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100644 index 0000000..f8e54af --- /dev/null +++ b/exam_20_13/preamble.tex @@ -0,0 +1,37 @@ +\usepackage{array} +\usepackage{amsmath, amssymb} +\usepackage{unicode-math} +\setmathfont{TeX Gyre Termes Math} + +\usepackage{graphicx} +\usepackage{forloop} +\usepackage{enumitem} +\usepackage{pgfplots} +\pgfplotsset{compat=1.18} +\pgfplotsset{ + every axis/.append style={ + axis line style={line width=1pt}, + tick style={line width=1pt}, + }, + every axis plot/.append style={ + line width=1pt + } +} +\usepackage[a4paper,margin=2cm]{geometry} +\usepackage{tasks} + +\usepackage{fontspec} +\setmainfont{TeX Gyre Termes} +% \setmainfont{Latin Modern Roman} + +\usepackage{setspace} +\setstretch{1.1} + +\usepackage{polyglossia} +\setdefaultlanguage{vietnamese} + +\usepackage{tkz-euclide} +\usetikzlibrary{calc} +\tkzSetUpLine[line width=0.8pt] +\tkzSetUpPoint[size=3] + diff --git a/exam_20_13/sections/fill-form.tex b/exam_20_13/sections/fill-form.tex new file mode 100644 index 0000000..520026d --- /dev/null +++ b/exam_20_13/sections/fill-form.tex @@ -0,0 +1,37 @@ +\newpage +\section{Phần trả lời} +\subsection{Phần trả lời trách nghiệm nhiều đáp án} +\renewcommand{\arraystretch}{2} % increase row height for padding +\begin{tabular}{|*{12}{>{\centering\arraybackslash}p{0.06\linewidth}|}} +\hline +1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ +\hline + & & & & & & & & & & & \\ +\hline +\end{tabular} + +\subsection{Phần trả lời trách nghiệm đúng sai} +\newcounter{x} +\forloop{x}{1}{\value{x} < 5} { + \begin{minipage}[c]{0.25\textwidth} + \textbf {Câu \arabic{x}.} + \hline + \begin{tabular}{|*{4}{>{\centering\arraybackslash}p{0.15\linewidth}|}} + \hline + 1 & 2 & 3 & 4\\ + \hline + & & &\\ + \hline + \end{tabular} + \end{minipage} +} + +\subsection{Phần trả lời ngắn} +\begin{tabular}{|*{6}{>{\centering\arraybackslash}p{0.1\linewidth}|}} +\hline +1 & 2 & 3 & 4 & 5 & 6\\ +\hline + & & & & &\\ +\hline +\end{tabular} + diff --git a/exam_20_13/sections/mulpc.tex b/exam_20_13/sections/mulpc.tex new file mode 100644 index 0000000..2b196f5 --- /dev/null +++ b/exam_20_13/sections/mulpc.tex @@ -0,0 +1,161 @@ +\settasks{ + label=(\Alph*), + label-offset = 2em, + label-format = {\bfseries}, + item-indent = 2em, + column-sep = 1em +} + +\section{Trắc nghiệm} +\textbf{1. }[Tây Hồ 23 - 24] Trong các khẳng định sau, khẳng định nào là sai?. +\begin{tasks}(2) + \task $\lim \frac{2n-1}{n+1} = 2$ + \task $\lim (\frac{2e}{\pi})^n = 0$ + \task $\lim (\frac{3n+1}{n-1} - 3) = 0$ + \task $\lim \frac{2n-1}{n+1} = 0$ +\end{tasks} +\textbf{2. }[CVA 24 - 25] Trong không gian, đường thẳng song song với mặt phẳng khi và chỉ khi:. +\begin{tasks} + \task Đường thẳng đó và mặt phẳng không có điểm chung. + \task Đường thẳng đó không có điểm chung với một đường thẳng thuộc mặt phẳng. + \task Đường thẳng đó song song với một đường thẳng thuộc mặt phẳng. + \task Đường thẳng đó không có điểm chung với hai đường thẳng thuộc mặt phẳng. +\end{tasks} + +\textbf{3. }[CTE] Cho dãy số $(u_n)$ xác định bởi: $u_1=\frac{5}{2}$ và $u_n=3u_{n-1}-1 \forall n \geq 2$. Biết dãy số $(v_n)$ xác định bởi: $v_n=u_n-\frac{1}{2} \forall n\geq1$ là một cấp số nhân. Hãy cho biết số hạng đầu và công bội của cấp số nhân đó. +\begin{tasks}(4) + \task $v_1 = 2, q=3$ + \task $v_1 = \frac{5}{2}, q=2$ + \task $v_1 = 2, q=2$ + \task $v_1 = 1, q=3$ +\end{tasks} + +\textbf{4. }[CTE] Cho số thực $a$ và hàm số $f(x)$ thỏa mãn $\lim\limits_{n\to a}f(x)=+\infty$. Tính giới hạn $\lim\limits_{x\to a}\frac{f(x)+1}{2-f(x)}$. +\begin{tasks}(4) + \task $+\infty$ + \task $-1$ + \task $-\infty$ + \task $0$ +\end{tasks} + +\textbf{5. }[PĐP 24 - 25] $ \lim\limits_{x\to\infty} (9^n - 5^n) $ bằng. +\begin{tasks}(4) + \task $3$ + \task $5$ + \task $+\infty$ + \task $-\infty$ +\end{tasks} +\textbf{6. }[CVA 23 - 24] Có bao nhiêu số nguyên dương $a$ thỏa mãn $\lim (an - \sqrt{27n^2+1}) = -\infty$?. +\begin{tasks}(4) + \task $4$ + \task $1$ + \task $5$ + \task $6$ +\end{tasks} + +\textbf{7. }[CVA 23 - 24] Bác An gửi tiền tiết kiệm vào ngân hàng theo thể thức lãi kép như sau: Lần đầu bác gửi 50 triệu đồng. Sau đó, cứ hết 1 tháng bác lại gửi thêm vào ngân hàng 5 triệu đồng. Biết lãi suất của ngân hàng là $0.5\%$ một tháng. Hỏi sau 2 năm, số tiền bác có trong ngân hàng là bao nhiêu triệu đồng? (làm tròn kết quả hàng đơn vị). +\begin{tasks}(4) + \task $180$ + \task $170$ + \task $185$ + \task $195$ +\end{tasks} + +\textbf{8. }[CVA 24 - 25] Cho hai dãy số $(u_{n}),(v_{n})$ với $u_{n}=1-\frac{2}{n}$ và $v_{n}=4+\frac{5}{n^2+2}$. Khi đó $\lim (u_{n} + \sqrt{v_{n}})$ bằng:. +\begin{tasks}(4) + \task $4$ + \task $2$ + \task $5$ + \task $3$ +\end{tasks} +\newpage +\textbf{9. }[CVA 24 - 25] Nếu mặt phẳng $(R)$ cắt hai mặt phẳng song song $(P)$ và $(Q)$ lần lượt theo hai giao tuyến $a$ $b$ thì vị trí tương đối giữa hai đường thẳng $a$ và $b$ là:. +\begin{tasks}(4) + \task Trùng nhau. + \task Song song. + \task Cắt nhau. + \task Chéo nhau. +\end{tasks} +\textbf{10. }[PĐP 24 - 25] Trong không gian, cho hai đường thẳng $a$, $b$ và mặt phẳng $(P)$. Khẳng định nào sau đây là đúng? +\begin{tasks}(2) + \task Nếu $\begin{cases} + a // b \\ + b \subset (P) \\ + a \not\subset (P) + \end{cases}\text{ thì } a // (P)$ + \task Nếu $ + \begin{cases} + a // (P) \\ + b // (P) +\end{cases}\text{ thì } a // b$ +\task Nếu $\begin{cases} + a // (P) \\ + b \subset (P) +\end{cases}\text{ thì }a//b$ +\task Nếu $ + \begin{cases} + a // b \\ + a \subset (P) +\end{cases}\text{ thì } a // (P) +$ +\end{tasks} +\textbf{11. }[PĐP 24 - 25] Cho hình chóp tứ giác $S.ABCD$. Gọi $O$ là giao điểm của $AC$ và $BD$. Lấy các điểm $E, F$ lần lượt thuộc đoạn thẳng $SB, SD$ (hai điểm $E,F$ không trùng với hai đầu mút đoạn thẳng tương ứng). Gọi $G$ là giao điểm của đường thẳng $EF$ với mặt phẳng $(SAC)$, gọi $H$ là giao điểm của đường thẳng $SC$ với mặt phẳng $(AEF)$ (tham khảo hình vẽ). Khẳng định nào sau đây là đúng? +\begin{minipage}[c]{0.47\textwidth} + \begin{center} + \begin{tasks}(1) + \task $B,D,E,F$ không đồng phẳng. + \task $C,G,H,O$ không đồng phẳng. + \task $A,E,F,D$ không đồng phẳng. + \task $A,D,E,O$ không đồng phẳng. + \end{tasks} + \end{center} +\end{minipage} +\hfill +\begin{minipage}[c]{0.47\textwidth} +\begin{center}\begin{tikzpicture} + \tkzDefPoints{1/0/A, 5/0/D, 4/-2.5/C, 2/-2/B, 3/3/S} + \tkzDrawPoints(A,B,C,D,S) + \tkzLabelPoints(B,C) + \tkzLabelPoints[above](S) + \tkzLabelPoints[left](A) + \tkzLabelPoints[right](D) + \tkzDrawSegments(A,B B,C C,D D,A S,A S,B S,D S,C) + \tkzDrawSegments[dashed](A,C B,D) + + \tkzDefPointWith[linear,K=.3](S,B) \tkzGetPoint{E} + \tkzDefPointWith[linear,K=.6](S,D) \tkzGetPoint{F} + \tkzInterLL(A,C)(D,B) \tkzGetPoint{O} + \tkzDrawPoints(O,E,F) + \tkzLabelPoints(O,E,F) +\end{tikzpicture} +\end{center} + +\end{minipage} +\textbf{12. }[PĐP 24 - 25] Cho hình lăng trụ $ABC.A'B'C'$ với $O_{1},O_{2}$ lần lượt là tâm các hình bình hành $ABB'A',BCC'B'$ (tham khảo hình vẽ). Khẳng định nào sau đây là sai?\\ +\begin{minipage}[c]{0.47\textwidth} +\begin{tasks}(1) + \task $O_{1}O_{2}//(AB'C)$. + \task $O_{1}O_{2}//(A'B'C')$. + \task $O_{1}O_{2}//(ACC'A')$. + \task $O_{1}O_{2}//(ABC)$. +\end{tasks} +\end{minipage} +\hfill +\begin{minipage}[c]{0.47\textwidth} + \begin{center} + \begin{tikzpicture} + \tkzDefPoints{0/0/A, 3/0/C, 1/-1/B, 0.3/2.4/A'} + \tkzDefPointWith[colinear= at B](A,A') \tkzGetPoint{B'} + \tkzDefPointWith[colinear= at C](A,A') \tkzGetPoint{C'} + \tkzInterLL(A',B)(A,B') \tkzGetPoint{O1} + \tkzInterLL(B',C)(B,C') \tkzGetPoint{O2} + \tkzLabelPoints(A,B,C,A',B',C') + \tkzLabelPoint(O1){$O_{1}$} + \tkzLabelPoint(O2){$O_{2}$} + \tkzDrawPoints(A,B,C,A',B',C',O1,O2) + \tkzDrawSegments(A,B B,C A,A' A',B' B',C' C',A' B,B' C,C') + \tkzDrawSegments[dashed](A,C) + \end{tikzpicture} +\end{center} +\end{minipage} + diff --git a/exam_20_13/sections/short.tex b/exam_20_13/sections/short.tex new file mode 100644 index 0000000..645c6e2 --- /dev/null +++ b/exam_20_13/sections/short.tex @@ -0,0 +1,16 @@ +\newpage +\section{Phần trắc nghiệm trả lời ngắn.