📚 Complete Mathematics for Cambridge Secondary 1 Book 2: Year 8 Core Revision | 剑桥初中数学第二册：八年级核心复习
This revision guide covers the main topics in Complete Mathematics for Cambridge Secondary 1 Book 2, designed for Year 8 learners following the CIE Lower Secondary Mathematics curriculum. Use it to consolidate key skills, spot common mistakes, and build confidence before assessments.
本复习指南涵盖《Complete Mathematics for Cambridge Secondary 1 Book 2》的主要专题，适用于学习剑桥初中数学课程的八年级学生。用它来巩固关键技能、发现常见错误，并在考前建立信心。
1. Integers, Powers and Roots | 整数、幂与平方根
, addition and subtraction (BIDMAS). For example, 5 + (−3)² × 2 = 5 + 9 × 2 = 5 + 18 = 23.
在第二册中，学生将整数运算扩展到负数、幂和平方根。必须始终遵循运算顺序：括号、指数、乘除、加减（BIDMAS）。例如 5 + (−3)² × 2 = 5 + 9 × 2 = 5 + 18 = 23。
ays negative: (−2)² = 4 and (−2)³ = −8. This often causes sign errors, so check carefully.
负底数的偶次幂为正，奇次幂仍为负：(−2)² = 4，(−2)³ = −8。这一点经常引起符号错误，请仔细检查。
Square roots and cube roots undo powers: √81 = 9 because 9² = 81; ∛64 = 4 because 4³ = 64. Estimating roots without a calculator is also tested, for example √50 lies between 7 and 8.
平方根和立方根是幂的逆运算：√81 = 9，因为 9² = 81；∛64 = 4，因为 4³ = 64。不借助计算器估算根号也是考点，例如 √50 介于 7 和 8 之间。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
vert between fractions, decimals and percentages fluently. For example, 3/8 = 0.375 = 37.5% o change a fraction to a decimal, and multiply by 100 to change a decimal to a percentage.
你必须能够熟练地在分数、小数和百分数之间转换。例如 3/8 = 0.375 = 37.5%。用除法将分数化为小数，再将小数乘以 100 化为百分数。
4, rewrite as 8/12 + 3/12 = 11/12. For mixed numbers, convert to improper fractions first.
分数的加减需要公分母。计算 2/3 + 1/4 时，先化为 8/12 + 3/12 = 11/12。带分数要先化为假分数。
Percentage increase and decrease are common in real-life problems. A 15% increase on $60 is found by multiplying 60 × 1.15 = $69. A 20% decrease is 60 × 0.80 = $48.
百分数增加和减少在现实问题中很常见。在 60 美元基础上增加 15%，用 60 × 1.15 = 69 美元；减少 20%，则 60 × 0.80 = 48 美元。
3. Ratio, Proportion and Rates | 比、比例与速率
Ratios compare quantities and can be simplified by dividing all parts by the same number. The ratio 24:36 simplifies to 2:3 because both divide by 12.
比用于比较数量，可通过将各部分同时除以同一个数来化简。24:36 化简为 2:3，因为两者都可以除以 12。
To divide a quantity in a given ratio, add the parts first. Divide $90 in the ratio 2:3: the total parts are 2 + 3 = 5, so each part is $18. The amounts are 2 × $18 = $36 and 3 × $18 = $54.
按给定比分配数量时，先求总份数。将 90 美元按 2:3 分配：总份数为 2 + 3 = 5，每份为 18 美元；因此两部分分别为 2 × 18 = 36 美元和 3 × 18 = 54 美元。
a speed = distance ÷ time. A car travelling 180 km in 2 hours has speed 180 ÷ 2 = 90 km/h.
正比例意味着两个量以相同的速率增加或减少。速率（如速度）使用公式：速度 = 路程 ÷ 时间。一辆汽车 2 小时行驶 180 千米，速度为 180 ÷ 2 = 90 千米/小时。
4. Algebraic Expressions and Formulae | 代数表达式与公式
3x + 5y − 2x + y = x + 6y. Only terms with exactly the same variable part can be combined.
第二册的代数重点是合并同类项来化简表达式。例如 3x + 5y − 2x + y = x + 6y。只有变量部分完全相同的项才能合并。
− 3) = 10x − 15. Be careful with signs when the bracket is negative: −2(x + 4) = −2x − 8.
去括号使用分配律：a(b + c) = ab + ac。例如 5(2x − 3) = 10x − 15。括号前为负号时要格外小心：−2(x + 4) = −2x − 8。
a − b² = 4(3) − (−2)² = 12 − 4 = 8. Always use brackets when substituting negative values.
代入法指用数字替换字母。若 a = 3、b = −2，则 4a − b² = 4(3) − (−2)² = 12 − 4 = 8。代入负值时请始终加括号。
5. Linear Equations and Inequalities | 线性方程与不等式
ing the same to both sides. For 3x + 5 = 20, subtract 5: 3x = 15, then divide by 3: x = 5.
解线性方程就是求出使等式成立的未知数值。使用逆运算，并在等式两边同时进行相同操作以保持平衡。例如 3x + 5 = 20，先减 5 得 3x = 15，再除以 3 得 x = 5。
rms. Solve 5x − 4 = 2x + 8: subtract 2x to get 3x − 4 = 8, add 4 to get 3x = 12, so x = 4.
未知数在等号两边的方程需要先移项。解 5x − 4 = 2x + 8：两边同时减去 2x 得 3x − 4 = 8，再加 4 得 3x = 12，因此 x = 4。
dividing by a negative number reverses the sign. For −2x ≤ 6, divide by −2 to get x ≥ −3.
不等式的解法与方程类似，但乘以或除以负数时不等号方向要改变。例如
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