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href="https://web.archive.org/web/20241002211008/https://yle.fi/urheilu" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Urheilu</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/saa" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Sää</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/uutiset/paikallisuutiset" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Paikallisuutiset</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-34837/fi" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Kotimaa</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-34953/fi" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Ulkomaat</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-220306/fi" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Politiikka</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-204933/fi" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Talous</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/kulttuuri" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Kulttuuri</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/tiede" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Tiede</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/luonto" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Luonto</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/oppiminen" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Oppiminen</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/abitreenit" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Abitreenit</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-215844/fi" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Kolumnit</span></a></li><li class="bqq79o2"><a href="https://web.archive.org/web/20241002211008/https://areena.yle.fi/1-3253227" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Uutiset viittomakielellä</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/selkouutiset" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Selkouutiset</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/uutisluokka" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Uutisluokka</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/elava-arkisto" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Elävä arkisto</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/tekstitv" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Teksti-TV</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://tunnus.yle.fi/viestiasetukset" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Uutiskirjeet</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://areena.yle.fi/tv/opas" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">TV-opas</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://areena.yle.fi/podcastit/opas" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Radio-opas</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/uutiset/rss" data-testid="header-drawer-submenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">RSS-syötteet</span></a></li></ul><div class="bqq79o0"><a href="https://web.archive.org/web/20241002211008/https://areena.yle.fi/" data-testid="header-areena-promo" class="_1m3quf81 eopu3j0"><svg viewbox="0 0 120 18" fill="none" xmlns="http://www.w3.org/2000/svg" class="_1m3quf80"><title>Yle Areena</title><path d="M17.9106 0.83486V17.1651C17.9106 17.6102 17.5266 18 17.1058 18H0.840919C0.383949 17.9992 0 17.6102 0 17.1644V0.83486C0 0.371663 0.383949 0 0.840919 0H17.1058C17.5266 0 17.9106 0.371663 17.9106 0.83486ZM6.94249 6.4098H6.65355C6.33634 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4.65407 7.89647 4.94919 8.41469 4.94919H8.53717V11C8.53717 11.3456 8.61648 11.5602 9.00906 11.5602H9.24697C9.64819 11.5602 9.70237 11.2769 9.70237 11V4.64697C9.70237 4.32818 9.70237 3.79633 9.11113 3.79633ZM14.7432 10.4239C14.667 10.4239 14.5901 10.4389 14.5006 10.4563L14.4668 10.4626C14.2862 10.4989 13.9831 10.5596 13.5042 10.5596C12.2636 10.5596 12.1176 10.349 12.0783 9.37285H14.4503C14.9976 9.37285 15.2418 9.15664 15.2418 8.67213C15.2418 7.64237 15.0266 6.27171 13.165 6.27171C11.5931 6.27171 10.8919 7.12946 10.8919 9.05247C10.8919 10.9297 11.5452 11.6281 13.3016 11.6281C14.0318 11.6281 14.6097 11.5152 14.8366 11.4111C14.9811 11.3495 15.1138 11.2572 15.1138 11V10.8122C15.113 10.5699 14.9748 10.4239 14.7432 10.4239Z" fill="currentColor"></path><path d="M12.0846 8.41359C12.1301 7.57715 12.4701 7.20312 13.1831 7.20312H13.1838C13.8614 7.20312 14.1661 7.56532 14.1975 8.41202L12.0846 8.41359Z" fill="currentColor"></path><path d="M31.4197 13.2932H25.348L23.7136 18.0002H20.0957L26.4898 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13.2932H107.759L106.129 18.0002H102.511L108.901 0.198242H113.186L119.455 18.0002H115.514L113.831 13.2932ZM110.884 3.60924L108.556 10.5302H113.087L110.884 3.60924Z" fill="currentColor"></path></svg><p class="_1m3quf82 fck75q2">Sarjat. Podcastit. Suorat.