📚 Year 12 Edexcel Maths: Unit Test Mock Paper Walkthrough | Year 12 Edexcel 数学：单元测试模拟卷解析
This walkthrough covers a mock unit test for Year 12 Edexcel Mathematics (Pure). Each question is carefully selected to reflect the style and difficulty of AS-level exams. Detailed solutions are provided to reinforce key concepts in algebra, functions, coordinate geometry, trigonometry, calculus, exponentials, sequences, and binomial expansion.
本解析涵盖一份针对 Year 12 Edexcel 数学（纯数学）的模拟单元测试卷。每道题目的选择均贴近 AS 考试风格与难度，并配有详细解答，旨在巩固代数、函数、坐标几何、三角学、微积分、指数、数列与二项展开等核心内容。
1. Quadratic Discriminant | 二次判别式
estion: The equation x² + (k - 3)x + 4 = 0 has equal roots. Find the possible values of k.
题目：方程 x² + (k - 3)x + 4 = 0 有等根，求 k 的可能取值。
tic ax² + bx + c = 0 to have equal roots, the discriminant must be zero: Δ = b² - 4ac = 0.
对于二次方程，有等根的条件是判别式为零：Δ = b² - 4ac = 0。
Here a = 1, b = k - 3, c = 4. So Δ = (k - 3)² - 4(1)(4) = (k - 3)² - 16.
这里 a = 1, b = k - 3, c = 4，因此 Δ = (k - 3)² - 16。
Δ = (k - 3)² - 16 = 0
Set Δ = 0: (k - 3)² = 16 → k - 3 = ±4.
令 Δ = 0 得：(k - 3)² = 16 → k - 3 = ±4。
k = 3 + 4 = 7 or k = 3 - 4 = -1. Always consider both positive and negative square roots.
因此 k = 3 + 4 = 7 或 k = 3 - 4 = -1。务必同时考虑正负平方根。
2. Function Composition | 函数复合
Given f(x) = 2x + 1 and g(x) = x² - 2. Find fg(x), gf(x), and solve fg(x) = gf(x).
已知 f(x) = 2x + 1, g(x) = x² - 2。求 fg(x)、
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