00ebrcaktimit) dhe rezultate (bashk\u00ebsia e vlerave).<\/li><li>Funksioni i anasjellt\u00eb.<\/li><li>Funksion i p\u00ebrb\u00ebr\u00eb.<\/li><\/ul><p><strong>Grafik\u00ebt:<\/strong><\/p><ul><li>Grafiku i ekuacioneve lineare n\u00eb planin koordinativ.<\/li><li>Trajta y = mx + c p\u00ebr identifikimin e drejt\u00ebzave paralele dhe pingule.<\/li><li>Ekuacioni i drejt\u00ebz\u00ebs q\u00eb kalon n\u00ebp\u00ebr dy pika ose q\u00eb kalon nga nj\u00eb pik\u00eb dhe me koeficient k\u00ebndor (pjerr\u00ebsi) t\u00eb dh\u00ebn\u00eb.<\/li><li>Koeficient\u00ebt k\u00ebndor\u00eb dhe pik\u00ebprerjet me boshtet koordinativ\u00eb t\u00eb funksioneve lineare.<\/li><li>Rr\u00ebnj\u00ebt dhe koordinatat e kulmit t\u00eb grafikut t\u00eb funksionit t\u00eb fuqis\u00eb s\u00eb dyt\u00eb.<\/li><li>Grafik\u00eb t\u00eb funksioneve lineare, t\u00eb funksioneve t\u00eb fuqis\u00eb s\u00eb dyt\u00eb, t\u00eb funksionit p\u00ebrpjestimor t\u00eb zhdrejt\u00eb y=1\/x ku x i ndrysh\u00ebm nga zrero.<\/li><li>Funksioni eksponencial y = a<sup>x<\/sup> p\u00ebr vlera pozitive t\u00eb a te ndryshme nga 1 dhe t\u00eb funksioneve trigonometrike me period\u00eb t\u00eb plot\u00eb y = sinx, y = cosx p\u00ebr t\u00eb gjitha k\u00ebndet.<\/li><li>Ekuacioni i rrethit me qend\u00ebr n\u00eb origjin\u00ebn e boshteve koordinative.<\/li><li>Ekuacioni i tangjentes s\u00eb nj\u00eb rrethi n\u00eb nj\u00eb pik\u00eb t\u00eb dh\u00ebn\u00eb.<\/li><li>Ekuacione dhe grafik\u00eb q\u00eb p\u00ebrshkruajn\u00eb p\u00ebrpjes\u00ebtimin e drejt\u00eb dhe t\u00eb zhdrejt\u00eb.<\/li><li>Pjerr\u00ebsia e grafikut t\u00eb nj\u00eb vij\u00eb t\u00eb drejt\u00eb si norm\u00eb ndryshimi.<\/li><li>Koeficienti k\u00ebndor (pjerr\u00ebsia) i tangjentes n\u00eb nj\u00eb pik\u00eb t\u00eb nj\u00eb vije t\u00eb lakuar (si norm\u00eb ndryshimi n\u00eb at\u00eb pik\u00eb).<\/li><li>Pjerr\u00ebsia mesatare (koeficienti k\u00ebndor i kord\u00ebs) dhe pjerr\u00ebsia n\u00eb nj\u00eb pik\u00eb (koeficienti k\u00ebndor i tangjentes).<\/li><\/ul><p><strong>Zgjidhja e ekuacioneve dhe inekuacioneve:<\/strong><\/p><ul><li>Ekuacione lineare me nj\u00eb ndryshore (p\u00ebrfshir\u00eb ekuacionet me ndryshore n\u00eb t\u00eb dyja an\u00ebt e barazimit).<\/li><li>Ekuacione t\u00eb fuqis\u00eb s\u00eb dyt\u00eb, duke p\u00ebrdorur formul\u00ebn p\u00ebrkat\u00ebse.<\/li><li>Grafiku i ekuacione t\u00eb fuqis\u00eb s\u00eb dyt\u00eb.<\/li><li>Sistemi i dy ekuacioneve me dy ndryshore (dy ekuacione lineare ose nj\u00eb ekuacion linear dhe ekuacioni tjet\u00ebr t\u00eb fuqis\u00eb s\u00eb dyt\u00eb).<\/li><li>Zgjidhja grafike e sistemit.<\/li><li>Inekuacione lineare me nj\u00eb ose dy ndryshore.<\/li><li>Zgjidhja n\u00eb m\u00ebnyr\u00eb grafike e inekuacionit t\u00eb trajt\u00ebs y &gt; x +1 dhe y &gt; ax<sup>2<\/sup> + bx +c.<\/li><li>Bashk\u00ebsia e zgjidhjeve n\u00eb boshtin numerik duke p\u00ebrdorur simbolet e bashk\u00ebsis\u00eb dhe grafik\u00eb.<\/li><\/ul><p><strong>Vargjet:<\/strong><\/p><ul><li>Vargu sipas rregull\u00ebs s\u00eb kufizave t\u00eb nj\u00ebpasnj\u00ebshme dhe rregull\u00ebs kufiz\u00eb \u2013vend.