</p></a></div><ul id="header-2023-drawer-sitemenu" class="bqq79o8 bqq79o0"><li><a href="https://web.archive.org/web/20241002211008/https://svenska.yle.fi/" lang="sv" data-testid="header-drawer-sitemenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Svenska</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/sapmi" lang="se" data-testid="header-drawer-sitemenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Sápmi</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/news" lang="en" data-testid="header-drawer-sitemenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">News</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/novosti" lang="ru" data-testid="header-drawer-sitemenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Новости</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/novyny" lang="uk" data-testid="header-drawer-sitemenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Новини</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-44136/fi" data-testid="header-drawer-sitemenu-link" class="_1bvm4mm2 eopu3j0"><span class="fck75q3">Uudizet karjalakse</span></a></li></ul><ul id="header-2023-drawer-links" class="bqq79o8 bqq79o0"><li class="bqq79o4"><a href="https://web.archive.org/web/20241002211008/https://yle.fi/a/74-20031519" data-testid="header-drawer-links-link" class="_1bvm4mm2 eopu3j0"><svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true" class="_1bvm4mm1"><path fill="currentColor" fill-rule="evenodd" d="M12 8a5 5 0 1 0 0 10 5 5 0 0 0 0-10m-3 5a3 3 0 1 1 6 0 3 3 0 0 1-6 0M9 2a1 1 0 0 0-.832.445L6.465 5H3a3 3 0 0 0-3 3v11a3 3 0 0 0 3 3h18a3 3 0 0 0 3-3V8a3 3 0 0 0-3-3h-3.465l-1.703-2.555A1 1 0 0 0 15 2zM7.832 6.555 9.535 4h4.93l1.703 2.555A1 1 0 0 0 17 7h4a1 1 0 0 1 1 1v11a1 1 0 0 1-1 1H3a1 1 0 0 1-1-1V8a1 1 0 0 1 1-1h4a1 1 0 0 0 .832-.445" clip-rule="evenodd"></path></svg><span class="fck75q3">Lähetä uutiskuva tai -video</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://asiakaspalvelu.yle.fi/" data-testid="header-drawer-links-link" class="_1bvm4mm2 eopu3j0"><svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true" class="_1bvm4mm1"><path fill="currentColor" fill-rule="evenodd" d="M4 3C2.348 3 1 4.348 1 6v12c0 1.652 1.348 3 3 3h16c1.652 0 3-1.348 3-3V6c0-1.652-1.348-3-3-3zm-.893 2.554C3.272 5.227 3.612 5 4 5h16c.388 0 .728.227.893.554L12 11.779zM3 7.92V18c0 .548.452 1 1 1h16c.548 0 1-.452 1-1V7.92l-8.426 5.9a1 1 0 0 1-1.147 0z" clip-rule="evenodd"></path></svg><span class="fck75q3">Asiakaspalvelu</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/yleisradio/ylen-yhteystiedot" data-testid="header-drawer-links-link" class="_1bvm4mm2 eopu3j0"><svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true" class="_1bvm4mm1"><path fill="currentColor" d="M13.26 8c0-.69-.56-1.25-1.25-1.25H12a1.25 1.25 0 0 0 0 2.5h.01c.69 0 1.25-.56 1.25-1.25M12 11c-.55 0-1 .45-1 1v4c0 .55.45 1 1 1s1-.45 1-1v-4c0-.55-.45-1-1-1M12 1C5.92 1 1 5.92 1 12s4.92 11 11 11 11-4.92 11-11S18.08 1 12 1m0 20a9 9 0 1 1 .001-18.001A9 9 0 0 1 12 21"></path></svg><span class="fck75q3">Ylen yhteystiedot</span></a></li><li><a href="https://web.archive.org/web/20241002211008/https://yle.fi/uutiset/yhteystiedot" data-testid="header-drawer-links-link" class="_1bvm4mm2 eopu3j0"><svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true" class="_1bvm4mm1"><path fill="currentColor" d="M13.26 8c0-.69-.56-1.25-1.25-1.25H12a1.25 1.25 0 0 0 0 2.5h.01c.69 0 1.25-.56 1.25-1.25M12 11c-.55 0-1 .45-1 1v4c0 .55.45 1 1 1s1-.45 1-1v-4c0-.55-.45-1-1-1M12 1C5.92 1 1 5.92 1 12s4.92 11 11 11 11-4.92 11-11S18.08 1 12 1m0 20a9 9 0 1 1 .001-18.001A9 9 0 0 1 12 21"></path></svg><span 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</div> <main id="main-content" class="mx-auto max-w-dog"> <div class="layout-content"> <div> <div id="block-yddrasil-content"> <article class="ydd-article" itemscope itemtype="http://schema.org/Article"> <meta itemscope itemtype="https://schema.org/WebPage" itemprop="mainEntityOfPage" itemid="https://yle.fi/aihe/a/20-10006784"> <div itemprop="publisher" itemscope itemtype="https://schema.org/Organization"> <div itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"> <meta itemprop="url" content="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/w_180,h_180/v1513081794/yle-logo-c-svg.png"> <meta itemprop="width" content="180"> <meta itemprop="height" content="180"> </div> <meta itemprop="name" content="Yle"> </div> <div class="mb-24 px-16 ram:px-0"> <h1 class="ydd-article-headline" itemprop="headline"> <span>Saisitko C:n pitkästä matematiikasta? Kokosimme testin ylioppilaskokeessa vaadittavista taidoista</span> </h1> <div class="flex items-center"> <span class="leading-none mr-4 text-gray-60"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" fill-rule="evenodd" d="M12 1C5.925 1 1 5.925 1 12s4.925 11 11 11 11-4.925 11-11S18.075 1 12 1M3 12a9 9 0 1 1 18 0 9 9 0 0 1-18 0m10-6a1 1 0 1 0-2 0v6a1 1 0 0 0 .553.894l4 2a1 1 0 1 0 .894-1.788L13 11.382z" clip-rule="evenodd"/></svg> </div> </span> <span class="text-gray-60 text-xs" property="dc:date dc:created" content="2024-09-25T09:15:25+03:00" datatype="xsd:dateTime" rel="sioc:has_creator"> <span class="published" itemprop="datePublished" content="2024-09-25T09:15:25+03:00">Julkaistu 25.09.2024 09:15.</span> <meta itemprop="dateModified" content="2024-09-25T09:15:25+03:00"> </span> </div> </div> <div class="mb-16"> <div itemprop="image" itemscope="" itemtype="https://schema.org/ImageObject" class="ydd-image relative "> <figure role="group"> <img alt="Sormi joka painaa nappia ja matemaattisia merkintöjä." itemprop="image" content="https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_5000/w_700/v1718723803/39-13053626671a482eeebb.jpg" data-yle-id="39-13053626671a482eeebb" data-crop-coords="w_5000" data-image-width="5000" data-image-version="1718723803" data-copyright="Janika Koli / Yle" data-caption="" data-ydd-modal-src="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_5000/w_1400/w_1400,h_788,c_fit/v1718723803/39-13053626671a482eeebb.jpg" data-ydd-modal-width="1400" data-ydd-modal-height="788" class="ydd-image__image js-ydd-image lazyload" src="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 5000 2813'%3E%3Cdefs%3E%3Cpattern id='blurhash' patternUnits='userSpaceOnUse' width='5000' height='2813'%3E%3Cimage