📚 Year 10 CIE Maths: Complete Syllabus Breakdown | CIE 十年级数学：课程大纲全面解析
If you're in Year 10 studying for the CIE IGCSE Mathematics (0580) exam, understanding the full syllabus is your first step towards exam success. This guide breaks down every topic, explains how the assessment works, and highlights exactly what you need to know – making it much easier to plan your revision and focus on the key areas that carry the most marks.
如果你正在十年级学习 CIE IGCSE 数学（0580），全面了解课程大纲是走向考试成功的第一步。这份指南逐一拆解全部课题，解释评估方式，并明确指出你需要掌握的核心内容——让你更轻松地规划复习，把精力集中在分值最高的关键板块。
1. Syllabus Overview | 课程大纲概览
The CIE IGCSE Mathematics syllabus (0580) covers a broad range of mathematical knowledge and skills, organised into nine content areas. It is available at two tiers: Core (grades C–G) and Extended (grades A*–E). Year 10 normally covers the initial half of the syllabus, building foundations before moving to more demanding topics in Year 11.
CIE IGCSE 数学大纲（0580）涵盖广泛的数学知识与技能，编排为九大内容领域。考试分为两个级别：核心课程（成绩等级 C 至 G）和扩展课程（A* 至 E）。十年级通常完成前半部分大纲的学习，为升入十一年级后接触更具挑战性的专题打好基础。
All candidates are assessed through two externally marked written papers, with no coursework. Both papers allow the use of a scientific calculator, and a formula sheet is provided in the exam for selected mensuration formulas. Knowing this structure early helps Year 10 students pace their learning effectively.
所有考生均通过两份外部评分的书面试卷进行评估，不设课程作业。两份试卷均允许使用科学计算器，考试时会提供包含部分测量公式的公式表。提前了解这一结构，能帮助十年级学生有效地把握学习节奏。
2. Assessment Objectives & Exam Structure | 评估目标与考试结构
The syllabus sets out four main assessment objectives: AO1 (Knowledge and understanding of mathematical techniques), AO2 (Application of techniques to solve problems), AO3 (Analysis and interpretation of mathematical information), and AO4 (Communication and reasoning). Throughout Year 10, teachers design lessons to develop all four skills simultaneously.
大纲规定了四项主要评估目标：AO1（对数学方法的知识与理解）、AO2（运用方法解决问题）、AO3（分析与解读数学信息）以及 AO4（交流与推理）。在整个十年级期间，教师设计的课堂活动会同步培养这四项能力。
Paper 1 is a non‑calculator short‑answer paper, while Paper 2 is a calculator structured‑question paper; both are equally weighted at 50% of the total mark. Students aiming for the highest grades must sit the Extended version, where questions demand greater depth. Year 10 is the ideal time to master core techniques before tackling multi‑step problems.
试卷一为不允许使用计算器的简答题卷，试卷二为允许使用计算器的结构化问题卷，各占总分的 50%。希望冲击高等级的学生必须参加扩展版考试，其题目要求更深的理解。十年级正是掌握基本方法的理想阶段，之后再应对多步骤复杂问题。
3. Number | 数
on. In Year 10, students consolidate operations with directed numbers, learn to use standard form A × 10ⁿ efficiently, and apply percentage change to real‑life contexts such as profit, loss and compound interest.
“数”这一主题贯穿整个大纲，内容包括基本运算、数字常识、分数、小数、百分数、比和比例。十年级学生要巩固正负数运算，学会高效使用科学记数法 A × 10ⁿ，并将百分比变化应用于盈亏、复利等实际场景。
Extended candidates also encounter surds, upper and lower bounds, and sequences with exponential patterns. For example, simplifying √50 to 5√2 and finding the bounds of a rounded measurement are typical Year 10 extension tasks that reappear in later topics like mensuration.
扩展课程考生还会接触根式、上下界以及指数型数列。例如，将 √50 化简为 5√2，或计算四舍五入测量值的上下界，都是十年级典型的拓展任务，这些技能随后会再次出现在测量等专题中。
4. Algebra – Core & Extended | 代数：核心与扩展
Algebra forms the heaviest and most interconnected part of the IGCSE syllabus. Year 10 starts with expanding brackets, factorising linear and quadratic expressions, and solving linear equations. Students then move on to rearranging formulas and understanding direct and inverse proportion in algebraic terms.
