Year 9 Cambridge Mathematics: Unit Test Mock Paper Walkthrough | 九年级剑桥数学：单元测试模拟卷解析

📚 Year 9 Cambridge Mathematics: Unit Test Mock Paper Walkthrough | 九年级剑桥数学：单元测试模拟卷解析

This article provides a complete walkthrough of a mock unit test designed for Year 9 Cambridge Mathematics. Working through typical exam-style questions will help you master key skills such as arithmetic, algebra, ratio, geometry, statistics and probability. Each question is broken down step by step, with strategies and common pitfalls explained.

本文完整解析了一份为九年级剑桥数学设计的单元模拟测试卷。通过练习典型的考试风格题目，你可以巩固算术、代数、比例、几何、统计和概率等关键技能。每道题都配有逐步分解的解答，并说明解题策略和常见错误。

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1. Order of Operations | 运算顺序

Question: Calculate 8 + 2 × (3² – ember to follow BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction).

题目：计算 8 + 2 × (3² – 5) ÷ 2。请遵循 BIDMAS 运算顺序（括号、指数、除法/乘法、加法/减法）。

First, work inside the brackets: 3² = 9, so 9 – 5 = 4.

首先，计算括号内部：3² = 9，因此 9 – 5 = 4。

. Next, perform multiplication and division from left to right: 2 × 4 = 8, then 8 ÷ 2 = 4.

此时表达式变为 8 + 2 × 4 ÷ 2。接着从左到右计算乘除法：2 × 4 = 8，然后 8 ÷ 2 = 4。

Finally, add: 8 + 4 = 12. The answer is 12.

最后做加法：8 + 4 = 12。答案是 12。

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2. Fractions, Decimals and Percentages | 分数、小数和百分数

Question: Express 3/5 as a decimal and as a percentage.

题目：将 3/5 表示为小数和百分数。

To convert a fraction to a decimal, divide the numerator by the denominator: 3 ÷ 5 = 0.6.

要将分数转换为小数，用分子除以分母：3 ÷ 5 = 0.6。

To change a decimal to a percentage, multiply by 100: 0.6 × 100 = 60%. Alternatively, find an equivalent fraction with denominator 100: 3/5 = 60/100 = 60%.

要将小数转换为百分数，乘以 100：0.6 × 100 = 60%。也可以先化为分母为 100 的等值分数：3/5 = 60/100 = 60%。

So, 3/5 = 0.6 = 60%.

因此，3/5 = 0.6 = 60%。

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3. Simplifying Algebraic Expressions | 化简代数表达式

Question: Simplify 3a + 2b – a + 4b.

题目：化简 3a + 2b – a + 4b。

Collect like terms: for a, we have 3a – a = 2a.

合并同类项：a 项，3a – a = 2a。

For b, we have 2b + 4b = 6b.

b 项，2b + 4b = 6b。

Therefore, the simplified expression is 2a + 6b.

因此，化简后的表达式为 2a + 6b。

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4. Solving Linear Equations | 解线性方程

Question: Solve for x: 5x – 7 = 3x + 9.

题目：解方程 5x – 7 = 3x + 9。

Start by getting all x-terms on one side. Subtract 3x from both sides: 5x – 7 – 3x = 3x + 9 – 3x, which gives 2x – 7 = 9.

首先将所有含 x 的项移到一边。两边同时减去 3x：5x – 7 – 3x = 3x + 9 – 3x，得到 2x – 7 = 9。

Then add 7 to both sides: 2x – 7 + 7 = 9 + 7, so 2x = 16.

然后两边加 7：2x – 7 + 7 = 9 + 7，得到 2x = 16。

Finally, divide both sides by 2: x = 8.

最后两边除以 2：x = 8。

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5. Ratios and Proportions | 比和比例

Question: The ratio of boys to girls in a class is 3:4. If there are 28 girls, how many boys are there?

题目：班级中男生与女生的比是 3:4。如果女生有 28 人，那么男生有多少人？

4 girls. The number of girls is known, so set up a proportion: boys / girls = 3/4 = b/28.

