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+\usepackage{lmodern} % Font Latin Modern +% \usepackage[margin=2.5cm]{geometry} % Marginesy 2.5 cm + +% Ulepszona mikrotypografia +\usepackage{microtype} + +% Pakiet do kolorowania tekstu +\usepackage{xcolor} + +% ----------------------------------- % +% Nagłówki/stopki: pakiet fancyhdr % +% ----------------------------------- % +\usepackage{fancyhdr} +\pagestyle{fancy} +\fancyhf{} % Wyczyść nagłówki i stopki + +\fancyhf{} % Wyczyść wszystkie pola nagłówka i stopki +\fancyhead[L]{\textbf{Szczegółowe Ocenianie z \textcolor{cviolet}{Matematyki}}} % Lewa strona nagłówka: tytuł dokumentu +\fancyhead[C]{--~\thepage~--} % Środek nagłówka: numer strony +\fancyhead[R]{\small \textcolor{cgreen}{Zakres Rozszerzony}, \textcolor{blue}{Poziom Nauczania: 1}} % Prawa strona nagłówka: dodatkowe informacje +\renewcommand{\headrulewidth}{1pt} % Linia w nagłówku o grubości 1pt +\renewcommand{\footrulewidth}{0pt} % Brak linii w stopce + +% ----------------------------- % +% Pakiet enumitem i styl % +% ----------------------------- % +\usepackage{enumitem} +\usepackage{hyperref} % Pakiet do obsługi linków + +% Define a new list environment +\newlist{longenum2}{enumerate}{2} + +% Adjust the first level: Ensure it fits within page width +\setlist[longenum2,1]{ + label=\arabic*., % Etykieta: "ust. 1." + leftmargin=2em, % Left margin adjusted to fit within header's width + labelsep=0.25em, % Space between label and text + labelwidth=1.5em, % Reserve enough space for the label + itemindent=0em, % No additional indentation for item content + align=left % Align the label to the left +} + +% Second level: Adjust similarly +\setlist[longenum2,2]{ + label=\arabic*), % Label format: "1.", "2.", etc. + leftmargin=2em, % Left margin adjusted to avoid overlap + labelsep=0.25em, % Space between label and text + labelwidth=1.5em, % Reserve enough space for the label + itemindent=0em, % No additional indentation + align=left % Align label to the left +} + +% Import necessary packages +\usepackage{enumitem} + +% Define a new list environment +\newlist{longenum}{enumerate}{7} + +% Adjust the first level: Ensure it fits within page width +\setlist[longenum,1]{ + label=\textbf{\arabic*}, % Etykieta: "ust. 1." + leftmargin=2em, % Left margin adjusted to fit within header's width + labelsep=0.5em, % Space between label and text + labelwidth=1.5em, % Reserve enough space for the label + itemindent=0em, % No additional indentation for item content + align=left % Align the label to the left +} + +% Second level: Adjust similarly +\setlist[longenum,2]{ + label=\arabic*., % Label format: "1.", "2.", etc. + leftmargin=2em, % Left margin adjusted to avoid overlap + labelsep=0.25em, % Space between label and text + labelwidth=1.5em, % Reserve enough space for the label + itemindent=0em, % No additional indentation + align=left % Align label to the left +} + +% Third level +\setlist[longenum,3]{ + label=\arabic*), % Label format: "1)", "2)", etc. + leftmargin=2em, % Increase indentation for clarity + labelsep=0.25em, + labelwidth=1.5em, + itemindent=0em, + align=left +} + +% Fourth level +\setlist[longenum,4]{ + label=\alph*., % Label format: "a.", "b.", etc. + leftmargin=2em, % Increase left margin for nested levels + labelsep=0.25em, + labelwidth=1.5em, + itemindent=0em, + align=left +} + +% Fifth level +\setlist[longenum,5]{ + label=\alph*), % Label format: "a)", "b)", etc. + leftmargin=2em, + labelsep=0.25em, + labelwidth=1.5em, + itemindent=0em, + align=left +} + +% Sixth level +\setlist[longenum,6]{ + label=\textbullet, % Label format: Bullet symbol + leftmargin=2em, + labelsep=0.25em, + labelwidth=1.5em, + align=left +} + +% Seventh level +\setlist[longenum,7]{ + label=--, % Label format: Dash symbol + leftmargin=2em, + labelsep=0.25em, + labelwidth=1.5em, + align=left +} + +% Custom configuration for lists with § and specified spacing +\newlist{customenum}{enumerate}{1} +\setlist[customenum,1]{ + label=\textbf{\S~\arabic*}, % Bold § and number + leftmargin=4em, % Indentation from the left margin + labelsep=0.5em, % Space between the label and the text + align=left, % Align label to the left + itemsep=0.5em, % Space between items + parsep=0em % No additional paragraph space +} +% +% ----------------------------- % +% Nagłówki sekcji % +% ----------------------------- % +\usepackage{titlesec} +\titleformat{\section} + {\normalfont\fontsize{14pt}{16pt}\bfseries\centering}{Rozdział \thesection}{1em}{} +\titleformat{\subsection} + {\normalfont\fontsize{12pt}{14pt}\bfseries\centering}{}{0em}{} + +% % Konfiguracja nagłówków +% \fancyhf{} +% \fancyhead[L]{\textbf{Wewnątrzszkolne Oceniania}} +% \fancyhead[C]{-- \thepage\ --} +% \fancyhead[R]{\textbf{Załącznik Nr 2}} +% \fancyfoot{} + +% Tytuł i odniesienia +\usepackage{titlesec} +\titleformat{\section} + {\normalfont\fontsize{14pt}{16pt}\bfseries\centering}{\thesection}{1em}{} +\titleformat{\subsection} + {\normalfont\fontsize{12pt}{14pt}\bfseries\centering}{}{0em}{} + +% Dodatkowe pakiety dla niestandardowego formatowania +\usepackage{xcolor} +\usepackage{sectsty} +\sectionfont{\centering\fontsize{16pt}{18pt}\selectfont} + +\definecolor{cred}{RGB}{255, 0, 0} +\definecolor{cviolet}{RGB}{148, 0, 211} +\definecolor{cgreen}{RGB}{0, 100, 0} +\definecolor{cblue}{RGB}{0, 0, 255} + +% Definiujemy nowy skrót, który pozwoli odwoływać się do numeru przypisu: +% \newcommand{\footref}[1]{\textsuperscript{\ref{#1}}} +\begin{document} + +% Wyłącz na moment fancyhdr, aby strona tytułowa nie miała nagłówka/stopki +% \thispagestyle{empty} +\thispagestyle{fancy} + + +% \begin{center} +% \textbf{Załącznik Nr 2}\\[0.5em] +% \textbf{do Statutu Zespołu Szkół Licealnych im. Zbigniewa Herberta w Słubicach}\\[3em] + +% {\Large \textbf{WEWNĄTRZSZKOLNE ZASADY OCENIANIA}}\\[1em] +% w~Zespole Szkół Licealnych im. Zbigniewa Herberta w Słubicach +% \end{center} + +% Wyłączenie nagłówków na pierwszej stronie +% \thispagestyle{plain} + +% Główna treść +\begin{flushright} + Zespołu Szkół Licealnych \\ + im. Zbigniewa Herberta w Słubicach \\ +\end{flushright} + +\vspace{1em} + + + \vspace{5em} + + \begin{center} + {\Large \textbf{SZCZEGÓŁOWE OCENIANIE Z \textcolor{cviolet}{MATEMATYKI}}}\\[1em] + \textbf{\textcolor{cgreen}{Zakres Rozszerzonym}, \textcolor{blue}{Poziom Nauczania: 1}}\\[1em] + \end{center} + + \vspace{5em} + + + System oceniania opracowany w oparciu o: + + \begin{enumerate}[noitemsep] + \item Wewnątrzszkolne Ocenianie jako Załącznik do Statutu Szkoły\footnotemark[1]. + \item Podstawę programową (\textbf{PP}) z~dnia 28 czerwca 2024 r.