Pre-U Cambridge Mathematics: Unit Test Mock Paper Analysis | Pre-U剑桥数学：单元测试模拟卷解析

📚 Pre-U Cambridge Mathematics: Unit Test Mock Paper Analysis | Pre-U剑桥数学：单元测试模拟卷解析

This article provides a detailed walkthrough of a mock unit test for Pre-U Cambridge Mathematics, covering essential topics such as polynomials, binomial expansion, calculus, trigonometry, and more. Each question is followed by step-by-step solutions in both English and Chinese, designed to reinforce understanding and exam technique.

本文详细解析Pre-U剑桥数学单元测试模拟卷，涵盖多项式、二项式展开、微积分、三角函数等核心主题。每道题目均配有中英双语逐步解答，旨在巩固理解并提升应试技巧。

1. Polynomial Division | 多项式除法

Question: Divide 4x³ – 3x² + 5x – 2 by (x – 2). State the quotient and remainder.

题目：用 (x – 2) 除 4x³ – 3x² + 5x – 2，给出商和余数。

Step 1: Set up the long division. Divide the leading term: 4x³ ÷ x = 4x². Write 4x² in the quotient.

步骤1：设立长除法。首项相除：4x³ ÷ x = 4x²，将4x²写入商中。

Step 2: Multiply (x – 2) by 4x² to obtain 4x³ – 8x², and subtract from the original polynomial: (4x³ – 3x²) – (4x³ – 8x²) = 5x².

步骤2：将 (x – 2) 乘以 4x² 得 4x³ – 8x²，从原多项式中减去：(4x³ – 3x²) – (4x³ – 8x²) = 5x²。

Step 3: Bring down the next term +5x to form 5x² + 5x. Divide 5x² ÷ x = 5x, and write +5x in the quotient.

步骤3：落下下一项 +5x，得到 5x² + 5x。5x² ÷ x = 5x，将 +5x 写入商中。

Step 4: Multiply (x – 2) by 5x to get 5x² – 10x, and subtract: (5x² + 5x) – (5x² – 10x) = 15x.

步骤

Published by TutorHao | Pre-U Mathematics Revision Series | aleveler.com

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