href='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAJCAIAAAC0SDtlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABJ0lEQVQYlSXNwU7cQBAE0KqeHmNHgBBS/v+U/0KJAmG1Cfaya3s8M105cHu3x9OvH0bmlHKyRIse+3Ysl/V0/vz9Z355W15O19dLXRrl2bO7EUaQIkCIkBFuHJJNgz+M+WnK66F+YAU74G4yIEFEADTIDaPb45Tb/RilWSCn4tf2VnTu8GwiQIZBFAlkA7NxyulxTKEEA9PBsqhuW/dEASIIkCKhBDEB2XTn7VsuR7+W/rD3aW8s4ZIIgIAEkJIkKBQhxZfBSBZDiqcc3kIkkpAIQJJ6RK1tLcdl3efr/nHbLtu+1+Ks34fwo8sIGUhSUKi1vu7HfN3O8+3933qa1/OtLLWZ4nmA15CRJFz4Kmrv21GXdX+fbz//fr5+3OZSZRrv7H5I/wGI79L1pculRAAAAABJRU5ErkJggg==' x='0' y='0' width='100%25' height='100%25' preserveAspectRatio='xMinYMin slice'%3E%3C/image%3E%3C/pattern%3E%3C/defs%3E%3Crect width='100%25' height='100%25' fill='url(%23blurhash)' /%3E%3C/svg%3E" width="5000" height="2813"> <meta itemprop="url" content="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_5000/w_700/v1718723803/39-13053626671a482eeebb.jpg"> <noscript class="absolute inset-0"><img class="ydd-image__image" src="https://web.archive.org/web/20241002211008im_/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_5000/w_400/v1718723803/39-13053626671a482eeebb.jpg" alt="Sormi joka painaa nappia ja matemaattisia merkintöjä."/></noscript> <figcaption class="ydd-image__captions text-xs pl-16 ram:pl-0 pt-8"> <div class="text-gray-60" itemprop="copyrightHolder">Kuva: Janika Koli / Yle</div> </figcaption> </figure> </div> </div> <div class="ydd-author-list border-b border-gray-10 border-t overflow-x-auto pl-16 pr-16 ram:pl-0 ram:pr-0 scrolling-touch whitespace-nowrap"> <div itemscope itemtype="http://schema.org/Person" itemprop="author" class="inline-flex flex-shrink-0 items-center pb-8 pr-24 pt-8"> <a class="focus-underline flex items-center" itemprop="url" href="/web/20241002211008/https://yle.fi/aihe/u/56-20-1762"> <div class="ydd-authors-list__placeholder-wrapper bg-gray-60 clip-path-circle flex-shrink-0 mr-8 overflow-hidden 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Näillä taidoilla läpäiset kirjoitukset helposti!</p> <p>Pitkän matematiikan kokeissa korostuvat aiheet, jotka testaavat opiskelijoiden kykyä ratkaista ongelmia ja soveltaa matemaattisia periaatteita monipuolisesti. A-osassa isoimmat teemat ovat yhtälöt, taso, derivaatta ja integraali sekä vektorit.</p><div class="ydd-article-image ydd-article-image--inline-svg mb-32 mt-32"> <div itemprop="image" itemscope itemtype="https://schema.org/ImageObject" class="ydd-image"> <figure role="group"> <svg class="highcharts-root" width="640" height="360" viewbox="0 0 640 360" aria-label="Interactive chart" aria-hidden="false" font-family=""Yle Next", Arial, sans-serif" font-size="1rem"> <desc>Yhtälöt ja suorat on kaikista kysytyin aihealue.</desc> <defs> <clippath id="highcharts-j115c9b-300-"> <path fill="none" d="M1 0H555V160H1z"/> </clippath> <filter id="highcharts-drop-shadow-7"> <fedropshadow dx="1" dy="1" flood-color="#000" flood-opacity=".75" stddeviation="2.5"/> </filter> </defs> <rect fill="#fff" class="highcharts-background" filter="none" width="640" height="360" rx="0" ry="0" aria-hidden="true"/> <path fill="none" class="highcharts-plot-background" filter="none" aria-hidden="true" d="M76 107H630V267H76z"/> <g class="highcharts-grid highcharts-xaxis-grid" aria-hidden="true" fill="none"> <path class="highcharts-grid-line" d="M186.5 107 186.5 267M297.5 107 297.5 267M408.5 107 408.5 267M519.5 107 519.5 267M630.5 107 630.5 267M76.5 107 76.5 267"/> </g> <g class="highcharts-grid highcharts-yaxis-grid" aria-hidden="true" fill="none" stroke="#b4b6b7"> <path class="highcharts-grid-line" d="M76 267.5 630 267.5M76 227.5 630 227.5M76 187.5 630 187.5M76 147.5 630 147.5M76 107.5 630 107.5"/> </g> <path fill="none" class="highcharts-plot-border" aria-hidden="true" d="M76 107H630V267H76z"/> <g class="highcharts-axis highcharts-xaxis" aria-hidden="true"> <path fill="none" class="highcharts-axis-line" stroke="#b4b6b7" d="M 76 267.5 L 630 267.5"/> </g> <g class="highcharts-axis highcharts-yaxis" aria-hidden="true"> <text x="32.26" text-anchor="middle" transform="rotate(-90 32.26 187)" class="highcharts-axis-title" y="187" color="#131415" font-size="18" font-weight="500" fill="#131415">pistettä</text> <path fill="none" class="highcharts-axis-line" stroke="#b4b6b7" d="M 76.5 107 L 76.5 267"/> </g> <g class="highcharts-series-group" filter="none" aria-hidden="false"> <g class="highcharts-series highcharts-series-8 highcharts-column-series highcharts-color-2" clip-path="url(#highcharts-j115c9b-300-)" aria-hidden="false" tabindex="-1" aria-label="20k, bar series 9 of 9 with 5 bars." style="outline:0" fill="#00b3ea" transform="translate(76 107)"> <path d="M 89 112 L 97 112 A 0 0 0 0 1 97 112 L 97 160 A 0 0 0 0 1 97 160 L 89 160 A 0 0 0 0 1 89 160 L 89 112 A 0 0 0 0 1 89 112 Z" filter="none" class="highcharts-point highcharts-color-2" tabindex="-1" aria-label="Yhtälöt ja suorat, 12. 20k." style="outline:0"/> <path d="M 200 72 L 208 72 A 0 0 0 0 1 208 72 L 208 160 A 0 0 0 0 1 208 160 L 200 160 A 0 0 0 0 1 200 160 L 200 72 A 0 0 0 0 1 200 72 Z" filter="none" class="highcharts-point highcharts-color-2" tabindex="-1" aria-label="Derivaatta ja integraali, 22. 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A 0 0 0 0 1 356 160 Z" filter="none" class="highcharts-point highcharts-color-1" tabindex="-1" aria-label="Geometriset muodot, 0. 23s." style="outline:0"/> <path d="M 467 160 L 475 160 A 0 0 0 0 1 475 160 L 475 160 A 0 0 0 0 1 475 160 L 467 160 A 0 0 0 0 1 467 160 L 467 160 A 0 0 0 0 1 467 160 Z" filter="none" class="highcharts-point highcharts-color-1" tabindex="-1" aria-label="Trigonometria, 0. 