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【摘要】介绍了英国高中课程数学科目的考试要求及其重要性，列举了数学科目四个单元（含纯数学1、纯数学3、力学1和概率与统计学1）的考试内容，分析了2014年夏季数学考试部分真题的关键英语词句，总结了数学考试常用的专业英语词汇，最后对准备留学英联邦国家需要具备的英语素质提出几点建议。
【关键词】英国高中课程 数学专业英语 留学 英语素质
【Abstract】The paper introduces test requirements and the importance of the subject mathematics of the General Certificate of Education Advanced Level，lists four units’ （pure mathematics 1，pure mathematics 3，Mechanics 1 and probability and statistics 1） content of the examination，analyzes the English keywords in the summer of 2014 mathematics examinations，summarizes the common English vocabulary in the mathematics examinations，and finally put forward some suggestions about the English requirements to prepare going abroad foreign Common wealth countries.
【Keywords】General Certificate of Education Advanced Level； Mathematical English Vocabularies； Going abroad； English qualities
一、背景介绍
英国高中课程（General Certificate of Education Advanced Level）简称A-level课程，A-level课程证书被几乎所有英语授课的大学作为招收新生的入学标准。目前为止，国内比较有影响力的A-level学校有深圳国际交流学院、华南师范大学国际预科中心和上海师范大学剑桥国际中心等。通常，留学英联邦国家的大学只需要提供三门A-level的成绩和雅思考试的成绩。而A-level课程体系中数学可选修两门。中国高中生的数学能力普遍比西方学生强，因此选择A-level数学就意味着一只脚已踏入了世界一流大学之门。
二、A-level数学考试
A-level数学科目考试代号为9709，包含四个单元：纯数学（Pure Mathematics）1、纯数学（Pure Mathematics）3、力学（Mechanics）1和概率与统计学（Probability and Statistics）1。这一部分先介绍每个单元的考试内容，然后分析2014年夏季的部分考试真题，最后列出数学考试常用的专业英语词汇。
1.单元考试内容。纯数学（Pure Mathematics）1包含：二次方程（Quadratics）、函数（Functions）、坐标几何（Coordinate geometry）、弧度制（Circular measure）、三角函数（Trigonometry）、向量（Vectors）、数列（Series）、导数（Differentiation）和积分（Integration）；纯数学（Pure Mathematics）3包含：代数（Algebra）、对数函数与指数函数（Logarithmic and exponential functions）、方程的数值解（Numerical solution of equations）、微分方程（Differential equations）和复数（Complex numbers）；力学（Mechanics）1包含：力与平衡（Forces and equilibrium）、直线运动学（Kinematics of motion in a straight line）、牛顿运动定律（Newton’s laws of motion）和能量、做功与功率（Energy，work and power）；概率与统计学（Probability and Statistics）1包含：数据表示（Representation of data）、置換与组合（Permutations and combinations）、概率（Probability）、离散随机变量（Discrete random variables）和正态分布（The normal distribution）。
2.数学2014年夏季部分真题分析。
Example 1（S14_9709_qp_13） A function f is such thatfor 0≤x≤6.
（i）Find an expression for f ’（x） and use your result to explain why f has an inverse.
（ii）Find an expression for f -1（x），and state the domain and range of f -1.
中国考生多数在回答第一问存在困难。这并不是要求从语言上回答为什么 f 是可逆的，而是要通过f ’ 的正负来判断 f 的单调性，进而证明 f 是一个1-1映射。
Example 2（S14_9709_qp_33） The diagram shows the curve for ，and its maximum point M. （i）Using the substitution ，find the exact value of the area of the shaded region bounded by the curve and the axes.
（ii）Find the x-coordinate of M，giving your answer correct to 3 decimal places.
中国考生在第一问容易犯错误，利用计算器计算并给出带小数点的结果。原因在于没有理解题目的要求“Find an exact value”，这是要求“给出完全精确的答案”。
Example 3（S14_9709_qp_43） A smooth inclined plane of length 160cm is fixed with one end at a height of 40cm above the other end，which is on horizontal ground. Particles P and Q，of masses 0.76 kg and 0.49 kg respectively，are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the top of the plane. Particle P is held at rest on the same line of greatest slope as the pulley and Q hangs vertically below the pulley at a height of 30 cm above the ground （see diagram）. P is released from rest. It starts to move up the plane and does not reach the pulley. Find
（i）The acceleration of the particles and the tension in the string before Q reaches the ground，
（ii）The speed with which Q reaches the ground，
（iii）The total distance travelled by before it comes to instantaneous rest.
力学的考试题目普遍信息量大，不容易读懂题意。尤其是第三问，难度在于 落地以后，所受的牵引力改变了，进而加速度也改变了。因此，理解几处关键用语“released from rest”，“move up the plane and does not reach the pully”，“before it comes to instantaneous rest” 是求解这道题的关键。
Example 4（S14_9709_qp_63） Nine cards are numbered 1，2，2，3，3，4，6，6，6.
