Đề thi giữa HK2 môn Toán 12 năm 2021 - Trường THPT...

A. \({x^2}.\sin x + x.\cos x - 2\sin x + C\).

B. \({x^2}.\sin x + 2x.\cos x - 2\sin x + C\).

C. \(x.\sin x + 2x.\cos x + C\). 

D. \(2x.\cos x + \sin  + C\).

A. \( - \dfrac{{{\pi ^2}}}{4}\)

B. \(\pi^2\)

C. \(\dfrac{{{\pi ^2}}}{2}\)

D. \(- \dfrac{{{\pi ^2}}}{2}\)

A. \( - \dfrac{1}{4}\cos 2x + C\)

B. \(\dfrac{1}{2}{\sin ^2}x + C\)

C. \( - \dfrac{1}{2}{\cos ^2}x + C\)

D. \(\dfrac{1}{2}\cos 2x + C\)

A. 32

B. 34

C. 46

D. 40

A. \(- \dfrac{1}{x} - \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\)

B. \(\dfrac{1}{x} - \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\)

C. \(- \dfrac{1}{x} - \dfrac{1}{{{x^2}}} - \dfrac{1}{{{x^3}}} + C\)

D. \(- \dfrac{1}{x} + \dfrac{2}{{{x^2}}} - \dfrac{4}{{3{x^2}}} + C\)

A. \({V_y} = 12\pi\)

B. \({V_y} = 8\pi\)

C. \({V_y} = 18\pi \)

D. \({V_y} = 16\pi\)

A. \({\left( {a - x} \right)^{\dfrac{5}{2}}} + ax + C\)

B. \(- \dfrac{2}{5}{\left( {a - x} \right)^{\dfrac{5}{2}}} + ax + C\)

C. \({\left( {a - x} \right)^{\dfrac{5}{2}}} - a + C\)

D. \(\dfrac{2}{5}{\left( {a - x} \right)^{\dfrac{5}{2}}} - \dfrac{2}{3}a{\left( {a - x} \right)^{\dfrac{3}{2}}} + C\)

A. \(\dfrac{6}{7}\)

B. \(\dfrac{7}{6}\)

C. 1

D. 2

A. \(\dfrac{1}{{x{{\ln }^3}x}}\)

B. \(x{\ln ^3}x\)

C. \(\dfrac{{{x^2}}}{{{{\ln }^3}x}}\)

D. \(\dfrac{{{{\ln }^3}x}}{x}\)

A. \({e^3} - \dfrac{7}{2}{e^2} + \ln \left( {1 + e} \right)\)

B. \({e^2} - 7e + \dfrac{1}{{e + 1}}\)

C. \({e^3} - \dfrac{7}{2}{e^2} - \dfrac{1}{{{{\left( {e + 1} \right)}^2}}}\)

D. \({e^3} - 7{e^2} - \ln \left( {1 + e} \right)\)

A. 6

B. 46

C. 26

D. 12

A. \(\int\limits_a^b {\left| {f(a)} \right|\,dx}\)

B. \( - \int\limits_a^b {f(x)\,dx}\)

C. \(\int\limits_b^a {f(x)\,dx}\)

D. \(\int\limits_a^b {f(x)\,dx}\)

A. 24

B. -7

C. -4

D. 8

A. \(\int\limits_a^b {f(x)\,dx = \int\limits_b^a {f(x)\,dx} }\)

B. \(\int\limits_a^b {k.dx = k\left( {b - a} \right),\,\forall k \in R}\)

C. \(\int\limits_a^b {f(x)\,dx = - \int\limits_b^a {f(x)\,dx} }\)

D. \(\int\limits_a^b {f(x)\,dx = \int\limits_a^c {f(x)\,dx + \int\limits_c^b {f(x)\,dx\,,\,\,\,c \in [a;b]} } }\)

A. \(I = \int\limits_{\dfrac{1}{2}}^1 {\dfrac{{2t}}{{1 + 1}}\,dt} \).  

B. \(I = \int\limits_{\dfrac{0}{2}}^{\dfrac{x}{4}} {\dfrac{{2t}}{{1 + 1}}\,dt} \).

C. \(I =  - \int\limits_{\dfrac{1}{2}}^1 {\dfrac{{2t}}{{1 + 1}}\,dt} \).

D. \(I =  - \int\limits_{\dfrac{0}{2}}^{\dfrac{x}{4}} {\dfrac{{2t}}{{1 + 1}}\,dt} \).

A. \(\left\{ \begin{array}{l}A =  - 2\\B =  - \dfrac{2}{\pi }\end{array} \right.\).  

B. \(\left\{ \begin{array}{l}A = 2\\B =  - \dfrac{2}{\pi }\end{array} \right.\).

C. \(\left\{ \begin{array}{l}A =  - 2\\B = \dfrac{2}{\pi }\end{array} \right.\). 

D. \(\left\{ \begin{array}{l}B = 2\\A =  - \dfrac{2}{\pi }\end{array} \right.\)

A. \(I = \dfrac{1}{2}\)

B. \(I = \dfrac{{3{e^2} + 1}}{4}\).

C. \(I = \dfrac{{{e^2} + 1}}{4}\).

D. \(I = \dfrac{{{e^2} - 1}}{4}\).

A. \(4\cos x + \ln x + C\). 

B. \(4\cos x + \dfrac{1}{x} + C\).

C. \(4\sin x - \dfrac{1}{x} + C\).

D. \(4\sin x + \dfrac{1}{x} + C\).

A. \(2\ln 2 + 3\).

B. \(\dfrac{{\ln 2}}{2} + \dfrac{3}{4}\).

C. \(\ln 2 + \dfrac{3}{2}\).

D. \(\ln 2 + 1\).

A. \(I = 2\int\limits_8^9 {\sqrt u du} \).

B. \(I = \dfrac{1}{2}\int\limits_8^9 {\sqrt u \,du} \).

C. \(I = \int\limits_8^9 {\sqrt u \,du} \).

D. \(I = \int\limits_9^8 {\sqrt u \,du} \)

A. \(\ln \dfrac{3}{2}\)

B. \(\dfrac{1}{2}\)

C. ln 2

D. ln 2 + 1

A. \(\pi \int\limits_0^\pi  {{{\sin }^2}x} \,dx\).

