📚 IGCSE Mathematics 0607: Complete Revision Guide | IGCSE 数学 0607 完整复习指南
This revision guide covers the key knowledge and skills required for Cambridge IGCSE International Mathematics 0607. It is designed to help you consolidate Core and Extended topics, build confidence with exam-style problem solving, and avoid common mistakes under timed conditions.
本复习指南涵盖剑桥 IGCSE 国际数学 0607 的核心知识与技能，帮助你巩固 Core 与 Extended 主题、提升考试型问题解决能力，并避免限时考试中的常见错误。
1. Course Structure: Core and Extended | 课程结构：Core 与 Extended
Cambridge IGCSE International Mathematics 0607 is offered at two tiers. Core covers grades D to G and concentrates on essential techniques; Extended covers grades A* to E and extends into algebraic manipulation, trigonometry, vectors and structured reasoning.
剑桥 IGCSE 国际数学 0607 分为两个层级。Core 覆盖 D 至 G 等级，侧重基本技能；Extended 覆盖 A* 至 E 等级，并在代数变形、三角、向量与结构化推理方面要求更高。
Core candidates normally sit the two Core written papers plus the Core investigation paper, while Extended candidates sit the two Extended written papers plus the Extended investigation paper. The non-calculator papers test fluency, the calculator papers test modelling and multi-step problem solving, and the final paper is an open-ended investigation or modelling task. Always confirm exact timings and weightings in the current syllabus.
Core 考生通常参加两份 Core 笔试卷与 Core 探究卷，Extended 考生参加两份 Extended 笔试卷与 Extended 探究卷。不允许使用计算器的试卷考查运算熟练度，允许使用计算器的试卷考查建模与多步问题解决，最后一份试卷是开放式探究或建模任务。具体时长与权重请以最新考纲为准。
| Component | Calculator | Focus |
| Paper 1 / Paper 3 | Not allowed | Number, algebra, exact values |
| Paper 2 / Paper 4 | Allowed | Applied and multi-step problems |
| Paper 5 / Paper 6 | Allowed | Investigation and modelling |
Because Extended work builds directly on Core content, the most efficient revision plan covers both: secure the Core techniques first, then push them into unfamiliar contexts, algebraic fractions and justification tasks.
由于 Extended 内容直接建立在 Core 之上，最高效的复习计划是两者兼顾：先牢固掌握 Core 技能，再拓展到陌生情境、代数分式与论证任务。
2. Number, Fractions, Decimals and Percentages | 数、分数、小数与百分数
Number is the foundation of all IGCSE topics. You must be confident with integers, fractions, decimals and percentages, and with the order of operations, usually remembered as BIDMAS: brackets, indices, division and multiplication, then addition and subtraction.
数是所有 IGCSE 主题的基础。你必须熟练掌握整数、分数、小数与百分数，以及运算顺序——通常记作 BIDMAS：括号、指数、乘除，最后加减。
Fraction skills include converting between mixed numbers and improper fractions, carrying out the four operations, and moving fluently between fractions, decimals and percentages. Percentage questions go well beyond simple calculation: expect percentage increase and decrease, reverse percentages, simple and compound interest, and percentage error.
分数技能包括带分数与假分数的互化、四则运算，以及在分数、小数、百分数之间灵活转换。百分数题目远不止简单计算：需要掌握百分数增减、逆百分数、单利与复利，以及百分误差。
Percentage change = (change ÷ original value) × 100%
Compound interest: A = P × (1 + r ÷ 100)ⁿ
Ratio, proportion and rate problems appear in both tiers. Use the unitary method for direct and inverse proportion, keep units consistent throughout a calculation, and treat map scales and unit conversions with care, because a single unit slip can lose all the method marks in a multi-step question.
比、比例与速率问题在两个层级都会出现。正比例与反比例可用归一法处理，计算过程中保持单位一致，并谨慎对待地图比例尺与单位换算，因为一次单位失误就可能让一道多步题失去全部方法分。
3. Powers, Surds and Standard Form | 幂、根式与标准形式
ᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1 and a⁻ⁿ = 1 ÷ aⁿ. Fractional indices link directly to roots, so a1/2 = √a and a1/3 = ∛a.
指数法则必须做到条件反射：aᵐ × aⁿ = aᵐ⁺ⁿ，aᵐ ÷ aⁿ = aᵐ⁻ⁿ，(aᵐ)ⁿ = aᵐⁿ，a⁰ = 1，a⁻ⁿ = 1 ÷ aⁿ。分数指数与根式直接相通，因此 a1/2 = √a，a1/3 = ∛a。
Surds should be simplified rather than approximated: √48 = 4√3, and √2 × √8 = 4. To rationalise a denominator such as 1 ÷ (3 + √2), multiply numerator and denominator by the conjugate 3 − √2. Leaving an answer as a simplified surd is usually required when the question asks for an exact value.
根式应化简而不应取近似值：√48 = 4√3，√2 × √8 = 4。要化简形如 1 ÷ (3 + √2) 的分母，可将分子分母同乘共轭式 3 − √2。当题目要求精确值时，通常需要保留化简后的根式。
s used for very large or very small quantities and for non-calculator work; remember that multiplying adds the indices while dividing subtracts them, and adjust the final answer if a falls outside the range.
标准形式写作 a × 10ⁿ，其中 1 ≤ a < 10，n 为整数。它用于表示极大或极小的量，也用于无计算器运算；记住乘法时指数相加、除法时指数相减，若 a 超出范围需再次调整。
4. Set Notation and Venn Diagrams | 集合记号与韦恩图
Set notation is essential for questions involving Venn diagrams, counting problems and probability. The symbol ∈ means "is a member of", ∉ means "is not a member of", and ∅ represents the empty set. For a set A, n(A) gives the number of elements.
集合记号在涉及韦恩图、计数问题与概率的题目中至关重要。符号 ∈ 表示"属于"，∉ 表示"不属于"，∅ 表示空集。对于集合 A，n(A) 表示其元素个数。
The complement A′ contains all elements not in A, A ∪ B means the union of A and B, and A ∩ B means the intersection. The universal set is written ξ and contains every element under discussion, while A ⊆ B means A is a subset of B.
补集 A′ 包含所有不在 A 中的元素，A ∪ B 表示 A 与 B 的并集，A ∩ B 表示交集。全集记作 ξ，包含所讨论的全部元素，A ⊆ B 表示 A 是 B 的子集。
three-set problems, start in the centre and work outwards, or use the counting formula n(A ∪ B) = n(A) + n(B) − n(A ∩ B) to check your diagram.
画两集合韦恩图时，先标出四个区域再开始计算，并记住交集同时属于两个集合。三
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