📚 Year 8 Cambridge Maths: Unit Test Mock Paper Walkthrough | 剑桥8年级数学：单元测试模拟卷解析
Welcome to our walkthrough of a Year 8 Cambridge Mathematics unit test mock paper. In this article, we present ten carefully selected questions that cover key topics from the Year 8 curriculum, including fractions, decimals, percentages, algebraic simplification, solving equations, ratio, area, circumference, statistics, and probability. Each question is followed by a detailed step-by-step solution, with explanations provided in both English and Chinese to support bilingual learning. Use this resource to check your understanding, identify common mistakes, and build confidence for your real tests.
欢迎来到我们的剑桥8年级数学单元测试模拟卷解析。在这篇文章中，我们精选了十道题目，涵盖分数、小数、百分数、代数化简、解方程、比率、面积、圆周长、统计和概率等8年级重要知识点。每道题都提供了详细的英文和中文分步解析，帮助你检验理解、发现常见错误，并为正式考试树立信心。
1. Multiplying Fractions | 分数乘法
Question: Evaluate 3/4 × 2/5, giving your answer in its simplest form.
问题：计算 3/4 × 2/5，并将结果化为最简分数。
To multiply fractions, multiply the numerators together and multiply the denominators together.
进行分数乘法时，将分子相乘，分母相乘。
Numerators: 3 × 2 = 6. Denominators: 4 × 5 = 20. This gives the fraction 6/20.
分子：3 × 2 = 6。分母：4 × 5 = 20。得到分数 6/20。
d the denominator by their greatest common factor, which is 2. 6 ÷ 2 = 3, and 20 ÷ 2 = 10.
现在化简 6/20，将分子和分母同时除以它们的最大公因数 2。6 ÷ 2 = 3，20 ÷ 2 = 10。
The simplified answer is therefore 3/10.
因此，化简后的答案为 3/10。
Always remember to check if your answer can be simplified. Leaving a fraction like 6/20 would lose marks in a test.
请始终记得检查答案是否可以化简。如果写成 6/20 而未化简，考试中会被扣分。
2. Decimals to Fractions and Percentages | 小数、分数和百分数转换
Question: Convert 0.875 to a fraction in its simplest form, and then express it as a percentage.
问题：将 0.875 化为最简分数，再用百分数表示。
sidering the place value. The last digit is in the thousandths place, so 0.875 = 875/1000.
根据数位将 0.875 写成分数。最后一位在千分位，因此 0.875 = 875/1000。
875 and 1000. Both are divisible by 25, and in fact by 125. 875 ÷ 125 = 7, 1000 ÷ 125 = 8.
化简这个分数，找到 875 和 1000 的最大公因数。它们都能被 25 整除，实际上最大公因数是 125。875 ÷ 125 = 7，1000 ÷ 125 = 8。
So the fraction in simplest form is 7/8.
因此最简分数为 7/8。
To convert a fraction to a percentage, multiply by 100%. 7/8 × 100% = (7 × 100)/8 % = 700/8 % = 87.5%.
要将分数化为百分数，乘以 100%。7/8 × 100% = (7 × 100)/8 % = 700/8 % = 87.5%。
Thus, 0.875 = 7/8 = 87.5%. Recognising common decimal-fraction equivalents like 0.875 = 7/8 can save time.
所以，0.875 = 7/8 = 87.5%。记住常见的分数小数等价关系（如 0.875 = 7/8）可以节省时间。
3. Simplifying Algebraic Expressions | 化简代数表达式
Question: Simplify 3a + 2b - a + 5b.
问题：化简 3a + 2b - a + 5b。
Identify like terms. Terms with 'a' are 3a and -a. Terms with 'b' are 2b and 5b.
找出同类项。含有 a 的项是 3a 和 -a。含有 b 的项是 2b 和 5b。
Combine the a terms: 3a - a = 2a.
合并 a 项：3a - a = 2a。
Combine the b terms: 2b + 5b = 7b.
合并 b 项：2b + 5b = 7b。
Write the simplified expression as 2a + 7b. You cannot combine 2a and 7b because they are unlike terms.