23s." style="outline:0"/> </g> <g class="highcharts-series highcharts-series-0 highcharts-column-series highcharts-color-0" clip-path="url(#highcharts-j115c9b-300-)" aria-hidden="false" tabindex="-1" aria-label="24k, bar series 1 of 9 with 5 bars." style="outline:0" fill="#00b4c8" transform="translate(76 107)"> <path d="M 14 88 L 22 88 A 0 0 0 0 1 22 88 L 22 160 A 0 0 0 0 1 22 160 L 14 160 A 0 0 0 0 1 14 160 L 14 88 A 0 0 0 0 1 14 88 Z" filter="none" class="highcharts-point highcharts-color-0" tabindex="-1" aria-label="Yhtälöt ja suorat, 18. 24k." style="outline:0"/> <path d="M 125 88 L 133 88 A 0 0 0 0 1 133 88 L 133 160 A 0 0 0 0 1 133 160 L 125 160 A 0 0 0 0 1 125 160 L 125 88 A 0 0 0 0 1 125 88 Z" filter="none" class="highcharts-point highcharts-color-0" tabindex="-1" aria-label="Derivaatta ja integraali, 18. 24k." style="outline:0"/> <path d="M 236 160 L 244 160 A 0 0 0 0 1 244 160 L 244 160 A 0 0 0 0 1 244 160 L 236 160 A 0 0 0 0 1 236 160 L 236 160 A 0 0 0 0 1 236 160 Z" filter="none" class="highcharts-point highcharts-color-0" tabindex="-1" aria-label="Vektorit ja taso, 0. 24k." style="outline:0"/> <path d="M 347 112 L 355 112 A 0 0 0 0 1 355 112 L 355 160 A 0 0 0 0 1 355 160 L 347 160 A 0 0 0 0 1 347 160 L 347 112 A 0 0 0 0 1 347 112 Z" filter="none" class="highcharts-point highcharts-color-0" tabindex="-1" aria-label="Geometriset muodot, 12. 24k." style="outline:0"/> <path d="M 457 160 L 465 160 A 0 0 0 0 1 465 160 L 465 160 A 0 0 0 0 1 465 160 L 457 160 A 0 0 0 0 1 457 160 L 457 160 A 0 0 0 0 1 457 160 Z" filter="none" class="highcharts-point highcharts-color-0" tabindex="-1" aria-label="Trigonometria, 0. 24k." style="outline:0"/> </g> </g> <text x="10" class="highcharts-title" y="32" aria-hidden="true" font-size="24" color="#131415" font-weight="900" fill="#131415">A-osan tehtävien jakautuminen</text> <g class="highcharts-legend highcharts-no-tooltip" transform="translate(6 55)" aria-hidden="true"> <rect fill="none" class="highcharts-legend-box" rx="0" ry="0" filter="none" width="596" height="22"/> <g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-0 highcharts-series-0" transform="translate(0 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">24k</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#00b4c8" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-1 highcharts-series-1" transform="translate(68.247 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">23s</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#2975d0" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-2 highcharts-series-2" transform="translate(134.327 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">23k</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#00b3ea" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-3 highcharts-series-3" transform="translate(202.574 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">22s</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#ffd435" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-4 highcharts-series-4" transform="translate(268.655 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">22k</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#ff8d34" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-5 highcharts-series-5" transform="translate(336.901 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">21s</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#ff4d5b" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-0 highcharts-series-6" transform="translate(402.982 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">21k</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#00b4c8" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-1 highcharts-series-7" transform="translate(471.229 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">20s</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#2975d0" class="highcharts-point"/> </g> <g class="highcharts-legend-item highcharts-column-series highcharts-color-2 highcharts-series-8" transform="translate(537.31 -5)"> <text x="26" y="23" color="#131415" font-size="18" font-weight="500" fill="#131415">20k</text> <rect x="3" y="6" rx="999" ry="999" width="18" height="18" fill="#00b3ea" class="highcharts-point"/> </g> </g> </g> <g class="highcharts-axis-labels highcharts-xaxis-labels" aria-hidden="true" text-anchor="middle" color="#131415" cursor="default" font-size="18" font-weight="500" fill="#131415"> <text x="131.4" y="292">Yhtälöt ja<tspan dy="21" x="131.4"></tspan>suorat</text> <text x="242.2" y="292">Derivaatta<tspan dy="21" x="242.2"></tspan>ja integraali</text> <text x="353" y="292">Vektorit ja<tspan dy="21" x="353"></tspan>taso</text> <text x="463.8" y="292">Geometris…</text> <text x="574.6" y="292">Trigonom…</text> </g> <g class="highcharts-axis-labels highcharts-yaxis-labels" aria-hidden="true" text-anchor="end" color="#131415" cursor="default" font-size="18" font-weight="500" fill="#131415"> <text x="64" y="272">0</text> <text x="64" y="232">10</text> <text x="64" y="192">20</text> <text x="64" y="152">30</text> <text x="64" y="112">40</text> </g> <text x="10" class="highcharts-credits" y="350" aria-label="Chart credits: Lähde: YTL, Katja Ylisiurua / Yle" aria-hidden="false" color="#131415" font-size="18" font-weight="400" fill="#131415">Lähde: YTL, Katja Ylisiurua / Yle</text> </svg> </figure> </div> </div><p>Maksimipistemäärä kokeen ensimmäisestä osasta on ollut viime vuosina 48 ja sen on saanut ratkaisemalla kaikki neljä tehtävää oikein. Syksyllä 2024 A-osan painoarvo nousee ja siinä on valinnaisia tehtäviä.