📚 Year 7 CCEA Maths: Unit Test Mock Paper Walkthrough | CCEA 7年级数学：单元测试模拟卷解析
This walkthrough breaks down a typical Year 7 CCEA unit test mock paper, covering number, algebra, geometry, and data handling. Each question is explained step by step in both English and Chinese, helping pupils spot common pitfalls, revise key skills, and build confidence before the real assessment.
本文详细解析一份模拟的 CCEA 7年级数学单元测试卷，涵盖数字、代数、几何与数据处理。每道题都提供逐步讲解与中英双语对照，帮助学生发现常见错误、巩固关键技能，并在真正考试前建立信心。
1. About the Mock Paper | 关于模拟卷
This mock paper is designed to reflect a 45‑minute unit test worth 50 marks. It is divided into three sections: Number & Arithmetic, Algebra & Equations, and Geometry & Data. You may encounter straightforward calculations, word problems, and at least one reasoning or multi‑step question meant to stretch your problem‑solving ability.
这份模拟卷模拟一份 45 分钟、总分 50 分的单元测试。试卷分为三大块：数与算术、代数与方程、几何与数据。你将碰到直接计算题、应用题，以及至少一道考查逻辑推理或多步运算的能力提升题。
Always read each question carefully. Underline key information like units, operations, and what the final answer should look like. Marks are often awarded not only for the final answer but also for showing your working.
一定要仔细读题，画出关键信息，如单位、运算符号以及答案要求的格式。评分通常不仅看最终答案，也看解题步骤，所以要养成写出完整计算过程的习惯。
2. Number and Place Value | 数字与位值
Question: Write down the value of the digit 7 in 3,405,072.
题目：写出数字 3,405,072 中数字 7 的位值。
The digit 7 sits in the tens column, so its value is 70. Remember to look at the position from the right: units, tens, hundreds, etc. In 3,405,072 the tens digit is 7, giving 7 × 10 = 70.
7 在十位上，因此它的值是 70。记住从右往左依次是个位、十位、百位…… 3,405,072 的十位数字是 7，所以是 7 × 10 = 70。
Another typical question asks you to compose a number: 600 + 40 + 2 + 0.5 + 0.03. Adding these gives 642.53. Be careful with decimal places so the tenths and hundredths line up correctly.
另一种常见题是组合数字：600 + 40 + 2 + 0.5 + 0.03。加在一起得到 642.53。注意对齐小数位，确保十分位和百分位正确。
Finally, compare 0.7 and 0.699. Because 0.7 = 0.700, it is greater than 0.699. Using a number line or converting to thousandths helps.
最后，比较 0.7 和 0.699。因为 0.7 = 0.700，所以 0.7 大于 0.699。借助数轴或都化成千分位可以看得更清楚。
0.7 = 0.700 > 0.699
3. Fractions, Decimals and Percentages | 分数、小数与百分比
Question: Add 3/4 and 1/6, giving your answer in its simplest form.
题目：计算 3/4 + 1/6，并化为最简分数。
Find a common denominator. The LCM of 4 and 6 is 12. Rewrite each fraction: 3/4 = 9/12, 1/6 = 2/12. Now add: 9/12 + 2/12 = 11/12. The fraction is already in its simplest form because 11 and 12 share no common factors.
先找公分母。4 和 6 的最小公倍数是 12。通分：3/4 = 9/12，1/6 = 2/12。相加得 9/12 + 2/12 = 11/12。11 和 12 互质，已经是最简分数。
Conversion question: Express 0.125 as a fraction and as a percentage.
转换题：将 0.125 写成分数和百分数。
Write 0.125 as 125/1000, then simplify by dividing numerator and denominator by 125: 125/1000 = 1/8. To change to a percentage, multiply by 100: 0.125 × 100% = 12.5%.
0.125 写成分数是 125/1000，分子分母同除以 125，得到 1/8。转为百分数：0.125 × 100% = 12.5%。
Context problem: In a class of 30 pupils, 30% are boys. How many boys are there?
应用题：班上有 30 名学生，30% 是男生，问男生有多少人？
Find 30% of 30: 30/100 × 30 = 900/100 = 9. So there are 9 boys. Always turn the percentage into a fraction or decimal to avoid errors.
求 30 的 30%：30/100 × 30 = 900/100 = 9。有 9 名男生。计算百分比时尽量先化成小数或分数，避免口算错误。
3/4 + 1/6 = 11/12 | 0.125 = 1/8 = 12.5%
4. Algebraic Expressions | 代数表达式
Question: Simplify 5x + 3y – 2x + y.
