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equation
058
n. 等式
D a statement showing that two amounts or values are equal, for example 2 x + y =54
E Sometimes you may need to add the two equations rather than subtracting them.
有时你可能需要把这两个等式相加而不是相减。
simultaneous equations
059
联立方程
D equations involving two or more unknown quantities that have the same values in each equation
E The point where the lines cross lies on both lines, so its coordinates satisfy both equations and therefore give the solution to the simultaneous equations.
两条直线的交点位于两条直线上，因此其坐标满足两个方程，从而给出联立方程的解。
solve
060
v. 求解
D to find an answer to a problem
E In Example 4.4 you can see how the same pair of simul-taneous equations are solved algebraically.
在例4.4中，你可以看到联立方程组是如何用代数方法求解的。
expression
061
n. 表达式
D a symbol or group of symbols that represent an amount
E It’s a good idea to write the positive term first since it is easy to lose a minus sign at the start of an expression.
以正数开头是一个好办法，因为在表达式的开头很容易丢失负号。
substitution
062
n. 代入
D the act of using something new or different instead of something else, or the new thing that is used
E Either the substitution method or the graphical method can be used to solve a pair of simultaneous equations.
联立方程组的求解可采用代入法或图解法。
elimination
063
n. 消元
D the process of removing something
E Solve the simultaneous equations 2 x +3 y =7 and 5 x –4 y =4 using the elimination method.
用消元法解联立方程组2 x +3 y =7和5 x –4 y =4。
solution
064
n. 解
D an answer to a puzzle or to a problem in mathematics
E She wrote the solution of the equation on the board.
她把方程的解写在黑板上。
linear
065
adj. 一次的
D able to be represented by a straight line on a graph
E We will learn to solve simultaneous equations in which one equation is linear and the other is quadratic in Chapter 4.
我们将在第四章学习求解联立方程组，其中一个方程是一次的，另一个方程是二次的。
quadratic
066
adj. 二次的
D involving an unknown quantity that is multiplied by itself once only
E Sridhara was one of the first mathematicians to give a rule to solve a quadratic equation.
Sridhara是最早提出求解二次方程方法的数学家之一。
cubic
067
adj. 三次的
D describes a mathematical expression or equation in which at least one variable is cubed but no variable is to be multiplied by itself more than two times
E This chapter will discuss how to solve the cubic equations using different methods.
本章将会探讨如何用不同方法求解三次方程。
quartic
068
adj. 四次的
D of or relating to the fourth degree
E Solve the quartic equation 4 x 4 –17 x 2 +4=0.
解四次方程4 x 4 –17 x 2 +4=0。
inequality
069
noun. 不等式
D an algebraic relation showing that a quantity is greater than or less than another quantity
E You must be careful when multiplying or dividing through an inequality by a negative number.
在不等式两边乘以或除以一个负数时，必须要小心。
factorise
070
v. 因式分解
D to express a number in terms of its factors
E Factorise the following expressions.
把下面的表达式进行因式分解。
perfect square
071
完全平方
D an integer that is the square of an integer
E If the discriminant is a perfect square, these roots are rational.
如果判别式是完全平方数，那么这些根是有理数。
complete the square
072
配方
D meaning manipulating the form of the equation so that the left side of the equation is a perfect square trinomial
E If a quadratic equation has real roots, the method of com-pleting the square can also be used to solve the equation.
如果一个二次方程有实根，也可以用配方的方法来求解。
discriminant
073
n. 判别式
D an algebraic expression related to the coefficients of a polynomial equation whose value gives information about the roots of the polynomial
E Use the discriminant to determine the number of roots of a quadratic equation.
用判别式来确定二次方程的根的个数。
simplify
074
v. 简化
D to make something less complicated and therefore easier to do or understand
E Find an expression for the gradient of the chord joining P and Q , simplifying your answer.
求出弦 PQ 的斜率的表达式并简化你的答案。
expand
075
v. 展开
D to increase in size, number, or importance, or to make something increase in this way
E Start by expanding the brackets.
从展开括号开始。
identical
076
adj. 同一的
D exactly the same, or very similar
E Marie has a bag of sweets which are all identical in shape.
玛丽有一袋形状完全相同的糖果。
identity
077
n. 恒等式
D an equation (=mathematical statement) that is true for every value given to a variable (=number that can change)
E The identity cos 2 θ +sin 2 θ =1 is essential for finding trigono-metric ratios.
恒等式cos 2 θ +sin 2 θ =1对于求三角函数比值是必不可少的。
distinct
078
adj. 有区别的
D clearly separate and different (from something else)
E The coins of most currencies have two distinct faces, usually referred to as ‘heads’ and ‘tails’.
大多数货币的硬币有两个不同的面，通常被称为“正面”和“反面”。
polynomial
079
n. 多项式
D a number or variable (=mathematical symbol), or the result of adding or subtracting two or more numbers or variables
E Quadratic functions are members of the family of polyno-mials.
二次函数是多项式函数的一种。
constant
080
n. 常数
D a particular number or amount that never changes
E We continue the process until we are left with a constant.