\footnotemark[2]. + \item Rozporządzenie\footnotemark[3] określające szczegółowe warunki oceniania, klasyfikowania i promowania uczniów. + \item Ustawę\footnotemark[4] \emph{Prawo oświatowe}. + \end{enumerate} + + \footnotetext[1]{Wewnątrzszkolne Ocenianie (WO) jako integralny załącznik do Statutu Szkoły, regulujący szczegółowe zasady oceniania, klasyfikowania i promowania uczniów.} + \footnotetext[2]{Podstawa programowa kształcenia ogólnego dla szkół podstawowych i ponadpodstawowych, zatwierdzona Rozporządzeniem Ministra Edukacji i Nauki z dnia 28 czerwca 2024 r.} + \footnotetext[3]{Rozporządzenie Ministra Edukacji Narodowej z dnia 25 sierpnia 2017 r. w~sprawie warunków i sposobu oceniania, klasyfikowania i promowania uczniów i słuchaczy w szkołach publicznych (Dz.U. z 2017 r. poz. 1534 z późn. zm.).} + \footnotetext[4]{Ustawa z dnia 14 grudnia 2016 r. – Prawo oświatowe (t.j. Dz.U. z 2021 r. poz. 1082 z późn. zm.).} + + + \begin{flushright} + \begin{minipage}{0.25\textwidth} % Szerokość na 25% strony + \raggedright % Wyrównanie tekstu do lewej wewnątrz minipage + \textit{Autorzy:}\\[0.5em] % Dodanie odstępu pod tytułem + \hspace{1em}M. Markiewicz\\ % Wcięcie dla pierwszego nazwiska + \hspace{1em}J. Góra % Wcięcie dla drugiego nazwiska + \end{minipage} + \end{flushright} + + +\thispagestyle{fancy} +%-------------------------------- +\newpage +\tableofcontents % Polecenie wstawiające spis treści + +\newpage +\section{Postanowienia ogólne} + +%----------------------------------------- +% § 1 +%----------------------------------------- +\paragraf{Cel i zakres Szczegółowego Oceniania (SO)} + +\begin{longenum} + \item \textbf{Cel główny:} Zapewnienie klarownych i jednolitych zasad oceniania + osiągnięć edukacyjnych uczniów, zgodnie z~Wewnątrzszkolnym Ocenianiem (\textbf{WO}). + \item \textbf{Cele szczegółowe:} + \begin{longenum} + \item Ujednolicenie wymagań edukacyjnych oraz sposobów sprawdzania wiedzy. + \item Zapewnienie przejrzystości kryteriów oceniania dla uczniów i rodziców (prawnych opiekunów). + \item Umożliwienie rzetelnej ewaluacji postępów uczniów i wspomaganie ich rozwoju. + \end{longenum} + \item \textbf{Zakres obowiązywania:} + \begin{longenum} + \item Niniejsze zasady dotyczą \textbf{\textcolor{cviolet}{matematyki} na \textcolor{blue}{1 poziomie nauczaniu} w~\textcolor{cgreen}{zakresie rozszerzonym}}. + % \item SO jest ściśle powiązane z \emph{Wewnątrzszkolnym Ocenianiem (WO)} + % oraz \emph{Statutem Szkoły} i nie może być z nimi sprzeczne. + \end{longenum} +\end{longenum} + +%----------------------------------------- +%----------------------------------------- +% § 2 +%----------------------------------------- +\footnotetext[5]{Rozkład materiału z~\textcolor{cviolet}{matematyki} dla danego \textcolor{blue}{poziomu nauczania}, opracowany na podstawie programu nauczania wydawnictwa Nowa Era, zgodny z \textbf{PP}\footnotemark[2].} + +\paragraf{SO obejmuje:} + +\begin{longenum} + \item Wymagania ogólne i~szczegółowe, wynikające z~\textbf{PP}\footnotemark[2]. + \item Punktację wymagań oraz określenie minimalnej liczby punktów, które zapewniają realizację wymagań edukacyjnych, zgodnie z~rozkładem materiału (\textbf{RM\footnotemark[5]}), w~którym przypisano działy z (\textbf{PP})\footnotemark[2] do danego \textcolor{blue}{poziomu nauczania}. + \item Zakres stosowania progów procentowych i~sposób ich przeliczania na oceny. + + % \item Sposoby i formy sprawdzania wiedzy (prace