📚 Cambridge KS3 Mathematics Practice Page p27_2: Core Skills and Worked Examples | 剑桥 KS3 数学 p27_2 练习页：核心技能与例题解析
, algebra, geometry and data skills that most students meet in Lower Secondary, with clear worked examples and paired bilingual explanations.
本文配套剑桥 KS3 数学练习页 p27_2，复习初中阶段最常见的数、代数、几何与数据核心技能，并配有清晰的例题和双语讲解。
1. Understanding Integers and Negative Numbers | 整数与负数运算
e number is the same as subtracting its positive value. For example, 7 + (-4) = 7 - 4 = 3.
加上一个负数等同于减去它的相反数。例如 7 + (-4) = 7 - 4 = 3。
When multiplying or dividing two numbers with the same sign, the result is positive; when the signs are different, the result is negative.
两个同号的数相乘或相除，结果为正；两个异号的数相乘或相除，结果为负。
(-6) × (-3) = 18 and (-8) ÷ 2 = -4
Use a number line if you are unsure: moving left subtracts, moving right adds.
如果不确定，可以使用数轴：向左移动表示减，向右移动表示加。
2. BIDMAS / Order of Operations | 运算顺序 BIDMAS
BIDMAS tells you the correct order: Brackets, Indices, Division and Multiplication, Addition and Subtraction.
BIDMAS 告诉你正确的运算顺序：括号、指数、除法和乘法、加法和减法。
Always complete division and multiplication from left to right, then addition and subtraction from left to right.
除法和乘法要按照从左到右的顺序完成，加法和减法也要按照从左到右的顺序完成。
20 - 3 × 4 = 20 - 12 = 8
ate 20 - 3 first. Because multiplication has a higher priority, you must find 3 × 4 first.
常见的错误是先计算 20 - 3。因为乘法的优先级更高，所以必须先计算 3 × 4。
3. Fractions: Simplify, Add and Subtract | 分数的化简、加法和减法
To simplify a fraction, divide the numerator and denominator by their highest common factor. For example, 12/16 simplifies to 3/4.
化简分数时，用分子和分母的最大公因数同时去除它们。例如 12/16 化简为 3/4。
To add or subtract fractions, first rewrite them with a common denominator. Then add or subtract the numerators only.
分数加减法需要先将它们化为同分母分数，然后只对分子进行加减。
1/4 + 1/6 = 3/12 + 2/12 = 5/12
When multiplying fractions, multiply the numerators and multiply the denominators. Simplify the result if possible.
分数相乘时，分子乘分子，分母乘分母。如果可能，最后要化简结果。
4. Decimals and Place Value | 小数与位值
Multiplying by 10 moves every digit one place to the left; dividing by 10 moves every digit one place to the right.
乘以 10 会使每个数字向左移动一位；除以 10 会使每个数字向右移动一位。
When you multiply decimals, first ignore the decimal points and multiply the whole numbers, then put the decimal point back according to the total number of decimal places.
小数相乘时，先忽略小数点并把它们当作整数相乘，然后根据小数位数的总和把小数点放回结果中。
0.6 × 0.2 = 0.12
Check place value carefully: 0.12 has 1 tenth and 2 hundredths, not 12 tenths.
仔细检查位值：0.12 表示 1 个十分位和 2 个百分位，而不是 12 个十分位。
5. Converting Fractions, Decimals and Percentages | 分数、小数和百分比的互化
To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100.
把分数化为小数时，用分子除以分母。把小数化为百分数时，乘以 100。
To change a percentage to a fraction, write it over 100 and simplify if possible.
把百分数化为分数时，先写成分母为 100 的分数，然后尽可能化简。
| Fraction 分数 | Decimal 小数 | Percentage 百分数 |
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 2/5 | 0.4 | 40% |
Knowing these common conversions by heart saves time in mental calculations and word problems.
熟记这些常见的互化关系可以节省心算和应用题的时间。
6. Introduction to Algebra: Collecting Like Terms | 代数入门：合并同类项
Like terms contain exactly the same letter or combination of letters. You can add or subtract their coefficients.
同类项含有完全相同的字母或字母组合。你可以对它们的系数进行加减。
3a + 2b - a + 5b = 2a + 7b
Expanding brackets means multiplying each term inside the bracket by the term outside.