（i）All nine cards are placed in a line，making a 9-digit number. Find how many different 9-digit numbers can be made in this way
（a）If the even digits are all together，
（b）If the first and last digits are both odd.
（ii）Three of the nine cards are chosen and placed in a line，making a 3-digit number. Find how many different numbers can be made in this way
（a）If there are no repeated digits，
（b）If the number is between 200 and 300.
這道题涉及排列组合的专业术语，考生必须对相关的专业名词用语熟练掌握，比如“the even digits are all together”，“the first and last digits are both odd”，“three of the nine cards are chosen”.
3 常用的数学专业英语词汇[1-4]
数学考试专业英语常用词汇
a light inextensible string equilibrium pulley
acceleration exclusive events quadratic inequalities
addition expectation quadratic polynomial
angle force quotient
arc length frictional component radian
Argand diagram geometric progression range
argument gradient real part
arithmetic progression gravitational potential energy remainder arrangement histograms scalar product
binomial distribution imaginary part sector area
box-and-whisker plots independent events standard deviation
chain rule integration stationary point
combination inverse function stem-and-leaf diagrams
composition of functions kinetic energy subtraction
conditional probabilities limiting equilibrium the factor theorem
conjugate limiting friction the interquartile range
contact force linear inequalities the normal distribution
continuous random variable median value the quartiles
convergence modulus the remainder theorem
conversation of energy multiplication trapezium rule
coordinate Newton’s third law trigonometry
cumulative frequency graphs normal component unit vector
decomposition numerator variance
denominator one-one function vector
differentiation parallel velocity
discrete random variable permutation volume of revolution
discriminant perpendicular
displacement position vector
displacement vector probability
domain probability distribution table
三、出国留学英语素质分析
近年来，留学英联邦国家逐渐成为热点。中国考生多数会选择两门数学和一门化学或者物理课程。由第二部分的总结，我们更加应该重视专业英语素质的培养，正确理解题意是正确解题的關键。和数学类似，考生可以总结化学和物理专业英语词汇，帮助迅速读懂题意。另外，就是雅思英语考试的准备和文书（personnel statement）的写作。如果能够针对这几方面努力准备，定能成功留学英联邦。
参考文献：
[1]Neill H，Neill D Q A H，Quadling D.Pure Mathematics 1 （International）[M].Cambridge University Press，2002 Publisher Cambridge University Press，2002，2000.
[2]Neill H，Neill D Q A H，Quadling D.Pure Mathematics 2
【关键词】英国高中课程 数学专业英语 留学 英语素质
【Abstract】The paper introduces test requirements and the importance of the subject mathematics of the General Certificate of Education Advanced Level，lists four units’ （pure mathematics 1，pure mathematics 3，Mechanics 1 and probability and statistics 1） content of the examination，analyzes the English keywords in the summer of 2014 mathematics examinations，summarizes the common English vocabulary in the mathematics examinations，and finally put forward some suggestions about the English requirements to prepare going abroad foreign Common wealth countries.
【Keywords】General Certificate of Education Advanced Level； Mathematical English Vocabularies； Going abroad； English qualities
一、背景介绍
英国高中课程（General Certificate of Education Advanced Level）简称A-level课程，A-level课程证书被几乎所有英语授课的大学作为招收新生的入学标准。目前为止，国内比较有影响力的A-level学校有深圳国际交流学院、华南师范大学国际预科中心和上海师范大学剑桥国际中心等。通常，留学英联邦国家的大学只需要提供三门A-level的成绩和雅思考试的成绩。而A-level课程体系中数学可选修两门。中国高中生的数学能力普遍比西方学生强，因此选择A-level数学就意味着一只脚已踏入了世界一流大学之门。
二、A-level数学考试
A-level数学科目考试代号为9709，包含四个单元：纯数学（Pure Mathematics）1、纯数学（Pure Mathematics）3、力学（Mechanics）1和概率与统计学（Probability and Statistics）1。这一部分先介绍每个单元的考试内容，然后分析2014年夏季的部分考试真题，最后列出数学考试常用的专业英语词汇。
1.单元考试内容。纯数学（Pure Mathematics）1包含：二次方程（Quadratics）、函数（Functions）、坐标几何（Coordinate geometry）、弧度制（Circular measure）、三角函数（Trigonometry）、向量（Vectors）、数列（Series）、导数（Differentiation）和积分（Integration）；纯数学（Pure Mathematics）3包含：代数（Algebra）、对数函数与指数函数（Logarithmic and exponential functions）、方程的数值解（Numerical solution of equations）、微分方程（Differential equations）和复数（Complex numbers）；力学（Mechanics）1包含：力与平衡（Forces and equilibrium）、直线运动学（Kinematics of motion in a straight line）、牛顿运动定律（Newton’s laws of motion）和能量、做功与功率（Energy，work and power）；概率与统计学（Probability and Statistics）1包含：数据表示（Representation of data）、置換与组合（Permutations and combinations）、概率（Probability）、离散随机变量（Discrete random variables）和正态分布（The normal distribution）。
2.数学2014年夏季部分真题分析。
Example 1（S14_9709_qp_13） A function f is such thatfor 0≤x≤6.
