引言

2009年的高考数学试卷，无论是选择题、填空题还是解答题，都充满了挑战。本文将带领大家回顾那些年我们一起攻克的难题与解题技巧，帮助读者更好地理解和掌握高中数学的精髓。

一、选择题与填空题

1. 选择题

2009年的选择题涉及了集合、三角函数、数列等多个知识点。以下是一个典型的例子：

题目：已知函数\(f(x) = \sin x + \cos x\)，求函数的最小正周期。

解答：

import math

# 定义函数f(x)
def f(x):
    return math.sin(x) + math.cos(x)

# 计算函数的最小正周期
period = 2 * math.pi / abs(math.cos(math.pi / 2))
print("函数的最小正周期为：", period)

2. 填空题

填空题主要考察学生对基础知识的掌握程度。以下是一个例子：

题目：若数列\(\{a_n\}\)的通项公式为\(a_n = 2^n - 1\)，则$a_5 = _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________