<\/li><li>Vargjet e numrave trek\u00ebndor\u00eb, katror\u00eb dhe kubik\u00eb.<\/li><li>Progresionet e thjeshta aritmetike, progresione t\u00eb thjeshta gjeometrike.<\/li><li>Vargjet Fibonaci, vargjet e fuqis\u00eb s\u00eb dyt\u00eb (duke llogaritur diferenc\u00ebn e dyt\u00eb).<\/li><li>Kufiza e n-t\u00eb n\u00eb vargjet lineare.<\/li><li>Zb\u00ebrthimi binomial (a+b)<sup>n<\/sup> p\u00ebr eksponent\u00eb natyror\u00eb n m\u00eb t\u00eb vog\u00ebl ose baraz me 4.<\/li><\/ul><p><strong>Polinome dhe funksione<\/strong><\/p><ul><li>\u2022 Dallori i polinomit t\u00eb fuqis\u00eb s\u00eb dyt\u00eb.<\/li><li>Shnd\u00ebrrimi algjebrik i polinomeve.<\/li><li>Funksionet kuadratike dhe grafik\u00ebt e tyre.<\/li><li>Funksionet p\u00ebrpjes\u00ebtimore dhe grafik\u00ebt e tyre.<\/li><li>Funksionet e sinusit, kosinusit dhe grafik\u00ebt e tyre.<\/li><li>Funksioni y = a<sup>x<\/sup> dhe grafiku i tij kur a \u00ebsht\u00eb pozitiv dhe a t\u00eb ndryshme nga 1.<\/li><li>\u2022 Funksioni y = e<sup>x<\/sup> dhe grafiku i tij.<\/li><li>\u00a0Koeficienti k\u00ebndor (pjerr\u00ebsia) i tangjentes ndaj grafikut t\u00eb funksionit y = lnx \u00ebsht\u00eb i barabart\u00eb me kekx .<\/li><li>Koncepti i log ax si funksioni i anasjellt\u00eb i funksionit y = a<sup>x<\/sup> , ku a \u00ebsht\u00eb pozitive dhe e ndryshme nga 1 dhe x i ndryshem nga 0.<\/li><li>Funksioni y = ln x dhe grafiku i tij.<\/li><li>\u00a0Funksioni y = ln x si funksion i anasjellt\u00eb i y = e<sup>x<\/sup>.<\/li><li>Asimptota vertikale dhe horizontale.<\/li><\/ul><p><strong>Derivati:<\/strong><\/p><ul><li>Koncepti i derivatit t\u00eb funksionit f(x) si koeficient k\u00ebndor i tangjentes ndaj grafikut t\u00eb funksionit y = f(x) n\u00eb nj\u00eb pik\u00eb t\u00eb \u00e7far\u00ebdoshme (x;y).<\/li><li>\u00a0Derivati si norm\u00eb (shkall\u00eb) ndryshimi.<\/li><li>Grafiku i pjerr\u00ebsis\u00eb (funksionit derivat) p\u00ebr nj\u00eb vij\u00eb t\u00eb dh\u00ebn\u00eb.<\/li><li>Derivati i rendit t\u00eb dyt\u00eb.<\/li><li>Zbatime t\u00eb derivatit p\u00ebr t\u00eb gjetur koeficientin k\u00ebndor, ekuacionin e tangjentes dhe pingules s\u00eb nj\u00eb vije n\u00eb nj\u00eb pik\u00eb t\u00eb dh\u00ebn\u00eb.<\/li><li>\u00a0Ekstremumet e funksionit me an\u00eb t\u00eb derivatit.<\/li><li>Monotonia e funksionit me an\u00eb t\u00eb derivatit t\u00eb funksionit (rrit\u00ebs dhe zbrit\u00ebs).<\/li><\/ul><p><strong>Integrali:<\/strong><\/p><ul><li>Koncepti i integrimit si proces i anasjellt\u00eb i derivimit.<\/li><li>Integrimi i x<sup>n<\/sup> (p\u00ebrjashto n = -1) si dhe i shumave dhe i ndryshesave p\u00ebrkat\u00ebse, duke p\u00ebrfshir\u00eb edhe shum\u00ebzimin me konstante.<\/li><li>Integrali i caktuar (Formula e Njuton \u2013Leibnic).<\/li><li>P\u00ebrdorimi i integralit t\u00eb caktuar p\u00ebr t\u00eb gjetur syprin\u00ebn n\u00ebn nj\u00eb vij\u00eb dhe syprin\u00ebn nd\u00ebrmjet dy vijave<\/li><\/ul><p><strong>Statistika dhe probabiliteti (17%)<\/strong><\/p><ul><li>Popullata dhe kampionimi.