原标题：CIE-A-level数学都考些什么？
A Level数学包括基础数学（Mathematics）和进阶数学（Further Mathematics）。两者之间关系是程连续性的，你只需要选择其中一门参加考试即可。
Mathematics 9709
基础数学可以说是一门必考科目。根据2020-2022年的syllabus, 基础数学包括三门课程纯数(其他机构会写P1、P2、P3),概率统计(其他机构会写S1、S2), 以及力学(其他机构会写M1)。 在选择Mathematics之前，学生应已有 IGCSE® Mathematics 0580 (Extended curriculum), or Cambridge International O Level (4024/4029)的数学基础。
基础数学一共有6份卷子：
Paper 1: Pure Mathematics 1
Paper 2: Pure Mathematics 2
Paper 3: Pure Mathematics 3
Paper 4: Mechanics
Paper 5: Probability & Statistics 1
Paper 6: Probability & Statistics 2
总的来说，AS Level 考生需要从中挑选两份paper进行考试. 而A Level考生一共需要考出4份paper的成绩. 考生可以分两年考完4张paper，或者在A Level这一年一次考完4张paper。
AS Level考生的选择组合有以下三个：
Pure Mathematics only (Paper 1 and Paper 2) - 不能进阶到A Level阶段考试
Pure Mathematics and Mechanics (Paper 1 and Paper 4)
Pure Mathematics and Probability & Statistics (Paper 1 and Paper 5).
A Level考生的选择组合有以下两个：
Pure Mathematics, Mechanics and Probability & Statistics (Papers 1, 3, 4 and 5)
Pure Mathematics and Probability & Statistics (Papers 1, 3, 5 and 6)
学生不允许选择Paper 4 + Paper 6， 因为paper 6需要有Paper 5的知识基础。
Paper3 和Paper6不能在AS Level阶段选考。
考卷概述如下：
每份Paper的考试内容如下：
Paper 1: Pure Mathematics 1 考核：
Quadratics, Functions,Coordinate geometry, Circular measure, Trigonometry, Series, Differentiation, Integration
Paper 2: Pure Mathematics 2 考核：
Algebra, Logarithmic and exponential functions, Trigonometry, Differentiation, Integration, Numerical solution of equations
Paper 3: Pure Mathematics 3考核：
Algebra, Logarithmic and exponential functions, Trigonometry, Differentiation, Integration, Numerical solution of equations, Vectors, Differential equations, Complex numbers,
Paper 4: Mechanics考核：
Forces and equilibrium, Kinematics of motion in a straight line, Momentum, Newton’s laws of motion, Energy, work and power
Paper 5: Probability & Statistics 1考核：
Representation of data, Permutations and combinations, Probability, Discrete random variables, The normal distribution
Paper 6: Probability & Statistics 2考核：
The Poisson distribution, Linear combinations of random variables, Continuous random variables, Sampling and estimation, Hypothesis tests
Further Mathematics 9231
进阶数学，是一门综合性强，对一般学生有一定挑战性的学科。进阶数学内容包括纯数学、统计学和力学三部分，模块和数学保持一致，但其内容更加广泛和深入。根据2020-2022年的syllabus, 基础数学包括三门课程进阶数学(其他机构会写FP1、FP2),概率统计(其他机构会写S3), 以及力学(其他机构会写M2)。 改革后的进阶数学比之前降低了一定的难度。在选择之前，要修读Cambridge International AS & A Level Mathematics (9709).
基础数学一共有4份卷子：
Paper 1: Further Pure Mathematics 1
Paper 2: Further Pure Mathematics 2
Paper 3: Further Mechanics
Paper 4: Further Probability & Statistics
总的来说，AS Level 考生需要从中挑选两份paper进行考试. 而A Level考生一共需要考出4份paper的成绩. 考生可以分两年考完4张paper，每年考2张paper，或者在A Level这一年一次考完4张paper。
AS Level Further Mathematics学生有2个试卷组合可以选择:
Further Pure Mathematics 1 and Further Mechanics (Paper 1 and Paper 3)
Further Pure Mathematics 1 and Further Probability & Statistics (Paper 1 and Paper 4).
A Level Further Mathematics 学生需要把剩下两份在AS Level没有进行考试的卷子进行考试。
Paper 1: Further Pure Mathematics 1
Paper 2: Further Pure Mathematics 2
Paper 3: Further Mechanics
Paper 4: Further Probability & Statistics.
考卷概述如下：
每份Paper的考试内容如下：
Further Pure Mathematics 1 Paper 1考核：
Roots of polynomial equations, Rational functions and graphs, Summation of series, Matrices , Polar coordinates, Vectors, Proof by induction
Further Pure Mathematics 2 Paper 2 考核：
Hyperbolic functions, Matrices, Differentiation, Integration, Complex numbers, Differential equations
Further Mechanics Paper 3考核：
Motion of a projectile, Equilibrium of a rigid body, Circular motion, Hooke’s law, Linear motion under a variable force, Momentum
Further Probability & Statistics Paper 4 考核：
Continuous random variables, Inference using normal and t-distributions, -tests, Non-parametric tests, Probability generating functions
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