化简后的表达式为 2a + 7b。不能将 2a 和 7b 进一步合并，因为它们不是同类项。
A common mistake is to treat 3a + 2b as 5ab, but that is incorrect – they must be kept separate.
一个常见错误是把 3a + 2b 写成 5ab，但这是不正确的——加法中不同字母的项必须分开。
4. Solving Linear Equations | 解一元一次方程
Question: Solve the equation 2(x + 3) = 14.
问题：解方程 2(x + 3) = 14。
irst, expand the left-hand side: 2 × x + 2 × 3 = 2x + 6. The equation becomes 2x + 6 = 14.
首先，展开左边：2 × x + 2 × 3 = 2x + 6。方程变为 2x + 6 = 14。
Subtract 6 from both sides to isolate the term with x: 2x = 8.
两边同时减去 6，以分离含 x 的项：2x = 8。
Divide both sides by 2: x = 4.
两边同时除以 2：x = 4。
bstituting x = 4 back into the original equation: 2(4 + 3) = 2 × 7 = 14, which is correct.
将 x = 4 代入原方程检验：2(4 + 3) = 2 × 7 = 14，结果正确。
Always perform the same operation on both sides of the equation to maintain balance.
在方程两边始终执行相同的运算，以保持等式平衡。
5. Dividing in a Given Ratio | 按给定比率分配
Question: Divide £120 between two people in the ratio 3 : 5. How much does each person receive?
问题：将 120 英镑按 3:5 的比率分配给两个人。每人各得多少？
Find the total number of parts in the ratio: 3 + 5 = 8 parts.
求出比率中的总份数：3 + 5 = 8 份。
Calculate the value of one part: £120 ÷ 8 = £15.
计算每份的金额：120 ÷ 8 = 15（英镑）。
The first person gets 3 parts: 3 × £15 = £45.
第一个人得到 3 份：3 × 15 = 45（英镑）。
The second person gets 5 parts: 5 × £15 = £75.
第二个人得到 5 份：5 × 15 = 75（英镑）。
Check: £45 + £75 = £120, and the ratio 45:75 simplifies to 3:5, confirming the answer.
检验：45 + 75 = 120，且 45:75 简化为 3:5，验证了答案。
6. Area of a Triangle | 三角形面积
Question: A triangle has a base of 8 cm and a perpendicular height of 5 cm. Calculate its area.
问题：一个三角形的底是 8 厘米，垂直高是 5 厘米。计算它的面积。
Recall the formula for the area of a triangle: Area = ½ × base × height.
回忆三角形面积公式：面积 = ½ × 底 × 高。
Substitute the given values: base = 8 cm, height = 5 cm. So Area = ½ × 8 × 5.
代入已知数值：底 = 8 厘米，高 = 5 厘米。因此面积 = ½ × 8 × 5。
Calculate: ½ × 8 = 4, then 4 × 5 = 20.
计算：½ × 8 = 4，然后 4 × 5 = 20。
The area is 20 cm². Remember that area is always expressed in square units.
面积为 20 cm²。记住面积始终以平方单位表示。
A common error is to forget the ½ factor and simply multiply base by height, giving 40 cm². The ½ is essential.
常见错误是忘记乘以 ½，直接将底乘以高，得到 40 cm²。这个 ½ 是必不可少的。
7. Circumference of a Circle | 圆的周长
Question: Find the circumference of a circle with radius 7 cm. Use π ≈ 22/7.
问题：计算半径为 7 厘米的圆的周长。使用 π ≈ 22/7。
The formula for circumference is C = 2πr, where r is the radius.
圆的周长公式为 C = 2πr，其中 r 是半径。
Substitute r = 7 and π = 22/7: C = 2 × (22/7) × 7.
代入 r = 7 及 π = 22/7：C = 2 × (22/7) × 7。
Notice that the 7 in the denominator cancels with the factor 7: (22/7) × 7 = 22.