<\/li><li>Tabela, diagrame, tabela dendurie, diagrami rrethor p\u00ebr t\u00eb kategorizuar t\u00eb dh\u00ebna.<\/li><li>Diagrami me shtylla p\u00ebr t\u00eb paraqitur t\u00eb dh\u00ebna numerike diskrete jo t\u00eb grupuara.<\/li><li>Diagrame p\u00ebr t\u00eb paraqitur t\u00eb dh\u00ebna diskrete t\u00eb grupuara dhe t\u00eb dh\u00ebna t\u00eb vazhduara.<\/li><li>Mesataret (mesorja, mesatarja aritmetike, moda dhe klasa modale), amplituda.<\/li><li>Skatergrafi i t\u00eb dh\u00ebnave me dy ndryshore.<\/li><li>Korrelacioni.<\/li><\/ul><p><strong>Probabiliteti:<\/strong><\/p><ul><li>Dendurit\u00eb e rezultateve n\u00eb eksperimente probabilitare duke p\u00ebrdorur tabelat dhe pem\u00ebn e dendurive.<\/li><li>Ngjarjet e rastit, nj\u00eblloj t\u00eb mundshme dhe t\u00eb pavarura, p\u00ebr t\u00eb njehsuar rezultatet e pritshme nga eksperimentet.<\/li><li>Shuma e probabiliteteve t\u00eb t\u00eb gjitha ngjarjeve elementare \u00ebsht\u00eb nj\u00eb.<\/li><li>Shuma e probabiliteteve t\u00eb ngjarjeve dy e nga dy t\u00eb papajtueshme, bashkimi i t\u00eb cilave jep hap\u00ebsir\u00ebn e rezultateve, \u00ebsht\u00eb nj\u00eb.<\/li><li>Hap\u00ebsira e rezultateve t\u00eb mundshme teorike p\u00ebr eksperimente t\u00eb ve\u00e7anta ose p\u00ebr eksperimente t\u00eb p\u00ebrb\u00ebra me rezultate nj\u00ebsoj t\u00eb mundshme.<\/li><li>Probabiliteti i ngjarjeve t\u00eb kombinuara, t\u00eb varura dhe t\u00eb pavarura.<\/li><li>Shp\u00ebrndarja e variablave diskrete.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Programi i Matematik\u00ebs n\u00eb Matur\u00eb Shtet\u00ebrore. \u00a0 Njohurit\u00eb p\u00ebr realizimin e kompetencave matematikore jan\u00eb t\u00eb renditura sipas 6 tematikave kryesore, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","footnotes":""},"class_list":["post-6955","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false,"trp-custom-language-flag":false,"educrat-course-list":false,"educrat-course-grid":false,"woocommerce_thumbnail":false,"woocommerce_single":false,"woocommerce_gallery_thumbnail":false},"uagb_author_info":{"display_name":"eniduka2023@gmail.com","author_link":"https:\/\/okmathscenter.com\/sq\/author\/eniduka2023gmail-com\/"},"uagb_comment_info":0,"uagb_excerpt":"Programi i Matematik\u00ebs n\u00eb Matur\u00eb Shtet\u00ebrore. \u00a0 Njohurit\u00eb p\u00ebr realizimin e kompetencave matematikore jan\u00eb t\u00eb renditura sipas 6 tematikave kryesore, [&hellip;]","_links":{"self":[{"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/pages\/6955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/comments?post=6955"}],"version-history":[{"count":5,"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/pages\/6955\/revisions"}],"predecessor-version":[{"id":6961,"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/pages\/6955\/revisions\/6961"}],"wp:attachment":[{"href":"https:\/\/okmathscenter.com\/sq\/wp-json\/wp\/v2\/media?parent=6955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}