📚 Cambridge KS3 Maths Paper 2 Revision: Core Skills | 剑桥KS3数学卷二复习：核心技能
This article reviews the core skills tested in the Cambridge KS3 mathematics Paper 2, focusing on number, algebra, geometry and data handling. Use it alongside your practice paper to spot gaps and improve accuracy.
本文复习剑桥KS3数学卷二考查的核心技能，重点包括数、代数、几何与数据处理。请结合练习卷使用，找出薄弱点并提高正确率。
1. Place Value and Rounding | 数位与四舍五入
Know place value from millions down to thousandths. When rounding to a given place, look at the next digit; if it is 5 or more, round up.
要掌握百万位到千分位的数位。四舍五入到某一位时，看下一位数字；如果是 5 或更大，就进位。
Example: 12345.678 rounded to two decimal places is 12345.68 because the third decimal digit is 8.
例如：12345.678 保留两位小数后是 12345.68，因为第三位小数是 8。
- Place value chart: millions, hundred thousands, ten thousands, thousands, hundreds, tens, units, tenths, hundredths, thousandths.
- 数位表：百万位、十万位、万位、千位、百位、十位、个位、十分位、百分位、千分位。
2. Factors, Multiples and Primes | 因数、倍数与质数
A factor divides exactly into a number. A multiple is the product of a number and an integer. Prime numbers have exactly two factors: 1 and themselves.
因数能整除一个数。倍数是一个数与整数相乘的结果。质数只有两个因数：1 和它本身。
Prime factorisation breaks a number into powers of primes. The lowest common multiple (LCM) and highest common factor (HCF) are useful when comparing fractions.
质因数分解把一个数拆成质数的幂。最小公倍数（LCM）和最大公因数（HCF）在比较分数时很有用。
72 = 2³ × 3²
The prime numbers below 20 are 2, 3, 5, 7, 11, 13, 17 and 19.
20 以内的质数有 2、3、5、7、11、13、17 和 19。
3. Fractions: Four Operations | 分数：四则运算
To add or subtract fractions, write them with a common denominator. To multiply, multiply numerators and multiply denominators. To divide, multiply by the reciprocal.
分数加减要先通分；乘法直接分子乘分子、分母乘分母；除法要乘以倒数。
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Mixed numbers should be changed to improper fractions before multiplying or dividing. Always simplify your final answer where possible.
带分数在乘除前要先化为假分数。最终答案要尽量约简。
- 2/3 × 3/4 = 6/12 = 1/2
- 2/3 × 3/4 = 6/12 = 1/2
4. Decimals and Percentages | 小数与百分数
Convert a percentage to a decimal by dividing by 100. To find a percentage of an amount, change the percentage to a decimal and multiply.
百分数除以 100 可化为小数。求一个数的百分之几，先把百分数化成小数再相乘。
| Fraction | Decimal | Percentage |
| 1/4 | 0.25 | 25% |
| 1/2 | 0.5 | 50% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
Percentage increase or decrease is found by working out the change and dividing by the original amount, then multiplying by 100.
百分数增减题：先算出变化量，除以原量，再乘以 100。
5. Ratio and Proportion | 比与比例
Share a quantity in a given ratio by dividing by the total number of parts and multiplying by each part. Direct proportion can be modelled with equivalent ratios.
按给定比例分配，先除以总份数，再乘以各部分份数。正比例可以用等值比来建模。
Example: divide £120 in the ratio 3:2. Total parts = 3 + 2 = 5, so one part is £120 ÷ 5 = £24. The shares are £72 and £48.
例如：把 120 英镑按 3:2 分配。总份数 = 3 + 2 = 5，一份为 120 ÷ 5 = 24 英镑。两部分分别是 72 英镑和 48 英镑。
al number of students is 5 + 7 = 12 parts; one part is 35 ÷ 7 = 5, so total = 12 × 5 = 60.
如果男孩与女孩的比是 5:7，女孩有 35 人，总份数为 5 + 7 = 12；一份为 35 ÷ 7 = 5，所以总人数 = 12 × 5 = 60。
6. Algebraic Expressions | 代数式
Collect like terms by adding or subtracting coefficients. Use the distributive law to expand brackets, then simplify.
