Đề thi thử THPT QG năm 2021 môn Toán - Trường THPT Nguyễn Du lần 3

A. \(A_{30}^{3}\).

B. \({{3}^{30}}\).

C. 10

D. \(C_{30}^{3}\).

A. 27

B. 31

C. 35

D. 29

A. \({{a}^{7}}\).

B. \({{a}^{\frac{5}{3}}}\).

C. \({{a}^{\frac{3}{5}}}\).

D. \({{a}^{\frac{1}{7}}}\).

A. Hàm số nghịch biến trên khoảng \(\left( 1;+\infty  \right)\).

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

C. Hàm số nghịch biến trên khoảng \(\left( -\infty ;1 \right)\).

D. Hàm số đồng biến trên khoảng \(\left( -1;+\infty  \right)\).

A. \(2-{{\log }_{5}}a\).

B. \(2{{\log }_{5}}a\).

C. \(\frac{2}{{{\log }_{5}}a}\).

D. \(2+{{\log }_{5}}a\).

A. \({y}'={{2021}^{x}}\ln 2021\).

B. \({y}'={{2021}^{x}}\).

C. \({y}'=\frac{{{2021}^{x}}}{\ln 2021}\).

D. \({y}'=x{{.2021}^{x-1}}\).

A. 0

B. 1

C. 2

D. 3

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

B. \(y={{x}^{4}}-4{{x}^{2}}-3\).

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

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

A. \(x=\frac{1}{2},\)\(y=-1\).

B. \(x=1,\)\(y=-2\).

C. \(x=-1,\)\(y=2\).

D. \(x=-1,\)\(y=\frac{1}{2}\).

A. 1

B. 2

C. 3

D. 4

A. x = 1

B. \(x=-2\).

C. \(x=2\).

D. \(x=-1\).

A. x = 3

B. x = 2

C. x = 1

D. x = -1

A. 2

B. 0

C. -3

D. 3

A. \(f\left( x \right)=\frac{{{x}^{4}}}{4}-\frac{2}{3}{{x}^{3}}+3x+1\).

B. \(f\left( x \right)=3{{x}^{2}}-4x\).

C. \(f\left( x \right)=\frac{{{x}^{4}}}{4}-\frac{2}{3}{{x}^{3}}+3x\).

D. \(f\left( x \right)=3{{x}^{2}}-4x+3\).

A. \(\frac{3}{2}\)

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

C. \(\frac{1}{2}\)

D. \(\frac{-1}{2}\)

A. -1

B. 1

C. 4

D. -4

A. \(S=\int\limits_{a}^{0}{f\left( x \right)}dx+\int\limits_{0}^{b}{f\left( x \right)dx}\).

B. \(S=\int\limits_{a}^{0}{f\left( x \right)}dx-\int\limits_{b}^{0}{f\left( x \right)dx}\).

C. \(S=\int\limits_{0}^{a}{f\left( x \right)}dx+\int\limits_{0}^{b}{f\left( x \right)dx}\).

D. \(S=\int\limits_{a}^{0}{f\left( x \right)}dx+\int\limits_{b}^{0}{f\left( x \right)dx}\).

A. -8

B. 8

C. 0

D. 3

A. \(-8-i.\)

B. \(-4-7i.\)

C. \(-4+7i.\)

D. \(-8+i.\)

A. \(\left( 4;2 \right).\)

B. \(\left( -4;2 \right).\)

C. \(\left( 4;-2 \right).\)

D. \(\left( -4;-2 \right)\).

A. 8

B. 4

C. 24

D. 6

A. 13

B. 30

C. 15

D. 6

A. \(V=\frac{\pi {{r}^{2}}h}{4}\)

B. \(V=\frac{\pi {{r}^{2}}h}{12}.\)

C. \(V=\frac{\pi {{r}^{2}}h}{24}\). 

D. \(V=\frac{\pi {{r}^{2}}h}{6}.\)

A. \(240\pi c{{m}^{2}}.\)

B. \(120\pi c{{m}^{2}}.\)

C. \(70\pi c{{m}^{2}}.\)

D. \(140\pi c{{m}^{2}}.\)

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

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

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

D. \(\sqrt{14}\).

A. \({{I}_{1}}\left( 0;-1;3 \right)\).

B. \({{I}_{2}}\left( 0;1;-3 \right)\).

C. \({{I}_{3}}\left( 0;-1;-3 \right)\).

D. \({{I}_{4}}\left( 0;1;3 \right)\).

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

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