klasowe, kartkówki, odpowiedzi ustne, projekty itp.). + % \item Sposób uwzględniania opinii/orzeczeń poradni psychologiczno-pedagogicznej w ocenianiu. + % \item Zasady gromadzenia informacji o postępach uczniów i formułowania ocen semestralnych/końcowych. +\end{longenum} + +%-------------------------------- +\section{Punktacja wymagań i minimalna liczba punktów} + +\paragraf{Cel i zakres punktacji wymagań i minimalnej liczby punktów} +\begin{longenum} + + \item Celem tak ustalonej punktacji jest \textbf{określenie wagi poszczególnych wymagań} + w procesie oceniania oraz zapewnienie \emph{rzetelnego} odniesienia do treści programowych. %wynikających z podstawy programowej. + + \item \textbf{Minimalną liczbę punktów} \(\,(P_{\min})\) ustala się w celu wyznaczenia + progu \emph{pełnej realizacji} wymaganych treści wynikających z \textbf{PP}\footnotemark[2] dla danego \textcolor{blue}{poziomu nauczania} w~zadanym zakresie, + przy założeniu, że zostają spełnione: + \begin{itemize}[noitemsep] + \item Wszystkie Wymagania Szczegółowe. + \item Wszystkie Wymagania Ogólne. + % \item nie dochodzi do \textbf{wielokrotnego naliczania} tego samego WO, nawet jeśli jest ono powiązane z kilkoma WS. + \end{itemize} + +\end{longenum} + +\paragraf{Punktacja wymagań} +\begin{longenum} + \item Każdemu \textbf{Wymaganiu Szczegółowemu} (oznaczonemu indeksem \(i\)) przypisuje się + \textbf{wagę punktową} \(w_{s_i}\), przy czym minimalna wartość tej wagi wynosi 1. + + \item Każdemu \textbf{Wymaganiu Ogólnemu} (oznaczonemu indeksem \(j\)) przypisuje się + \textbf{wagę punktową} \(w_{o_j}\), przy czym minimalna wartość tej wagi wynosi 1. + + \item \textbf{Łączna liczba punktów} przysługujących danemu działowi określonemu w~\textbf{PP}\footnotemark[2], uwzględniająca wszystkie powiązania + między Wymaganiami Szczegółowymi i Wymaganiami Ogólnymi, obliczana jest według następującej formuły: + + % \begin{equation} + % P_{\text{sum}} + % = + % \sum_{i=1}^{N_{W_S}} + % \Bigl( + % w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} + % \Bigr), + % \label{wzor:punktacja} + % \end{equation} + % gdzie: + % \begin{itemize}[noitemsep] + % \item \(N_{W_S}\) oznacza całkowitą liczbę Wymagań Szczegółowych w danym dziale, + % \item \(N^i_{W_O}\) oznacza liczbę Wymagań Ogólnych powiązanych z \(i\)-tym Wymaganiem Szczegółowym. + % \end{itemize} + + \begin{equation} + P_{\text{sum}} = \sum_{i=1}^{N_{W_S}} \Bigl( w_{s_i} \times \sum_{j=1}^{N^i_{W_O}} w_{o_j} \Bigr) + \label{wzor:punktacja} + \end{equation} + + gdzie: + \begin{itemize}[noitemsep] + \item \(N_{W_S}\) oznacza całkowitą liczbę Wymagań Szczegółowych w~danym dziale, + \item \(N^i_{W_O}\) oznacza liczbę Wymagań Ogólnych powiązanych z~\(i\)-tym Wymaganiem Szczegółowym, + \item \(N^i_{W_O} \geq 1\) dla każdego \(i\). + \end{itemize} + + {\small + \textbf{Uwaga:} Wzór (\ref{wzor:punktacja})służy do określenia \emph{całkowitej} liczby punktów możliwej + do uzyskania za pełne zrealizowanie danego działu, z uwzględnieniem konkretnych + powiązań pomiędzy Wymaganiami Szczegółowymi i Wymaganiami Ogólnymi. + } + + \item Celem tak ustalonej punktacji jest określenie wagi poszczególnych wymagań edukacyjnych + w~procesie oceniania osiągnięć edukacyjnychs. + + \item \textbf{Punktacja} przypisana poszczególnym działom oraz łączna liczba punktów + \(\bigl(P_{\text{sum}}\bigr)\), obliczona