合并同类项时只加减系数；用分配律去括号，再化简。
3(x + 4) - 2(x - 1) = 3x + 12 - 2x + 2 = x + 14
Remember to multiply every term inside the bracket by the term outside. Be careful with negative signs.
记住括号外的项要乘括号内每一项。注意负号处理。
- 4a + 3b - 2a + b = 2a + 4b
- 4a + 3b - 2a + b = 2a + 4b
7. Solving Linear Equations | 解一元一次方程
Use inverse operations in balance steps. Keep the equation balanced by doing the same operation to both sides.
用逆运算逐步解方程；两边同时进行相同运算以保持平衡。
2x + 3 = 11 → 2x = 8 → x = 4
When letters appear on both sides, collect the variable terms on one side first. Then isolate the variable by using inverse operations.
当未知数在等号两边时，先把含未知数的项移到同一边。再用逆运算求出未知数。
Check your answer by substituting it back into the original equation.
把答案代回原方程检验。
8. Angles and Triangles | 角与三角形
Angles on a straight line add to 180°, angles around a point add to 360°, and the angles in a triangle add to 180°.
平角为 180°，周角为 360°，三角形内角和为 180°。
An equilateral triangle has three 60° angles. An isosceles triangle has two equal sides and two equal base angles. A right-angled triangle has one 90° angle.
等边三角形三个角都是 60°。等腰三角形有两条等边和两个相等的底角。直角三角形有一个 90° 角。
- If a triangle has angles 45° and 60°, the third angle = 180° - 45° - 60° = 75°.
- 如果一个三角形两角为 45° 和 60°，第三个角 = 180° - 45° - 60° = 75°。
9. Perimeter, Area and Volume | 周长、面积与体积
shape. Area of a rectangle = length × width. Volume of a cuboid = length × width × height.
周长是图形一周的长度；长方形面积 = 长 × 宽；长方体体积 = 长 × 宽 × 高。
Area triangle = ½ × base × height
For compound shapes, split them into rectangles or triangles, find each area, then add or subtract as needed.
对组合图形，可拆分成矩形或三角形，分别求面积，再按需要加减。
Volume of a cuboid is found by multiplying the three dimensions. Units must be cubic, such as cm³ or m³.
长方体体积用三条边相乘求得。单位要使用立方单位，例如 cm³ 或 m³。
10. Coordinates and Graphs | 坐标与图像
Plot points using (x, y). The x-coordinate moves left or right; the y-coordinate moves up or down. Straight-line graphs can be drawn from a table of values.
用 (x, y) 描点；x 坐标控制左右移动，y 坐标控制上下移动。直线图可从数值表画出。
values might be (0,1), (1,3), (2,5). Plot these points and join them with a straight line.
对于 y = 2x + 1，数值表可以是 (0,1)、(1,3)、(2,5)。描点后用直线连接。
Midpoint of two points is found by averaging the x-coordinates and averaging the y-coordinates.
两点的中点坐标：将两个 x 坐标求平均，再将两个 y 坐标求平均。
11. Averages and Data Handling | 平均数与数据处理
Mean is the sum divided by the number of values. Median is the middle value when ordered; mode is most frequent; range is highest minus lowest.
平均数 = 总和 ÷ 个数；中位数是排序后中间的数；众数是出现最多的数；极差 = 最大值减最小值。
Example: data 4, 7, 7, 9, 10 has mean 7.4, median 7, mode 7, and range 6.
例如：数据 4、7、7、9、10 的平均数为 7.4，中位数为 7，众数为 7，极差为 6。
When reading bar charts, pictograms or pie charts, check the key or scale carefully before answering frequency questions.
阅读条形图、象形图或饼图时，先仔细查看图例或刻度，再回答频数问题。
12. Problem-Solving Checklist | 问题解决检查清单
Read carefully, underline key numbers, choose a strategy, show clear working, check units and reasonableness. Use estimation to catch silly mistakes.
仔细读题，圈画关键数字，选择策略，展示清晰步骤，检查单位与合理性。用估算找出低级错误。
- Understand the problem and identify what is asked.
- 理解题意，明确要求什么。
- Plan a method: equation, ratio, table, diagram or trial and improvement.
- 制定方法：方程、比例、表格、图形或试错法。
- Execute the plan step by step and show all working.
- 按步骤执行并展示全部过程。
- Check the answer in the original context.
- 把答案放回原题情境中检查。
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