兴国县中考数学试卷真题

一、选择题（每题3分，共30分）
1. 下列各数中，有理数是（）
A. $\sqrt{3}$
B. $\pi$
C. $\frac{1}{2}$
D. $\sqrt{2} - 1$
2. 已知$a$，$b$是实数，且$a + b = 0$，则下列等式中不正确的是（）
A. $a^2 + b^2 = 0$
B. $a^2 - b^2 = 0$
C. $ab = 0$
D. $a^2 \cdot b^2 = 0$
3. 在$\triangle ABC$中，$\angle A = 60^\circ$，$\angle B = 45^\circ$，则$\angle C$的度数是（）
A. $60^\circ$
B. $75^\circ$
C. $45^\circ$
D. $90^\circ$
4. 已知一元二次方程$ax^2 + bx + c = 0$（$a \neq 0$）的解为$x_1$和$x_2$，则下列结论正确的是（）
A. $x_1 + x_2 = \frac{b}{a}$
B. $x_1 \cdot x_2 = \frac{c}{a}$
C. $x_1 +
x_2 = \frac{b}{a} + 1$ D. $x_1 \cdot x_2 = \frac{c}{a} + 1$
5. 下列函数中，是奇函数的是（）
A. $y = x^2 + 1$
B. $y = x^3 - 2x$
C. $y = \sqrt{x}$
D. $y = \frac{1}{x} + 1$
6. 若$a$，$b$，$c$是等差数列，且$a + b + c = 12$，则下列结论正确的是（）
A. $a = 4$
B. $b = 4$
C. $c = 4$
D. $a + b + c = 4$
7. 下列各图中，面积最大的图形是（）
A. 矩形
B. 正方形
C. 菱形
D. 梯形
8. 已知$A(1, 2)$，$B(3, 4)$，则$\overrightarrow{AB}$的坐标是（）
A. $(2, 2)$
B. $(2, -2)$
C. $(-2, 2)$
D. $(-2, -2)$
9. 若$y = 2x - 3$是直线$l$的解析式，则下列结论正确的是（）
A. $l$的斜率为$2$，截距为$-3$
B. $l$的斜率为$-2$，截距为$3$
C. $l$的斜率为$-3$，截距为$2$
D. $l$的斜率为$3$，截距为$-2$
10. 已知一元二次方程$2x^2 - 5x + 3 = 0$的解为$x_1$和$x_2$，则下列结论正确的是（）
A. $x_1 + x_2 = \frac{5}{2}$
B. $x_1 \cdot x_2 = \frac{3}{2}$
C. $x_1 + x_2 = \frac{5}{2} + \sqrt{2}$
D. $x_1 \cdot x_2 = \frac{3}{2} +
\sqrt{2}$
二、填空题（每题3分，共30分）
11. 已知$x + 1 = 0$，则$x =
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