Year 8 OCR Mathematics: Mock Test Walkthrough | Year 8 OCR 数学：单元测试模拟卷解析

📚 Year 8 OCR Mathematics: Mock Test Walkthrough | Year 8 OCR 数学：单元测试模拟卷解析

Welcome to the Year 8 OCR Mathematics mock test walkthrough. This article provides detailed solutions and explanations for a representative set of questions, covering key topics from Number, Algebra, Geometry, Statistics and more. Each solution is broken down step by step to help you understand the methods and improve your problem-solving skills.

欢迎来到 Year 8 OCR 数学模拟卷解析。本文对一套代表性题目提供详细解答和讲解，涵盖数、代数、几何、统计等关键主题。每题会逐步拆解，帮助你掌握方法，提升解题能力。

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1. Number: Mixed Operations with Fractions | 数：分数的混合运算

A typical question asks: Evaluate 2½ + 1¼ × 3⅓, giving your answer as a mixed number in simplest form.

典型题目要求：计算 2½ + 1¼ × 3⅓，并将答案写成最简带分数。

Follow the order of operations (BIDMAS): multiplication before addition. First, convert mixed numbers to improper fractions: 2½ = 5/2, 1¼ = 5/4, 3⅓ = 10/3.

遵循运算顺序（BIDMAS）：先乘后加。首先，把带分数化为假分数：2½ = 5/2，1¼ = 5/4，3⅓ = 10/3。

Multiply the fractions: 5/4 × 10/3.

5/4 × 10/3 = (5×10)/(4×3) = 50/12

计算分数乘法。

Simplify 50/12 by dividing numerator and denominator by 2: 50/12 = 25/6.

化简 50/12，分子分母同除以2：50/12 = 25/6。

Convert 25/6 to a mixed number: 25 ÷ 6 = 4 remainder 1, so 25/6 = 4⅙.

把 25/6 化成带分数：25 ÷ 6 = 4 余 1，所以 25/6 = 4⅙。

Now add 2½ (which is 5/2) to 4⅙. Write both with a common denominator of 6: 5/2 = 15/6, 4⅙ = 25/6.

现在将 2½（即 5/2）与 4⅙ 相加。通分，公分母为6：5/2 = 15/6，4⅙ = 25/6。

Add: 15/6 + 25/6 = 40/6.

15/6 + 25/6 = 40/6

相加。

Simplify 40/6 by dividing by 2: 40/6 = 20/3.

化简 40/6，分子分母同除以2：40/6 = 20/3。

Convert to a mixed number: 20 ÷ 3 = 6 remainder 2, giving 6⅔.

Answer: 6⅔

化成带分数：20 ÷ 3 = 6 余 2，得到 6⅔。

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2. Decimals and Percentages | 小数与百分数

Question: A laptop costs £480. In a sale, there is a 15% discount. Find the sale price. You also need to convert 0.875 to a fraction in its simplest form.

题目：一台笔记本电脑原价 £480，打折 15%。求折后价。还需要将 0.875 化为最简分数。

To find 15% of £480, multiply 480 by 0.15.

480 × 0.15 = 72

计算 480 的 15%，用 480 乘以 0.15。

The discount is £72. Subtract this from the original price: £480 – £72 = £408.

折扣为 £72。从原价中减去：£480 – £72 = £408。

For the decimal conversion, write 0.875 as a fraction over 1,000: 875/1000.

小数化分数，将 0.875 写成分母为 1000 的分数：875/1000。

Simplify by dividing numerator and denominator by 125: 875 ÷ 125 = 7, 1000 ÷ 125 = 8. So the simplest fraction is ⅞.

0.875 = ⅞

分子分母同除以 125：875 ÷ 125 = 7，1000 ÷ 125 = 8。最简分数为 ⅞。

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3. Algebra: Simplifying Expressions | 代数：化简表达式

Simplify the expression: 7x – 2y + 3x + 5y – 4x² – x² + 2.

化简表达式：7x – 2y + 3x + 5y – 4x² – x² + 2。

Identify and group like terms. For x terms: 7x + 3x = 10x.

识别并合并同类项。关于 x 的项：7x + 3x = 10x。

For y terms: -2y + 5y = 3y.

关于 y 的项：-2y + 5y = 3y。

For x² terms: -4x² – x² = -5x².

关于 x² 的项：-4x² – x² = -5x²。

The constant +2 remains unchanged.

常数 +2 保持不变。

Write the simplified expression, usually ordering by descending powers of x: -5x² + 10x + 3y + 2.

Answer: -5x² + 10x + 3y + 2

写出化简后的表达式，通常按 x 的降幂排列：-5x² + 10x + 3y + 2。

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4. Algebra: Solving Equations | 代数：解方程

Solve the equation: 4(x – 3) = 20.

解方程：4(x – 3) = 20。

First, expand the bracket: 4 × x – 4 × 3 = 4x – 12. The equation becomes

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