} +\textbf{1. }[Tây Hồ 23 - 24] Cho $b>0$ và $\lim\frac{\sqrt{bn^2+2n}-\sqrt{4n+3}}{2n-1}=1$. Tìm giá trị của tham số $b$. \\ +\textbf{2. }[CTE] Tìm $m$ để phương trình $x^3-(3m+1)x^2+(5m+4)x-8=0$ có ba nghiệm lập thành một cấp số nhân. \\ +\textbf{3. }[PĐP 24 - 25] Cho hình chóp $S.ABCD$ có đáy là hình bình hành. Gọi $M$ là trung điểm của $CD$, điểm $N$ thuộc đoạn $SM$ sao cho $NS=3NM$, điểm $P$ thuộc đoạn $AM$ sao cho $NP$ song song với mặt phẳng $(SAB)$. Tỉ số $\frac{MP}{MA}$ bằng bao nhiêu? \\ +\textbf{4. }[CVA 24 - 25] Cho hình chóp $S.ABCD$ có đáy là hình thang với hai đáy là $AB$ và $CD$ thỏa mãn $AB=2DC$. Gọi $M$ là trung điểm $BC$. Mặt phẳng qua $AM$ song song với $SD$ cắt $SB$ tại $N$ (tham khảo hình vẽ). Tính tỉ số $\frac{SB}{SN}$ (làm tròn kết quả đến hàng phần mười). +\begin{center} + \begin{tikzpicture} + \tkzDefPoints{0/0/A, 5/0/B, 1/-1/D, 3.5/-1/C, 2/3/S} + \tkzDefMidPoint(B,C) \tkzGetPoint{M} + \tkzLabelPoints(A,B,C,D,S,M) + \tkzDrawPoints(A,B,C,D,S,M) + \tkzDrawSegments(B,C C,D D,A S,A S,D S,C S,B) + \tkzDrawSegments[dashed](A,B A,M) + \end{tikzpicture} +\end{center} diff --git a/exam_20_13/sections/writing.tex b/exam_20_13/sections/writing.tex new file mode 100644 index 0000000..6f89df4 --- /dev/null +++ b/exam_20_13/sections/writing.tex @@ -0,0 +1,7 @@ +\section{Tự luận} +\text [PĐP 24 - 25] Cho hình chóp $S.ABCD$ có đáy $ABCD$ là hình bình hành tâm $O$. Gọi $M,N$ lần lượt là trung điểm của đoạn thẳng $AB,AD$ và $G$ là trọng tâm $\triangle SAC$. +\begin{enumerate} + \item Tìm giao tuyến của hai mặt phẳng $(SMN)$ và $(SBD)$. + \item Mặt phẳng $(\alpha)$ chứa $AG$ và song song với $BD$ cắt $SB$ và $SD$ lần lượt tại $J,K$. Nêu cách xác định hai điểm $J, K$ và chứng minh $JK=\frac{4}{3}MN$. + \item Gọi $I$ là điểm thuộc cạnh $SC$ sao cho $CI=\frac{2}{5}SC$. Chứng minh $(BDI)//(MNG)$. +\end{enumerate} diff --git a/exam_20_13/sections/yesno.tex b/exam_20_13/sections/yesno.tex new file mode 100644 index 0000000..941ca49 --- /dev/null +++ b/exam_20_13/sections/yesno.tex @@ -0,0 +1,58 @@ +\section{Trắc nghiệm đúng sai} +\textbf{1. }[CTE] Cho đồ thị hàm số $y=f(x)$ như hình vẽ. Khi đó:. \\ +\begin{minipage}[c]{0.47\textwidth} +\begin{enumerate} + \item $\lim\limits_{x\to1} f(x)=0$ + \item $\lim\limits_{x\to+\infty} f(x)=2$ + \item $\lim\limits_{x\to-1} f(x)=+\infty$ + \item $\lim\limits_{x\to-\infty} \frac{\sqrt{x^2 + 1}\cdot f(x)}{x}=2$ +\end{enumerate} +\end{minipage} +\hfill +\begin{minipage}[c]{0.47\textwidth} +\begin{center} +\begin{tikzpicture} +\begin{axis}[ + axis lines=middle, + ticks=none, + xmin=-6, xmax=6, + ymin=-2, ymax=10, + samples=300, +] +\addplot[domain=-6:-1]{2 - 4/(x+1)}; +\addplot[domain=-1:1] {2/(x+1) - 1}; +\addplot[domain=1:6] {2 - 4/(x+1)}; +\addplot[dashed, domain=-6:6] {2}; +\addplot[dashed] coordinates {(-1,-6) (-1,12)}; +\node at (axis cs:1,0) [below] {$1$}; +\node at (axis cs:-1,0) [below] {$-1$}; +\node at (axis cs:0,2) [above right] {$2$}; +\end{axis} +\end{tikzpicture} +\end{center} +\end{minipage} \\ +\textbf{2. }[CVA 24 - 25] Cho hai hàm số $f(x)=x^2-3x+2$ và $g(x)=\sqrt{2x^2+1}$. Khi đó:. +\begin{enumerate} + \item $\lim\limits_{x\to1}\frac{f(x)}{x^2-1}=\frac{1}{2}$ + \item $\lim\limits_{x\to+\infty}\frac{g(x)}{f(x)}=+\infty$ + \item $\lim\limits_{x\to1}f(x)=0$ + \item $\lim\limits_{x\to+\infty}g(x)=+\infty$\\ +\end{enumerate} +\textbf{3. }[CVA 24 - 25] Cho dãy số $(u_n)$ với $\begin{cases} + u_1=3\\ + u_{n+1}=2u_n, \forall n \in \mathbb{N}^* +\end{cases}$ +\begin{enumerate} + \item $(u_n)$ là cấp số nhân có công bội là $q=3$ + \item $(u_n)$ là dãy số bị chặn. + \item Tổng 7 số hạng đầu của dãy số $(u_n)$ là 381 + \item 72 là một số hạng của dãy số trên. +\end{enumerate} + +\textbf{4. }[CTE] Cho hình chóp $S.ABCD$ có đáy $ABCD$ là hình bình hành. Các điểm $M,N$ lần lượt là trung điểm của đoạn thẳng $SB,SD$. +\begin{enumerate} + \item Giao tuyến của hai mặt phẳng $(SAB)$ và $(SCD)$ là đường thẳng song song với $AD$. + \item Đường thẳng MN song song với mặt phẳng $(SBD)$. + \item Mặt phẳng $(SAC)$ đi qua trung điểm của đoạn thẳng $MN$. + \item Nếu gọi $I$ là giao điểm của mặt phẳng $(AMN)$ với đường thẳng $SC$ thì $SI=\frac{1}{2}IC$. +\end{enumerate} diff --git a/miscs/main.pdf b/miscs/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..72d9cc9e08532e3d66cf611c897ccca0e5f8f6f4 GIT binary patch literal 12023 zcmbVy1yq~e)+Sn9i))~`ySrO)FAl*WxJz-T#fww4xVu|{;%>#=rNM3Z=AT(#XWiaA z-?~}J%KM(2oV}B?&$I2JRF;rpWM$$;q#T*;p6Oqh==+Yy1z-VyOso+F1OUuZR<-_!KWRh)%Y6Mo_qlE@~43d$qy`xpTQIcLc z~xQ2{q6$l7q*|jRwIk9cqX@`3vF$GT z(0;us(r|X*((dN-dRN3r?qnb)whjGO!q#YDcXUXsuH+mK^T5T~01~;IGVDA)xM!IH z4c{fT*LCMUPpS4ZV|LsYUY%Pwv$vl1j*$VO3~Ijz;ysX%35zenpz8|!t0!A#5%3s@ z{EpiZK2Xc-@dciAC7WS|_OW>~v!`-}b-)luD1VeP8=Pr%UZ%EwsNV9_iLI&kTK;%v9B-Zbz(4QuLhSh4-pqVH+@Z&%{g0Kj$CE-mR z@)?Ck@^LzepWSdGkR7K<1dY|`-8ow=a1B@SOEk&jf$_#0%@-|0AZhwr6AvG{EfaSs zjG`Cz1I72V;u~bTV9u*o3WHB~QWE5+|&UxaZ5! 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