代数是 IGCSE 大纲中最厚重、相互联系最紧密的部分。十年级从展开括号、因式分解一次式和二次式、解线性方程开始，随后进入公式变形，以及用代数方式理解正比例与反比例。
For the Extended tier, Year 10 also introduces quadratic equations, both by factorisation and by the quadratic formula:
x = (-b ± √b² - 4ac) / 2a
. Inequalities, simultaneous equations and graphical representation of functions are covered in depth, preparing students for the curve-sketching and transformation of graphs they will meet in Year 11.在扩展级别，十年级还会介绍二次方程的因式分解解法和求根公式法：
x = (-b ± √b² - 4ac) / 2a
。不等式、联立方程组以及函数的图像表示都会深入学习，为学生十一年级将要面对的曲线绘制与图像变换做好准备。5. Co-ordinate Geometry | 坐标几何
This section develops the link between algebra and geometry. Year 10 students learn to plot straight‑line graphs, understand the gradient‑intercept form
y = mx + c
, and calculate the gradient between two points. They also explore parallel and perpendicular lines, recognising that the product of the gradients of perpendicular lines is −1.该部分搭建起代数与几何之间的桥梁。十年级学生学习绘制一次函数图像，理解斜截式
y = mx + c
，并计算两点间的斜率。他们还会探究平行线与垂直线，认识到垂线斜率的乘积为 −1。Midpoint and distance problems provide excellent practice for substituting into formulas. By the end of Year 10, Extended students are comfortable finding the equation of a straight line given two points or one point and the gradient, skills that appear repeatedly in past papers.
中点与距离问题为公式代入提供了绝佳的练习。到十年级结束时，扩展课程学生能够熟练地根据两点或一点和斜率求出直线方程，这些技能在历年考题中反复出现。
6. Geometry | 几何
Geometry in the CIE syllabus involves properties of angles, triangles, quadrilaterals, polygons and circles. Year 10 begins with angle facts – including angles on parallel lines – and moves to congruence and similarity. The interior and exterior angle sums of polygons are derived and used in problem‑solving.
CIE 大纲中的几何学涵盖角、三角形、四边形、多边形和圆的性质。十年级从角度事实（包括平行线上的角）入手，延伸至全等与相似。多边形的内角和外角和公式会被推导出来并用于解题。
Circle theorems form a significant part of the Extended course. Year 10 students usually learn the theorem that the angle at the centre is twice the angle at the circumference, the angle in a semicircle is a right angle, and how to apply alternate segment theorem. These require precise notation and logical reasoning, making them an excellent vehicle for developing AO4 (communication).
圆定理是扩展课程的重要组成部分。十年级学生通常会学习圆心角等于圆周角的两倍、半圆上的圆周角是直角，以及弦切角定理的应用。这些内容需要严谨的符号和逻辑推理，是培养 AO4（交流能力）的绝佳载体。
7. Mensuration | 测量
s such as arc length = (θ/360) × 2πr and sector area = (θ/360) × πr². Compound shapes and frustums of cones challenge students to combine several formulas in one question.
测量涵盖二维与三维图形的周长、面积、体积和表面积。十年级的学习内容包括扇形，推导如弧长 = (θ/360) × 2πr 和扇形面积 = (θ/360) × πr² 等公式。组合图形和圆锥台则考验学生在一道题中综合运用多个公式的能力。
Unit conversion is heavily tested, especially between cm³ and litres. Extended candidates must also work with pyramids, spheres and cones, and use similar shape relationships to find linear, area and volume scale factors. Year 10 is the time to build fluency with the formula sheet so that examination time is saved.
单位换算考查频繁，尤其在立方厘米与升之间。扩展考生还需处理棱锥、球体和圆锥，并利用相似形关系求出长度比、面积比和体积比。十年级正是熟悉公式表并提高熟练度的时期，以便在考试中节省时间。
8. Trigonometry | 三角学
Trigonometry is introduced gradually. In Year 10, students first meet the sine, cosine and tangent ratios for right‑angled triangles, using SOHCAHTOA to find unknown sides and angles. Applications to angles of elevation and depression, and bearings, connect trigonometry directly to real‑world problems.
三角学是逐步引入的。十年级学生首先接触直角三角形中的正弦、余弦和正切比，利用 SOHCAHTOA 求未知边和角。仰角、俯角以及方位角的应用将三角学与现实问题直接联系起来。
Extended learners then progress to the sine rule and cosine rule for non‑right‑angled triangles:
a/sin A = b/sin B = c/sin C
anda² = b² + c² - 2bc cos A
. The area formula ½ ab sin C is also covered. Grasping these rules in Year 10 leaves more time in Year 11 for the 3D trigonometry and exact trigonometric values needed for A*.扩展课程学生随后学习用于非直角三角形的正弦定理和余弦定理：
a/sin A = b/sin B = c/sin C
和a² = b² + c² - 2bc cos A
。面积公式 ½ ab sin C 也会涉及。在十年级掌握这些定理，可为十一年级留出更多时间钻研三维三角学及特殊角精确值，冲击 A*。9. Vectors & Transformations | 向量与变换
Transformations – reflection, rotation, translation and enlargement – artesian plane. Year 10 pupils learn to describe transformations fully using words such as 'reflect in the line y = x' or 'rotate 90° clockwise about the origin'. Enlargement with a negative scale factor is often introduced as an extension task.
