📚 Exam-style Practice: Paper 2 Pure Mathematics | 考试风格练习：试卷2 纯数学
This article provides a set of exam-style practice questions for Edexcel A-Level Mathematics Paper 2 (Pure Mathematics). Working through these examples will help you revise core techniques in algebra, functions, coordinate geometry, sequences, trigonometry, exponentials, calculus, vectors and proof. Each topic includes a typical question followed by a step-by-step solution.
本文提供了一套针对爱德思A-Level数学试卷2（纯数学）的考试风格练习题。通过这些例题，你可以巩固代数、函数、坐标几何、数列、三角学、指数与对数、微积分、向量和证明等核心技巧。每个主题都包含一道典型题目及其分步解答。
1. Algebraic Methods | 代数方法
Question: Show that (x-2) is a factor of f(x)=x³ – 4x² + x + 6 and hence factorise f(x) completely.
问题：证明 (x-2) 是 f(x)=x³ – 4x² + x + 6 的因式，并由此将 f(x) 完全分解因式。
To check if (x-2) is a factor, evaluate f(2): f(2) = (2)³ – 4(2)² + 2 + 6 = 8 – 16 + 2 + 6 = 0. Since f(2)=0, the Factor Theorem confirms (x-2) is a factor.
检验 (x-2) 是否为因式，计算 f(2)：f(2) = 8 – 16 + 2 + 6 = 0。由因式定理，f(2)=0 说明 (x-2) 是因式。
Now divide f(x) by (x-2). Using polynomial division or comparing coefficients, we obtain the quotient x² – 2x – 3.
接下来用 f(x) 除以 (x-2)。通过多项式除法或系数比较，得到商 x² – 2x – 3。
Factorise the quadratic: x² – 2x – 3 = (x-3)(x+1).
对二次式因式分解：x² – 2x – 3 = (x-3)(x+1)。
Therefore, the complete factorisation is f(x) = (x-2)(x-3)(x+1).
因此，完全分解为 f(x) = (x-2)(x-3)(x+1)。
2. Functions and Graphs | 函数与图像
Published by TutorHao | A-Level Mathematics Revision Series | aleveler.com
Find Edexcel A Level Maths Textbooks on eBay UK
New, used and second-hand copies of textbooks and revision guides are often much cheaper than retail — check current listings and prices before you buy.
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导