B. \(\dfrac{\pi }{2}\int\limits_0^\pi  {{{\sin }^2}x} \,dx\).

C. \(\dfrac{\pi }{2}\int\limits_0^\pi  {{{\sin }^4}x} \,dx\).

D. \(\pi \int\limits_0^\pi  {\sin x} \,dx\).

A. \(I = 2\int\limits_0^1 {dt} \). 

B. \(I = 2\int\limits_0^{\dfrac{\pi }{4}} {dt} \).

C. \(I = \int\limits_0^{\dfrac{\pi }{3}} {dt} \).

D. \(I = 2\int\limits_0^{\dfrac{\pi }{6}} {dt} \).

A. -2

B. \(\dfrac{{13}}{6}\)

C. \(\ln 2 - \dfrac{3}{4}\)

D. \(\ln 3 - \dfrac{3}{5}\).

A. \(\int {\dfrac{{dx}}{{6x - 2}} = 6\ln |6x - 2| + C} \).

B. \(\int {\dfrac{{dx}}{{6x - 2}} = \dfrac{1}{6}\ln |6x - 2| + C} \).

C. \(\int {\dfrac{{dx}}{{6x - 2}} = \dfrac{1}{2}\ln |6x - 2| + C} \).

D. \(\int {\dfrac{{dx}}{{6x - 2}} = \ln |6x - 2| + C} \).

A. \(\overrightarrow {OM}  = x.\overrightarrow i  + y.\overrightarrow j  + z.\overrightarrow k \)

B. \(\overrightarrow {OM}  = z.\overrightarrow i  + y.\overrightarrow j  + x.\overrightarrow k \)

C. \(\overrightarrow {OM}  = x.\overrightarrow j  + y.k + z.\overrightarrow i \)

D. \(\overrightarrow {OM}  = x.\overrightarrow k  + y.\overrightarrow j  + z.\overrightarrow i \)

A. \(M\left( {1;1; - 3} \right)\)

B. \(M\left( {1; - 1; - 3} \right)\)

C. \(M\left( {1; - 3;1} \right)\)

D. \(M\left( { - 1; - 3;1} \right)\)

A. -1

B. 1

C. 2

D. -2

A. \(N\left( {x;y;z} \right)\)

B. \(N\left( {x;y;0} \right)\)

C. \(N\left( {0;0;z} \right)\)

D. \(N\left( {0;0;1} \right)\)

A. \(C\left( { - 1;3;2} \right)\)

B. \(C\left( {11; - 2;10} \right)\)

C. \(C\left( {5; - 6;2} \right)\)

D. \(C\left( {13; - 8;8} \right)\)

A. \(G\left( {0;\dfrac{3}{4};1} \right)\)

B. \(G\left( {0;3;4} \right)\)

C. \(G\left( {\dfrac{1}{2}; - \dfrac{1}{2}; - \dfrac{1}{2}} \right)\) 

D. \(G\left( {0;\dfrac{3}{2};2} \right)\)

A. \(\overrightarrow u  = k\overrightarrow n \left( {k \ne 0} \right)\)

B. \(\overrightarrow n  = k\overrightarrow u \)

C. \(\overrightarrow n .\overrightarrow u  = 0\) 

D. \(\overrightarrow n .\overrightarrow u  = \overrightarrow 0 \)

A. \(d//\left( P \right)\)

B. \(d \subset \left( P \right)\)

C. \(\left( P \right) \subset d\)

D. \(d \bot \left( P \right)\)

A. \(\left( { - 1;1; - 3} \right)\)

B. \(\left( {1;2;0} \right)\)

C. \(\left( {2; - 2;3} \right)\)

D. \(\left( {2; - 2; - 3} \right)\)

A. \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] = \overrightarrow 0 \)

B.  \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] = \left[ {\overrightarrow u ,\overrightarrow {MM'} } \right]\)

C. \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] = \left[ {\overrightarrow u ,\overrightarrow {MM'} } \right] = \overrightarrow 0 \)

D. \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] \ne \left[ {\overrightarrow u ,\overrightarrow {MM'} } \right]\)

A. d // d'

B. \(d \equiv d'\)

C. d cắt d'

D. A hoặc B đúng

A. \(\left\{ \begin{array}{l}\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] \ne \overrightarrow 0 \\\left[ {\overrightarrow u ,\overrightarrow {u'} } \right]\overrightarrow {MM'}  = 0\end{array} \right.\)

B. \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] \ne \overrightarrow 0 \)

C. \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right]\overrightarrow {MM'}  = 0\)

D. \(\left[ {\overrightarrow u ,\overrightarrow {u'} } \right] = \overrightarrow 0 \)

A. d // d'

B. \(d \equiv d'\)

C. d cắt d'

D. d chéo d'

A. d // d'

B. \(d \bot d'\)

C. \(d \equiv d'\)

D. d cắt d'

A. cắt nhau

B. song song

C. chéo nhau

D. trùng nhau