去括号是指用括号外的项乘以括号内的每一项。
3(x + 4) = 3x + 12
After expanding, always check whether any like terms can be collected to simplify further.
去括号后，要检查是否可以合并同类项，以便进一步化简。
7. Solving One-Step and Two-Step Equations | 解一步和两步方程
An equation is like a balance: whatever you do to one side, you must do to the other side.
方程就像一个天平：你对一边做什么，就必须对另一边做同样的操作。
ne-step equation, use the inverse operation. For example, x + 7 = 12 gives x = 12 - 7 = 5.
解一步方程时，使用逆运算。例如 x + 7 = 12，得到 x = 12 - 7 = 5。
For a two-step equation, undo addition or subtraction first, then undo multiplication or division.
解两步方程时，先处理加法或减法，再处理乘法或除法。
2x - 3 = 9 → 2x = 12 → x = 6
Always substitute your answer back into the original equation to check it works.
一定要把答案代回原方程检验它是否正确。
8. Area and Perimeter of Rectangles | 矩形的面积与周长
imeter is the total distance around the outside of a shape. For a rectangle, P = 2(l + w).
周长是图形外边线的总长度。对于矩形，P = 2(l + w)。
Area measures the space inside a shape. For a rectangle, A = l × w.
面积度量图形内部的空间。对于矩形，A = l × w。
For l = 8 cm and w = 5 cm: P = 26 cm, A = 40 cm²
Always write the correct units: cm for perimeter, cm² for area, and m² for larger spaces.
一定要写对单位：周长用 cm，面积用 cm²，较大的空间用 m²。
9. Angles on a Straight Line and Around a Point | 平角与周角
Angles on a straight line add up to 180°. Angles around a point add up to 360°.
平角上的角度之和为 180°。绕一点一周的角度之和为 360°。
Vertically opposite angles formed by two crossing lines are equal.
两条相交直线形成的对顶角相等。
If one angle is 65° on a straight line, the other is 180° - 65° = 115°
Look for straight lines and full turns in diagrams to set up simple angle equations.
在图中寻找直线和完整的一周，可以帮助建立简单的角度方程。
10. Mean, Median, Mode and Range | 平均数、中位数、众数和极差
The mean is found by adding all values and dividing by the number of values.
平均数是将所有数值相加后除以数值的个数。
The median is the middle value after the data has been put in order. If there are two middle numbers, find their average.
中位数是将数据排序后位于中间的数。如果有两个中间数，就取它们的平均数。
The mode is the most frequent value, and the range is the largest value minus the smallest value.
众数是出现次数最多的值，极差是最大值减去最小值。
For 4, 7, 8, 10, 10, 12: mean = 8.5, median = 9, mode = 10, range = 8
Ordering the data first makes the median and range much easier to find accurately.
先将数据排序，能更准确地找到中位数和极差。
11. Probability Scale and Simple Events | 概率刻度与简单事件
Probability is a number from 0 to 1, where 0 means impossible and 1 means certain.
概率是 0 到 1 之间的一个数，0 表示不可能，1 表示必然发生。
For equally likely outcomes, probability equals the number of favourable outcomes divided by the total number of outcomes.
对于等可能的结果，概率等于有利结果的数量除以总结果的数量。
P(red) from 3 red and 5 blue counters = 3/8
A probability closer to 1 means the event is more likely; closer to 0 means it is less likely.
概率越接近 1，事件越可能发生；越接近 0，则越不可能发生。
12. Exam-Style Tips for p27_2 | p27_2 考试风格提示
Always show your method, even for short questions. Marks are given for correct working, not just the final answer.
即使是简答题也要写出解题过程。评分不仅看最终答案，也看正确的步骤。
Use estimation to check whether your answer is sensible, especially when working with decimals and fractions.
用估算检查答案是否合理，尤其是在处理小数和分数时。
Keep an eye on units, signs and order of operations. Small accuracy errors are often the difference between full marks and lost marks.
注意单位、符号和运算顺序。小的准确性错误常常是满分与失分之间的差别。
If you are stuck on a multi-step problem, break it into smaller parts and write down what you already know.
如果多步问题卡住了，把它拆成几个小部分，并写下你已经知道的条件。
Published by TutorHao | Mathematics Revision Series | aleveler.com
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