变换——反射、旋转、平移和放大（放缩）——应用于笛卡尔平面上的点和图形。十年级学生要学会使用完备的数学语言描述变换，如“关于直线 y = x 反射”或“绕原点顺时针旋转 90°”。负比例因子的放大通常作为拓展任务引入。
tion and scalar multiplication. Extended students also work with the magnitude of a vector |a| = √x² + y² and position vectors, laying the foundation for vector geometry proofs in Year 11.
向量用于描述运动和位置。十年级涵盖列向量、向量加法和数乘。扩展课程学生还会接触向量的模 |a| = √x² + y² 以及位置向量，为十一年级的向量几何证明打下基础。
10. Probability | 概率
Probability starts with simple experiments, sample spaces and the 0‑ ear 10 deepens understanding by introducing tree diagrams, conditional probability and the 'and'/'or' rules. Correct use of the addition rule P(A or B) = P(A) + P(B) – P(A and B) reduces common errors.
概率从简单实验、样本空间和 0–1 概率尺度开始。十年级通过引入树状图、条件概率以及“且/或”规则来加深理解。正确使用加法法则 P(A or B) = P(A) + P(B) – P(A and B) 可减少常见错误。
Venn diagrams are used to represent sets and probabilities. Extended candidates are expected to handle replacement and non‑replacement scenarios on tree diagrams and to interpret the meaning of mutually exclusive and independent events. Year 10 teachers often link probability to percentage work to make the context more concrete.
维恩图用于表示集合与概率。扩展考生需要处理树状图中放回与不放回的情境，并解读互斥事件和独立事件的意义。十年级教师常将概率与百分数相联系，使情境更加具体。
11. Statistics | 统计
Statistics skills are tested in both IGCSE papers. Year 10 covers collection of data, frequency tables, bar charts, pie charts, histograms with equal class widths and scatter diagrams. Students learn to calculate mean, median, mode and range from both raw data and grouped frequency tables.
统计技能在 IGCSE 两份试卷中均有考查。十年级涉及数据收集、频数表、条形图、饼图、等宽直方图和散点图。学生要学会从原始数据和分组频数表中计算平均数、中位数、众数和极差。
The Extended tier adds cumulative frequency curves, quartiles and interquartile range, and interpretation of correlation. Drawing a cumulative frequency diagram and reading off the median and upper/lower quartiles is a high‑scoring structured question that Year 10 pupils can master thoroughly.
扩展级别增加了累积频数曲线、四分位数和四分位距，以及相关性的解释。绘制累积频数曲线图并读取中位数和上、下四分位数是一道高分结构化题，十年级学生完全可以扎实掌握。
12. Tips for Year 10 Success | 十年级成功建议
Build a strong foundation now. Every Year 10 topic reappears in more complex forms in Year 11, so treat every homework and class test as an opportunity to eliminate weak areas. Use the official CIE syllabus document to tick off the subtopics you have mastered and make a note of those that need extra work.
现在打下坚实基础。十年级的每一个课题都会以更复杂的形式在十一年级重现，因此把每次作业和课堂测验都当作消除薄弱环节的机会。利用 CIE 官方大纲文件，勾掉已掌握的子课题，并标记出需要额外努力的部分。
Practise past paper questions regularly, even if you have not yet covered all the material. Start with Paper 1 short questions to improve speed and accuracy without a calculator. As you progress through Year 10, attempt the corresponding questions from Paper 2 to become comfortable with calculator techniques and multi‑step reasoning.
定期练习历年真题，即使你还没有学完全部内容。从试卷一的简答题开始，提高没有计算器时的速度和准确度。随着十年级课程的推进，尝试试卷二中对应的题目，熟悉计算器使用技巧和多步骤推理。
Finally, use online resources and revision guides that match the 0580 syllabus. Keep a formula notebook and revise it weekly. CIE examiners reward clear working and proper mathematical communication, so always show your steps. Year 10 is the perfect time to build the habits that lead to top grades.
最后，使用与 0580 大纲匹配的在线资源和复习指南。准备一个公式笔记本，每周复习。CIE 考官看重清晰的解题步骤和规范的数学表达，因此务必展示你的计算过程。十年级正是养成这些高分习惯的最佳时机。
Published by TutorHao | Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图