{"id":240,"date":"2026-03-05T15:21:58","date_gmt":"2026-03-05T14:21:58","guid":{"rendered":"https:\/\/zalapto.pl\/baza\/?p=240"},"modified":"2026-03-05T15:26:38","modified_gmt":"2026-03-05T14:26:38","slug":"zadanie-6-matura-probna-matematyka-marzec-2026","status":"publish","type":"post","link":"https:\/\/zalapto.pl\/baza\/zadanie-6-matura-probna-matematyka-marzec-2026\/","title":{"rendered":"Zadanie 6 \u2013 Matura pr\u00f3bna matematyka CKE (Marzec 2026)"},"content":{"rendered":"\n\n\n
\n \n <\/i> Wr\u00f3\u0107 do pe\u0142nego arkusza z marcem 2026\n <\/a>\n<\/div>\n\n
\n
\n \n

Tre\u015b\u0107 zadania<\/h2>\n
\n Doko\u0144cz zdanie. Wybierz w\u0142a\u015bciw\u0105 odpowied\u017a spo\u015br\u00f3d podanych.

\n Dla ka\u017cdej liczby rzeczywistej \\(x\\) r\u00f3\u017cnej od \\((-10 )\\) oraz r\u00f3\u017cnej od \\(0\\) warto\u015b\u0107 wyra\u017cenia \\(\\frac{x^2+20x+100}{x^3}\\cdot\\frac{x^2}{x+10}\\) jest r\u00f3wna warto\u015bci wyra\u017cenia:
\n A. \\(20x+10\\)
\n B. \\(\\frac{1}{x}\\)
\n C. \\(\\frac{x+10}{x}\\)
\n D. \\(\\frac{x^2+30}{x}\\)\n <\/div>\n\n

Rozwi\u0105zanie krok po kroku<\/h2>\n \n
\n \n <\/i> Zobacz podpowied\u017a\n <\/summary>\n
\n Zwr\u00f3\u0107 uwag\u0119 na licznik pierwszego u\u0142amka (\\(x^2 + 20x + 100\\)). Przypomina Ci to co\u015b? To rozwini\u0119ty wz\u00f3r skr\u00f3conego mno\u017cenia na kwadrat sumy: \\((a+b)^2 = a^2 + 2ab + b^2\\). Zwi\u0144 go, a potem mn\u00f3\u017c i skracaj „na krzy\u017c”.\n <\/div>\n <\/details>\n\n
\n \n <\/i> Sprawd\u017a pe\u0142ne rozwi\u0105zanie\n <\/summary>\n
\n \n

1. Zwijamy licznik ze wzoru skr\u00f3conego mno\u017cenia:<\/strong><\/p>\n Zauwa\u017camy, \u017ce \\(x^2 + 20x + 100\\) to po prostu \\((x + 10)^2\\). Podstawmy to do naszego wyra\u017cenia:\n

\n $$ \\frac{(x+10)^2}{x^3} \\cdot \\frac{x^2}{x+10} $$\n <\/div>\n \n

2. Mno\u017cymy i zapisujemy na jednej kresce u\u0142amkowej:<\/strong><\/p>\n

\n $$ \\frac{(x+10)^2 \\cdot x^2}{x^3 \\cdot (x+10)} $$\n <\/div>\n \n

3. Skracamy u\u0142amek:<\/strong><\/p>\n Z licznika skracamy jeden nawias \\((x+10)\\) z mianownikiem. Nast\u0119pnie skracamy \\(x^2\\) z licznika z B. \\(x^3\\) w mianowniku (w mianowniku zostanie nam po prostu \\(x\\)):\n $$ \\frac{(x+10) \\cdot 1}{x \\cdot 1} = \\frac{x+10}{x} $$\n \n

\n

Poprawna odpowied\u017a: C<\/p>\n \n <\/div>\n <\/details>\n\n <\/div>\n<\/div>\n\n

\n

Skracanie u\u0142amk\u00f3w algebraicznych sprawia Ci problemy?<\/p>\n

Zosta\u0142o ma\u0142o czasu do maja, ale z nami na pewno to Za\u0142apiesz<\/strong>. Przer\u00f3bmy to razem na wirtualnej tablicy.<\/p>\n Zapisz si\u0119 na korepetycje<\/a>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Wr\u00f3\u0107 do pe\u0142nego arkusza z marcem 2026 Tre\u015b\u0107 zadania Doko\u0144cz zdanie. Wybierz w\u0142a\u015bciw\u0105 odpowied\u017a spo\u015br\u00f3d podanych. Dla ka\u017cdej liczby rzeczywistej \\(x\\) r\u00f3\u017cnej od \\((-10 )\\) oraz r\u00f3\u017cnej od \\(0\\) warto\u015b\u0107 wyra\u017cenia \\(\\frac{x^2+20x+100}{x^3}\\cdot\\frac{x^2}{x+10}\\) jest r\u00f3wna warto\u015bci wyra\u017cenia: A. \\(20x+10\\) B. \\(\\frac{1}{x}\\) C. \\(\\frac{x+10}{x}\\) D. \\(\\frac{x^2+30}{x}\\) Rozwi\u0105zanie krok po kroku Zobacz podpowied\u017a Zwr\u00f3\u0107 uwag\u0119 na licznik pierwszego […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3,26],"tags":[],"class_list":["post-240","post","type-post","status-publish","format-standard","hentry","category-matura-podstawowa","category-zadania"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts\/240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/comments?post=240"}],"version-history":[{"count":4,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts\/240\/revisions"}],"predecessor-version":[{"id":248,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/posts\/240\/revisions\/248"}],"wp:attachment":[{"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/media?parent=240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/categories?post=240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zalapto.pl\/baza\/wp-json\/wp\/v2\/tags?post=240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}