Year 11 CIE Additional Mathematics: Core Concepts Review | 11年级CIE进阶数学核心知识点梳理

📚 Year 11 CIE Additional Mathematics: Core Concepts Review | 11年级CIE进阶数学核心知识点梳理

The Cambridge IGCSE Additional Mathematics (0606) syllabus extends beyond the standard IGCSE Mathematics, introducing advanced topics such as functions, calculus, and trigonometry in greater depth. This article provides a comprehensive review of the core concepts that Year 11 students must master for success in examinations.

剑桥IGCSE附加数学（0606）课程在标准IGCSE数学的基础上进行了拓展，深入介绍了函数、微积分和三角学等高等主题。本文全面梳理了11年级学生必须掌握的核心知识点，助力考试成功。

1. Functions | 函数基础

Functions map each input (x) to exactly one output (y). The domain is the set of all possible inputs, and the range is the set of all possible outputs. A function must have a unique y for each x.

函数将每个输入(x)映射到唯一的输出(y)。定义域是所有可能输入的集合，值域是所有可能输出的集合。每个x必须对应唯一的y。

Composite functions are written as gf(x) = g(f(x)) – apply f first, then g. The domain of gf must ensure f(x) is in the domain of g.

复合函数记作gf(x) = g(f(x))——先应用f，再应用g。gf的定义域必须保证f(x)落在g的定义域内。

Inverse functions f⁻¹(x) reverse the mapping. A function must be one-to-one to have an inverse. You swap x and y and rearrange; the range of f⁻¹ equals the domain of f.

反函数f⁻¹(x)反转映射关系。函数必须是一一对应才有反函数。交换x和y并重新整理，且f⁻¹的值域等于f的定义域。

2. Quadratic Functions | 二次函数

The general quadratic is f(x) = ax² + bx + c. By completing the square, you can express it as a(x + p)² + q, where the vertex is at (-p, q).

一般二次式为f(x) = ax² + bx + c。通过配方法，可以将其写成a(x + p)² + q，其顶点坐标为(-p, q)。

The discriminant Δ = b² – 4ac determines the nature of roots: Δ > 0 (two distinct real roots), Δ = 0 (one repeated root), Δ < 0 (no real roots).

判别式Δ = b² – 4ac决定根的性质：Δ > 0（两个不等实根），Δ = 0（一个重根），Δ < 0（无实根）。

To solve a quadratic inequality such as ax² + bx + c > 0, find the critical values where the quadratic equals zero, then test intervals or use a sketch. The solution is written in interval notation.

求解二次不等式如ax² + bx + c > 0，先求出二次式等于零的临界值，然后通过区间测试或草图确定解集，解用区间表示。

3. Indices and Surds | 指数与根式

The laws of indices: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a

Published by TutorHao | Year 11 进阶数学 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）