KS3 Maths: Common Errors Explained | KS3 数学：易错题精讲

📚 KS3 Maths: Common Errors Explained | KS3 数学：易错题精讲

Many KS3 students lose marks not because they don’t know the methods, but because they fall into common traps set by typical exam questions. This article breaks down the most frequent mistakes in number, algebra, geometry and data handling, and shows you how to avoid them.

许多KS3学生丢分不是因为他们不懂方法，而是因为掉进了常见考题的陷阱。本文剖析了在数、代数、几何和数据处理中最常见的错误，并教你如何避免它们。

1. Negative Number Operations | 负数运算

A classic mistake is multiplying two negative numbers and still getting a negative. Remember: a negative times a negative makes a positive.

一个经典的错误是两负数相乘结果还是负数。记住：负负得正。

Wrong: (-3) × (-2) = -6 → Correct: (-3) × (-2) = 6

错误: (-3) × (-2) = -6 → 正确: (-3) × (-2) = 6

Another tricky area is adding and subtracting negatives. For example, 5 – (-2) becomes 5 + 2 = 7, not 3. Students often treat subtracting a negative as just subtracting a positive.

另一个容易出错的地方是加减负数。例如，5 – (-2) 变成 5 + 2 = 7，而不是 3。学生常把减去负数当作仅仅减去正数。

Also, when a number is written as -5 – 3, the correct result is -8, but many pupils mistakenly give -2 because they incorrectly combine signs.

还有，当算式写成 -5 – 3 时，正确结果是 -8，但许多学生错写成 -2，因为他们错误地合并了符号。

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2. Adding and Subtracting Fractions | 分数加减

The most common error is adding numerators and denominators directly. For instance, 1/2 + 1/3 is not 2/5. You must find a common denominator first.

最常见的错误是直接分子加分子、分母加分母。例如，1/2 + 1/3 不是 2/5。你必须先求公分母。

Correct: 1/2 = 3/6, 1/3 = 2/6, so 3/6 + 2/6 = 5/6.

正确: 1/2 = 3/6, 1/3 = 2/6, 所以 3/6 + 2/6 = 5/6.

When subtracting, the same rule applies: convert to equivalent fractions with the same denominator. Many students also forget to simplify their final answer.

减法同样适用：转换成同分母的等价分数后再减。许多学生还忘记化简最终答案。

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3. Algebraic Simplification | 代数化简

One of the biggest misconceptions is adding unlike terms. For example, 3a + 2b cannot be simplified to 5ab. Only like terms (same letter and same power) can be added or subtracted.

最大的误解之一是不同类项相加。例如，3a + 2b 不能化简成 5ab。只有同类项（字母和指数都相同）才能加减。

Mistake: 5x – x = 5 → Correct: 5x – x = 4x

错误: 5x – x = 5 → 正确: 5x – x = 4x

When multiplying terms, however, you can combine letters: 2a × 3b = 6ab. But (a + b)² is not a² + b² – a common expansion error.

然而，在乘法中可以组合字母：2a × 3b = 6ab。但是 (a + b)² 不等于 a² + b² —— 这是一个常见的展开错误。

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4. Solving Linear Equations | 解一次方程

Solving equations like 2x + 3 = 11 often trips up students when moving terms. The key is to perform the same operation on both sides. Common mistake: subtracting 3 from the left but not from the right.

解像 2x + 3 = 11 这样的方程时，学生常在移项时出错。关键是要在等号两边执行相同的运算。常见错误：左边减了3，右边却忘了减。

Correct steps: 2x + 3 = 11 → 2x = 8 → x = 4.

正确步骤: 2x + 3 = 11 → 2x = 8 → x = 4.

With brackets, many try to divide first but forget to divide every term. For 3(x – 2) = 12, you can either expand: 3x – 6 = 12 → 3x = 18 → x = 6, or divide both sides by 3 first: x – 2 = 4 → x = 6. Avoid the trap of writing 3x – 2 = 12.

