Đề thi giữa HK2 môn Toán 12 năm 2021 - Trường THPT Lê Thị Hồng Gấm

A. \(I = \ln |x - 3| - \dfrac{{16}}{{x - 3}} + C\)

B. \(I = \dfrac{1}{5}\ln |x - 3| - \dfrac{{16}}{{x - 3}} + C\)

C. \(I = \ln |x - 3| + \dfrac{{16}}{{x - 3}} + C\)

D. \(I = 5\ln |x - 3| - \dfrac{{16}}{{x - 3}} + C\)

A. \(\sqrt 3 - \dfrac{\pi }{3}\)

B. \(\dfrac{\pi }{3} - 3\)

C. \(\dfrac{{{\pi ^2}}}{3} - \pi \sqrt 3 \)

D. \(\pi \sqrt 3 - \dfrac{{{\pi ^2}}}{3}\)

A. \(I = \sin \left( {4x + 2} \right) + C\)

B. \(I = - \sin \left( {4x + 3} \right) + C\)

C. \(I = \dfrac{1}{4}\sin \left( {4x + 3} \right) + C\)

D. \(I = 4\sin \left( {4x + 3} \right) + C\)

A. F’(x) = x.

B. F’(x) = 1.

C. F’(x) = x - 1.

D. F’(x) = \(\dfrac{{{x^2}}}{2} - \dfrac{1}{2}\).

A. \(2\ln |x + 1| + \dfrac{{2{x^2} + 2x + 4}}{{x + 1}}\).

B. \(\ln \left( {x + 1} \right) + \dfrac{{2{x^2} + 2x + 4}}{{x + 1}}\).

C. \(\ln {\left( {x + 1} \right)^2} + \dfrac{{2{x^2} + 3x + 5}}{{x + 1}}\). 

D. \(\dfrac{{2{x^2} + 3x + 5}}{{x + 1}} + \ln {e^2}{\left( {x + 1} \right)^2}\).

A. Nếu V₁ = V₂ thì chắc chắn suy ra \(f(x) = g(x),\forall x \in [a;b]\).

B.  S₁>S₂.

C. V₁ > V₂.

D. Cả 3 phương án trên đều sai.

A. 27ln2.

B. 72ln27

C. 3ln72.

D. Một kết quả khác.

A. \( - \dfrac{1}{4}\sin \left( {\pi  - 2a} \right) - \sin 2a + \pi  - 4a\).

B. \(  \dfrac{1}{4}\left( {\sin \left( {\pi  - 2a} \right) - \sin 2a + \pi  - 4a} \right)\).

C. \( - \dfrac{1}{4}\left( {\sin \left( {\pi  - 2a} \right) - \sin 2a + \pi  - 4a} \right)\).

D. 0

A. 2

B. 4

C. 3

D. 5

A. \(f(x) = {\pi ^x}\ln x\).

B. \(f(x0 =  - {\pi ^x}\ln x\).

C. \(f(x) = \dfrac{{{\pi ^x}}}{{\ln \pi }}\).

D. \(f(x) = \dfrac{{{\pi ^x}}}{{\ln x}}\).

A. \(F(3) = \dfrac{1}{2}\).

B. \(F(3) = \ln \dfrac{3}{2}\).

C. F(3) = ln2.

D. F(3) = ln2 + 1.

A. \(f(x) = {x^3} - 2\sqrt x  - \dfrac{1}{x} - x\).

B. \(f(x) = {x^3} - \sqrt x  - \dfrac{1}{{\sqrt x }} - x\).

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

D. \(f(x{x^3} - \dfrac{1}{2}\sqrt x  - \dfrac{1}{x} - x\).

A. \(\dfrac{9}{2}\).

B. 3

C. \(\dfrac{9}{4}\)

D. \(\dfrac{7}{2}\).

A. \(\dfrac{3}{2}\) 

B. \( - \dfrac{3}{2}\)

C. \(\dfrac{5}{2}\)

D. \( - \dfrac{5}{2}\)

A. \(I =  - \dfrac{1}{5}\cos 5x + C\). 

B. \(I = \dfrac{1}{5}\cos 5x + C\).

C. \(I =  - \dfrac{1}{8}\cos 4x - \dfrac{1}{{12}}\cos 6x + C\).

D. \(I = \dfrac{1}{8}\cos 4x + \dfrac{1}{{12}}\cos 6x + C\).

A. \(e + \dfrac{1}{e} - 2\)

B. 0

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

D. \(e + \dfrac{1}{e}\).

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

B. \(\dfrac{{{x^2}}}{2}\left( {2x + {x^3}} \right) + C\).

C. \({x^2}\left( {2 + 6x} \right) + C\).

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

A. \(\cos \left( {\dfrac{\pi }{3} - 2x} \right) + C\).

B. \( - \dfrac{1}{2}\cos \left( {\dfrac{\pi }{3} - 2x} \right) + C\).

C. \(\dfrac{1}{2}\cos \left( {\dfrac{\pi }{3} - 2x} \right) + C\).

D. \( - \cos \left( {\dfrac{\pi }{3} - 2x} \right) + C\).

A. \(2\sqrt x  + 2\ln \left( {\sqrt x  + 1} \right) + C\).

B. \(2 - 2\ln \left( {\sqrt x  + 1} \right) + C\).

C. \(2\sqrt x  - 2\ln \left( {\sqrt x  + 1} \right) + C\).

D. \(2 + 2\ln \left( {\sqrt x  + 1} \right) + C\).

A. S= ln 2 – 1

B. S = ln 4 – 1

C. S =ln 4 + 1

D. S = ln 2 + 1

A. m = 1, m = - 6

