Year 10 CIE Additional Mathematics: Full Syllabus Breakdown | Year 10 CIE 进阶数学：课程大纲全面解析

📚 Year 10 CIE Additional Mathematics: Full Syllabus Breakdown | Year 10 CIE 进阶数学：课程大纲全面解析

CIE IGCSE Additional Mathematics (0606) is an advanced course designed for Year 10 students who have a strong foundation in core mathematics. This syllabus builds upon basic algebra and geometry, introducing higher-level concepts such as functions, calculus, and trigonometry to prepare students for A-Level and beyond. In this article, we break down the entire syllabus topic by topic, highlighting what Year 10 learners typically encounter in their first year of the course.

CIE IGCSE 进阶数学（0606）是为具备扎实数学基础的 Year 10 学生设计的高级课程。该大纲在初等代数与几何的基础上引入函数、微积分和三角学等高阶概念，帮助学生为 A-Level 及以后的学习做好准备。本文将逐主题拆解整个课程大纲，并指出 Year 10 学生在第一年通常需要掌握的内容。

1. Functions | 函数

Students must understand the definition of a function, including domain, range, and one-to-one mappings. They should be able to use function notation f(x), find composite functions fg(x), and determine inverse functions f⁻¹(x). Graphical interpretation of functions is also emphasised.

学生需理解函数的定义，包括定义域、值域和一一映射。他们应能使用函数记号 f(x)，求复合函数 fg(x)，并确定反函数 f⁻¹(x)。对函数图像的解读也是重点内容。

Key notation includes f: x ↦ 2x + 3, and understanding that the graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x.

关键记号包括 f: x ↦ 2x + 3，并理解 y = f⁻¹(x) 的图像是 y = f(x) 关于直线 y = x 的反射。

2. Quadratic Functions | 二次函数

The syllabus covers quadratic expressions of the form ax² + bx + c. Learners should be able to complete the square, identify the vertex of a parabola, and sketch graphs. The discriminant Δ = b² – 4ac determines the nature of roots: real and distinct, real and equal, or no real roots.

大纲涵盖形如 ax² + bx + c 的二次表达式。学生应能配平方式、确定抛物线的顶点并描绘图像。判别式 Δ = b² – 4ac 用于判定根的性质：实不等根、实等根或无实根。

The quadratic formula is given by:

x = [-b ± √(b² – 4ac)] / 2a

Quadratic inequalities such as x² – 5x + 6 ≤ 0 are solved by sketching the parabola or using sign diagrams.

二次公式为：

x = [-b ± √(b² – 4ac)] / 2a

形如 x² – 5x + 6 ≤ 0 的二次不等式可通过画抛物线或使用符号表来求解。

3. Equations, Inequalities and Graphs | 方程、不等式与图像

This topic extends equation-solving to include modulus functions, like |2x – 1| = 3. Students learn to solve inequalities involving modulus, for instance |x – 4| < 2, and represent solutions on number lines. Graphical methods are used to solve equations such as |x + 1| = 2x - 3 by considering intersection points.

本主题将方程求解拓展到含绝对值函数的情形，如 |2x – 1| = 3。学生将学习求解含绝对值的不等式，例如 |x – 4| < 2，并在数轴上表示解集。通过寻找交点，可利用图像法求解形如 |x + 1| = 2x - 3 的方程。

Cubic and reciprocal graphs may also be introduced, and learners should be able to transform graphs using translations and reflections.

还可能引入三次函数与倒函数的图像，学生应能利用平移和反射对图像进行变换。

4. Indices and Surds | 指数与根式

Mastery of the laws of indices for rational exponents is essential. Students simplify expressions like (a²b³)⁴ and solve equations such as 2ˣ = 2³. Surds, including simplification, rationalising the denominator, and operations with square roots, are covered.

熟练掌握有理指数幂的指数运算法则至关重要。学生需化简如 (a²b³)⁴ 的表达式并求解 2ˣ = 2³ 这样的方程。根式部分涵盖化简、分母有理化以及平方根的运算。

Examples include expressing √48 in the form a√3 and rationalising 1/(√2 – 1) by multiplying numerator and denominator by √2 + 1.

例如，将 √48 写成 a√3 的形式，并通过乘以 √2 + 1 对 1/(√2 – 1) 进行分母有理化。

5. Logarithmic and Exponential Functions | 对数与指数函数

Students learn the relationship between logarithms and exponentials: if aˣ = y, then x = logₐ y. They apply the laws of logarithms: logₐ (xy) = logₐ x + logₐ y, logₐ (x/y) = logₐ x – logₐ y, and logₐ xⁿ = n logₐ x. Solving exponential equations using logarithms, such as 3ˣ = 7, is required.

学生将学习对数与指数的关系：若 aˣ = y，则 x = logₐ y。他们会应用对数运算法则：logₐ (xy) = logₐ x + logₐ y，logₐ (x/y) = logₐ x – logₐ y，以及 logₐ xⁿ = n logₐ x。还要求会用对数求解指数方程，如 3ˣ = 7。

The natural logarithm ln x = logₑ x and the exponential function eˣ appear frequently in calculus and growth/decay

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