题目：化简 5x + 3y – 2x + y。
Collect like terms: the x‑terms are 5x and –2x, giving 3x. The y‑terms are 3y and y (which is +1y), giving 4y. So the simplified expression is 3x + 4y.
合并同类项：x 项有 5x 和 –2x，得 3x；y 项有 3y 和 y（即 +1y），得 4y。化简结果为 3x + 4y。
Writing an expression: ‘Multiply n by 6, then add 3.’ The expression is 6n + 3. Pay attention to the order: multiplication before addition unless parentheses change it.
写出表达式：“把 n 乘以 6，再加 3”。表达式为 6n + 3。注意运算顺序是先乘后加，除非括号改变了顺序。
Substitution: Given a = 4, b = –2, evaluate 3a + 2b.
代入求值：已知 a = 4，b = –2，求 3a + 2b 的值。
Replace a with 4 and b with –2: 3 × 4 + 2 × (–2) = 12 – 4 = 8. Watch the negative sign when multiplying.
用 4 替换 a，–2 替换 b：3×4 + 2×(–2) = 12 – 4 = 8。代入时注意负号运算。
3a + 2b = 3(4) + 2(–2) = 8
5. Solving Simple Equations | 解简单方程
Question: Solve 2x + 7 = 19.
题目：解方程 2x + 7 = 19。
Subtract 7 from both sides: 2x = 12. Then divide by 2: x = 6. Always check by putting 6 back into the equation: 2 × 6 + 7 = 12 + 7 = 19, which works.
两边同时减去 7：2x = 12。再除以 2：x = 6。把 6 代回原方程检验：2×6 + 7 = 12 + 7 = 19，吻合。
Now solve 5y – 3 = 2y + 9.
现在解 5y – 3 = 2y + 9。
Bring y‑terms to one side and constants to the other. Subtract 2y from both sides: 3y – 3 = 9. Add 3 to both sides: 3y = 12. Divide by 3: y = 4. Check: 5×4 – 3 = 20 – 3 = 17; 2×4 + 9 = 8 + 9 = 17. Correct.
将含 y 的项移到一边，常数移到另一边。两边减去 2y：3y – 3 = 9。两边加 3：3y = 12。除以 3：y = 4。检验：5×4 – 3 = 17，2×4 + 9 = 17，两边相等。
x = 6 | y = 4
6. Angles and Geometry | 角度与几何
Question: In a triangle, two angles are 48° and 73°. Find the third angle.
题目：三角形中两个角分别是 48° 和 73°，求第三个角。
The sum of angles in a triangle is 180°. Add the known angles: 48° + 73° = 121°. Subtract from 180°: 180° – 121° = 59°. The missing angle is 59°.
三角形内角和为 180°。先加已知角：48° + 73° = 121°。180° – 121° = 59°，所以第三个角是 59°。
Angles on a straight line: If one angle is 115°, the supplementary angle is 180° – 115° = 65°. Remember that angles around a point sum to 360°, and in a quadrilateral they sum to 360°.
直线上的角：若一个角为 115°，补角是 180° – 115° = 65°。还要记住围绕一个点的角度和为 360°，四边形内角和也是 360°。
180° – (48° + 73°) = 59° | 180° – 115° = 65°
7. Perimeter and Area | 周长与面积
Question: A rectangle has length 8 cm and width 5 cm. Find its perimeter and area.
题目：一个长方形的长是 8 cm，宽是 5 cm，求它的周长和面积。
Perimeter = 2 × (length + width) = 2 × (8 + 5) = 2 × 13 = 26 cm. Area = length × width = 8 × 5 = 40 cm². Always write the correct unit after the number.
周长 = 2 × (长 + 宽) = 2 × (8 + 5) = 26 cm。面积 = 长 × 宽 = 8 × 5 = 40 cm²。最后一定要写上正确单位。
A compound shape is formed by two rectangles: one is 4 cm by 3 cm, the other is 5 cm by 2 cm, joined along a side. Find the total area.
一个组合图形由两个矩形拼接而成：一个长 4 cm、宽 3 cm，另一个长 5 cm、宽 2 cm。求总面积。
Calculate each area separately: 4 × 3 = 12 cm², 5 × 2 = 10 cm². Total area = 12 + 10 = 22 cm². The perimeter may require you to add only the outer edges, so be careful not to count the shared side.
分别计算面积：4 × 3 = 12 cm²，5 × 2 = 10 cm²。总面积 = 22 cm²。求周长时只需计算外边框，注意不要去数重叠的那条边。
Perimeter = 26 cm | Area = 40 cm²
8. Data Handling and Averages | 数据处理与平均数
Question: Here are the scores of a quiz: 5, 8, 12, 14, 8, 7. Find the mean, median and mode.
