📚 Year 9 Edexcel Maths: Unit Test Mock Paper Walkthrough | Year 9 Edexcel 数学：单元测试模拟卷解析
Preparing for your Year 9 Edexcel maths unit test? This walkthrough takes you through a full mock paper, covering key topics from number operations to geometry and statistics. Each section presents a typical question, a detailed step-by-step solution, and highlights common pitfalls, so you can build confidence and improve your exam technique.
正在为 Year 9 Edexcel 数学单元测试做准备吗？这篇解析将带你完成一套完整的模拟卷，涵盖从数字运算到几何与统计的重点主题。每节将展示一道典型题目，给出详细的分步解答并指出常见错误，帮助你积累信心、优化考试技巧。
1. Number Skills and Fractions | 数字技能与分数
Calculate 3½ ÷ 2⅓
First, convert both mixed numbers to improper fractions. For 3½, multiply the whole number 3 by the denominator 2 to get 6, then add the numerator 1 to obtain 7. The improper fraction is 7/2.
首先，把两个带分数都转换为假分数。对于 3½，将整数 3 乘以分母 2 得到 6，再加上分子 1 得到 7。假分数是 7/2。
For 2⅓, multiply 2 by 3 to get 6, add the numerator 1 to get 7. The improper fraction is 7/3.
对于 2⅓，将 2 乘以 3 得到 6，再加分子 1 得到 7。假分数是 7/3。
Now rewrite the division as multiplying by the reciprocal: 7/2 ÷ 7/3 becomes 7/2 × 3/7.
现在把除法改写为乘以倒数：7/2 ÷ 7/3 变成 7/2 × 3/7。
Cancel the common factor 7 in the numerator and denominator: 7/2 × 3/7 = 1/2 × 3/1.
约去分子与分母中的公因数 7：7/2 × 3/7 = 1/2 × 3/1。
Multiply across: 1 × 3 = 3 and 2 × 1 = 2. The result is 3/2, which simplifies to 1½.
分子相乘、分母相乘：1 × 3 = 3，2 × 1 = 2。结果是 3/2，化简为 1½。
Many students forget to flip the second fraction. Always remember: keep, change, flip.
很多学生会忘记翻转第二个分数。务必记住口诀：保留、变号、翻转。
2. Algebraic Simplification and Substitution | 代数化简与代入
Simplify 4a − 3b + 2a − 5b, then evaluate when a = 3, b = −2
: 4a + 2a = 6a. Collect the b-terms: −3b − 5b = −8b. The simplified expression is 6a − 8b.
合并 a 项：4a + 2a = 6a。合并 b 项：−3b − 5b = −8b。化简后的表达式是 6a − 8b。
Now substitute a = 3 and b = −2 into the simplified expression: 6(3) − 8(−2).
现在将 a = 3 和 b = −2 代入化简后的表达式：6(3) − 8(−2)。
3 = 18. For −8 × (−2), recall that a negative times a negative is positive, so we get +16.
计算 6 × 3 = 18。对于 −8 × (−2)，注意负数乘负数得正，因此得到 +16。
Add the results: 18 + 16 = 34. Always simplify before substituting – it reduces errors with negative numbers.
结果相加：18 + 16 = 34。务必先化简再代入，这能减少处理负数时出错。
Common error comparison | 常见错误对比
| Mistake | Why it's wrong | Correct approach |
|---|---|---|
| Writing −8(−2) as −8 × (−2) = −16 | Forgets the sign rule for negative numbers | −8 × (−2) = +16 |
| Substituting directly without simplifying first | More steps lead to arithmetic errors | Always collect like terms first |
3. Solving Linear Equations | 解线性方程
Solve 2(x + 3) = 3x − 5
d the bracket on the left: 2 × x = 2x and 2 × 3 = 6. The equation becomes 2x + 6 = 3x − 5.
展开左边的括号：2 × x = 2x，2 × 3 = 6。方程变为 2x + 6 = 3x − 5。
Bring x-terms to one side. Subtract 2x from both sides: 6 = x − 5.
将含 x 的项移到同一边。两边同时减去 2x，得到 6 = x − 5。
Isolate x by adding 5 to both sides: 6 + 5 = x, so x = 11.