比 3:4 表示每 3 个男生对应 4 个女生。已知女生人数，列比例式：男生/女生 = 3/4 = b/28。

Solve the equation by multiplying both sides by 28: b = (3/4) × 28 = 21.

解比例式，两边乘 28：b = (3/4) × 28 = 21。

ultiplier: 28 ÷ 4 = 7, so multiply the number of boys by 7: 3 × 7 = 21. There are 21 boys.

另一方法，求倍数：28 ÷ 4 = 7，然后将男生份数乘 7：3 × 7 = 21。所以男生有 21 人。

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6. Angles and Parallel Lines | 角与平行线

Question: In a triangle, two angles are 50° and 60°. Find the third angle.

题目：在一个三角形中，两个角分别是 50° 和 60°。求第三个角。

The sum of interior angles in any triangle is 180°. Let the missing angle be x.

任何三角形的内角和为 180°。设未知角为 x。

So, 50° + 60° + x = 180° → 110° + x = 180°.

因此，50° + 60° + x = 180° → 110° + x = 180°。

Subtract 110° from both sides: x = 70°.

两边减去 110°：x = 70°。

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7. Perimeter and Area | 周长与面积

Question: A rectangle has length 10 cm and width 6 cm. Find its perimeter and area, including units.

题目：一个长方形的长为 10 cm，宽为 6 cm。求它的周长和面积，注明单位。

Perimeter of a rectangle = 2 × (length + width) = 2 × (10 + 6) = 2 × 16 = 32 cm.

长方形的周长 = 2 ×（长 + 宽）= 2 × (10 + 6) = 2 × 16 = 32 cm。

Area = length × width = 10 × 6 = 60 cm².

面积 = 长 × 宽 = 10 × 6 = 60 cm²。

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8. Volume and Surface Area | 体积与表面积

Question: A cube has side length 4 cm. Calculate its volume and total surface area.

题目：一个立方体的棱长为 4 cm。计算它的体积和总表面积。

Volume of a cube = side³ = 4³ = 4 × 4 × 4 = 64 cm³.

立方体体积 = 棱长³ = 4³ = 4 × 4 × 4 = 64 cm³。

Surface area of a cube = 6 × (side²) = 6 × (4²) = 6 × 16 = 96 cm².

立方体表面积 = 6 ×（棱长²）= 6 × (4²) = 6 × 16 = 96 cm²。

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9. Mean, Median and Mode | 平均数、中位数和众数

Question: Five students scored the following marks in a test: 8, 7, 9, 10, 6. Find the mean, median and mode.

题目：五名学生在测验中的分数为：8, 7, 9, 10, 6。求平均数、中位数和众数。

mber of values. Sum = 8 + 7 + 9 + 10 + 6 = 40. Number of scores = 5, so mean = 40 ÷ 5 = 8.

平均数：所有值相加除以个数。总和 = 8 + 7 + 9 + 10 + 6 = 40。有 5 个分数，所以平均数 = 40 ÷ 5 = 8。

Median: Arrange in order: 6, 7, 8, 9, 10. The middle value is 8, so median = 8.

中位数：按顺序排列：6, 7, 8, 9, 10。中间值为 8，因此中位数 = 8。

Mode: The number that appears most often. Here each number appears once, so there is no mode (or the data set has no repeated value).

众数：出现次数最多的数。这里每个数都只出现一次，因此没有众数（或数据集无重复值）。

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10. Probability | 概率

Question: A bag contains 4 red, 3 blue and 2 green marbles. One marble is picked at random. Find the probability that it is not red.

题目：一个袋子中有 4 个红色、3 个蓝色和 2 个绿色弹珠。随机抽取一个。求抽到的不是红色的概率。

Total number of marbles = 4 + 3 + 2 = 9. The probability of picking a red marble is 4/9.

弹珠总数 = 4 + 3 + 2 = 9。抽到红色的概率是 4/9。

Therefore, probability of not red = 1 – 4/9 = 5/9.

因此，不是红色的概率 = 1 – 4/9 = 5/9。

ternatively, count favourable outcomes: blue plus green = 3 + 2 = 5, so probability = 5/9.

另一种方法，数有利情况：蓝色加绿色 = 3 + 2 = 5，所以概率 = 5/9。

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