📚 Essential Maths 9C Homework Answers: Common Mistakes Summary | Essential Maths 9C 作业答案易错点总结
When marking Essential Maths 9C homework, teachers often see the same mistakes appearing again and again. Understanding these common errors can help you avoid them in tests and build stronger foundations. This article summarises the key pitfalls and shows how to correct them.
在批改Essential Maths 9C作业时，老师们经常发现同样的错误反复出现。了解这些常见错误能帮助你避免在考试中丢分，打下更扎实的基础。本文总结了重点易错点，并展示正确解法。
1. Adding and Subtracting Fractions | 分数加减法
Mistake: Simply adding numerators and denominators, e.g. 1/2 + 1/3 = (1+1)/(2+3) = 2/5.
错误：直接将分子与分母分别相加，如 1/2 + 1/3 = (1+1)/(2+3) = 2/5。
Correct: Find the lowest common denominator (LCD). Here LCD is 6. 1/2 = 3/6, 1/3 = 2/6, so 3/6 + 2/6 = 5/6.
正确：先找最小公分母（LCD），此处为6。1/2 = 3/6, 1/3 = 2/6，因此相加得5/6。
Another common slip is forgetting to simplify the answer, e.g. leaving 4/8 instead of 1/2.
另一个常见问题是忘记约分，如结果4/8却未化为1/2。
2. Negative Numbers and BIDMAS | 负数与运算顺序
Mistake: Treating −3² as (−3)², giving 9. However, the index applies only to the 3, so −3² = −9.
错误：将−3²当作(−3)²，得9。但指数仅作用于3，因此−3² = −9。
Correct order (BIDMAS): Brackets, Indices, Division/Multiplication, Addition/Subtraction. For −5², calculate 5² = 25 first, then apply the negative sign → −25.
正确顺序（BIDMAS）：括号、指数、乘除、加减。对于−5²，先算5²=25，再带负号得−25。
Another mistake: 4 − 3 × 2. Some students calculate 4 − 3 = 1, then 1 × 2 = 2. The correct way: multiplication first: 3 × 2 = 6, then 4 − 6 = −2.
另一个错误：4 − 3 × 2。有学生先算4−3=1，然后1×2=2。正确是先乘：3×2=6，然后4−6=−2。
3. Expanding Brackets | 去括号
Common mistake: 3(x + 4) = 3x + 4, forgetting to multiply the 4 by 3.
常见错误：3(x + 4) = 3x + 4，漏乘了4。
Correct: Multiply every term inside the bracket: 3 × x = 3x, 3 × 4 = 12, so 3x + 12.
正确：括号内每一项都要乘：3×x=3x, 3×4=12，得3x+12。
When a negative sign is outside: −2(3x − 5). Error: −2 × 3x = −6x and −2 × −5 = −10, giving −6x − 10. The correct is −6x + 10 because negative × negative = positive.
括号外是负号时：−2(3x − 5)。错误：−6x − 10。正确为−6x + 10，因为负负得正。
4. Solving Linear Equations | 解一元一次方程
Example: 2x + 3 = 11. Incorrect working: 2x = 11 + 3 → 2x = 14 → x = 7.
例：2x + 3 = 11。错误过程：2x = 11 + 3 → 2x = 14 → x = 7。
Correct: To isolate 2x, subtract 3 from both sides: 2x = 11 − 3 = 8, so x = 4.
正确：为了分离2x，两边同时减3：2x = 11 − 3 = 8，因此x = 4。
Another pitfall: After finding 3x = 12, some divide by 3 incorrectly, or forget to divide the constant term. Always perform the same operation on both sides.
另一个陷阱：得到3x=12后，有的人除以3时算错，或忘记常数项也要除。切记等式两边进行相同运算。
5. Angle Facts in Triangles | 三角形角度
Mistake: Given two angles 50° and 60°, using 180° − 50° + 60° = 190° (mixing operations). The sum of angles in a triangle is 180°, so the third angle = 180° − (50° + 60°) = 70°.
错误：已知两角50°和60°，错误地计算180° − 50° + 60° = 190°（运算符号混淆）。三角形内角和180°，第三角 = 180° − (50°+60°) = 70°。
In isosceles triangles, if the vertex angle is 40°, some incorrectly set both base angles to 40° as well. The correct method: (180° − 40°) ÷ 2 = 70° each.
在等腰三角形中，若顶角为40°，有的学生会误将两底角也设为40°。正确：(180°−40°)÷2 = 70°。
6. Area and Perimeter | 面积与周长
Confusion: A rectangle with length 5 cm and width 3 cm. Students often give the area as 16 cm (using perimeter formula). Area = length × width = 15 cm². Perimeter = 2×(5+3) = 16 cm.
混淆：长5厘米、宽3厘米的矩形，学生常常给出面积16厘米（用了周长公式）。面积 = 长×宽 = 15 cm²。周长 = 2×(5+3) = 16 cm。
With compound shapes, forgetting to split into simpler parts or double-counting edges. Always label each section and sum areas correctly.
对于复合图形，忘记分割成简单图形或重复计算边长。务必对各部分标注清楚，正确求和面积。
7. Percentage Increase and Decrease | 百分比增减
Error: Increasing £50 by 20% by simply adding 20 → £70. This treats the percentage as a raw number, not a proportion.
错误：将£50增加20%，直接加20得£70。这错把百分数当成纯数字，而非比例。
Correct: A 20% increase uses the multiplier 1.20. New amount = £50 × 1.20 = £60.
正确：增加20%使用乘数1.20。新金额 = £50 × 1.20 = £60。
Similarly, for a 15% decrease, multiply by 0.85, not subtract 15.
类似地，减少15%应乘以0.85，而非直接减15。
8. Finding the nth Term | 求第n项
Sequence: 5, 9, 13, 17, … Common error: nth term = 4n + 5. Checking n=1 gives 9, not 5.
数列：5, 9, 13, 17, … 常见错误：第n项 = 4n + 5。检验n=1得9，不是5。
Correct: The difference is 4, so the rule is 4n + c. For n=1, 4×1 + c = 5 → c = 1. Hence nth term = 4n + 1.
正确：差为4，所以通项为4n + c。n=
Published by TutorHao | KS3 Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导