Year 12 Edexcel Maths: Unit Test Mock Paper Walkthrough | Year 12 Edexcel 数学：单元测试模拟卷解析

📚 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

Question: 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。

For a quadratic 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。

Hence 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)、

Published by TutorHao | Year 12 Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）