zgodnie ze wzorem~(\ref{wzor:punktacja}), + znajduje się w~\textbf{Rozdziale~1~załącznika~1}. + +\end{longenum} + +\paragraf{Ustalanie minimalnej liczby punktów} +\begin{longenum} + \item \textbf{Minimalną liczbę punktów} \(P_{\min}\) opisaną wzorem (\ref{eq:pmin}) ustala się w celu wyznaczenia + progu \emph{pełnej realizacji} wymaganych treści wynikających z~\textbf{PP}\footnotemark[2]. + +\begin{equation} + P_{\min} = \min \left\{ \sum_{i=1}^{N_{W_S}} \left( w_{s_i} \times w_{o_j(i)} \right) \right\} + \label{eq:pmin} + \end{equation} + Gdzie: + \begin{itemize} + \item \( P_{\min} \) to minimalna wartość całkowitej punktacji, + \item \( N_{W_S} \) to liczba wymagań szczegółowych, + \item \( w_{s_i} \) to waga \( i \)-tego wymagania szczegółowego, + \item \( w_{o_j(i)} \) to waga wybranego wymagania ogólnego dla \( i \)-tego wymagania szczegółowego, + \item \( j(i) \) to indeks wybranego wymagania ogólnego dla \( i \)-tego wymagania szczegółowego. + \end{itemize} + + \begin{equation} + \forall i \in \{1, \dots, N_{W_S}\}, \quad \exists j(i) \in \{1, \dots, N_{W_O}^i\} + \label{eq:warunek} + \end{equation} + Warunek określony wzorem (\ref{eq:warunek}) zapewnia, że dla każdego wymagania szczegółowego wybrane jest dokładnie jedno wymaganie ogólne, a jednocześnie wszystkie wymagania są zrealizowane. + + \textbf{Uwaga:} W przypadku, gdy każdemu Wymaganiu Szczegółowemu i Ogólnemu przypisuje się \textbf{1~punkt}, wówczas minimalna liczba punktów \( P_{\min} \) realizujących obowiązkowe wymagania edukacyjne z~podstawy programowej dla danego działu wyraża się wzorem (\ref{eq:min_points}). + + \begin{equation} + \label{eq:min_points} + P_{\min} = N_{W_S} + \end{equation} + + Gdzie \( N_{W_S} \) oznacza liczbę Wymagań Szczegółowych. + + \item Minimalna liczba punktów \(\bigl(P_{\text{sum}}\bigr)\) realizująca obowiązkowe wymagania zgodnie z \textbf{PP}\footnotemark[2], znajduje się w~\textbf{Rozdziale~1~załącznika~1}. + +\end{longenum} + +%--------------------------------- +%------------------------------------ + +\section{Wymagania ogólne i szczegółowe} + +\paragraf{Cel i zakres wymagań ogólnych i szczegółowych} + +\begin{longenum} + \item \textbf{Cel:} Zapewnienie jasnych i jednolitych zasad oceniania osiągnięć uczniów + z~\textcolor{cviolet}{matematyki} na \textcolor{cgreen}{zakresie rozszerzonym} na \textcolor{cblue}{1 poziomie nauczania} liceum ogólnokształcącego, + zgodnie z \textbf{Podstawą Programową}\footnotemark[2] i~\textbf{Rozkładem Materiału}\footnotemark[5]. + + \item \textbf{Zakres:} Wymagania określone w niniejszym dokumencie obowiązują nauczycieli realizujących treści kształcenia z~\textbf{\textcolor{cviolet}{matematyki} na \textcolor{blue}{pierwszym poziomie nauczania} (\textcolor{cgreen}{zakres rozszerzonym})}, uwzględniając: + \begin{longenum} + \item Działy z \textbf{RM}\footnotemark[5] – obszary tematyczne przypisane do pierwszego \textcolor{blue}{poziomu nauczania}, które wyznaczają strukturę nauczania \textcolor{cviolet}{matematyki}. + \item Pełną realizację obowiązkowych wymagań edukacyjnych – zgodnie z wytycznymi zawartymi w aktualnej \textbf{PP}\footnotemark[2], które określają minimalne wymagania do opanowania przez uczniów w ramach każdego działu. + \end{longenum} +\end{longenum} + + + +\paragraf{Wymagania ogólne} + +\begin{longtable}{|p{0.05\textwidth}|p{0.85\textwidth}|} + \hline + \textbf{Lp.