遇到括号时，很多学生想先除以系数却忘了除以每一项。对于 3(x – 2) = 12，你可以先展开：3x – 6 = 12 → 3x = 18 → x = 6，或者两边先除以 3：x – 2 = 4 → x = 6。避免写出 3x – 2 = 12 这样的陷阱式写法。

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5. Area and Perimeter Confusion | 面积与周长混淆

Students frequently mix up the formulas for area and perimeter of rectangles. Perimeter is the distance around the shape (add all sides), area is the space inside (length × width).

学生常常把矩形的面积和周长公式搞混。周长是围绕形状一周的长度（所有边长相加），面积是内部的区域大小（长 × 宽）。

A rectangle with length 8 cm and width 5 cm: Perimeter = 2×(8+5) = 26 cm. Area = 8×5 = 40 cm². Students often give area as 26 cm² or perimeter as 40 cm.

一个长8厘米、宽5厘米的矩形：周长 = 2×(8+5) = 26 厘米。面积 = 8×5 = 40 平方厘米。学生常常把面积错写成 26 平方厘米，或把周长写成 40 厘米。

For triangles, the area formula is ½ × base × height. Forgetting the ½ is a typical error. Using a slanted side as the height is another.

对于三角形，面积公式是 ½ × 底 × 高。忘记乘 ½ 是典型的错误。把斜边当作高来用也是另一个错误。

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6. Ratio and Proportion | 比和比例

When sharing a quantity in a given ratio, students sometimes just use the ratio numbers as the amounts. For example, share £50 in the ratio 2:3. The correct method is to add the parts: 2+3=5, then £50÷5=£10 per part. So amounts are 2×£10=£20 and 3×£10=£30. Not £2 and £3!

当按给定比例分配一个数量时，学生有时直接用比例数字作为数量。例如，按 2:3 分配 50 英镑。正确方法是先求总份数：2+3=5，然后 50÷5=10 每份。所以金额是 2×10=20 英镑和 3×10=30 英镑。而不是 2 英镑和 3 英镑！

Another frequent error is simplifying ratios incorrectly. 8:12 simplifies to 2:3, not 4:6 because 4:6 can be simplified further.

另一个常见错误是化简比不正确。8:12 化简后是 2:3，而不是 4:6，因为 4:6 还能继续化简。

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7. Percentage Calculations | 百分数计算

Many believe that if you increase a number by 10% and then decrease the result by 10%, you get the original. This is false. An increase of 10% multiplies by 1.1, a decrease of 10% multiplies by 0.9. Together: 1.1 × 0.9 = 0.99, so you end up with 99% of the original.

许多人以为一个数先增加10%再减少10%会回到原数。这是错误的。增加10%是乘以 1.1，减少10%是乘以 0.9。综合：1.1 × 0.9 = 0.99，最终得到原数的 99%。

Also, when finding a percentage of an amount, students sometimes misplace the decimal point. 15% of 60 is 0.15 × 60 = 9, not 1.5 × 60 = 90.

还有，在求一个数的百分之几时，学生会点错小数点。60的15%是 0.15 × 60 = 9，而不是 1.5 × 60 = 90。

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8. Powers and Indices | 幂与指数

A power like 2³ means 2 × 2 × 2 = 8, not 2 × 3 = 6. This misunderstanding leads to many errors.

像 2³ 这样的幂表示 2 × 2 × 2 = 8，而不是 2 × 3 = 6。这种误解导致很多错误。

When raising a product to a power, the exponent applies to all factors inside the parentheses: (2x)² = 2² × x² = 4x². It is wrong to write 2x².

当把乘积做乘方时，指数作用于括号内的每一个因子：(2x)² = 2² × x² = 4x²。写成 2x² 是错误的。

Even with numerical bases, (3+2)² is not 3² + 2², it’s 5² = 25. Always follow order of operations.

即使是数字底数，(3+2)² 不等于 3² + 2²，而是 5² = 25。一定要遵循运算顺序。

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9. Rounding and Significant Figures | 四舍五入与

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