我们继续这个过程，直到得出一个常数。
variable
081
n. 变量
D a number, amount, or situation that can change
E A zero of a polynomial is a value of the variable which makes the polynomial equal to zero.
多项式的零点是代入之后多项式为零的变量值。
degree
082
n. 次数；度
D (an) amount or level of something
E Two polynomials are equal if and only if they have the same degree (order), and corresponding terms have equal coefficients.
两个多项式相等的充要条件是它们具有相同的次数，并且对应项有相等的系数。
order
083
n. 阶数
D the way in which data or information is arranged
E The order of a polynomial is the highest power of the variable it contains, so a quadratic is a polynomial of order 2, a cubic has order 3 and so on.
多项式的阶数是所含变量的最高次幂，因此二次多项式是2阶，三次多项式是3阶，依此类推。
coefficient
084
n. 系数
D a number or symbol that is written in front of and multiplies another number or symbol
E To calculate the other binomial coefficients we can use a formula.
我们可以用一个公式来计算其他二项式系数。
term
085
n. （代数式等的）项
D any number, variable (=symbol), or product (= result of mutiplying)
E Write down the general term of the expansion.
写下展开式的通项公式。
like term
086
同类项
D terms that have the same variables and powers
E Polynomials are added by collecting like terms.
多项式相加通过合并同类项得到。
dominant term
087
主项
D the mathematical term greater in absolute value than any other (as in a set) or than the sum of the others
E The term x 3 makes by far the largest contribution to the answers. It is the dominant term.
x 3 这一项对结果的贡献最大，它是主项。
long division
088
长除法
D a method of dividing one large number by another by writing down each stage of the work
E One method is to set out the polynomial division rather like arithmetic long division.
一种方法是多项式除法，就像算术长除法那样。
factor theorem
089
因子定理；因式定理
D a theorem linking factors and zeros of a polynomial
E The factor theorem states that if ( x–a ) is a factor of a poly-nomial f ( x ), then f ( a )=0 and a is a root of the equation f ( x )=0.
因式定理指出，如果（ x–a ）是多项式 f （ x ）的因子，那么 f （ a ）=0， a 是方程 f （ x ）=0的根。
partial fraction
090
部分分式
D the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator
E In some cases， it is necessary to factorise the denominator before finding the partial fractions.
在某些情况下，在计算部分分式之前要对分母进行因式分解。
exponent
091
n. 指数
D a number or sign that shows how many times another number is to be multiplied by itself
E Understand and use the laws of indices for all rational exponents.
理解并使用所有有理指数的指数定律。
power
092
n. 幂
D the number of times that a number is to be multiplied by itself
E The most important clues to the shape of the curve are the order of the polynomial and the sign of the highest power of the variable.
曲线形状最重要的线索是多项式的阶数和变量最高次幂的符号。
index
093
n. 指数
D an indirect shortcut derived from and pointing into a greater volume of values, data, information or knowledge
E The following numerical examples show the methods for simplifying expressions using index notation.
下面的数值例子展示了使用指数符号简化表达式的方法。
base
094
n. 底
D the number on which a counting system is built
E A negative base raised to an odd exponent is negative.
底为负数、指数为奇数的数是负数。
logarithm
095
n. 对数
D The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number.
E The logarithm in base 10 of a positive number is the power that 10 must be raised to in order to obtain the number.
以10为底的某个正数的对数，表示10的这个对数的幂等于这个正数。
surd
096
n. 无理数
D
an irrational number, such as
E Real numbers are all the positive and negative numbers, or zero, including fractions and surds.
实数是所有的正数和负数，或零，包括分数和无理数。
common logarithm
097
常用对数
D the logarithm with base 10
E Most textbooks in calculus and the sciences, as well as calculators, use the notation ln x for the natural logarithm and lg x for the common logarithm, log 10 x .
大多数微积分和科学教科书，以及计算器中，使用符号ln x 表示自然对数，lg x 表示常用对数log 10 x 。
natural logarithm
098
自然对数
D The natural logarithm of a number is its logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828. The natural logarithm of x is generally written as ln x , log e x , or sometimes, if the base e is implicit, simply log x .
E The laws for natural logarithms are the laws for logarithms written in base e.
自然对数的运算规则是以e为底的对数的运算规则。
binomial expansion
099
二项展开式
D the algebraic expansion of powers of a binomial
E A binomial expression has two terms. The binomial expan-sion allows you to expand powers of binomial expressions.
二项式有两个项。二项展开式可以将二项式的幂进行展开。
Pascal’s triangle
100
帕斯卡三角形
D a system of numbers arranged in rows resembling a triangle with each row consisting of the coefficients in the expansion of ( a + b ) n for n =0, 1, 2, 3, …
E You can see that these numbers, 1, 5, 10, 10, 5, 1, are row 5 of Pascal’s triangle.
你可以看到数字1、5、10、10、5、1是帕斯卡三角形的第5行。
ascending power
101
升幂
D the power of a term increases for each succeeding term
E Expand each of the following as a series of ascending powers of x .
