Year 11 OCR Maths: Unit Test Mock Paper Walkthrough | OCR 数学单元测试模拟卷解析

📚 Year 11 OCR Maths: Unit Test Mock Paper Walkthrough | OCR 数学单元测试模拟卷解析

This walkthrough guides you through a representative unit test mock paper for the OCR Year 11 Mathematics course. Each question is broken down step by step, with clear explanations in both English and Chinese, so you can master the essential techniques and avoid common pitfalls. Use this resource to revise key topics, check your understanding, and build exam confidence.

本解析将带你演练一份具有代表性的OCR 11年级数学单元测试模拟卷。每道题目都配有分步拆解，并提供清晰的中英双语解释，帮助你掌握基本技巧并避开常见陷阱。利用这份资料复习关键课题、检验理解程度、树立考试信心。

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1. Simplifying Algebraic Expressions | 代数表达式的化简

Question: Simplify 3x² + 5x – 2x² + 7.

题目：化简 3x² + 5x – 2x² + 7。

Step 1: Identify the like terms. The x² terms are 3x² and –2x². The x term is 5x. The constant is 7. Always underline or circle groups to avoid mixing them.

步骤1：找出同类项。x² 项为 3x² 和 –2x²；x 项为 5x；常数项为 7。养成画线或圈出的习惯，避免混淆。

Step 2: Combine the x² terms by adding their coefficients: 3 – 2 = 1, so 3x² – 2x² = x².

步骤2：合并 x² 项，系数相加：3 – 2 = 1，因此 3x² – 2x² = x²。

Step 3: Bring down the remaining terms. The simplified expression is x² + 5x + 7. There are no more like terms, so this is the final answer.

步骤3：写下其余各项。化简后的表达式为 x² + 5x + 7。没有其他同类项，这就是最终答案。

ick check: if x = 1, original gives 3+5-2+7 = 13, simplified gives 1+5+7 = 13. They match.

快速检验：令 x = 1，原式得 3+5-2+7 = 13，化简后得 1+5+7 = 13。两者相等。

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2. Solving Linear Equations | 解一元一次方程

Question: Solve for x: 2(x – 3) = 4x + 2.

题目：解 x 的方程：2(x – 3) = 4x + 2。

First, expand the bracket on the left-hand side: 2x – 6 = 4x + 2. Multiplying a negative inside the bracket is a frequent source of sign errors.

首先，展开左边的括号：2x – 6 = 4x + 2。括号内的负数相乘是符号错误的常见来源。

Collect the x terms on one side. Subtract 2x from both sides: –6 = 2x + 2. This avoids negative coefficients on the variable.

将含 x 的项移到一边。两边同时减去 2x：–6 = 2x + 2。这样做可避免变量系数为负。

Isolate the x term by subtracting 2 from both sides: –8 = 2x.

通过两边减 2 分离出含 x 的项：–8 = 2x。

Divide both sides by 2: x = –4.

两边除以 2：x = –4。

Verify: substitute x = –4 back: 2(–4–3) = 2(–7) = –14, and 4(–4)+2 = –16+2 = –14. Correct.

验证：将 x = –4 代回原方程：2(–4–3) = 2(–7) = –14，而 4(–4)+2 = –16+2 = –14。正确。

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3. Solving Inequalities | 解不等式

Question: Solve the inequality 4x – 7 > 5x + 3 and represent the solution on a number line.

题目：解不等式 4x – 7 > 5x + 3，并在数轴上表示解集。

Move the x terms to one side. Subtract 4x from both sides: –7 > x + 3. Remember that if you multiply or divide by a negative, you must flip the inequality sign – but here we avoid that.

将 x 项移到一边。两边减去 4x：–7 > x + 3。记住，如果乘以或除以负数，必须反转不等号——但这里我们避免了该情况。

Subtract 3 from both sides: –10 > x, which can be rewritten as x < –10.

两边再减 3：–10 > x，可改写为 x < –10。

On a number line, draw an open circle at –10 (because x is strictly less than –10, not equal to) and shade all values to the left.

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