Year 9 CIE Maths: Unit Test Mock Paper Walkthrough | Year 9 CIE数学：单元测试模拟卷解析

📚 Year 9 CIE Maths: Unit Test Mock Paper Walkthrough | Year 9 CIE数学：单元测试模拟卷解析

This walkthrough presents a mock unit test covering core Year 9 CIE Mathematics topics. Each question is broken down step‑by‑step to help you build confidence and accuracy ahead of your real assessment.

本文解析一份模拟单元测试卷，覆盖Year 9 CIE数学核心主题。每道题均配有分步详解，帮助你在正式评估前建立信心与准确度。

1. Solving Linear Equations | 解线性方程

Question: Solve for x: 3x − 7 = 2x + 5.

题目：解方程求 x：3x − 7 = 2x + 5。

Step 1: Subtract 2x from both sides to collect the x‑terms on the left.

步骤1：方程两边同时减去 2x，将含 x 的项集中到左边。

3x − 7 − 2x = 2x + 5 − 2x

x − 7 = 5

Step 2: Add 7 to both sides to isolate x.

步骤2：两边同时加上 7，使 x 单独留在方程一侧。

x − 7 + 7 = 5 + 7

x = 12

Therefore, the solution is x = 12.

因此，方程的解为 x = 12。

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2. Expanding Brackets | 展开括号

Question: Expand and simplify (x + 4)(x − 3).

题目：展开并化简 (x + 4)(x − 3)。

Use the FOIL method: First, Outer, Inner, Last.

使用 FOIL 方法：先乘首项，再乘外项、内项、末项。

First: x × x = x²

首项：x × x = x²

Outer: x × (−3) = −3x

外项：x × (−3) = −3x

Inner: 4 × x = 4x

内项：4 × x = 4x

Last: 4 × (−3) = −12

末项：4 × (−3) = −12

Now combine the like terms: x² − 3x + 4x − 12 = x² + x − 12.

合并同类项：x² − 3x + 4x − 12 = x² + x − 12。

The simplified expression is x² + x − 12.

化简后的表达式为 x² + x − 12。

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3. Direct Proportion | 正比例关系

Question: If 5 pens cost $3.50, find the cost of 8 pens.

题目：若 5 支笔的售价为 $3.50，求 8 支笔的售价。

First, find the unit price of one pen.

首先，计算一支笔的单价。

Cost per pen = $3.50 ÷ 5 = $0.70.

每支笔价格 = $3.50 ÷ 5 = $0.70。

Then multiply the unit cost by 8: 8 × $0.70 = $5.60.

再将单价乘以 8：8 × $0.70 = $5.60。

Alternatively, set up a proportion: 5/3.50 = 8/x → x = (8 × 3.50) ÷ 5 = 28 ÷ 5 = 5.60.

也可列比例式：5/3.50 = 8/x，得 x = (8 × 3.50) ÷ 5 = 28 ÷ 5 = 5.60。

So, 8 pens cost $5.60.

因此，8 支笔的售价为 $5.60。

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4. Angles in a Triangle | 三角形内角和

Question: In triangle ABC, ∠A = 40°, ∠B = (2x)°, ∠C = (3x)°. Find the value of x and the size of ∠C.

题目：在 △ABC 中，∠A = 40°，∠B = (2x)°，∠C = (3x)°。求 x 的值及 ∠C 的大小。

The sum of angles in a triangle is always 180°.

三角形内角和恒为 180°。

Form the equation: 40 + 2x + 3x = 180

列出方程：40 + 2x + 3x = 180

Combine like terms: 40 + 5x = 180.

合并同类项：40 + 5x = 180。

Subtract 40 from both sides: 5x = 140.

两边同时减去 40：5x = 140。

Divide by 5: x = 28.

两边除以 5：x = 28。

Now find ∠C = 3 × 28° = 84°.

计算 ∠C = 3 × 28° = 84°。

Thus, x = 28 and ∠C = 84°.

因此，x = 28，∠C = 84°。

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5. Pythagoras' Theorem | 勾股定理

Question: A right‑angled triangle has legs of length 6 cm and 8 cm. Calculate the hypotenuse.

题目：一直角三角形的两条直角边分别为 6 cm 和 8 cm。求斜边的长度。

By Pythagoras' theorem: a² + b² = c², where c is the hypotenuse.

根据勾股定理：a² + b² = c²，其中 c 为斜边。

Substitute the given lengths:

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