} & \textbf{Treści kształcenia} \\ + \hline + \endhead + + 1. & \textbf{Kształcenie sprawności rachunkowej oraz rozumienia pojęć i procedur matematycznych.} \\ + \hline + 1.1 & Uczeń posługuje się liczbami rzeczywistymi, dokonuje obliczeń i przekształceń wyrażeń algebraicznych oraz poprawnie interpretuje wynik każdego działania w kontekście zadania. \\ + \hline + 1.2 & Uczeń stosuje właściwą terminologię i zapis symboliczny, wynikający z podstawowych struktur matematycznych. \\ + \hline + + 2. & \textbf{Rozwiązywanie problemów, modelowanie matematyczne i wnioskowanie.} \\ + \hline + 2.1 & Uczeń formułuje i rozwiązuje typowe zadania problemowe z zastosowaniem właściwych metod i narzędzi matematycznych. \\ + \hline + 2.2 & Uczeń interpretuje otrzymane wyniki, uwzględniając kontekst zadania, i przedstawia logiczne uzasadnienia. \\ + \hline + + 3. & \textbf{Analiza danych, stosowanie elementów rachunku prawdopodobieństwa i statystyki opisowej.} \\ + \hline + 3.1 & Uczeń odczytuje, interpretuje i tworzy proste reprezentacje graficzne (tabele, wykresy, diagramy), korzystając z podstawowych metod statystycznych. \\ + \hline + 3.2 & Uczeń stosuje podstawowe zasady rachunku prawdopodobieństwa do opisu prostych zjawisk losowych, w szczególności wykorzystując definicję klasyczną prawdopodobieństwa. \\ + \hline + + 4. & \textbf{Rozwijanie umiejętności argumentacji i komunikowania się językiem matematyki.} \\ + \hline + 4.1 & Uczeń interpretuje i tworzy wypowiedzi o treściach matematycznych w formie ustnej i pisemnej, posługując się poprawnymi definicjami, twierdzeniami i notacją. \\ + \hline + 4.2 & Uczeń wyjaśnia zależności między wielkościami, formułuje wnioski oraz prowadzi rozumowania dotyczące analizowanych zadań. \\ + \hline +\end{longtable} + +\newpage +\paragraf{Wymagania szczegółowe} + +\begin{longtable}{|p{0.95\textwidth}|} + \hline + \textbf{I. Liczby rzeczywiste.} \\ + + \hline + \hspace{0.25em}\textbf{Zakres podstawowy}. Uczeń: \\ + \hline + \hspace{0.5em} 1) Wykonuje działania (dodawanie, odejmowanie, mnożenie, dzielenie, potęgowanie, pierwiastkowanie, logarytmowanie) w zbiorze liczb rzeczywistych. \\ + \hline + \hspace{0.5em} 2) Przeprowadza proste dowody dotyczące podzielności liczb całkowitych i reszt z dzielenia, np. \\ + \hline + \hspace{1em} a) Dowód podzielności przez 24 iloczynu czterech kolejnych liczb naturalnych, \\ + \hspace{1em} b) Dowód własności: jeśli liczba przy dzieleniu przez 4 daje resztę 3, to nie jest kwadratem liczby całkowitej. \\ + \hline + \hspace{0.5em} 3) Stosuje własności pierwiastków dowolnego stopnia, w tym pierwiastków stopnia nieparzystego z liczb ujemnych. \\ + \hline + \hspace{0.5em} 4) Stosuje związek pierwiastkowania z potęgowaniem oraz prawa działań na potęgach i pierwiastkach. \\ + \hline + \hspace{0.5em} 5) Stosuje monotoniczność potęgowania, w szczególności własności: jeśli \( x < y \) oraz \( a > 1 \), to \( a^x < a^y \), zaś gdy \( x < y \) i \( 0 < a < 1 \), to \( a^x > a^y \). \\ + \hline + \hspace{0.5em} 6) Posługuje się pojęciem przedziału liczbowego, zaznacza przedziały na osi liczbowej. \\ + \hline + \hspace{0.5em} 7) Stosuje interpretację geometryczną i algebraiczną wartości bezwzględnej, rozwiązuje równania typu: \( |x + 4| = 5 \). \\ + \hline + \hspace{0.5em} 8) Wykorzystuje własności potęgowania i