Đề thi thử THPT QG năm 2021 môn Toán - Trường THPT Thành Nhân lần 2

A. \(\frac{{4\pi {a^3}}}{3}.\)

B. \(4\pi {a^3}.\)

C. \(\frac{{\pi {a^3}}}{3}.\)

D. \(2\pi {a^3}.\)

A. \(2\log a + \log b.\)

B. \(\log a + 2\log b.\)

C. \(2\left( {\log a + \log b} \right).\)

D. \(\log a + \frac{1}{2}\log b.\)

A. 19

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

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

D. 13

A. 6

B. 10

C. 18

D. 0

A. (1;3)

B. (-1;1)

C. (-2;0)

D. (1;2)

A. x = 9

B. x = 7

C. x = 8

D. x = 10

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

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

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

D. \(y={{x}^{3}}+3{{x}^{2}}+2\)

A. \(\left( 3;1;3 \right)\)

B. \(\left( 2;1;3 \right)\)

C. \(\left( 3;1;2 \right)\)

D. \(\left( 3;2;3 \right)\)

A. \(\frac{\pi {{a}^{3}}\sqrt{3}}{3}\)

B. \(\frac{\pi {{a}^{3}}}{3\sqrt{3}}\)

C. \(\frac{\pi {{a}^{3}}\sqrt{2}}{3}\)

D. \(\frac{\pi {{a}^{3}}}{3}\)

A. \(x+y=0\)

B. \(x=0\)

C. \(y=0\)

D. \(z=0\)

A. -2

B. 12

C. 22

D. 2

A. \(\frac{{{a}^{3}}\sqrt{2}}{3}\)

B. \(\frac{{{a}^{3}}}{2}\)

C. \(\frac{{{a}^{3}}\sqrt{3}}{4}\)

D. \(\frac{{{a}^{3}}\sqrt{3}}{2}\)

A. \(\pi \int\limits_{0}^{2}{{{\left( {{x}^{2}}-2x \right)}^{2}}\text{d}x}\)

B. \(\pi \int\limits_{0}^{2}{4{{x}^{2}}\text{d}x}-\pi \int\limits_{0}^{2}{{{x}^{4}}\text{d}x}\)

C. \(\pi \int\limits_{0}^{2}{4{{x}^{2}}\text{d}x}+\pi \int\limits_{0}^{2}{{{x}^{4}}\text{d}x}\)

D. \(\pi \int\limits_{0}^{2}{\left( 2x-{{x}^{2}} \right)\text{d}x}\)

A. \(S=\left( -\infty ;2 \right)\)

B. \(S=\left( -\infty ;1 \right)\)

C. \(S=\left( 1;+\infty  \right)\)

D. \(S=\left( 2;+\infty  \right)\)

A. 4040

B. 4400

C. 4038

D. 4037

A. \(\left( 2;1 \right)\)

B. \(\left( 1;2 \right)\)

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

D. \(\left( 2;-1 \right)\)

A. 2

B. 3

C. 4

D. 5

A. \(F\left( x \right)={{e}^{2x}}+{{x}^{3}}+C\)

B. \(F\left( x \right)=\frac{{{e}^{2x}}}{2}+\frac{{{x}^{3}}}{3}+C\)

C. \(F\left( x \right)=2{{e}^{2x}}+2x+C\)

D. \(F\left( x \right)={{e}^{2x}}+\frac{{{x}^{3}}}{3}+C\)

A. \(y=-9x+22\).

B. \(y=9x+22\).

C. \(y=9x+14\).

D. \(y=-9x+14\).

A. \(\underset{[-2;\ 2]}{\mathop{\max }}\,f\left( x \right)=5\)

B. \(\underset{[-2;\ 2]}{\mathop{\max }}\,f\left( x \right)=17\)

C. \(\underset{[-2;\ 2]}{\mathop{\max }}\,f\left( x \right)=-15\)

D. \(\underset{[-2;\ 2]}{\mathop{\max }}\,f\left( x \right)=15\).

A. \(\left[ 3;5 \right]\)

B. \(\left( 1;3 \right]\)

C. \(\left[ 1;3 \right]\)

D. \(\left( 1;5 \right)\)

A. \(\frac{{{a}^{3}}\sqrt{2}}{3}\)

B. \(\frac{{{a}^{3}}\sqrt{2}}{6}\)

C. \({{a}^{3}}\)

D. \(\frac{{{a}^{3}}}{3}\)

A. \(T=-2\)

B. \(T=-\frac{2}{5}\)

C. \(T=-\frac{1}{5}\)

D. \(T=5\)

A. \(y'=\left( 1-x \right){{e}^{x+1}}\)

B. \(y'=\left( 1+x \right){{e}^{x+1}}\)

C. \(y'={{e}^{x+1}}\)

D. \(y'=x{{e}^{x}}\)

A. 0

B. -9

C. -10

D. -1

A. \({{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=\frac{121}{9}\)

