Year 11 CAIE Additional Mathematics (Further Maths) Syllabus Breakdown | Year 11 CAIE 进阶数学课程大纲全面解析

📚 Year 11 CAIE Additional Mathematics (Further Maths) Syllabus Breakdown | Year 11 CAIE 进阶数学课程大纲全面解析

The CAIE IGCSE Additional Mathematics (0606) syllabus, often called ‘Further Mathematics’ in Year 11, is designed for high-achieving students who want to deepen their mathematical understanding beyond the standard IGCSE Mathematics course. This syllabus lays a robust foundation for A Level Mathematics and Further Mathematics. In this article, we break down the entire syllabus, highlighting key topics, assessment structure, and the essential concepts you need to master.

CAIE IGCSE 附加数学（0606）教学大纲，在Year 11常被称为‘进阶数学’，专为希望在标准IGCSE数学之外深化理解的高水平学生设计。该大纲为A Level数学与进阶数学奠定了坚实基础。本文将全面解析整个课程大纲，重点介绍关键主题、评估结构以及需要掌握的核心概念。

1. Syllabus at a Glance | 大纲速览

The syllabus is assessed through two written papers, each lasting 2 hours. Paper 1 covers algebra, functions, trigonometry, series and coordinate geometry. Paper 2 focuses on vectors, calculus and kinematics. Both papers are compulsory, and calculators are allowed. However, no formula sheet is provided — you must memorise all key formulae.

本课程通过两份书面试卷评估，每份时长2小时。试卷一涵盖代数、函数、三角学、级数与坐标几何。试卷二则聚焦向量、微积分与运动学。两份试卷均为必考，且允许使用计算器。但不提供公式表——你必须熟记所有关键公式。

2. Functions | 函数

A function f maps each element in its domain to exactly one element in its range. You must be able to find the range for a given domain, form composite functions such as fg(x) = f(g(x)), and determine inverse functions f⁻¹(x) provided the function is one-to-one. Quadratic functions reappear: completing the square, the discriminant Δ = b² − 4ac, and the coordinates of the vertex are essential.

函数 f 将定义域中的每个元素恰好映射到值域中的一个元素。你必须能够根据给定定义域求值域，构建如 fg(x) = f(g(x)) 的复合函数，并在函数一一对应时求其反函数 f⁻¹(x)。二次函数也会再次出现：配方法、判别式 Δ = b² − 4ac 以及顶点坐标都是核心内容。

Modulus functions |x| and graphs of y = |f(x)| are also included, as well as transformations of graphs (translations, stretches and reflections).

绝对值函数 |x| 以及 y = |f(x)| 的图像也包含在内，同时还会涉及图像的变换（平移、伸缩和反射）。

3. Quadratic Functions | 二次函数

The standard form is f(x) = ax² + bx + c. Completing the square helps locate the vertex (h, k) and the axis of symmetry x = h. The discriminant Δ determines the nature of roots: Δ > 0 gives two distinct real roots, Δ = 0 gives one repeated real root, and Δ < 0 yields no real roots.

标准形式为 f(x) = ax² + bx + c。配方法有助于找到顶点 (h, k) 和对称轴 x = h。判别式 Δ 决定了根的性质：Δ > 0 时有两个不等实根，Δ = 0 时有一个重根，Δ < 0 时无实根。

Solving quadratic inequalities such as ax² + bx + c > 0 is approached by sketching the parabola and identifying where the curve lies above the x-axis. You will also work with intersections of lines and parabolas.

求解如 ax² + bx + c > 0 的二次不等式时，需先绘制抛物线草图，找出曲线位于 x 轴上方的部分。此外，还会处理直线与抛物线的交点问题。

4. Equations, Inequalities and Simultaneous Equations | 方程、不等式与联立方程

This topic extends to solving a linear–quadratic pair of simultaneous equations, usually by substitution. Inequalities involving rational expressions, e.g. (x − 1)/(x + 2) > 0, and absolute value inequalities like |2x − 3| ≤ 5 must be solved analytically or graphically.

本主题延伸至联立求解线性方程与二次方程，通常采用代入法。含有理分式的不等式，如 (x − 1)/(x + 2) > 0，以及绝对值不等式如 |2x − 3| ≤ 5，需用解析法或图像法求解。

Graphs of functions such as y = axⁿ, exponential and logarithmic curves, and their transformations (translations, stretches, reflections) are fundamental for interpreting solutions.

函数图像，如 y = axⁿ、指数曲线与对数曲线，以及它们的变换（平移、伸缩、反射），是解读解集的基础。

5. Indices, Surds and Logarithms | 指数、根式与对数

Laws of indices: aᵐ × aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁻ⁿ = 1/aⁿ. Surds are simplified using √(ab) = √a √b and √(a/b) = √a/√b, and denominators are rationalised. Logarithms are introduced: if aˣ = b then x = logₐb. Key rules are logₐ(xy) = logₐx + logₐy, logₐ(x/y) = logₐx − logₐy, and logₐxⁿ = n logₐx. The change‑of‑base formula logₐx = (log_b x) / (log_b a) is essential for solving logarithmic and exponential equations.

指数律：aᵐ × aⁿ = aᵐ⁺ⁿ，(aᵐ)ⁿ = aᵐⁿ，a⁻ⁿ = 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）