Year 8 CCEA Further Mathematics: Mock Unit Test Walkthrough | Year 8 CCEA 进阶数学：单元测试模拟卷解析

📚 Year 8 CCEA Further Mathematics: Mock Unit Test Walkthrough | Year 8 CCEA 进阶数学：单元测试模拟卷解析

This article provides a detailed walkthrough of a mock unit test for Year 8 CCEA Further Mathematics. Each question is carefully explained, covering key topics like algebra, ratios, geometry, probability and volume. Work through the solutions to strengthen your problem-solving skills and exam confidence.

本文详细解析了一份 Year 8 CCEA 进阶数学单元测试模拟卷，涵盖代数、比例、几何、概率和体积等核心主题。通过逐步解答每道题目，帮助你巩固解题技巧，增强考试信心。

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

Question: Simplify 3a + 5b − a + 2b − 4.

题目：化简 3a + 5b − a + 2b − 4。

To simplify, we collect like terms. The 'a' terms are 3a and −a, the 'b' down −4. The expression reduces to a single term in a, a single term in b, and the number.

化简时，我们合并同类项。含 a 的项有 3a 和 −a，含 b 的项有 5b 和 2b，常数项为 −4。逐步合并：3a − a = 2a；5b + 2b = 7b；然后写下 −4。表达式化为了一个 a 项、一个 b 项与常数。

2a + 7b − 4

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2. Solving Linear Equations | 解线性方程

Question: Solve the equation 5x − 2 = 3x + 10.

题目：解方程 5x − 2 = 3x + 10。

y adding 2 to both sides: 2x = 12. Finally, divide both sides by 2 to find the value of x.

首先将含 x 的项移到一侧。两边同时减去 3x：5x − 2 − 3x = 3x + 10 − 3x，化简得 2x − 2 = 10。接着，将常数项移到右侧，两边加 2：2x = 12。最后，两边除以 2，求出 x 的值。

x = 6

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3. Finding the nth Term | 求第 n 项公式

Question: Find the nth term of the sequence: 3, 7, 11, 15, …

题目：求数列 3, 7, 11, 15, … 的第 n 项。

st term. Here a = 3, so the nth term is 3 + (n − 1) × 4 = 3 + 4n − 4. Simplifying gives the final expression.

该数列每次增加 4，因此公差 d = 4。等差数列第 n 项的公式为 a + (n − 1)d，其中 a 为首项。这里 a = 3，所以第 n 项为 3 + (n − 1) × 4 = 3 + 4n − 4。化简后得到最终表达式。

4n − 1

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4. Percentage Discounts | 百分比折扣

Question: A shirt costs £40 before a 15% discount. Work out the sale price.

题目：一件衬衫原价 £40，现打 15% 折扣。计算折后价格。

A 15% discount means you pay 85% of the original price. Convert 85% decimal (0.85) and multiply by the original price: 0.85 × 40 = 34. Alternatively, find 15% first: 0.15 × 40 = 6, then subtract from £40 to get £34. Either method gives the sale price.

15% 的折扣意味着你需要支付原价的 85%。将 85% 化为小数 0.85，乘以原价：0.85 × 40 = 34。也可以先计算 15%：0.15 × 40 = 6，再用 £40 减去 £6 得到 £34。两种方法均得出折后价格。

£34

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5. Ratio Problems | 比例问题

Question: The ratio of boys to girls in a class is 3:2. If there are 15 boys, how many students are there in total?

题目：某班级男生与女生的人数比为 3:2。若男生有 15 人，全班共有多少学生？

udents is 5 × 5 = 25. You can also work out that there are 2 × 5 = 10 girls, then add 15 + 10.

在比例 3:2 中，男生对应 3 份。因为 3 份 = 15，所以 1 份为 15 ÷ 3 = 5。总份数为 3 + 2 = 5 份。因此全班总人数为 5 × 5 = 25。也可先求出女生人数 2 × 5 = 10，再与男生相加得 25。

25 students

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6. Angles in a Triangle Using Ratios | 三角形内角按比例分配

Question: A triangle has angles in the ratio 1:2:3. Find the size of each angle.

题目：一个三角形三个内角的度数比为 1:2:3。求每个角的度数。

= 30°, the middle angle is 2 × 30° = 60°, and the largest angle is 3 × 30° = 90°. Notice that this is a right‑angled triangle.

三角形内角和为 180°。比例 1:2:3 的总份数为 1 + 2 + 3 = 6 份。每份是 180° ÷ 6 = 30°。因此，最小角为 1 × 30° = 30°，中间角为 2 × 30° = 60°，最大角为 3 × 30° = 90°。可以看出这是一个直角三角形。

30°, 60°, 90°

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7. Area of a Circle | 圆的面积

Question: Find the area of a circle with radius 7 cm. Use π ≈ 22/7.

题目：求半径为 7 cm 的圆的面积。使用 π ≈ 22/7。

nominator cancels with a factor from 49 (since 49 = 7 × 7), leaving 22 × 7 = 154. Remember to include the correct units cm².

圆的面积公式为 A = πr²。代入 r = 7 和 π = 22/7：A = (22/7) × 7²。7² = 49，所以式子变为 (22/7) × 49。分母的 7 和 49 的因数约分（49 = 7 × 7），得到 22 × 7 = 154。注意加上正确的单位 cm²。

154 cm²

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8. Probability with a Fair Dice | 公平骰子的概率

Question: A fair six-sided dice is rolled. What is the probability of getting a prime number?

题目：掷一枚均匀的六面骰子。掷出质数的概率是多少？

The possible outcomes are 1, 2, 3, 4, 5, 6. Among these, the prime numbers are 2, 3 and 5. That gives three favourable outcomes out of six equally likely outcomes. Probability is calculated as favourable / total, so the answer can be written as a fraction or simplified.

可能的结果为 1, 2, 3, 4, 5, 6。其中质数有 2, 3 和 5，即三个有利结果。共有六个等可能结果。概率 = 有利结果数 / 总结果数，因此答案可以写成分数或约简。

1/2

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9. Solving a Linear Inequality | 解一元一次不等式

Question: Solve the inequality 3(x − 1) ≤ 6.

题目：解不等式 3(x − 1) ≤ 6。

h sides by 3 (the inequality sign stays the same because we divide by a positive number). This gives the solution set of all x that satisfy the restriction.

首先展开括号：3x − 3 ≤ 6。然后两边加 3，使含 x 的项单独在一侧：3x ≤ 9。最后两边除以 3（除以正数，不等号方向不变）。得到所有满足条件的 x 的集合。

x ≤ 3

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10. Expanding Double Brackets | 展开双括号

Question: Expand and simplify (x + 3)(x − 2).

题目：展开并化简 (x + 3)(x − 2)。

= x. Write the terms in descending order of powers, giving the final simplified quadratic expression.

使用 FOIL 方法（首、外、内、尾）。首项：x × x = x²。外项：x × (−2) = −2x。内项：3 × x = 3x。尾项：3 × (−2) = −6。合并 x 项：−2x + 3x = x。按幂次降序排列，得到化简后的二次式。

x² + x − 6

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11. Volume of a Cuboid | 长方体的体积

Question: A cuboid measures 5 cm by 3 cm by 2 cm. Calculate its volume.

题目：一个长方体长 5 cm、宽 3 cm、高 2 cm。计算其体积。

stitute the given measurements: V = 5 × 3 × 2. Multiply the numbers: 5 × 3 = 15, then 15 ×

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