B. m = - 1 , m = - 6

C. m = - 1, m = 6

D. m = 1, m = 6

A. \(P =  - \dfrac{3}{2}\).

B. \(P = \dfrac{3}{2}\).

C. \(P =  - \dfrac{5}{3}\). 

D. \(P = \dfrac{5}{3}\).

A. \(d\left( {A,d'} \right) = \frac{{\left| {\left[ {\overrightarrow {AM'} ,\overrightarrow {u'} } \right]} \right|}}{{\left| {\overrightarrow {u'} } \right|}}\)

B. \(d\left( {A,d'} \right) = \frac{{\left| {\left[ {\overrightarrow {AM'} ,\overrightarrow {u'} } \right]} \right|}}{{\overrightarrow {u'} }}\)

C. \(d\left( {A,d'} \right) = \frac{{\left[ {\overrightarrow {AM'} ,\overrightarrow {u'} } \right]}}{{\overrightarrow {u'} }}\)

D. \(d\left( {A,d'} \right) = \frac{{\left| {\overrightarrow {AM'} .\overrightarrow {u'} } \right|}}{{\left| {\overrightarrow {u'} } \right|}}\)

A. \(\left( {1;0;0} \right).\)

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

C. \(\left( {0;1;0} \right).\)

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

A. \(\left( {3;\dfrac{8}{3}; - \dfrac{8}{3}} \right).\)

B. \(\left( {3;\dfrac{8}{3};\dfrac{8}{3}} \right).\)

C. \(\left( {3;3; - \dfrac{8}{3}} \right).\)

D. \(\left( {1;2;\dfrac{1}{3}} \right).\)

A. 43

B. 44

C. 42

D. 45

A. D(0;1;3)

B. D(0;3;1)

C. D(0; - 3;1)

D. D(0;3; - 1)

A. \(I(\dfrac{8}{3};\dfrac{5}{3};\dfrac{8}{3})\).

B. \(I(\dfrac{5}{3};\dfrac{8}{3};\dfrac{8}{3})\).

C. \(I( - \dfrac{5}{3};\dfrac{8}{3};\dfrac{8}{3}).\)

D. \(I(\dfrac{8}{3};\dfrac{8}{3};\dfrac{5}{3})\).

A. \(\cos \left( {\overrightarrow b ,\overrightarrow c } \right) = \dfrac{{\sqrt 6 }}{3}.\)

B. \(\overrightarrow a  + \overrightarrow b  + \overrightarrow c  = \overrightarrow 0 .\)

C. \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c \) đồng phẳng.

D. \(\overrightarrow a .\overrightarrow b  = 1.\)

A. \(\dfrac{2}{{\sqrt {13} }}.\)

B. \(\dfrac{1}{{\sqrt {13} }}.\)

C. \(\dfrac{{\sqrt {13} }}{2}.\)

D. \(\dfrac{{3\sqrt {13} }}{{13}}.\)

A. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 20.\)

B. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 40.\)

C. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 52.\)

D. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 56.\)

A. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 20.\)

B. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 40.\)

C. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 52.\)

D. \({\left( {x - 2} \right)^2} + {\left( {y - 4} \right)^2} + {\left( {z - 6} \right)^2} = 56.\)

A. \({\left( {x + 1} \right)^2} + {\left( {y + 2} \right)^2} + {\left( {z + 3} \right)^2} = 9.\)

B. \({\left( {x + 1} \right)^2} + {\left( {y - 2} \right)^2} + {\left( {z + 3} \right)^2} = 9.\)

C. \({\left( {x - 1} \right)^2} + {\left( {y + 2} \right)^2} + {\left( {z + 3} \right)^2} = 9.\)

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

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

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

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

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

A. \(\sqrt 7 \pi .\)

B. \(2\sqrt 7 \pi .\)

C. \(7\pi .\)

D. \(14\pi .\)

A. \(M\left( {0; - 3;0} \right)\).

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

C. \(M\left( {0; - 2;0} \right)\).

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