江苏省南京市、盐城市2026届高三数学一模试题(含解析)苏教版(.docx

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1. 若函数 \( f(x) = ax^2 + bx + c \) 的图象开口向上，且顶点坐标为 \( (1, -2) \)，则下列选项中正确的是：
A. \( a > 0, b > 0, c > 0 \)
B. \( a > 0, b < 0, c > 0 \)
C. \( a < 0, b > 0, c < 0 \)
D. \( a < 0, b < 0, c < 0 \)
2. 已知等差数列 \( \{a_n\} \) 的前 \( n \) 项和为 \( S_n \)，若 \( S_3 = 9 \)，\( S_5 = 25 \)，则该数列的公差为：
A. 2
B. 3
C. 4
D. 5
3. 下列函数中，在定义域内是奇函数的是：
A. \( f(x) = x^2 1 \)
B. \( f(x) = \frac{1}{x} \)
C. \( f(x) = |x| \)
D. \( f(x) = x^3 \)
4. 在极坐标系中，点 \( P(2, \frac{\pi}{3}) \) 对应的直角坐标为：
A. \( (1, \sqrt{3}) \)
B. \( (2, \sqrt{3}) \)
C. \( (1, \frac{\pi}{3}) \)
D. \( (2, \frac{\pi}{3}) \)
5. 若复数 \( z \) 满足 \( |z - 1| = |z + 1| \)，则 \( z \) 在复平面上的几何意义是：
A. 位于实轴上
B. 位于虚轴上
C. 位于第一象限
D. 位于第二象限
二、填空题
6. 若函数 \( f(x) = \frac{x^2 - 1}{x - 1} \)，则 \( f(2) = ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________\