1. Given sets $A = \{ x \mid - 1 < x < 2 \} , B = \{ x \mid 0 < x < 3 \}$, then $A \cup B =$
A. $( - 1,3 )$
B. $( - 1,0 )$
C. $( 0,2 )$
D. $( 2,3 )$

1. Let set $A = \{ \mathrm { x } / ( \mathrm { x } + 1 ) ( \mathrm { x } - 2 ) < 0 \}$, set $B = \{ \mathrm { x } / 1 < \mathrm { x } < 3 \}$, then $A \cup B =$
A. $\{ X / - 1 < X < 3 \}$ B. $\{ X / - 1 < X < 1 \}$ C. $\{ X / 1 < X < 2 \}$ D. $\{ X / 2 < X < 3 \}$

1. Given the universal set $U = \{ 1,2,3,4,5,6 \}$, set $A = \{ 2,3,4 \}$, set $B = \{ 1,3,4,6 \}$, then set $A \cap C _ { U } B =$
(A) $\{ 3 \}$
(B) $\{ 2,5 \}$
(C) $\{ 1,4,6 \}$
(D) $\{ 2,3,5 \}$

1. Given sets $\mathrm { P } = \left\{ x \mid x ^ { 2 } - 2 x \geq 3 \right\} , \mathrm { Q } = \{ x \mid 2 < x < 4 \}$ , then $\mathrm { P } \cap \mathrm { Q } =$ $\_\_\_\_$

1. Given sets $P = \left\{ x \mid x ^ { 2 } - 2 x \geq 0 \right\} , Q = \{ x \mid 1 < x \leq 2 \}$ , then $\left( \complement _ { \mathbb{R} } P \right) \cap Q =$
A. $[0,1)$
B. $( 0,2 ]$
C. $( 1,2 )$
D. $[ 1,2 ]$

2. Let variables $x , y$ satisfy the constraint conditions $x - 2y \geq 0$, $x \leq 2$, $y \geq 0$. Then the maximum value of the objective function $z = 3x + y$ is
(A) 7
(B) 8
(C) 9
(D) 14

Variables $x, y$ satisfy the constraints $\left\{\begin{array}{c}x + 2 \geq 0, \\ x - y + 3 \geq 0, \\ 2x + y - 3 \leq 0,\end{array}\right.$ then the maximum value of the objective function $Z = x + 6y$ is
(A) 3
(B) 4
(C) 18
(D) 40

3. Let $x \in R$. Then ``$x > 1$'' is ``$x ^ { 3 } > 1$'' a
A. sufficient but not necessary condition
B. necessary but not sufficient condition
C. necessary and sufficient condition
D. neither sufficient nor necessary condition

4. Let $x \in \mathbb{R}$. Then ``$1 < x < 2$'' is ``$|x - 2| < 1$'' a
(A) sufficient but not necessary condition
(B) necessary but not sufficient condition
(C) necessary and sufficient condition
(D) neither sufficient nor necessary condition

Let $x \in \mathbb{R}$. Then ``$|x - 2| < 1$'' is ``$x^2 + x - 2 > 0$'' a
(A) sufficient but not necessary condition
(B) necessary but not sufficient condition
(C) necessary and sufficient condition
(D) neither sufficient nor necessary condition

5. Given that $\mathrm { x } , \mathrm { y }$ satisfy the constraints $\left\{ \begin{array} { c } x - y \geq 0 \\ x + y - 4 \leq 0 \\ y \geq 1 \end{array} \right.$, then the maximum value of $\mathrm { z } = - 2 \mathrm { x } + \mathrm { y }$ is
(A) $- 1$
(B) $- 2$
(C) $- 5$
(D) $1$

5. If variables $x$ and $y$ satisfy the constraint conditions $\left\{ \begin{array} { l } x + 2 y \geq 0 , \\ x - y \leq 0 , \\ x - 2 y + 2 \geq 0 , \end{array} \right.$ then the minimum value of $z = 2 x - y$ equals
A. $- \frac { 5 } { 2 }$
B. $- 2$
C. $- \frac { 3 } { 2 }$
D. 2

If the system of inequalities $\left\{ \begin{array} { c } x + y - 2 \leq 0 \\ x + 2 y - 2 \geq 0 \\ x - y + 2 m \geq 0 \end{array} \right.$ represents a triangular region with area equal to $\frac { 4 } { 3 }$, then the value of $m$ is
(A) $-3$
(B) $1$
(C) $\frac { 4 } { 3 }$
(D) $3$

14. If $x , y$ satisfy the constraint conditions $\left\{ \begin{array} { c } x + y - 5 \leq 0 \\ 2 x - y - 1 \geq 0 \\ x - 2 y + 1 \leq 0 \end{array} \right.$, then the maximum value of $z = 2 x + y$ is $\_\_\_\_$ .

