📚 Year 7 CCEA Maths: Unit Test Mock Paper Walkthrough | Year 7 CCEA 数学: 单元测试模拟卷解析
This article provides a complete walkthrough of a specially designed Year 7 CCEA Mathematics unit test mock paper. Each question is carefully explained step by step, helping you review key topics such as number, algebra, geometry and data handling while building exam confidence.
本文为你详细解析一套专门设计的CCEA Year 7数学单元测试模拟卷。每道题目都配有逐步讲解，帮助你在复习数字、代数、几何和数据处理等重要知识点的同时，提升考试信心。
1. Number and Place Value | 数字与数位
Question: Write down the value of the digit 7 in the number 3,725, and then round 3,725 to the nearest hundred.
题目：写出数字3,725中数字7的数值，并将3,725四舍五入到最近的百位。
The number 3,725 has four digits. The 7 is in the hundreds place, so its value is 700. To round to the nearest hundred, look at the tens digit, which is 2. Since 2 is less than 5, we round down and keep the hundreds digit as 7, giving 3,700.
数字3,725有四个数位。7位于百位，因此其数值为700。要四舍五入到最近的百位，需要看十位上的数字，这里是2。由于2小于5，我们向下舍入，百位保持为7，得到3,700。
2. Addition and Subtraction | 加法与减法
Question: Calculate 5,436 + 2,789 and 8,200 – 3,456.
题目：计算 5,436 + 2,789 和 8,200 – 3,456。
For the addition, line up the numbers by place value: 5,436 + 2,789. 6+9=15, write 5 carry 1; 3+8+1=12, write 2 carry 1; 4+7+1=12, write 2 carry 1; 5+2+1=8. The sum is 8,225. For the subtraction, 8,200 – 3,456: we need to borrow. 0-6 borrow from 0, so borrow across to hundreds. 8,200 becomes 7,1(10),(10). Finally 10-6=4, 9-5=4, 11-4=7, 7-3=4, giving 4,744.
加法计算要对齐数位：5,436 + 2,789。6+9=15，写5进1；3+8+1=12，写2进1；4+7+1=12，写2进1；5+2+1=8。总和为8,225。减法计算 8,200 – 3,456：需要借位。0减6不够，向十位借，但十位也是0，需要连续借到位。8,200变成7,1(10),(10)。最后10-6=4，9-5=4，11-4=7，7-3=4，得到4,744。
3. Multiplication and Division | 乘法与除法
Question: Find 234 × 56 and 1,092 ÷ 13.
题目：计算 234 × 56 和 1,092 ÷ 13。
Multiply 234 by 56: first 234 × 6 = 1,404. Then 234 × 50 = 11,700. Add the two products: 1,404 + 11,700 = 13,104. For the division, use long division: 13 goes into 109 eight times (13×8=104), remainder 5. Bring down the 2, making 52. 13 goes into 52 exactly four times. So 1,092 ÷ 13 = 84.
计算 234 × 56：先计算 234 × 6 = 1,404。再计算 234 × 50 = 11,700。将两个积相加：1,404 + 11,700 = 13,104。除法用长除法：13 除 109 商 8（13×8=104），余数5。落下2得到52。13 除 52 正好是4。因此 1,092 ÷ 13 = 84。
4. Fractions | 分数
Question: Simplify 15/25, and then calculate 2/5 + 1/3.
题目：化简 15/25，然后计算 2/5 + 1/3。
Simplify 15/25 by dividing numerator and denominator by their highest common factor, which is 5. 15 ÷ 5 = 3 and 25 ÷ 5 = 5, giving 3/5. For the addition, find a common denominator for 5 and 3, which is 15. Convert: 2/5 = 6/15, 1/3 = 5/15. Add the numerators: 6 + 5 = 11, so the answer is 11/15.
化简 15/25，需要将分子和分母同时除以它们的最大公因数5。15 ÷ 5 = 3，25 ÷ 5 = 5，得到 3/5。计算加法时，找出5和3的公分母15。转换分数：2/5 = 6/15，1/3 = 5/15。分子相加：6 + 5 = 11，答案为 11/15。
5. Decimals and Fractions | 小数与分数
Question: Convert 0.875 into a fraction in simplest form, and write 3/8 as a decimal.
题目：将小数0.875化为最简分数，并将分数3/8化成小数。
0.875 means 875 thousandths, so write it as 875/1000. Divide numerator and denominator by 125 to simplify: 875 ÷ 125 = 7, 1000 ÷ 125 = 8, giving 7/8. To convert 3/8 to a decimal, divide 3 by 8: 8 into 3 goes 0.375, so the decimal is 0.375.
0.875 表示875个千分之一，因此写成分数 875/1000。分子分母同时除以125化简：875 ÷ 125 = 7，1000 ÷ 125 = 8，得到 7/8。要将 3/8 化成小数，用3除以8：3 ÷ 8 = 0.375，所以小数是0.375。
6. Percentages | 百分数
Question: Find 15% of 240, and increase 80 by 25%.
