优优班--学霸训练营 > 知识点挑题
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            • 1.
              设全集\(U=\{(x,y)|x\),\(y∈R\}\),集合\(M=\{(x,y)| \dfrac {y-3}{x-2}=1\}\),\(N=\{(x,y)|y\neq x+1\}\),则\(∁_{U}(M∪N)\)等于\((\)  \()\)
              A.\(\varnothing \)
              B.\(\{(2,3)\}\)
              C.\((2,3)\)
              D.\(\{(x,y)|y=x+1\}\)
            • 2.

              已知集合\(A=\{x|x^{2}-x-2 > 0\}\),则\(C_{R}A=\)

              A.\(\{x|-1 < x < 2\}\)

              B.\(\{x|-1\leqslant x\leqslant 2\}\)

              C.\(\{x|x < -1\}∪\{x|x > 2\}\)

              D.\(\{x|x\leqslant -1\}∪\{x|x\geqslant 2\}\)
            • 3.

              已知集合\(A=\left\{ x|{{x}^{2}}-3x+2=0 \right\}\),\(B=\left\{ x|x > 1 \right\}\),则\(A∩{C}_{R}B= (\)   \()\)

              A.\(\left\{ -1 \right\}\)
              B.\(\left\{ 1 \right\}\)
              C.\(\left\{ 1{,}2 \right\}\)
              D.\(\left\{ -1{,}-2 \right\}\)
            • 4.

              已知集合\(P=\left\{ x\left| x-1\leqslant 0 \right. \right\}\),\(Q=\left\{ x\left| \dfrac{x-2}{x}\leqslant 0 \right. \right\}\),则\(\left( {{C}_{R}}P \right)\cap Q\)(    )

              A.\((0,1)\)
              B.\(\left( 0,2 \right]\)
              C.\(\left( 1,2 \right]\)
              D.\(\left[ 1,2 \right]\) 
            • 5.

              已知集合\(A{=}\{ x{|}x^{2}{-}2x{-}3{ < }0\}\),集合\(B{=}\{ x{|}2^{x{+}1}{ > }1\}\),则\({{∁}}_{B}A{=}({  })\)

              A.\({[}3{,}{+∞})\)
              B.\((3{,}{+∞})\)
              C.\(({-∞}{,}{-}1{]∪[}3{,}{+∞})\)
              D.\(({-∞}{,}{-}1){∪}(3{,}{+∞})\)
            • 6.

              设\(U=R\),已知集合\(A=\{x|x > 1\}\),\(B=\{x|x > a\}\),且\(({{\complement }_{U}}A)\bigcup B=R\),则实数\(A\)的 取值范围是

              A.\((-\infty ,1)\)
              B.\((1,+\infty )\)
              C.\(\left( -\infty ,1 \right]\)
              D.\(\left[ 1,+\infty \right) \)
            • 7.

              已知集合\(A=\{x|x^{2}-2x > 0\}\),\(B=\{x|-\sqrt{5} < x < \sqrt{5}\}\),则\((\)  \()\)

              A.\(A∩B=\varnothing \)
              B.\(A∪B=R\)
              C.\(B\subseteq A\)          
              D.\(A\subseteq B\)
            • 8. 已知集合\(A=\left\{x|x > 1\right\} \),\(B=\left\{0,1,2,4\right\} \),则\(\left({C}_{R}A\right)∩B =\)
              A.\(\left\{0,1\right\} \)
              B.\(\left\{0\right\} \)
              C.\(\left\{2,4\right\} \)
              D.\(Φ \)
            • 9.

              \((1)\)复数\(\dfrac{2{+}i}{1{-}2i}\)的共轭复数是______.

              \((2)\)若下列两个方程\(x^{2}{+}(a{-}1)x{+}a^{2}{=}0{,}x^{2}{+}2ax{-}2a{=}0\)中至少有一个方程有实数根,则实数\(a\)的取值范围是______ .

              \((3)\)已知\(\sqrt{2{+}\dfrac{2}{3}}{=}2\sqrt{\dfrac{2}{3}}{,}\sqrt{3{+}\dfrac{3}{8}}{=}3\sqrt{\dfrac{3}{8}}{,}\sqrt{4{+}\dfrac{4}{15}}{=}4\sqrt{\dfrac{4}{15}}{,}{…}\),若\(\sqrt{6{+}\dfrac{a}{b}}{=}6\sqrt{\dfrac{a}{b}}{,}(a{,}b{∈}R)\),则\(a{+}b{=}\) ______ .

              \((4)\)在平面内,如果用一条直线去截正方形的一个角,那么截下的一个直角三角形按图\(1\)所标边长,由勾股定理有:\(c^{2}{=}a^{2}{+}b^{2}{.}\)设想正方形换成正方体,把截线换成如图\(2\)所示的截面,这时从正方体上截下三条侧棱两两垂直的三棱锥\(O{-}LMN\),如果用\(S_{1}{,}S_{2}{,}S_{3}\)表示三个侧面面积,\(S_{4}\)表示截面面积,那么你类比得到的结论是______ .

            • 10.

              已知集合\(U=\{x|x > 0\}\),\(A{= }\!\!\{\!\!{ }x|x\geqslant 2{ }\!\!\}\!\!{ }\),则\({{\complement }_{\ U}}A=\)______.

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