两边加 5 解出 x：6 + 5 = x，因此 x = 11。
Check in the original equation: Left = 2(11+3)=28, Right = 3×11−5=28. Both sides match.
代回原方程检验：左边 = 2(11+3)=28，右边 = 3×11−5=28。两边相等。
A frequent mistake is expanding the bracket incorrectly. Always multiply every term inside by the factor outside.
常见错误是括号展开不正确。务必用外面的因数乘以括号内的每一项。
Avoid this trap | 避开这个陷阱
| Incorrect step | Consequence | Correct expansion |
|---|---|---|
| 2(x+3) = 2x + 3 | Lost the multiplication by 2 for 3 | 2x + 6 |
| Moving terms without sign change | Gets wrong constant | Keep the balance – whatever you do to one side, do to the other |
4. Inequalities | 不等式
Solve 3x + 4 ≤ 2x + 9 and represent the solution on a number line
Subtract 2x from both sides: x + 4 ≤ 9.
两边同时减去 2x：x + 4 ≤ 9。
Subtract 4 from both sides: x ≤ 5.
再减去 4：x ≤ 5。
On a number line, draw a solid circle at 5 (since 5 is included) and shade to the left.
在数轴上，在 5 处画一个实心圆（因为 5 包含在解集中），并向左画阴影区域。
to use a solid circle for ≤ or ≥. A hollow circle is only for strict inequalities: < or >.
一些学生忘记用实心圆表示 ≤ 或 ≥。空心圆仅用于严格不等式 < 或 >。
When multiplying or dividing by a negative, you must flip the inequality sign. In this question no negative operations are needed, but always watch out.
乘或除以负数时，必须翻转不等号。本题无需这类运算，但需要始终留心。
5. Ratio and Proportion | 比与比例
Divide £360 in the ratio 2 : 3 : 5
First, find the total number of parts: 2 + 3 + 5 = 10 parts.
先求总份数：2 + 3 + 5 = 10 份。
Calculate the value of one part: £360 ÷ 10 = £36.
计算每份的金额：£360 ÷ 10 = £36。
Multiply each part by this unit value: first share = 2 × £36 = £72, second share = 3 × £36 = £108, third share = 5 × £36 = £180.
用每份金额乘以各份数：第一份 = 2 × £36 = £72，第二份 = 3 × £36 = £108，第三份 = 5 × £36 = £180。
Quick check: £72 + £108 + £180 = £360. Always add the shares to confirm the total.
快速检验：£72 + £108 + £180 = £360。务必把各份加总来验证总和。
Mixing up the order of the ratio is a typical slip. Stick to the sequence given in the problem.
搞混比例的顺序是常见的疏忽，一定要严格按照题目给出的顺序分配。
6. Area of a Trapezium | 梯形面积
A trapezium has parallel sides of lengths 8 cm and 12 cm and a perpendicular height of 5 cm. Find its area.
formula for the area of a trapezium: A = ½(a + b)h, where a and b are the parallel sides.
回忆梯形面积公式：A = ½(a + b)h，其中 a 和 b 是平行边长。
Substitute the values: a = 8, b = 12, h = 5. So A = ½ (8 + 12) × 5.
代入数值：a = 8, b = 12, h = 5。因此 A = ½ (8 + 12) × 5。
ide the bracket: 8 + 12 = 20. Multiply: ½ × 20 = 10, then 10 × 5 = 50. The area is 50 cm².
先算括号内：8 + 12 = 20。接着相乘：½ × 20 = 10，10 × 5 = 50。面积是 50 cm²。
Don't forget to square the units when giving an area. Writing 'cm' instead of 'cm²' loses a mark.
给出面积时别忘了单位的平方。写成 'cm' 而不是 'cm²' 会丢分。
7. Volume of a Cylinder | 圆柱体积
Find the volume of a cylinder with base radius 4 cm and height 10 cm. (Use π ≈ 3.14)
The volume of a cylinder is V = πr²h.
圆柱的体积公式为 V = πr²h。
Identify r = 4 cm and h = 10 cm. Square the radius: r² = 4² = 16.