</p><p>Arvosana A on irronnut noin 20 pisteellä, B noin 30 pisteellä ja C on vaatinut lähes neljän tehtävän edestä pisteitä. Tutki aikaisempien vuosien pisterajoja <a class="link" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/a/20-10006648">Abitreenien pisterajakoneessa</a>.</p><p>Yhtälönratkaisutaitoja on testattu viime vuosina vähintään kahdessa A-osan tehtävässä. Muistettavia asioita ovat olleet itseisarvot, osittelulaki ja polynomien asteet.</p><details> <summary class="cursor-pointer flex gap-5 summary-reset"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" d="M19 3.172a1.83 1.83 0 0 0-1.293.535L4.395 17.02l-.97 3.556 3.556-.97L20.293 6.293a1.827 1.827 0 0 0-.593-2.982 1.8 1.8 0 0 0-.7-.14Zm-1.465-1.709a3.829 3.829 0 0 1 4.172 6.244l-13.5 13.5a1 1 0 0 1-.444.258l-5.5 1.5a1 1 0 0 1-1.228-1.228l1.5-5.5a1 1 0 0 1 .258-.444l13.5-13.5a3.8 3.8 0 0 1 1.242-.83"/></svg> </div> <span class="link">Yhtälöt ja suorat</span> </summary> <div class="js-ydd-yle-tehtava ydd-yle-tehtava ydd-yle-tehtava--exam" data-ydd-tehtava-options="{"darkMode":"auto","lang":"fi-FI"}" data-ydd-tehtava-type="exam" data-ydd-tehtava-exam-id="47-aa5e5c70-e44d-4df9-a50a-61abb0a7d072"></div> </details><p>A-osassa on ollut joka vuosi yksi derivaatta- tai integraalitehtävä. Tyypillisesti derivattatehtävä on ollut vähemmän pisteitä tuottava yksinkertainen derivointiharjoitus ja integraalitehtävässä ratkaistava lauseke on pitänyt osata muodostaa itse. Kokeile, miten sinulta luonnistuvat derivointi ja integrointi!</p><details> <summary class="cursor-pointer flex gap-5 summary-reset"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" d="M19 3.172a1.83 1.83 0 0 0-1.293.535L4.395 17.02l-.97 3.556 3.556-.97L20.293 6.293a1.827 1.827 0 0 0-.593-2.982 1.8 1.8 0 0 0-.7-.14Zm-1.465-1.709a3.829 3.829 0 0 1 4.172 6.244l-13.5 13.5a1 1 0 0 1-.444.258l-5.5 1.5a1 1 0 0 1-1.228-1.228l1.5-5.5a1 1 0 0 1 .258-.444l13.5-13.5a3.8 3.8 0 0 1 1.242-.83"/></svg> </div> <span class="link">Derivaatta ja integraali</span> </summary> <div class="js-ydd-yle-tehtava ydd-yle-tehtava ydd-yle-tehtava--exam" data-ydd-tehtava-options="{"darkMode":"auto","lang":"fi-FI"}" data-ydd-tehtava-type="exam" data-ydd-tehtava-exam-id="47-7235f7d3-2aa7-419c-8d10-8506310aa935"></div> </details><p>Vektoreita käsitteleviä tehtäviä ei ole näkynyt jokaisessa kokeessa, mutta silloin kun niitä on ollut kokeessa, on niiden painoarvo ollut suuri. Pitkän matematiikan kirjoittajien on syytä kerrata, mitä eroa on piste- ja ristitulolla ja miten tietää, ovatko vektorin yhdensuuntaisia.</p><details> <summary class="cursor-pointer flex gap-5 summary-reset"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" d="M19 3.172a1.83 1.83 0 0 0-1.293.535L4.395 17.02l-.97 3.556 3.556-.97L20.293 6.293a1.827 1.827 0 0 0-.593-2.982 1.8 1.8 0 0 0-.7-.14Zm-1.465-1.709a3.829 3.829 0 0 1 4.172 6.244l-13.5 13.5a1 1 0 0 1-.444.258l-5.5 1.5a1 1 0 0 1-1.228-1.228l1.5-5.5a1 1 0 0 1 .258-.444l13.5-13.5a3.8 3.8 0 0 1 1.242-.83"/></svg> </div> <span class="link">Vektorit</span> </summary> <div class="js-ydd-yle-tehtava ydd-yle-tehtava ydd-yle-tehtava--exam" data-ydd-tehtava-options="{"darkMode":"auto","lang":"fi-FI"}" data-ydd-tehtava-type="exam" data-ydd-tehtava-exam-id="47-e7f1edb9-0a1e-45a8-8ebb-a24e4b3978d3"></div> </details><p>Saitko tehtävistä yhteensä yli 40 pistettä? Jos sait, pisteesi riitäisivät arvosanaan C!</p><div class="bg-gray-5 dark:bg-lock-gray-90 my-24 p-16 owl:p-24 text-center"> <h2 class="font-black mb-16 text-lg owl:text-2xl">Harjoittele lisää matematiikan yo-kokeiden tehtäviä </h2> <a class="bg-dark border-transparent text-light ydd-button border-2 font-bold inline-flex items-center justify-center leading-150 focus:outline-none focus:outline-3 focus:outline-turquoise-60 rounded-full shrink-0 hover:bg-[#000]/70 hover:dark:bg-[#fff]/70 cursor-pointer pb-[7px] pt-8 px-24 text-sm" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/abitreenit/harjoittele"> Abitreenien yo-koekoneeseen </a> </div> </div> <div class="-ml-16 -mr-16"> <details class="ydd-article-tags__details group/details mb-32 ml-16 mt-32"> <summary class="ydd-article-tags__summary cursor-pointer flex group/summary pb-16 pointer-events-none relative select-none summary-reset"> <div class="flex"> <div class="ydd-article-tags__pill bg-gray-5 border border-gray-10 flex items-center pointer-events-auto rounded-4xl"> <span id="aria-article-tags" class="ydd-article-tags__pill-text text-gray-60 truncate">Lisää aiheesta: <span aria-hidden="true" itemprop="keywords" content="koulutus, matematiikka, ylioppilaskirjoitukset, Abitreenit">Koulutus, Matematiikka</span> </span> <span class="group-focus/summary:bg-red-60 group-focus/summary:text-light group-open/details:rotate-180 h-20 ml-8 rounded-full shrink-0 text-gray-60 w-20"> <div class="size-20 [&>svg]:h-full [&>svg]:w-full"> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" d="M5.293 9.293a1 1 0 0 1 1.414 0L12 14.586l5.293-5.293a1 1 0 1 1 1.414 1.414l-6 6a1 1 0 0 1-1.414 0l-6-6a1 1 0 0 1 0-1.414"/></svg> </div> </span> </div> </div> </summary> <div class="ydd-article-tags__content pl-8"> <ul class="ydd-article-tags__list break-word list-reset relative w-full" aria-labelledby="aria-article-tags"> <li class="ydd-article-tags__list-item mb-16 pl-16 relative"> <a class="link" href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-212557/fi">Koulutus</a> </li> <li class="ydd-article-tags__list-item mb-16 pl-16 relative"> <a class="link" href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-218531/fi">Matematiikka</a> </li> <li class="ydd-article-tags__list-item mb-16 pl-16 relative"> <a class="link" href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-204541/fi">Ylioppilaskirjoitukset</a> </li> <li