pierwiastkowania w sytuacjach praktycznych, w tym do obliczania procentów składanych, zysków z lokat i kosztów kredytów. \\ + \hline + \hspace{0.5em} 9) Stosuje związek logarytmowania z potęgowaniem, posługuje się wzorami na logarytm iloczynu, logarytm ilorazu i logarytm potęgi. \\ + + \hline + \hspace{0.25em}\textbf{Zakres rozszerzony}. Uczeń: \\ + \hspace{0.5em} 1) Spełnia wymagania określone dla zakresu podstawowego. \\ + \hspace{0.5em} 2) Ponadto stosuje wzór na zamianę podstawy logarytmu. \\ + + % \hline +\end{longtable} + +\begin{longtable}{|p{0.95\textwidth}|} + \hline + \textbf{II. Wyrażenia algebraiczne.} \\ + \hline + Zakres podstawowy. Uczeń: \\ + 1) stosuje wzory skróconego mnożenia na: \( (a + b)^2 \), \( (a - b)^2 \), \( a^2 - b^2 \); \\ + 2) dodaje, odejmuje i mnoży wielomiany jednej i wielu zmiennych; \\ + 3) wyłącza poza nawias jednomian z sumy algebraicznej; \\ + 4) mnoży i dzieli wyrażenia wymierne. \\ + \hline + Zakres rozszerzony. Uczeń spełnia wymagania określone dla zakresu podstawowego, a ponadto: \\ + 1) dzieli wielomian jednej zmiennej \( W(x) \) przez dwumian postaci \( x - a \); \\ + 2) rozkłada wielomiany na czynniki metodą wyłączania wspólnego czynnika przed nawias oraz metodą grupowania wyrazów; \\ + 3) znajduje pierwiastki całkowite wielomianu o współczynnikach całkowitych; \\ + 4) stosuje podstawowe własności trójkąta Pascala oraz następujące własności współczynnika dwumianowego (symbolu Newtona): \( \binom{n}{0} = 1 \), \( \binom{n}{1} = n \), \( \binom{n}{n-1} = n \), \( \binom{n}{k} = \binom{n}{n-k} \), \( \binom{n}{k} + \binom{n}{k+1} = \binom{n+1}{k+1} \); \\ + 5) korzysta ze wzorów na: \( a^3 + b^3 \), \( a^3 - b^3 \), \( a^n - b^n \), \( (a + b)^n \) i \( (a - b)^n \); \\ + 6) dodaje i odejmuje wyrażenia wymierne, np.: \( \frac{1}{x} + 1 - \frac{1}{x} \), \( \frac{1}{x} + \frac{1}{x^2} + \frac{1}{x^3} \), \( \frac{x + 1}{x + 2} + \frac{x - 1}{x + 1} \). + + % \hline +\end{longtable} + +\begin{longtable}{|p{0.95\textwidth}|} + \hline + \textbf{III. Równania i nierówności.} \\ + \hline + Zakres podstawowy. Uczeń: \\ + 1) przekształca równania i nierówności w sposób równoważny, w tym np. przekształca równoważnie równanie \( \frac{5}{x} + 1 = \frac{x + 3}{2x - 1} \); \\ + 2) interpretuje równania i nierówności liniowe sprzeczne oraz tożsamościowe; \\ + 3) rozwiązuje nierówności liniowe z jedną niewiadomą; \\ + 4) rozwiązuje równania i nierówności kwadratowe; \\ + 5) rozwiązuje równania wielomianowe postaci \( W(x) = 0 \) dla wielomianów doprowadzonych do postaci iloczynowej. \\ + \hline + Zakres rozszerzony. Uczeń spełnia wymagania określone dla zakresu podstawowego, a ponadto: \\ + 1) rozwiązuje równania wielomianowe postaci \( W(x) = 0 \) oraz nierówności wielomianowe typu: \( W(x) > 0 \), \( W(x) \geq 0 \), \( W(x) < 0 \), \( W(x) \leq 0 \) dla wielomianów doprowadzonych do postaci iloczynowej lub takich, które dają się doprowadzić do postaci iloczynowej metodą wyłączania wspólnego czynnika przed nawias lub metodą grupowania; \\ + 2) rozwiązuje równania i nierówności wymierne, które dadzą się sprowadzić do równania lub nierówności liniowej lub kwadratowej; \\ + 3) stosuje wzory Viète’a dla równań kwadratowych; \\ + 4) rozwiązuje równania i nierówności z wartością bezwzględną; \\ + 5) analizuje równania i nierówności liniowe z parametrami oraz równania