题目：求240的15%，并将80增加25%。
To find 15% of 240, convert 15% to a decimal (0.15) and multiply: 0.15 × 240 = 36. Increasing 80 by 25% means finding 25% of 80 (0.25 × 80 = 20) and adding it to the original: 80 + 20 = 100. Alternatively, multiply 80 by 1.25.
求240的15%时，将15%转换成小数0.15，然后相乘：0.15 × 240 = 36。将80增加25%，意思是先求80的25%（0.25 × 80 = 20），然后加到原数上：80 + 20 = 100。另一种方法是直接用80乘以1.25。
7. Algebraic Expressions | 代数表达式
Question: If a = 4 and b = 7, evaluate 3a + 2b – 5.
题目：已知 a = 4，b = 7，求 3a + 2b – 5 的值。
Substitute the values directly into the expression: 3(4) + 2(7) – 5. Multiply first: 3 × 4 = 12, 2 × 7 = 14. Then add and subtract: 12 + 14 = 26, 26 – 5 = 21. The final result is 21.
将数值直接代入表达式：3(4) + 2(7) – 5。先做乘法：3 × 4 = 12，2 × 7 = 14。然后加减：12 + 14 = 26，26 – 5 = 21。最终结果为21。
8. Solving Simple Equations | 解简单方程
Question: Solve for x: 5x – 7 = 18.
题目：解方程求出 x：5x – 7 = 18。
Start by adding 7 to both sides to isolate the term with x. This gives 5x = 25. Then divide both sides by 5 to find x: x = 25 ÷ 5 = 5. Always check: 5 × 5 – 7 = 25 – 7 = 18, which is correct.
首先在方程两边同时加上7，将含有x的项隔离开，得到 5x = 25。然后两边除以5求出x：x = 25 ÷ 5 = 5。记得检验：5 × 5 – 7 = 25 – 7 = 18，结果正确。
5x – 7 = 18 → 5x = 25 → x = 5
9. Angles | 角
Question: Find the missing angle in a triangle if two angles are 45° and 63°.
题目：一个三角形的两个角分别为45°和63°，求第三个角的度数。
The angles in a triangle always sum to 180°. Add the two known angles: 45° + 63° = 108°. Subtract this sum from 180° to find the missing angle: 180° – 108° = 72°. Therefore, the third angle measures 72°.
三角形的三个内角和总是180°。将两个已知角的度数相加：45° + 63° = 108°。从180°中减去这个和，得到缺失的角：180° – 108° = 72°。因此第三个角为72°。
10. Perimeter and Area | 周长与面积
Question: A rectangle has length 12 cm and width 8 cm. Find its perimeter and area.
题目：一个长方形的长为12 cm，宽为8 cm。求它的周长和面积。
Perimeter is the distance around the shape. For a rectangle, perimeter = 2 × (length + width) = 2 × (12 + 8) = 2 × 20 = 40 cm. Area measures the space inside and is found by length × width = 12 × 8 = 96 cm².
周长是图形一周的长度。长方形周长 = 2 × (长 + 宽) = 2 × (12 + 8) = 2 × 20 = 40 cm。面积测量内部空间的大小，用长 × 宽计算 = 12 × 8 = 96 cm²。
11. Data Handling | 数据处理
Question: Find the mean, median, and mode of the following data set: 8, 12, 7, 9, 12, 6, 10.
题目：求以下数据集的平均数、中位数和众数：8, 12, 7, 9, 12, 6, 10。
First, put the numbers in order: 6, 7, 8, 9, 10, 12, 12. The mode is the most frequent value, which is 12. The median is the middle value in the ordered list: the 4th number is 9. To find the mean, add all values: 6+7+8+9+10+12+12 = 64, then divide by the count (7): 64 ÷ 7 ≈ 9.14 (to 2 decimal places).
首先将数字按顺序排列：6, 7, 8, 9, 10, 12, 12。众数是出现次数最多的值，为12。中位数是排序后中间位置的数，第4个数是9。求平均数时，将所有数值相加：6+7+8+9+10+12+12 = 64，然后除以数据个数7：64 ÷ 7 ≈ 9.14（保留两位小数）。
12. Coordinates and Symmetry | 坐标与对称
Question: Plot the points A(2,3), B(5,3), C(5,6) and D(2,6) on a coordinate grid. Name the shape formed and state how many lines of symmetry it has.
题目：在坐标网格上标出点 A(2,3)、B(5,3)、C(5,6) 和 D(2,6)。说出形成的图形名称，并写出它有几条对称轴。
Plotting the points shows a horizontal distance of 3 units between A and B, and a vertical distance of 3 units between A and D. All sides are equal in length and the angles are right angles, so the shape is a square. A square has 4 lines of symmetry: two through the midpoints of opposite sides, and two through opposite vertices.
描点后发现，点A和B之间的水平距离为3个单位，A和D之间的垂直距离也为3个单位。四条边长度相等，且内角都是直角，因此图形是一个正方形。正方形有4条对称轴：两条分别通过对边中点，两条通过对角顶点。
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