📚 Year 10 CAIE Additional Mathematics: Core Topics Overview | Year 10 CAIE 进阶数学：核心知识点梳理
This article provides a structured review of the essential topics typically covered in Year 10 CAIE Additional Mathematics (0606). Mastery of these core concepts will build a strong foundation for further study in pure mathematics, mechanics and statistics.
本文系统梳理了 Year 10 CAIE 附加数学（0606）通常涵盖的核心知识点。掌握这些核心概念，将为后续学习纯数学、力学和统计学打下坚实基础。
1. Functions and Mappings | 函数与映射
A function is a rule that assigns each element from the domain to exactly one element in the codomain. The set of all outputs is called the range. A mapping is one-to-one if each input maps to a distinct output.
函数是一种规则，它将定义域的每个元素对应到值域中唯一的元素。所有输出值的集合称为值域。若每个输入对应不同输出，则映射是一一映射。
is the independent variable. The domain and range can be represented as intervals, e.g., x ∈ ℝ or f(x) ≥ 0.
函数记作 f(x)，其中 x 是自变量。定义域和值域可用区间表示，例如 x ∈ ℝ 或 f(x) ≥ 0。
Composite functions: (f ∘ g)(x) = f(g(x)). The order matters; f ∘ g is generally not the same as g ∘ ion, the range of the inner function must be a subset of the domain of the outer function.
复合函数：(f ∘ g)(x) = f(g(x))。顺序很重要，f ∘ g 通常不等于 g ∘ f。构成复合函数时，内层函数的值域必须是外层函数定义域的子集。
nd f⁻¹(f(x)) = x. The graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x.
反函数 f⁻¹(x) 仅当 f 为一一映射时存在。它满足 f(f⁻¹(x)) = x 和 f⁻¹(f(x)) = x。y = f⁻¹(x) 的图像是 y = f(x) 关于直线 y = x 的对称图像。
2. Quadratic Functions and Their Graphs | 二次函数及其图像
e written as f(x) = a(x − h)² + k, revealing the vertex (h, k) and axis of symmetry x = h.
二次函数的标准形式为 f(x) = ax² + bx + c（a ≠ 0）。通过配方法，可写为 f(x) = a(x − h)² + k，从而得到顶点 (h, k) 和对称轴 x = h。
s. If Δ > 0, two distinct real roots; Δ = 0, one repeated real root; Δ < 0, no real roots.
判别式 Δ = b² − 4ac 决定根的数量与类型。Δ > 0 时有两个不等实根；Δ = 0 时有一个重实根；Δ < 0 时无实根。
For solving quadratic inequalities, sketch the graph to identify intervals where f(x) > 0 or f(x) < 0. Be careful with the sign of a and boundary points.
解二次不等式时，画出函数图像以确定 f(x) > 0 或 f(x) < 0 的区间。注意 a 的符号和边界点。
3. Solving Equations and Inequalities | 解方程与不等式
atic equations, use factorising, completing the square or the quadratic formula: x = [−b ± √b² − 4ac] / (2a). Choose the method that best suits the given form.
解二次方程，可用因式分解、配方法或求根公式：x = [−b ± √b² − 4ac] / (2a)。选择最适合给定形式的方法。
Simultaneous equations involve finding intersection points of lines and curves. Substitute the linear equation into the quadratic to form a single equation in one variable. Always check for extraneous solutions after solving rational equations.
联立方程需求出直线与曲线的交点。
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