i nierówności kwadratowe z parametrami, w szczególności: wyznacza liczbę rozwiązań w zależności od parametrów, podaje warunki, przy których rozwiązania mają określone znaki bądź należą do określonego przedziału, wyznacza rozwiązania w zależności od parametrów; \\ + 6) rozwiązuje równania wielomianowe, które dają się doprowadzić do równania kwadratowego, w szczególności równania dwukwadratowe; \\ + 7) rozwiązuje równania wymierne postaci \( \frac{V(x)}{W(x)} = 0 \), gdzie wielomiany \( V(x) \) i \( W(x) \) są zapisane w postaci iloczynowej. \\ + \hline + \end{longtable} + + + \section{Postanowienia końcowe} + + \paragraf{Zasady obowiązywania} + \begin{longenum} + \item Niniejszy dokument określa szczegółowe zasady oceniania uczniów na \textcolor{blue}{1~poziomie edukacyjnym} na \textcolor{cgreen}{zakresie rozszerzonym} i~obowiązuje wszystkich nauczycieli oraz uczniów w~Zespole Szkół Licealnych im. Zbigniewa Herberta w~Słubicach. + \item Szczegółowe Ocenianie (SO) jest zgodne z: + \begin{longenum} + \item \textbf{Podstawą programową} kształcenia ogólnego\footnotemark[2]. + \item \textbf{Wewnątrzszkolnym Ocenianiem} (WO), stanowiącym integralną część Statutu Szkoły\footnotemark[1]. + \item Obowiązującymi \textbf{przepisami prawa oświatowego}\footnotemark[4]. + \end{longenum} + \item Dokument może być aktualizowany zgodnie z nowelizacją przepisów prawa oraz wewnętrznymi regulacjami szkoły. + \end{longenum} + + \paragraf{Postanowienia końcowe} + \begin{longenum} + \item Każdy uczeń oraz jego rodzice (prawni opiekunowie) mają prawo do pełnej informacji na temat zasad oceniania określonych w~niniejszym dokumencie. + \item Nauczyciel jest zobowiązany do przestrzegania zasad oceniania zgodnie z~wytycznymi zawartymi w~SO. + \item W~przypadku wątpliwości interpretacyjnych związanych z~ocenianiem, decyzje podejmuje nauczyciel przedmiotu w~porozumieniu z~zespołem przedmiotowym. + \item Niniejsze zasady wchodzą w~życie z~dniem zatwierdzenia przez dyrektora szkoły i~obowiązują do momentu wprowadzenia ich nowelizacji. + \end{longenum} + + \begin{flushright} + \textbf{Nauczyciele zespołu przedmiotowego:} \\ + \vspace{2em} % Miejsce na podpisy + \rule{6cm}{0.4pt} \\ % Linia do podpisu pierwszego nauczyciela \\ + \textit{(podpis nauczyciela)} \\[1.5em] + + \rule{6cm}{0.4pt} \\ % Linia do podpisu drugiego nauczyciela \\ + \textit{(podpis nauczyciela)} \\[1.5em] + + \rule{6cm}{0.4pt} \\ % Linia do podpisu trzeciego nauczyciela (opcjonalnie) \\ + \textit{(podpis nauczyciela)} +\end{flushright} + + + +--- +% \begin{longenum} +% \item Nauczyciel, uwzględniając potrzeby i możliwości edukacyjne uczniów, zobowiązany jest do zapewnienia +% realizacji wszystkich powyższych wymagań szczegółowych w ramach programu nauczania przewidzianego +% w klasie pierwszej liceum ogólnokształcącego na poziomie podstawowym. + +% \item Niniejsze wymagania stanowią uszczegółowienie podstawy programowej i są podstawą do +% formułowania \textbf{przedmiotowych zasad oceniania}, w szczególności \emph{Szczegółowego Oceniania (SO)} +% z matematyki, określającego kryteria przyznawania ocen bieżących, semestralnych i końcoworocznych. +% \end{longenum} + + + +% \end{customenum} + +\end{document} + +% Liczby rzeczywiste +% Wyrażenia algebraiczne +% Równania i nierówności +% Funkcje +% Trygonometria +% Planimetria +% Geometria analityczna