class="ydd-article-tags__list-item mb-16 pl-16 relative"> <a class="link" href="https://web.archive.org/web/20241002211008/https://yle.fi/t/18-193891/fi">Abitreenit</a> </li> </ul> </div> </details> <div class="mb-32 min-h-[64px] px-12" id="comments"> <h2 class="sr-only">Keskustelu</h2> <div class="js-ydd-comments-plugin lazyload" data-id="20-10006784" data-ydd-yle-comments-plugin-language="fi"></div> </div> <aside id="ydd-article-related-content"> <div class="border-b-4 border-gray-10 deco-line-title mb-16 mt-8 pl-16 pr-16 w-full"> <div class="items-center flex justify-between"> <h3 class="text-lg" id="aria-articles-list-related-content"> Matematiikka </h3> </div> </div> <div class="ydd-cards w-full list-"> <div class="ydd-card ydd-card--s-extended" data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006761","ui_element_id":"related-content","ui_element_position":1}"> <div class="ydd-card__wrap"> <div class="ydd-card__content mr-16 ml-16 flex flex-wrap"> <div class="w-full"> <a data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006761","ui_element_id":"related-content","ui_element_position":1}" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/a/20-10006761"> <div class="ml-16 mb-8 w-1/4 float-right cod:w-1/6"> <div class="relative"> <div itemprop="image" itemscope="" itemtype="https://schema.org/ImageObject" class="ydd-image relative "> <figure role="group"> <img alt="Kuva lukion käytävältä ja Abitreenien logo." itemprop="image" content="https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_2813,h_2813,c_crop,x_2187,y_0/w_700/v1718614070/39-1303441666c2b58b100f.jpg" data-yle-id="39-1303441666c2b58b100f" data-crop-coords="w_2813,h_2813,c_crop,x_2187,y_0" data-image-width="2813" data-image-version="1718614070" class="ydd-image__image js-ydd-image lazyload" src="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 2813 2813'%3E%3Cdefs%3E%3Cpattern id='blurhash' patternUnits='userSpaceOnUse' width='2813' height='2813'%3E%3Cimage 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inset-0"><img class="ydd-image__image" src="https://web.archive.org/web/20241002211008im_/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_2813,h_2813,c_crop,x_2187,y_0/w_400/v1718614070/39-1303441666c2b58b100f.jpg" alt="Kuva lukion käytävältä ja Abitreenien logo."/></noscript> </figure> </div> </div> </div> <h3 class="mb-16 text-md dog:text-lg">Tavoitteeksi B lyhyestä matematiikasta – tällä nopealla treenipaketilla läpäiset kirjoitukset kirkkaasti</h3> </a> <p class="mb-0 text-gray-95 text-md">Kertaa A-osan useimmin kysyttyjä asioita aikaisempien vuosien ylioppilaskokeiden tehtävillä ja katso, mitkä ovat 2020-luvun tärkeimmät taidot matematiikan kirjoituksissa. </p> <div class="ydd-card__footer flex flex-wrap gap-8 items-center mb-8 mt-16"> <div class="flex items-center"> <span class="leading-none mr-4 text-gray-60"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" fill-rule="evenodd" d="M12 1C5.925 1 1 5.925 1 12s4.925 11 11 11 11-4.925 11-11S18.075 1 12 1M3 12a9 9 0 1 1 18 0 9 9 0 0 1-18 0m10-6a1 1 0 1 0-2 0v6a1 1 0 0 0 .553.894l4 2a1 1 0 1 0 .894-1.788L13 11.382z" clip-rule="evenodd"/></svg> </div> </span> <div aria-label="Julkaistu" class="text-gray-60 text-xs">19.9.2024</div> </div> </div> </div> </div> </div> </div> <div class="border-gray-10 border-t mx-16"></div> <div class="ydd-card ydd-card--s-extended" data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006816","ui_element_id":"related-content","ui_element_position":2}"> <div class="ydd-card__wrap"> <div class="ydd-card__content mr-16 ml-16 flex flex-wrap"> <div class="w-full"> <a data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006816","ui_element_id":"related-content","ui_element_position":2}" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/a/20-10006816"> <div class="ml-16 mb-8 w-1/4 float-right cod:w-1/6"> <div class="relative"> <div itemprop="image" itemscope="" itemtype="https://schema.org/ImageObject" class="ydd-image relative "> <figure role="group"> <img alt="Matematiikan ainesivu. Musta fontti vaalealla taustalla." itemprop="image" content="https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_1080,h_1080,c_crop,x_410,y_0/w_700/v1698317104/39-1191630653a42c938480.jpg" data-yle-id="39-1191630653a42c938480" data-crop-coords="w_1080,h_1080,c_crop,x_410,y_0" data-image-width="1080" data-image-version="1698317104" class="ydd-image__image js-ydd-image lazyload" src="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 1080 1080'%3E%3Cdefs%3E%3Cpattern id='blurhash' patternUnits='userSpaceOnUse' width='1080' height='1080'%3E%3Cimage href='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAJCAIAAAC0SDtlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVQYlS3CSVbcQBAFwJ9DpRowcP8jcAWvfChoSZXDZ+MXIf/+fs30nXnm3l0QPY6Xj7f3zz8f769vjwiFZO7zPH9+vp/X00ECEIiKmBhUXc1UVQQA+B8AEVGoc4akiixdplDzIx7hYWoCkAOCMyAU6ure3QAUcvgSdfeIiIcfS02I6eFMd3NGIKbuVSmipu7usR5rHRHha5koyarq7s7KrO7BwHemqskyFVu+joi1wkwp6O7qqszM6qyunqFfud1czSkUE3NVV4iQk9333vu+996V2TUc+l3ZoDEapIAKKAj0THZduc/7vK4rc3c1Z3x3jSCmGzMyFBAk2Jya3pVX7ue+7vuuSs78AlMm06eDeXtvAAAAAElFTkSuQmCC' x='0' y='0' width='100%25' height='100%25' preserveAspectRatio='xMinYMin slice'%3E%3C/image%3E%3C/pattern%3E%3C/defs%3E%3Crect width='100%25' height='100%25' fill='url(%23blurhash)' /%3E%3C/svg%3E" width="1080" height="1080"> <meta itemprop="url" content="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_1080,h_1080,c_crop,x_410,y_0/w_700/v1698317104/39-1191630653a42c938480.jpg"> <noscript class="absolute inset-0"><img class="ydd-image__image" src="https://web.archive.org/web/20241002211008im_/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_1080,h_1080,c_crop,x_410,y_0/w_400/v1698317104/39-1191630653a42c938480.jpg" alt="Matematiikan ainesivu. Musta fontti vaalealla taustalla."