If $\mathrm { x } , \mathrm { y }$ satisfy the constraint conditions $\left\{ \begin{array} { l } x - y + 1 \geqslant 0 , \\ x - 2 y \leqslant 0 , \\ x + 2 y - 2 \leqslant 0 , \end{array} \right.$ then the maximum value of $z = x + y$ is $\_\_\_\_$ .

14. Given that real numbers $x , y$ satisfy $x ^ { 2 } + y ^ { 2 } \leq 1$ , then the maximum value of $| 2 x + y - 4 | + | 6 - x - 3 y |$ is $\_\_\_\_$ .

Let $A = \left\{ x \mid x ^ { 2 } - 4 x + 3 < 0 \right\} , B = \{ x \mid 2 x - 3 > 0 \}$, then $A \cap B =$
(A) $\left( - 3 , - \frac { 3 } { 2 } \right)$
(B) $\left( - 3 , \frac { 3 } { 2 } \right)$
(C) $\left( 1 , \frac { 3 } { 2 } \right)$
(D) $\left( \frac { 3 } { 2 } , 3 \right)$

Given sets $A = \{ x \mid x < 2 \}$, $B = \{ x \mid 3 - 2x > 0 \}$, then
A. $A \cap B = \{ x \mid x \leq \frac{3}{2} \}$
B. $A \cap B = \varnothing$
C. $A \cup B = \left\{ x \left\lvert \, x < \frac{3}{2} \right. \right\}$
D. $A \cup B = \mathbf{R}$

If $a > 1$, then the range of values of $x$ satisfying $\log_a(x^2 - 2) < \log_a x$ is
A. $(\sqrt{2}, +\infty)$
B. $(\sqrt{2}, 2)$
C. $(1, \sqrt{2})$
D. $(1, 2)$

Let $x, y$ satisfy the constraint conditions $\left\{ \begin{array}{l} x - y \geq 1 \\ y \geq 0 \end{array} \right.$. Then the maximum value of $z = x + y$ is
A. 0
B. 1
C. 2
D. 3

Let $x, y$ satisfy the linear constraints $\left\{\begin{array}{l} 2x - 3y + 3 \geq 0, \\ y + 3 \geq 0, \\ 3x - 3 \leq 0 \end{array}\right.$ and let $z = 2x + y$. The minimum value of $z$ is
A. $-15$
B. $-9$
C. $1$
D. $9$

Let $x$ and $y$ satisfy the constraints $\left\{ \begin{array} { l } x + 2 y \leqslant 1, \\ 2 x + y \geqslant - 1, \\ x - y \leqslant 0, \end{array} \right.$ then the minimum value of $z = 3 x - 2 y$ is \_\_\_\_

[Optional 4-5: Inequalities] (10 points)
Given functions $f(x) = -x^2 + ax + 4$ and $g(x) = |x + 1| + |x - 1|$.
(2) If the solution set of the inequality $f(x) \geq g(x)$ contains $[-1, 1]$, find the range of values for $a$.

Given the set $A = \left\{ x \mid x ^ { 2 } - x - 2 > 0 \right\}$, then $\mathrm { C } _ { \mathrm { R } } A =$
A. $\{ x \mid - 1 < x < 2 \}$
B. $\{ x \mid - 1 \leqslant x \leqslant 2 \}$
C. $\{ x \mid x < - 1 \} \cup \{ x \mid x > 2 \}$
D. $\{ x \mid x \leqslant - 1 \} \cup \{ x \mid x \geqslant 2 \}$

If $x , y$ satisfy the constraints $\left\{ \begin{array} { l } x - 2 y - 2 \leqslant 0 , \\ x - y + 1 \geqslant 0 , \\ y \leqslant 0 , \end{array} \right.$ then the maximum value of $z = 3 x + 2 y$ is $\_\_\_\_$