📚 IGCSE Maths Practice Workbook: 100 Core Questions | IGCSE 数学练习册 100 道核心题
This workbook brings together 100 carefully selected IGCSE Mathematics questions that target the most common skills tested in Papers 1-4. Working through them helps students improve accuracy, speed and confidence across number, algebra, geometry, statistics and probability.
本练习册汇集了 100 道精选 IGCSE 数学题，针对 Paper 1-4 中最常考查的技能。逐题训练有助于提升学生在数、代数、几何、统计与概率等模块中的准确率、速度与信心。
1. Number and Sets | 数与集合
Number work underpins almost every IGCSE topic. Make sure you can move confidently between integers, fractions, decimals, surds and standard form, and that you understand set notation such as A ∪ B, A ∩ B and A' because these appear regularly in both core and extended papers.
数的运算是 IGCSE 几乎所有主题的基础。要确保自己能熟练地在整数、分数、小数、根式与科学记数法之间转换，并理解 A ∪ B、A ∩ B 和 A' 等集合符号，因为这些内容在 Core 和 Extended 试卷中都经常出现。
Standard form: a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
科学记数法：a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。
ess 0.00046 in standard form. Move the decimal point four places to the right: 4.6 × 10⁻⁴.
示例：将 0.00046 写成科学记数法。把小数点向右移动四位：4.6 × 10⁻⁴。
2. Fractions, Decimals and Percentages | 分数、小数与百分数
Percentages are often tested through word problems. You should be able to convert between forms, calculate percentage change, and work backwards from a final value to find the original amount.
百分数常以应用题形式考查。你应当能够完成各类形式之间的转换，计算百分比变化，并从最终值倒推出原始量。
Percentage change = (change ÷ original) × 100%.
百分比变化 =（变化量 ÷ 原值）× 100%。
Example: A price increases by 15% to $92. The multiplier is 1.15, so original price = 92 ÷ 1.15 = $80.
示例：某商品价格上涨 15% 后为 92 美元。倍数为 1.15，因此原价 = 92 ÷ 1.15 = 80 美元。
3. Ratio and Proportion | 比与比例
een two variables. Direct proportion gives y = kx, while inverse proportion gives y = k/x.
比与比例问题要求你按比例分配数量，并判断两个变量之间的比例类型。正比例对应 y = kx，反比例对应 y = k/x。
Direct proportion: y = kx; In inverse proportion: y = k/x.
正比例：y = kx；反比例：y = k/x。
nal to x and y = 8 when x = 3, find y when x = 6. First k = 8 × 3 = 24, so y = 24 ÷ 6 = 4.
示例：若 y 与 x 成反比，且 x = 3 时 y = 8，求 x = 6 时 y 的值。先算 k = 8 × 3 = 24，所以 y = 24 ÷ 6 = 4。
4. Algebraic Expressions | 代数式
Algebraic manipulation is a high-mark area. Practise expanding products such as (x + a)(x + b), factorising quadratics, using the difference of two squares, and simplifying algebraic fractions with common factors.
代数变形是分值较高的模块。要练习展开形如 (x + a)(x + b) 的乘积、因式分解二次式、运用平方差公式，并化简含公因式的代数分式。
Difference of two squares: a² − b² = (a − b)(a + b).
平方差公式：a² − b² = (a − b)(a + b)。
Example: Factorise 3x² − 12. First take out the common factor: 3(x² − 4), then use the difference of two squares: 3(x − 2)(x + 2).
示例：因式分解 3x² − 12。先提取公因式：3(x² − 4)，再用平方差公式：3(x − 2)(x + 2)。
5. Linear Equations and Inequalities | 线性方程与不等式
Linear equations and inequalities often appear early in Papers 1 and 2. When solving inequalities, remember that multiplying or dividing by a negative number reverses the direction of the inequality sign.
线性方程与不等式常出现在 Paper 1 和 Paper 2 的前半部分。解不等式时，记住乘以或除以负数会改变不等号的方向。
If a < b and c < 0, then ac > bc.
若 a < b 且 c < 0，则 ac > bc。
Example: Solve −2x ≤ 6. Divide
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