B. \({{\left( x+1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z+3 \right)}^{2}}=\frac{11}{3}\)

C. \({{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z-3 \right)}^{2}}=\frac{49}{5}\)

D. \({{\left( x+1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z+3 \right)}^{2}}=\frac{49}{5}\)

A. \(30{}^\circ\)

B. \(45{}^\circ\)

C. \(60{}^\circ\)

D. \(90{}^\circ\)

A. \(V=12{{a}^{3}}\)

B. \(V=36{{a}^{3}}\)

C. \(V=54{{a}^{3}}\)

D. \(V=18{{a}^{3}}\)

A. Đường tròn \({{\left( x-3 \right)}^{2}}+{{\left( y+1 \right)}^{2}}=4\).

B. Đường tròn \({{\left( x+1 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=4\).

C. Đường tròn \({{\left( x+1 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=16\).

D. Đường thẳng \(x-3y=3\).

A. 1

B. 3

C. 4

D. 2

A. 15

B. 9

C. 36

D. 27

A. \(x+y-3z+9=0\)

B. \(x+y-3z+2=0\)

C. \(\frac{x-3}{1}=\frac{y-5}{1}=\frac{z+4}{-3}\)

D. \(x+y-3z-9=0\)

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

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

C. \(\frac{x-2}{1}=\frac{y-1}{1}=\frac{z-3}{-1}\)

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

A. 6

B. 3

C. 1

D. 2

A. Hàm số \(\left( C \right)\) đồng biến trên khoảng \(\left( 0;2 \right)\).

B. Hàm số \(\left( C \right)\) đồng biến trên khoảng \(\left( -\infty ;-2 \right)\).

C. Hàm số \(\left( C \right)\) nghịch biến trên khoảng \(\left( 2;4 \right)\).

D. Hàm số \(\left( C \right)\) nghịch biến trên khoảng \(\left( -4;-3 \right)\).

A. \(\frac{5}{42}\)

B. \(\frac{37}{42}\)

C. \(\frac{2}{7}\)

D. \(\frac{1}{21}\)

A. \(62c{{m}^{3}}\)

B. \(15c{{m}^{3}}\)

C. \(108c{{m}^{3}}\)

D. \(16c{{m}^{3}}\)

A. \(\frac{1}{4}\)

B. \(\frac{5}{12}\)

C. \(-\frac{1}{3}\)

D. \(\frac{1}{12}\)

A. \({{2019}^{1009}}\)

B. \({{2019}^{1009}}+1\)

C. \(-{{2019}^{1009}}+1\)

D. \(-{{2019}^{1009}}-1\)

A. \(\frac{2a\sqrt{21}}{21}\)

B. \(\frac{a\sqrt{6}}{4}\)

C. \(\frac{a\sqrt{15}}{5}\)

D. \(\frac{2a}{3}\)

A. \(I=-\frac{1}{2}\)

B. \(I=0\)

C. \(I=-2\)

D. \(I=4\)

A. \(\left\{ \begin{align} & x=4+7t \\ & y=-2-2t \\ & z=3+5t \\ \end{align} \right. \)

B. \(\left\{ \begin{align} & x=4+7t \\ & y=-2+2t \\ & z=3+5t \\ \end{align} \right. \)

C. \(\left\{ \begin{align} & x=-4+7t \\ & y=-2-2t \\ & z=3+5t \\ \end{align} \right.\)

D. \(\left\{ \begin{align} & x=4+7t \\ & y=-2-2t \\ & z=-3+5t \\ \end{align} \right.\)

A. 3

B. 4

C. 5

D. Vô số

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

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

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

D. \(\left( -\frac{1}{3};0 \right)\)

A. 4

B. 5

C. 6

D. 3

A. \(\sqrt{2}\)

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

C. \(\frac{2\sqrt{3}}{3}\)

D. \(\sqrt{\frac{35}{6}}\)

A. 4

B. 5

C. 6

D. 7

A. \({{P}_{\max }}=2\)

B. \({{P}_{\max }}=3\)

C. \({{P}_{\max }}=4\)

D. \({{P}_{\max }}=5\)

A. T = 10

B. \(T=\frac{21}{2}\)

C. \(T=\frac{19}{2}\)

D. T = 15