/></noscript> </figure> </div> </div> </div> <h3 class="mb-16 text-md dog:text-lg">2024 syksy: matematiikka, lyhyt oppimäärä</h3> </a> <p class="mb-0 text-gray-95 text-md">Katso Ylioppilastutkintolautakunnan laatima koe (katseluversio) tai tee Abitreenien harjoittelukoe. Tältä sivulta löydät myös hyvän vastauksen piirteet.</p> <div class="ydd-card__footer flex flex-wrap gap-8 items-center mb-8 mt-16"> <div class="flex items-center"> <span class="leading-none mr-4 text-gray-60"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" fill-rule="evenodd" d="M12 1C5.925 1 1 5.925 1 12s4.925 11 11 11 11-4.925 11-11S18.075 1 12 1M3 12a9 9 0 1 1 18 0 9 9 0 0 1-18 0m10-6a1 1 0 1 0-2 0v6a1 1 0 0 0 .553.894l4 2a1 1 0 1 0 .894-1.788L13 11.382z" clip-rule="evenodd"/></svg> </div> </span> <div aria-label="Julkaistu" class="text-gray-60 text-xs">19.8.2024</div> </div> </div> </div> </div> </div> </div> <div class="border-gray-10 border-t mx-16"></div> <div class="ydd-card ydd-card--s-extended" data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006815","ui_element_id":"related-content","ui_element_position":3}"> <div class="ydd-card__wrap"> <div class="ydd-card__content mr-16 ml-16 flex flex-wrap"> <div class="w-full"> <a data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006815","ui_element_id":"related-content","ui_element_position":3}" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/a/20-10006815"> <div class="ml-16 mb-8 w-1/4 float-right cod:w-1/6"> <div class="relative"> <div itemprop="image" itemscope="" itemtype="https://schema.org/ImageObject" class="ydd-image relative "> <figure role="group"> <img alt="Matematiikan ainesivu. Musta fontti vaalealla taustalla." itemprop="image" content="https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_1080,h_1080,c_crop,x_410,y_0/w_700/v1698317104/39-1191630653a42c938480.jpg" data-yle-id="39-1191630653a42c938480" data-crop-coords="w_1080,h_1080,c_crop,x_410,y_0" data-image-width="1080" data-image-version="1698317104" class="ydd-image__image js-ydd-image lazyload" src="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 1080 1080'%3E%3Cdefs%3E%3Cpattern id='blurhash' patternUnits='userSpaceOnUse' width='1080' height='1080'%3E%3Cimage href='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAJCAIAAAC0SDtlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABC0lEQVQYlS3CSVbcQBAFwJ9DpRowcP8jcAWvfChoSZXDZ+MXIf/+fs30nXnm3l0QPY6Xj7f3zz8f769vjwiFZO7zPH9+vp/X00ECEIiKmBhUXc1UVQQA+B8AEVGoc4akiixdplDzIx7hYWoCkAOCMyAU6ure3QAUcvgSdfeIiIcfS02I6eFMd3NGIKbuVSmipu7usR5rHRHha5koyarq7s7KrO7BwHemqskyFVu+joi1wkwp6O7qqszM6qyunqFfud1czSkUE3NVV4iQk9333vu+996V2TUc+l3ZoDEapIAKKAj0THZduc/7vK4rc3c1Z3x3jSCmGzMyFBAk2Jya3pVX7ue+7vuuSs78AlMm06eDeXtvAAAAAElFTkSuQmCC' x='0' y='0' width='100%25' height='100%25' preserveAspectRatio='xMinYMin slice'%3E%3C/image%3E%3C/pattern%3E%3C/defs%3E%3Crect width='100%25' height='100%25' fill='url(%23blurhash)' /%3E%3C/svg%3E" width="1080" height="1080"> <meta itemprop="url" content="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_1080,h_1080,c_crop,x_410,y_0/w_700/v1698317104/39-1191630653a42c938480.jpg"> <noscript class="absolute inset-0"><img class="ydd-image__image" src="https://web.archive.org/web/20241002211008im_/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_1080,h_1080,c_crop,x_410,y_0/w_400/v1698317104/39-1191630653a42c938480.jpg" alt="Matematiikan ainesivu. Musta fontti vaalealla taustalla."/></noscript> </figure> </div> </div> </div> <h3 class="mb-16 text-md dog:text-lg">2024 syksy: matematiikka, pitkä oppimäärä</h3> </a> <p class="mb-0 text-gray-95 text-md">Katso Ylioppilastutkintolautakunnan laatima koe (katseluversio) tai tee Abitreenien harjoittelukoe. 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Etumerkit menevät kuitenkin helposti sekaisin. </p> <div class="ydd-card__footer flex flex-wrap gap-8 items-center mb-8 mt-16"> <div class="flex items-center"> <span class="leading-none mr-4 text-gray-60"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" fill-rule="evenodd" d="M12 1C5.925 1 1 5.925 1 12s4.925 11 11 11 11-4.925 11-11S18.075 1 12 1M3 12a9 9 0 1 1 18 0 9 9 0 0 1-18 0m10-6a1 1 0 1 0-2 0v6a1 1 0 0 0 .553.894l4 2a1 1 0 1 0 .894-1.788L13 11.382z" clip-rule="evenodd"/></svg> </div> </span> <div aria-label="Julkaistu" class="text-gray-60 text-xs">30.5.2024</div> </div> </div> </div> </div> </div> </div> <div class="border-gray-10 border-t mx-16"></div> <div class="ydd-card ydd-card--s-extended" data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006075","ui_element_id":"related-content","ui_element_position":5}"> <div class="ydd-card__wrap"> <div class="ydd-card__content mr-16 ml-16 flex flex-wrap"> <div class="w-full"> <a data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006075","ui_element_id":"related-content","ui_element_position":5}" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/a/20-10006075"> <div class="ml-16 mb-8 w-1/4 float-right cod:w-1/6"> <div class="relative"> <div itemprop="image" itemscope="" itemtype="https://schema.org/ImageObject" class="ydd-image relative "> <figure role="group"> <img alt="Matemaattisia merkkejä ja numeroita keltaisella pohjalla." itemprop="image" content="https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_2813,h_2813,c_crop,x_2021,y_0/w_700/v1705487592/39-122903665a7ac7616d74.jpg" data-yle-id="39-122903665a7ac7616d74" data-crop-coords="w_2813,h_2813,c_crop,x_2021,y_0" data-image-width="2813" data-image-version="1705487592" class="ydd-image__image