8 szkoły podstawowej

Matematyka 8

Matematyka

Egzamin ósmoklasisty. Matematyka

Egzamin ósmoklasisty Matematyka. 2018/2019. Arkusz przykładowy

Egzamin ósmoklasisty Matematyka. Czerwiec 2020

Egzamin ósmoklasisty Matematyka. Grudzień 2018. Arkusz próbny

Egzamin ósmoklasisty Matematyka. Grudzień 2019. Arkusz próbny

Egzamin ósmoklasisty Matematyka. Kwiecień 2019

Egzamin ósmoklasisty Matematyka. Listopad 2018. Arkusz próbny

Egzamin ósmoklasisty Matematyka. Maj 2021

Egzamin ósmoklasisty Matematyka. Maj 2022

Egzamin ósmoklasisty Matematyka. Marzec 2020. Arkusz próbny

Egzamin ósmoklasisty Matematyka. Marzec 2021. Arkusz próbny

Matematyka 8. Ćwiczenia podstawowe

Matematyka 8. Podręcznik cz.1

Matematyka 8. Podręcznik cz.2

Matematyka 8. Zestawy zadań

Matematyka. Kalendarz ósmoklasisty

Matematyka. Przygotowanie do egzaminu ósmoklasisty. Repetytorium

Matematyka wokół nas 8

Matematyka z kluczem 8

Matematyka z plusem 8

Tak, zdam! Egzamin ósmoklasisty. Repetytorium Matematyka

Teraz egzamin ósmoklasisty. Arkusze

Teraz egzamin ósmoklasisty. Repetytorium

Sprawdźmy, które liczby spełniają warunek: −85​&lt;a&lt;−83​ &nbsp; -sprawdźmy czy liczba&nbsp; &nbsp; −3211​ &nbsp; &nbsp;spełnia ten warunek: −85​=−3220​ &nbsp; &nbsp;

Wiemy, że: -samochód zużywa 7,1 litra benzyny na 100 km -1 litr benzyny kosztuje 4,94 zł skoro samochód ten zużywa 7,1 litra benzyny na 100 km, to na 50 km&nbsp; zużyje on dwa razy mniej benzyny czyli:&nbsp;

Przedstawmy podaną sumę w postaci iloczynu wyłączając wspólny czynnik przed nawias:&nbsp;

Obliczmy wartość danego wyrażenia: (232<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​+38<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​−98<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​):2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​=(2⋅42<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​+3⋅22<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​−72<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​):2<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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M834 80h400000v40h-400000z'/></svg>​= &nbsp;&nbsp;

Wiemy, że: - cena jednego loda wynosi 2,50 zł - w opakowaniu jest 60 sztuk lodów - przy zakupie 4 opakowań udzielany jest 8% rabat Obliczmy, w ilu opakowaniach zmieści się 1500 sztuk lodów:&nbsp;&nbsp;

a) Województwa, w których wyprodukowano więcej niż 2000 ton miodu: wielkopolskie,

Sprawdźmy, które liczby spełniają warunek: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/3119b6b922026bde91433bb8a9ff878c035fe807ca65ae66d8ff51d67b568b15_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/3119b6b922026bde91433bb8a9ff878c035fe807ca65ae66d8ff51d67b568b15_big.svg" type="image/svg+xml"></object> &nbsp; -sprawdźmy czy liczba&nbsp; &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b88452503419abdf6ade7da2e2292f89c77313af909f0ec295fad73aba091759_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b88452503419abdf6ade7da2e2292f89c77313af909f0ec295fad73aba091759_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp;spełnia ten warunek: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ec154cd6e1f9b91fc8b65c83252803c16c1fb5d83d9363fa14da786a35bc7cc1_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ec154cd6e1f9b91fc8b65c83252803c16c1fb5d83d9363fa14da786a35bc7cc1_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp;

Obliczmy wartość danego wyrażenia: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/a3b1332f05a677e690d49a0e24ed05d5df7df6d57f5762dc6bbfe9d5d70ec9a5_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/a3b1332f05a677e690d49a0e24ed05d5df7df6d57f5762dc6bbfe9d5d70ec9a5_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp;

Zauważmy, że: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4982dd244bda8b0cbe471b46a0a4f1d4db78e565d70ca3f5949e92b4e540755f_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4982dd244bda8b0cbe471b46a0a4f1d4db78e565d70ca3f5949e92b4e540755f_big.svg" type="image/svg+xml"></object> &nbsp; &nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/27fcf18bf640871c01419e0046f8486dbde47e9b5401c5fa49b656bae32fa49c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/27fcf18bf640871c01419e0046f8486dbde47e9b5401c5fa49b656bae32fa49c_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7304d05483fdd914520042cf334ed8941508a33916cf14ec40f986d163dd3000_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7304d05483fdd914520042cf334ed8941508a33916cf14ec40f986d163dd3000_big.svg" type="image/svg+xml"></object> &nbsp; ta liczba jest równa 3, zatem jest to liczba naturalna

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