确定 r = 4 cm，h = 10 cm。将半径平方：r² = 4² = 16。
Multiply: π × 16 × 10. Using π ≈ 3.14, first find π × 16 = 3.14 × 16 = 50.24.
相乘：π × 16 × 10。用 π ≈ 3.14，先计算 π × 16 = 3.14 × 16 = 50.24。
Then multiply by 10: 50.24 × 10 = 502.4. The volume is 502.4 cm³.
再乘以 10：50.24 × 10 = 502.4。体积是 502.4 cm³。
Many pupils confuse volume with surface area. Volume fills the inside; surface area covers the outside. Always include the correct units – cm³ for volume.
很多学生混淆体积与表面积。体积是内部容积，表面积是外部覆盖面积。一定要用对单位——体积用 cm³。
8. Pythagoras' Theorem | 勾股定理
A 10 m ladder leans against a vertical wall. The foot of the ladder is 6 m from the base of the wall. How high up the wall does the ladder reach?
m), the distance from the wall is one leg (a = 6 m), and the height is the other leg (b).
梯子、墙壁和地面构成一个直角三角形。梯子是斜边（c = 10 m），梯子底端到墙的距离是一条直角边（a = 6 m），梯子顶端距地面的高度是另一条直角边（b）。
Apply Pythagoras' theorem: a² + b² = c². Substitute: 6² + b² = 10².
应用勾股定理：a² + b² = c²。代入数值：6² + b² = 10²。
Evaluate the squares: 36 + b² = 100. Subtract 36 from both sides: b² = 64.
计算平方：36 + b² = 100。两边减去 36：b² = 64。
Take the square root: b = √64 = 8. The ladder reaches 8 m up the wall.
开平方根：b = √64 = 8。梯子顶端距地面 8 m。
Always check if you are asked to find a leg or the hypotenuse. If the hypotenuse is given, subtract the squares; if finding the hypotenuse, add them.
务必弄清楚题目要求的是直角边还是斜边。已知斜边求直角边用减法平方；求斜边则用加法。
9. Angles in Polygons | 多边形内角和
A regular octagon has 8 sides. Find the sum of its interior angles and the size of one interior angle.
he sum of interior angles of any polygon = (n - 2) × 180°, where n is the number of sides.
任意多边形的内角和 = (n - 2) × 180°，其中 n 是边数。
For an octagon, n = 8. Sum = (8 - 2) × 180° = 6 × 180° = 1080°.
对于八边形，n = 8。内角和 = (8 - 2) × 180° = 6 × 180° = 1080°。
all interior angles are equal. Divide the sum by 8: one interior angle = 1080° ÷ 8 = 135°.
因为这是一个正八边形，所有内角相等。用内角和除以 8：一个内角 = 1080° ÷ 8 = 135°。
A common slip is using the wrong multiplier: some use (n - 3) or forget to subtract 2. The formula comes from triangulating the polygon.
常见毛病是用错乘数：有人用 (n - 3) 或忘记减 2。该公式源于将多边形划分为三角形的方法。
10. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph shows ice cream sales plotted against noon temperature. The points slope upward to the right. Describe the correlation and explain what it means in context.
The pattern shows a positive correlation: as the temperature increases, ice cream sales tend to increase as well.
散点图显示出正相关：随着气温升高，冰淇淋销量也往往增加。
This does not mean temperature directly causes sales, but the data suggests a strong association. In context, hotter weather likely encourages more people to buy ice cream.
这并不意味着气温直接导致销售变化，但数据表明存在很强的关联。在实际场景中，天气越热，越多人可能会购买冰淇淋。
If the points are tightly grouped along a line, the correlation is strong. If they are widely scattered, the correlation is weak.
如果数据点紧密分布在某条线附近，则相关性较强；如果分布得很散，则相关性较弱。
When interpreting, always state the variables and link the trend to the real-world situation. Avoid saying “one causes the other” unless you have evidence.
解释时，务必指明变量并将趋势与现实情境联系起来。避免说“一个导致另一个”，除非有证据支持。
Some graphs show a negative correlation (as one variable rises, the other falls) or no correlation at all. Identifying the direction is key.
有些图呈现负相关（一个变量上升，另一个下降）或完全没有相关性。识别方向是关键。
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