GCSE Maths Complete Study Guide | GCSE数学完整学习指南
Everything you need to ace GCSE Mathematics — from Foundation basics to Grade 9 Higher tier mastery.
攻克GCSE数学所需的一切——从基础入门到9分高级掌握。
📐 Foundation vs Higher Tier | 基础级 vs 高级
| Foundation 基础 | Higher 高级 |
|---|---|
| Grades 1-5 | Grades 4-9 |
| Covers basic arithmetic to simple algebra | Includes advanced algebra, trigonometry, vectors |
| Best for: Students targeting a pass (Grade 4-5) | Best for: Students targeting Grade 6+ for A-Level Maths |
Rule of thumb: If you’re considering A-Level Maths or sciences, take Higher tier. Foundation caps at Grade 5.
经验法则: 若考虑A-Level数学或科学，选Higher。Foundation最高只能拿到Grade 5。
📊 Key Topics Breakdown | 核心主题
1. Number / 数 (15-25% of exam)
Fractions, decimals, percentages, HCF/LCM, standard form, surds (Higher), bounds. Calculator and non-calculator skills essential.
分数、小数、百分比、最大公约数/最小公倍数、标准形式、根式(Higher)、界限。计算器和非计算器技能都很重要。
2. Algebra / 代数 (20-30%)
Equations, inequalities, sequences, graphs, quadratic equations, simultaneous equations, functions (Higher), iteration (Higher). The biggest section — master this.
方程、不等式、数列、图像、二次方程、联立方程、函数(Higher)、迭代(Higher)。最大章节——必须掌握。
3. Ratio, Proportion & Rates of Change / 比率与比例 (15-25%)
Ratio notation, direct/inverse proportion, compound measures (speed, density), percentage change, growth and decay. Real-world applications.
比率表示法、正/反比例、复合度量(速度、密度)、百分比变化、增长与衰减。实际应用。
4. Geometry & Measures / 几何与测量 (15-20%)
Angles, circles, Pythagoras, trigonometry, vectors (Higher), transformations, area/volume, congruence and similarity.
角、圆、勾股定理、三角学、向量(Higher)、变换、面积/体积、全等与相似。
5. Probability & Statistics / 概率与统计 (10-15%)
Venn diagrams, tree diagrams, conditional probability (Higher), mean/median/mode, cumulative frequency, box plots, histograms (Higher).
维恩图、树形图、条件概率(Higher)、平均数/中位数/众数、累积频率、箱线图、直方图(Higher)。
🏫 Exam Board Differences | 考试局差异
- Edexcel: Most popular. 3 papers (1 non-calc + 2 calc). Well-structured with clear mark schemes.
最流行。3张卷（1非计算器+2计算器）。结构清晰，评分标准明确。 - AQA: Slightly more wordy questions. Emphasis on problem-solving in context.
题目文字稍多。重视情境中的问题解决。 - OCR: Includes more “explain your reasoning” style questions. Foundation has less algebra than Edexcel.
包含更多”解释你的推理”式问题。Foundation代数少于Edexcel。
🔢 Calculator Tips & Common Mistakes | 计算器技巧与常见错误
- Always check calculator mode: Degrees vs radians — wrong mode can lose you 10+ marks on trigonometry.
始终检查计算器模式：角度vs弧度——模式错误可在三角题丢10+分。 - Show your working: Even if you get the final answer wrong, method marks can save you.
展示计算过程：即使最终答案错误，方法分可以救你。 - Units, units, units: Forgetting to convert cm² to m² is the #1 silly mistake.
单位、单位、单位：忘记cm²转m²是头号低级错误。 - Check your answer makes sense: A probability of 2.5 or a negative length means you’ve gone wrong.
检查答案是否合理：概率2.5或负数长度意味着你算错了。
📅 Study Schedule Template | 学习计划模板
| Week | Focus | Practice |
|---|---|---|
| 1-2 | Number + Algebra basics | 30 min daily, Paper 1 non-calc each weekend |
| 3-4 | Geometry + Ratio | Topic-specific worksheets, 1 timed paper |
| 5-6 | Advanced Algebra + Statistics | 2 full papers per week, timed |
| 7-8 | Weak areas + Exam technique | 3 papers/week, review mistakes in detail |
📞 Need GCSE Maths tutoring? | 需要GCSE数学辅导？
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