题目：以下是测验分数：5, 8, 12, 14, 8, 7。求平均数、中位数和众数。
First, order the data: 5, 7, 8, 8, 12, 14. Mean = sum ÷ number of values. Sum = 5+7+8+8+12+14 = 54. Divide by 6: 54 ÷ 6 = 9. So the mean is 9.
先把数据排序：5, 7, 8, 8, 12, 14。平均数 = 总和 ÷ 数据个数。总和 = 5+7+8+8+12+14 = 54。54 ÷ 6 = 9，平均数是 9。
Median is the middle value. With 6 numbers, the median lies between the 3rd and 4th values: (8 + 8) ÷ 2 = 8. The mode is the most frequent score, which is 8 (appears twice).
中位数是中间值。有 6 个数，中位数在第 3 和第 4 个数的中间：(8 + 8) ÷ 2 = 8。众数是出现次数最多的分数，即 8（出现两次）。
A quick summary table can help you organise these measures.
下面的总结表格帮助你理清这些统计量。
| Mean | 9 |
| Median | 8 |
| Mode | 8 |
When reading a bar chart, always check the scale on the axis. One small square might represent 2, 5 or 10 units, so read the labels carefully before calculating totals or averages.
阅读柱状图时，一定要看清轴上的刻度。一个小格可能代表 2、5 或 10 个单位，因此在计算总和或平均数前务必先确认坐标刻度。
9. Problem‑Solving Strategies | 问题解决策略
Word problem: Tom has £x. He spends £3 on stationery, then spends half of the remaining money on a book. He has £2 left. Find x.
文字题：Tom 有 £x。他花 £3 买文具，然后把剩下钱的一半用来买书，最后还剩 £2。求 x。
Work backwards. Before buying the book, he had twice the £2 left: £4. Before buying stationery, he had £3 more: £4 + £3 = £7. So x = 7. Then check: start 7, spend 3 → 4, half of 4 is 2, left 2. Correct.
逆向推理。买书前，他剩的钱是 £2 的两倍：£4。买文具前，再多 £3：£4 + £3 = £7。因此 x = 7。验证：7 – 3 = 4，花一半买书剩 2。正确。
Cost problem: A fence costs £12 per metre. A gardener needs to fence a rectangular garden 6 m by 4 m. How much does the fencing cost?
费用问题：篱笆每米 £12。一个园丁要给一块 6 m 长、4 m 宽的长方形花园围上篱笆，要花多少钱？
Perimeter = 2 × (6 + 4) = 20 m. Cost = 20 × £12 = £240. Always underline ‘per metre’ so you remember to multiply.
周长 = 2 × (6 + 4) = 20 m。费用 = 20 × £12 = £240。要圈出“每米”这样的词，提醒自己要用乘法。
x = 7 | Cost = £240
10. Common Mistakes and Tips | 常见错误与提分技巧
Mistake 1: Forgetting to use a common denominator when adding fractions. Always convert to equivalent fractions with the same denominator first.
错误 1：分数相加时忘记通分。一定要先把分数化成同分母的等价分数再相加。
Mistake 2: Losing negative signs when substituting values. Write the value in brackets, especially when it is negative, e.g., 2b with b = –2 becomes 2(–2) = –4.
错误 2：代入求值时丢掉负号。代入负数时要用括号括起来，如 b = –2 代入 2b，应写成 2(–2) = –4。
Mistake 3: Confusing perimeter and area. Perimeter is the distance around the edge (add side lengths), while area is the space inside (multiply two dimensions for rectangles).
错误 3：混淆周长和面积。周长是绕图形一周的长度（各边相加），面积是内部的区域大小（长方形用长乘宽）。
Mistake 4: Not writing units. Always include units such as cm, m, cm² or degrees. A number alone does not tell the full story.
错误 4：不写单位。答案必须带单位，如 cm、m、cm² 或 °（度）。光秃秃的数字不能完整表达含义。
Tip: Underline key information in the question and show all your working. Even if your final answer is slightly wrong, you can earn method marks.
提分技巧：圈出题目中的关键信息，并写出完整运算步骤。即使最终答案有小错，步骤分仍能帮你拿到不少分数。
Lastly, manage your time. Spend roughly one minute per mark, and leave a few minutes to check answers, especially equations and conversions.
最后，合理分配时间。大约一分钟做一分的题，留几分钟检查答案，尤其是方程题和单位换算。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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