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

A. \(\mathop \smallint \nolimits_{}^{} \frac{{dx}}{x} = \ln \;x\; + \,C\)

B. \(\mathop \smallint \nolimits_{}^{} {x^\alpha }dx = \frac{{{x^{\alpha  + 1}}}}{{\alpha  + 1}}\; + \,C\left( {\alpha  \ne  - 1} \right)\)

C. \(\mathop \smallint \nolimits_{}^{} {\alpha ^x}dx = \frac{{{\alpha ^x}}}{{\ln \;\alpha }}\; + \,C\left( {0 < \alpha  \ne  - 1} \right)\)

D. \(\mathop \smallint \nolimits_{}^{} \frac{1}{{{{\cos }^2}x}}dx = \tan \;x + C\)

A. \(\tan x-\cot x+C\)

B. \(\cot 2 x+C\)

C. \(\tan 2 x-x+C\)

D. \(-\tan x+\cot x+C\)

A. \(f(x)=-\sin x+7 \cos x\)

B. \(f(x)=\sin x+7 \cos x\)

C. \(f(x)=\sin x-7 \cos x\)

D. \(f(x)=-\sin x-7 \cos x\)

A. \(\ln \;x - \ln \;{x^2} + C\)

B. \(\ln \;x - \frac{1}{x} + C\)

C. \(\ln \;x + \frac{1}{x} + C\)

D. \(\ln \;\left| x \right| + \frac{1}{x} + C\)

A. \(F(x)=\tan x-x+C\)

B. \(F(x)=-\tan x+x+C\)

C. \(F(x)=\tan x+x+C\)

D. \(F(x)=-\tan x-x+C\)

A. \(\frac{2}{3} \int_{1}^{3} u^{2} d u\)

B. \(\frac{2}{3} \int_{0}^{2} u^{2} d u\)

C. \(\left.\frac{2}{9} u^{3}\right|_{1} ^{2}\)

D. \(\int_{1}^{3} u^{2} d u\)

A. 11

B. 9

C. 7

D. 12,5

A. \(\ln 3-\frac{3}{5}\)

B. \(\ln 2-2\)

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

D. \(\ln 2-\frac{3}{8}\)

A. \(4 \sqrt{2}\)

B. \(3 \sqrt{2}\)

C. \( \sqrt{2}\)

D. \(- \sqrt{2}\)

A. \(\frac{-5 \pi}{8}\)

B. \(\frac{\pi}{2}\)

C. \(\frac{3 \pi}{8}\)

D. \(\frac{\pi}{8}\)

A. \(-\left.\left(x^{2}-5 x\right) \ln x\right|_{1} ^{e}-\int_{1}^{e}(x-5) d x\)

B. \(\left.\left(x^{2}-5 x\right) \ln x\right|_{1} ^{e}+\int_{1}^{e}(x-5) d x\)

C. \(\left.(x-5) \ln x\right|_{1} ^{e}-\int_{1}^{e}\left(x^{2}-5 x\right) d x\)

D. \(\left.\left(x^{2}-5 x\right) \ln x\right|_{1} ^{e}-\int_{1}^{e}(x-5) d x\)

A. 7

B. 5

C. 2

D. \(\frac{5}{2}\)

A. 5

B. -6

C. 9

D. -9

A. \( {S_H} = \mathop \smallint \limits_a^b \left| {f\left( x \right)} \right|{\rm{d}}x - \mathop \smallint \limits_a^b \left| {g\left( x \right)} \right|{\rm{d}}x.\)

B. \( {S_H} = \mathop \smallint \limits_a^b \left| {f\left( x \right) - g\left( x \right)} \right|{\rm{d}}x.\)

C. \( {S_H} = \left| {\mathop \smallint \limits_a^b \left[ {f\left( x \right) - g\left( x \right)} \right]{\rm{d}}x} \right|.\)

D. \( {S_H} = \mathop \smallint \limits_a^b \left[ {f\left( x \right) - g\left( x \right)} \right]{\rm{d}}x.\)

A. \( S = \mathop \smallint \limits_a^b \left( {f\left( x \right) - g\left( x \right)} \right)dx\)

B. \( S = \mathop \smallint \limits_a^b \left( {g\left( x \right) - f\left( x \right)} \right)dx\)

C. \( S = \mathop \smallint \limits_a^b \left| {f\left( x \right) - g\left( x \right)} \right|dx\)

D. \( S = \mathop \smallint \limits_a^b \left| {f\left( x \right)} \right|dx - \mathop \smallint \limits_a^b \left| {g\left( x \right)} \right|dx\)