js-ydd-image lazyload" src="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 2813 2813'%3E%3Cdefs%3E%3Cpattern id='blurhash' patternUnits='userSpaceOnUse' width='2813' height='2813'%3E%3Cimage href='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAJCAIAAAC0SDtlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA3klEQVQYlSXPsYEbMRRDwQeQUvFX48Uuwdbu8gMOFE80+vP7w8AN/6S/4iMdC7PFq92Jz+Sac8258jxbNVBAqi0bG4QkFUnU2l3TBrTp+jLL3Yv3wqayJdUae0VL3drvdLa6qSp37b53tbSWI4oVK+hkjfyyZ9StqjVa8c56wZYWIweIGMnosBYrdTZtSevASJUlfwOuhFwoDVELuxyqlNQTJ1JpRaumPe5JnjlnNKPsche1yXSmc8pMYgpMOMqTXJP75JnMhru4TdIcctrZrQUo6aPcOZ95Ps99zbn/AypqxKcEEitDAAAAAElFTkSuQmCC' x='0' y='0' width='100%25' height='100%25' preserveAspectRatio='xMinYMin slice'%3E%3C/image%3E%3C/pattern%3E%3C/defs%3E%3Crect width='100%25' height='100%25' fill='url(%23blurhash)' /%3E%3C/svg%3E" width="2813" height="2813"> <meta itemprop="url" content="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_2813,h_2813,c_crop,x_2021,y_0/w_700/v1705487592/39-122903665a7ac7616d74.jpg"> <noscript class="absolute inset-0"><img class="ydd-image__image" src="https://web.archive.org/web/20241002211008im_/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_2813,h_2813,c_crop,x_2021,y_0/w_400/v1705487592/39-122903665a7ac7616d74.jpg" alt="Matemaattisia merkkejä ja numeroita keltaisella pohjalla."/></noscript> </figure> </div> </div> </div> <h3 class="mb-16 text-md dog:text-lg">Kolme nopeaa tekniikkaa päässälaskutaitojesi parantamiseen – tehosta matematiikan taitojasi</h3> </a> <p class="mb-0 text-gray-95 text-md">Haluatko sinäkin olla nopeampi laskija? Kokeile Abitreenien uudet tekniikat!</p> <div class="ydd-card__footer flex flex-wrap gap-8 items-center mb-8 mt-16"> <div class="flex items-center"> <span class="leading-none mr-4 text-gray-60"> <div class="size-14 [&>svg]:h-full [&>svg]:w-full"> <svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" fill="none" viewbox="0 0 24 24" aria-hidden="true"><path fill="currentColor" fill-rule="evenodd" d="M12 1C5.925 1 1 5.925 1 12s4.925 11 11 11 11-4.925 11-11S18.075 1 12 1M3 12a9 9 0 1 1 18 0 9 9 0 0 1-18 0m10-6a1 1 0 1 0-2 0v6a1 1 0 0 0 .553.894l4 2a1 1 0 1 0 .894-1.788L13 11.382z" clip-rule="evenodd"/></svg> </div> </span> <div aria-label="Julkaistu" class="text-gray-60 text-xs">20.3.2024</div> </div> </div> </div> </div> </div> </div> <div class="border-gray-10 border-t mx-16"></div> <div class="ydd-card ydd-card--s-extended" data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006378","ui_element_id":"related-content","ui_element_position":6}"> <div class="ydd-card__wrap"> <div class="ydd-card__content mr-16 ml-16 flex flex-wrap"> <div class="w-full"> <a data-ydd-impression-data="{"service_id":"yddrasil-fi","yle_id":"20-10006378","ui_element_id":"related-content","ui_element_position":6}" href="https://web.archive.org/web/20241002211008/https://yle.fi/aihe/a/20-10006378"> <div class="ml-16 mb-8 w-1/4 float-right cod:w-1/6"> <div class="relative"> <div itemprop="image" itemscope="" itemtype="https://schema.org/ImageObject" class="ydd-image relative "> <figure role="group"> <img alt="Abitreenien juontajat Katja Ylisiurua ja Roosa Laksio matematiikan suoran yo-koelähetyksen promokuvassa." itemprop="image" content="https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_1081,h_1081,c_crop,x_413,y_2/w_700/v1709039036/39-124991065ddd43b8c1a4.jpg" data-yle-id="39-124991065ddd43b8c1a4" data-crop-coords="w_1081,h_1081,c_crop,x_413,y_2" data-image-width="1081" data-image-version="1709039036" class="ydd-image__image js-ydd-image lazyload" src="data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 1081 1081'%3E%3Cdefs%3E%3Cpattern id='blurhash' patternUnits='userSpaceOnUse' width='1081' height='1081'%3E%3Cimage href='data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAAJCAIAAAC0SDtlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVQYlQXBAWLbMAwDQACk5Ly0/94XtraJLZLYHb//fMGexjSn6A5MAktaUihEmRqwwAI6uwbGDF2Y4jQxBNC0ZPYoQJkkKBL5/ikYnnCnK6ZiOmZo2GqKCiggKSSS+f33gYUhCj7qk106xfI0bEGpTK2MlZlS/v5r2OjE4dyqR+fWffDpOZiRY3lvvbaulSsyzw0YPpgb/cbzi/uN941P4yFmITdeF+pCL+xkBsNWD/vg+fjz4/eP3zdus1I0KHWyDwrDrtx7TxMdRfTMOf08OKUJKZgbe3MvZY54gMq9cxpuPmFzGt2gSYVia1+6XrgWVjjYsv8Db9O211F3RnoAAAAASUVORK5CYII=' x='0' y='0' width='100%25' height='100%25' preserveAspectRatio='xMinYMin slice'%3E%3C/image%3E%3C/pattern%3E%3C/defs%3E%3Crect width='100%25' height='100%25' fill='url(%23blurhash)' /%3E%3C/svg%3E" width="1081" height="1081"> <meta itemprop="url" content="https://web.archive.org/web/20241002211008/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/fl_keep_iptc/q_88/w_1081,h_1081,c_crop,x_413,y_2/w_700/v1709039036/39-124991065ddd43b8c1a4.jpg"> <noscript class="absolute inset-0"><img class="ydd-image__image" src="https://web.archive.org/web/20241002211008im_/https://images.cdn.yle.fi/image/upload/f_auto,fl_progressive/q_auto/w_1081,h_1081,c_crop,x_413,y_2/w_400/v1709039036/39-124991065ddd43b8c1a4.jpg" alt="Abitreenien juontajat Katja Ylisiurua ja Roosa Laksio matematiikan suoran yo-koelähetyksen promokuvassa."/></noscript> </figure> </div> </div> </div> <h3 class="mb-16 text-md dog:text-lg">Näin YTL:n asiantuntijat analysoivat kevään 2024 matematiikan kokeita Abitreenien lähetyksessä</h3> </a> <p class="mb-0 text-gray-95 text-md">Abitreenien yo-koelähetyksessä Ylioppilastutkintolautakunnan sensorit, aineenopettaja ja kokeen tehnyt abi kävivät päivän yo-kokeita läpi kohta kohdalta.</p> <div class="ydd-card__footer flex 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