（i）Find an expression for f ’（x） and use your result to explain why f has an inverse.
（ii）Find an expression for f -1（x），and state the domain and range of f -1.
中国考生多数在回答第一问存在困难。这并不是要求从语言上回答为什么 f 是可逆的，而是要通过f ’ 的正负来判断 f 的单调性，进而证明 f 是一个1-1映射。
Example 2（S14_9709_qp_33） The diagram shows the curve for ，and its maximum point M. （i）Using the substitution ，find the exact value of the area of the shaded region bounded by the curve and the axes.
（ii）Find the x-coordinate of M，giving your answer correct to 3 decimal places.
中国考生在第一问容易犯错误，利用计算器计算并给出带小数点的结果。原因在于没有理解题目的要求“Find an exact value”，这是要求“给出完全精确的答案”。
Example 3（S14_9709_qp_43） A smooth inclined plane of length 160cm is fixed with one end at a height of 40cm above the other end，which is on horizontal ground. Particles P and Q，of masses 0.76 kg and 0.49 kg respectively，are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the top of the plane. Particle P is held at rest on the same line of greatest slope as the pulley and Q hangs vertically below the pulley at a height of 30 cm above the ground （see diagram）. P is released from rest. It starts to move up the plane and does not reach the pulley. Find
（i）The acceleration of the particles and the tension in the string before Q reaches the ground，
（ii）The speed with which Q reaches the ground，
（iii）The total distance travelled by before it comes to instantaneous rest.
力学的考试题目普遍信息量大，不容易读懂题意。尤其是第三问，难度在于 落地以后，所受的牵引力改变了，进而加速度也改变了。因此，理解几处关键用语“released from rest”，“move up the plane and does not reach the pully”，“before it comes to instantaneous rest” 是求解这道题的关键。
Example 4（S14_9709_qp_63） Nine cards are numbered 1，2，2，3，3，4，6，6，6.
（i）All nine cards are placed in a line，making a 9-digit number. Find how many different 9-digit numbers can be made in this way
（a）If the even digits are all together，
（b）If the first and last digits are both odd.
（ii）Three of the nine cards are chosen and placed in a line，making a 3-digit number. Find how many different numbers can be made in this way
（a）If there are no repeated digits，
（b）If the number is between 200 and 300.
這道题涉及排列组合的专业术语，考生必须对相关的专业名词用语熟练掌握，比如“the even digits are all together”，“the first and last digits are both odd”，“three of the nine cards are chosen”.
3 常用的数学专业英语词汇[1-4]
数学考试专业英语常用词汇
a light inextensible string equilibrium pulley
acceleration exclusive events quadratic inequalities
addition expectation quadratic polynomial
angle force quotient
arc length frictional component radian
Argand diagram geometric progression range
argument gradient real part
arithmetic progression gravitational potential energy remainder arrangement histograms scalar product
binomial distribution imaginary part sector area
box-and-whisker plots independent events standard deviation
chain rule integration stationary point
combination inverse function stem-and-leaf diagrams
composition of functions kinetic energy subtraction
conditional probabilities limiting equilibrium the factor theorem
conjugate limiting friction the interquartile range
contact force linear inequalities the normal distribution
continuous random variable median value the quartiles
convergence modulus the remainder theorem
conversation of energy multiplication trapezium rule
coordinate Newton’s third law trigonometry
cumulative frequency graphs normal component unit vector
decomposition numerator variance
denominator one-one function vector
differentiation parallel velocity
discrete random variable permutation volume of revolution
discriminant perpendicular
displacement position vector
displacement vector probability
domain probability distribution table
三、出国留学英语素质分析
近年来，留学英联邦国家逐渐成为热点。中国考生多数会选择两门数学和一门化学或者物理课程。由第二部分的总结，我们更加应该重视专业英语素质的培养，正确理解题意是正确解题的關键。和数学类似，考生可以总结化学和物理专业英语词汇，帮助迅速读懂题意。另外，就是雅思英语考试的准备和文书（personnel statement）的写作。如果能够针对这几方面努力准备，定能成功留学英联邦。
参考文献：
[1]Neill H，Neill D Q A H，Quadling D.Pure Mathematics 1 （International）[M].Cambridge University Press，2002 Publisher Cambridge University Press，2002，2000.
[2]Neill H，Neill D Q A H，Quadling D.Pure Mathematics 2