A. \( S = \mathop \smallint \limits_{ - 2}^{ - 3} 2xdx\)

B. \(S = \pi \mathop \smallint \limits_{ - 3}^{ - 2} 4{x^2}dx\)

C. \( S = \mathop \smallint \limits_{ - 3}^{ - 2} 2xdx\)

D. \( S = \mathop \smallint \limits_{ - 3}^{ - 2} (2x)^2dx\)

A. \( S = \mathop \smallint \limits_1^3 f\left( x \right)dx.\)

B. \( S = \mathop \smallint \limits_1^3 \left| {f\left( x \right)} \right|dx\)

C. \( S = \mathop \smallint \limits_3^1 f\left( x \right)dx.\)

D. \( S = \mathop \smallint \limits_3^1 \left| {f\left( x \right)} \right|dx.\)

A. \( S = \mathop \smallint \limits_{ - 3}^{ - 1} \left| {{x^2} - 1} \right|dx\)

B. \( S = \mathop \smallint \limits_{ - 1}^{ - 3} \left| {{x^2} - 1} \right|dx\)

C. \( S = \mathop \smallint \limits_{ - 3}^{ 0} \left| {{x^2} - 1} \right|dx\)

D. \( S = \mathop \smallint \limits_{ - 3}^{ - 1} \left( {1 - {x^2}} \right)dx\)

A. A′(3;−2;1).

B. A′(3;2;−1).

C. A′(3;−2;−1).

D. A′(3;2;1)

A. \( M\left( {\frac{{ - {x_A} + {x_B}}}{2};\frac{{ - {y_A} + {y_B}}}{2};\frac{{ - {z_A} + {z_B}}}{2}} \right)\)

B. \( M\left( {\frac{{{x_A} + {x_B}}}{3};\frac{{{y_A} + {y_B}}}{3};\frac{{{z_A} + {z_B}}}{3}} \right)\)

C. \(M\left( {\frac{{{x_A} - {x_B}}}{2};\frac{{{y_A} - {y_B}}}{2};\frac{{{z_A} - {z_B}}}{2}} \right)\)

D. \( M\left( {\frac{{{x_A} + {x_B}}}{2};\frac{{{y_A} + {y_B}}}{2};\frac{{{z_A} + {z_B}}}{2}} \right)\)

A. M∈(Oxz).

B. M∈(Oyz).

C. M∈Oy.

D. M∈(Oxy).

A. K(0;2;3).

B. H(1;2;0).

C. F(0;2;0).

D. E(1;0;3).

A. Mặt phẳng (Oxy).

B. Trục Oy.

C. Mặt phẳng (Oyz).

D. Mặt phẳng (Oxz).

A. H(3 ; 0 ; 2)

B. H(-3 ; 0 ; -2)

C. H(-1 ; 4 ; 4)

D. H(-1 ; -1 ; 0)

A. (0 ;-3 ; 5)

B. (1 ;-3 ; 0)

C. (0 ;-3 ; 0)

D. (0 ;-3 ; -5)

A. (-2 ; 2 ; 0)

B. (-2 ; 0 ; 2)

C. (-1 ; 1 ; 0)

D. (-1 ; 0 ; 1)

A. \(H(6 ; 7 ; 8)\)

B. \(H(1 ; 2 ; 2)\)

C. \(H(2 ; 5 ; 3)\)

D. \(H(2 ;-3 ;-1)\)

A. (1 ; 1 ; 3)

B. (5 ; 2 ; 2)

C. (0 ; 0 ;-3)

D. (3 ; 0 ; 3)

A. \((x-1)^{2}+y^{2}+(z+2)^{2}+25=0\)

B. \((x+1)^{2}+y^{2}+(z-2)^{2}=25\)

C. \((x-1)^{2}+y^{2}+(z-2)^{2}=25\)

D. \((x-1)^{2}+y^{2}+(z+2)^{2}=25\)

A. \((x-1)^{2}+(y-2)^{2}+(z+3)^{2}=14\)

B. \((x+1)^{2}+(y+2)^{2}+(z-3)^{2}=53\)

C. \((x-1)^{2}+(y-2)^{2}+(z+3)^{2}=17\)

D. \((x-1)^{2}+(y-2)^{2}+(z+3)^{2}=53\)

A. \((x+1)^{2}+(y+1)^{2}+(z+1)^{2}=62\)

B. \((x+5)^{2}+(y+1)^{2}+(z-6)^{2}=62\)

C. \((x-1)^{2}+(y-1)^{2}+(z-1)^{2}=62\)

D. \((x-5)^{2}+(y-1)^{2}+(z+6)^{2}=62\)

A. \((S):(x-1)^{2}+y^{2}+(z+3)^{2}=9\)

B. \((S):(x+1)^{2}+y^{2}+(z-3)^{2}=3\)

C. \((S):(x-1)^{2}+y^{2}+(z+3)^{2}=3\)

D. \((S):(x+1)^{2}+y^{2}+(z-3)^{2}=9\)

A. \((x-1)^{2}+y^{2}+(z+2)^{2}=4\)

B. \((x+1)^{2}+y^{2}+(z-2)^{2}=16\)

C. \((x+1)^{2}+y^{2}+(z-2)^{2}=4\)

D. \((x-1)^{2}+y^{2}+(z+2)^{2}=16\)

A. \(3\over2\)

B. 3

C. \(\sqrt5\over2\)

D. 2

A. \(9\over7\)

B. \(9\over7\sqrt2\)

C. \(9\over14\)

D. \(9\over\sqrt2\)

A. \(\sqrt {\frac{19}{86}}\)

B. \(\sqrt {\frac{86}{19}}\)

C. 11

D. \(\sqrt {\frac{19}{2}}\)

A. 1

B. 2

C. 2 hoặc 32

D. 32

A. \(1\over9\)

B. \(1\over3\)

C. \(1\over6\)

D. \(1\over2\)