注意到分母中的 7 与 7 约分：(22/7) × 7 = 22。
So C = 2 × 22 = 44 cm.
因此 C = 2 × 22 = 44 cm。
ou would get approximately 43.96 cm, but with 22/7 the exact value is a nice whole number.
如果使用 π ≈ 3.14，你会得到大约 43.96 cm，但用 22/7 则得到一个整齐的整数结果。
8. Mean and Range | 平均数和范围
Question: Find the mean and the range of the following set of numbers: 12, 15, 18, 22, 10.
问题：求下列一组数的平均数和范围：12, 15, 18, 22, 10。
To find the mean, first add all the numbers together: 12 + 15 + 18 + 22 + 10 = 77.
要求平均数，先把所有数相加：12 + 15 + 18 + 22 + 10 = 77。
There are 5 numbers in the set, so divide the total by 5: 77 ÷ 5 = 15.4.
这组数据共有 5 个数，因此用总数除以 5：77 ÷ 5 = 15.4。
The mean is 15.4.
平均数为 15.4。
rgest number (22) and the smallest number (10). Subtract the smallest from the largest: 22 – 10 = 12.
求范围时，找出最大值（22）和最小值（10）。用最大值减去最小值：22 – 10 = 12。
The range is 12. The range gives a measure of how spread out the data is.
范围是 12。范围衡量了数据的分散程度。
9. Probability of 'Not' an Event | “非”事件的概率
Question: A bag contains 4 red, 3 blue and 5 green marbles. One marble is picked at random. What is the probability that it is NOT red?
问题：一个袋子里有 4 颗红色弹珠、3 颗蓝色弹珠和 5 颗绿色弹珠。随机抽取一颗，抽出的弹珠不是红色的概率是多少？
First find the total number of marbles: 4 + 3 + 5 = 12.
首先计算弹珠总数：4 + 3 + 5 = 12。
The number of marbles that are not red is the sum of blue and green marbles: 3 + 5 = 8.
非红色弹珠的数量是蓝色和绿色之和：3 + 5 = 8。
e probability (not red) = number of favourable outcomes / total number of outcomes = 8/12.
因此概率（非红）= 有利结果数 / 总结果数 = 8/12。
viding both numerator and denominator by 4: 8 ÷ 4 = 2, 12 ÷ 4 = 3. The probability is 2/3.
化简 8/12，分子分母同时除以 4：8 ÷ 4 = 2，12 ÷ 4 = 3。概率为 2/3。
Alternatively, P(not red) = 1 – P(red) = 1 – 4/12 = 1 – 1/3 = 2/3. This is a good check.
另一种方法：P(非红) = 1 – P(红) = 1 – 4/12 = 1 – 1/3 = 2/3。这可以作为验证。
10. Interpreting a Pie Chart | 饼图解读
Question: A pie chart shows the favourite sports of students: 40% chose football, 25% chose cricket, and the rest chose tennis. What fraction and what percentage of the students prefer tennis?
问题：一个饼图显示了学生最喜欢的运动：40% 选择足球，25% 选择板球，其余选择网球。喜欢网球的学生占几分之几？百分比是多少？
The whole pie chart represents 100%. Add the given percentages: 40% + 25% = 65%.
整个饼图代表 100%。将已知百分比相加：40% + 25% = 65%。
Subtract from 100% to find the tennis percentage: 100% – 65% = 35%.
从 100% 中减去，得到网球的百分比：100% – 65% = 35%。
To express this as a fraction, write 35% 5/100. Simplify by dividing both numerator and denominator by 5: 35 ÷ 5 = 7, 100 ÷ 5 = 20.
要表示为分数，将 35% 写成 35/100。化简，分子分母同时除以 5：35 ÷ 5 = 7，100 ÷ 5 = 20。
The fraction is 7/20. So tennis is preferred by 7/20 of the students, or 35%.
分数为 7/20。因此喜欢网球的学生占 7/20，即 35%。
Always check that the fractions and percentages you calculate from a pie chart add up to the whole.
从饼图计算分数和百分比时，务必检验各部分之和是否等于整体。
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