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

D. \(\vec{h}\left( 1;1;1 \right)\).

A. \(\left\{ \begin{align} & x=1+t \\ & y=t \\ & z=1-t \\ \end{align} \right. \)

B. \(\left\{ \begin{align} & x=1+t \\ & y=1-t \\ & z=t \\ \end{align} \right. \)

C. \(\left\{ \begin{align} & x=1+t \\ & y=t \\ & z=t \\ \end{align} \right. \)

D. \(\left\{ \begin{align} & x=t \\ & y=1+t \\ & z=1-t \\ \end{align} \right. \)

A. \(\frac{3}{10}\).

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

C. \(\frac{1}{2}\).

D. \(\frac{1}{5}\).

A. \(\frac{2x+1}{x-2}\).

B. \(\frac{x-3}{x-4}\).

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

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

A. 0

B. 18

C. 10

D. 11

A. \(\left( -5;-4 \right]\cup \left[ 4;5 \right)\).

B. \(\left( -\infty ;-4 \right]\cup \left[ 4;+\infty  \right)\).

C. \(\left( 4;5 \right)\).

D. \(\left[ 4;+\infty  \right)\).

A. \(\frac{1011}{1010}\).

B. 1

C. \(\frac{2021}{2020}\).

D. -1

A. 2010

B. 2014

C. 2028

D. 2032

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

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

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

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

A. \(\frac{2\sqrt{57}a}{19}\).

B. \(\frac{\sqrt{57}a}{19}\).

C. \(\frac{2\sqrt{5}a}{5}\).

D. \(\frac{\sqrt{5}a}{5}\).

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

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

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

D. \({{\left( x+3 \right)}^{2}}+{{\left( y-1 \right)}^{2}}+{{\left( z+2 \right)}^{2}}=4\)

A. \(\left\{ \begin{align} & x=1+t \\ & y=5-t \\ & z=-1+t \\ \end{align} \right. \)

B. \(\left\{ \begin{align} & x=1-t \\ & y=5-t \\ & z=-1+t \\ \end{align} \right. \)

C. \(\left\{ \begin{align} & x=1+3t \\ & y=5+3t \\ & z=-1+3t \\ \end{align} \right. \)

D. \(\left\{ \begin{align} & x=-1+t \\ & y=-5-t \\ & z=1+t \\ \end{align} \right. \)

A. \(f(2)-2.\)

B. \(f\left( \frac{1}{2} \right)+2.\)

C. \(f(2)+2\).

D. \(f\left( \frac{3}{2} \right)-1\).

A. \(59149\).

B. \(59050\).

C. \(59049\)

D. \(59048\).

A. \(\frac{28}{3}\).

B. 8

C. \(\frac{341}{48}\).

D. \(\frac{341}{96}\).

A. 1

B. 0

C. 3

D. 2

A. \(\frac{{{a}^{3}}}{6}\).

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

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

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

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

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

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

D. \(\frac{1}{3}\).

A. \(M\left( 1;1;-4 \right)\).

B. \(N\left( 0;-5;6 \right)\).

C. \(P\left( 0;5;-6 \right)\).

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

A. 0

B. 3

C. 1

D. 2

A. 211

B. 2020

C. 2023

D. 212

A. \(\frac{2\sqrt{6}}{3}\).

B. \(\frac{\sqrt{6}}{2}\).

C. \(\frac{5\sqrt{3}}{6}\).

D. \(\frac{3\sqrt{3}}{4}\).

A. 9

B. 8

C. 7

D. 6

A. 0

B. 1

C. -1

D. 2