把下面的每一个式子按照 x 的升幂展开。
descending power
102
降幂
D the power of a term decreases for each succeeding term
E In binomial expansion, the second element is arranged in descending power.
在二项展开式中，第二个元素按降幂排列。
factorial
103
adj. 阶乘的
D The factorial of a non-negative integer n , denoted by n !, is the product of all positive integers less than or equal to n .
E You can use combinations and factorial notation to help you expand binomial expressions.
你可以使用组合和阶乘符号来帮助展开二项表达式。
permutation
104
n. 排列
D any of the various arrangements in which a set of objects can be organised
E The solution required a permutation of three objects from twenty-six.
这个解要从26个物体中选3个进行排列。
combination
105
n. 组合
D a result of two or more things joining together
E You can use the combination formula to calculate the number of possible arrangements.
你可以利用组合公式来计算可能的排列数量。
percentage error
106
误差百分比
D a measure of the accuracy of a measurement relative to a true or estimated value
E Use your calculator to find the percentage error in your answer.
用计算器算出你答案中的误差百分比。
relative error
107
相对误差
D The relative error is defined as the ratio of the absolute error of the measurement to the actual measurement.
E Thus the relative error in the volume is about three times the relative error in the radius.
因此体积的相对误差大约是半径相对误差的三倍。
approximation
108
n. 近似值
D a guess of a number that is not exact but that is close
E You can find an approximation for the area using rectangular strips.
你可以用矩形条找到面积的近似值。
sequence
109
n. 序列
D a series of related things or events, or the order in which things or events follow each other
E Express in words the rule for generating the sequence of numbered balls.
用文字表达生成球的编号序列的规则。
progression
110
n. 数列
D a sequence of numbers in which each term is related to its predecessor by a uniform law
E Write down the fifth term, the common ratio and the n th term of the following geometric progressions.
写出下列等比数列的第五项、公比和第 n 项。
series
111
n. 级数
D a number of similar or related events or things, one following another
E Explain why the geometric series with a =1 and r =–1 does not converge.
解释为什么 a =1和 r =–1的几何级数不收敛。
finite
112
adj. 有限的
D having a limit or end
E A line segment is a finite part of a straight line with two distinct endpoints.
线段是具有两个不同端点的直线的有限部分。
infinite
113
adj. 无限的
D without limits; extremely large or great
E The first three terms of an infinite geometric sequence are 9, 6 and 4.
无穷等比数列的前三项是9、6和4。
summation
114
n. 求和
D the act or process of forming a sum
E Summation is indicated by the use of the symbol Σ (sigma).
求和是用符号∑（sigma）来表示的。
arithmetic sequence
115
等差数列
D a sequence (=an ordered series of numbers) in which the numbers get bigger or smaller by the same amount, such as 3, 6, 9, ..., or 9, 6, 3, ...
E An arithmetic sequence is sometimes called an arithmetic progression.
等差数列（arithmetic sequence）有时称为等差数列（arith-metic progression）。
common difference
116
公差
D the fixed difference between any term in an arithmetic progression and the preceding term
E With an arithmetic sequence, the rule for the n th term can easily be deduced by looking at the common difference.
对于一个等差数列，第 n 项可以很容易地通过观察公差来推导。
geometric sequence
117
等比数列
D a sequence (such as 1, ½, ¼) in which the ratio of a term to its predecessor is always the same
E A geometric sequence has a common ratio between con-secutive terms.
一个等比数列在连续项之间有一个公比。
common ratio
118
公比
D the ratio of each term of a geometric progression to the term preceding it
E Find the first term and the common ratio.
求首项和公比。
periodic
119
adj. 周期的
D happening repeatedly over a period of time
E This periodic feature is an important property of the trigonometric functions.
这种周期性是三角函数的一个重要性质。
converge
120
v. 收敛，聚合
D to move toward the same point and come closer together or meet
E In this case, f ( x ) is said to converge to A as x approaches a .
在这种情况下，当 x 接近 a 时， f （ x ）收敛于 A 。
diverge
121
v. 发散
D to follow a different direction, or to be or become different: If a series of approximations to some value get progressively further from it, then the series is said to diverge.
E If the initial value is not close to the root, then the iteration may converge to another root or diverge.
如果初始值不接近这个根，则迭代的结果可能收敛到另一个根或者发散。
general term
122
通项
D a mathematical expression composed of variables and constants that yields the successive terms of a sequence or series when integers are substituted for one of the variables often denoted by k
E Find a formula for the general term Un .
找到 Un 的通项公式。
sigma notation
123
sigma求和
D a notation of calculating the sum of a group of values
E You can also use a calculator to evaluate the sum of a series in sigma notation.
你可以使用计算器来计算sigma求和。
algebraic fraction
124
代数分式
D a fraction whose numerator and denominator are algebraic expressions
E You can simplify algebraic fractions using division.
你可以用除法简化代数分式。
rational expression
125
有理表达式
D an expression that is the ratio of two polynomials
E Simplify rational expressions by factorising and cancelling.
通过因式分解和约分化简有理表达式。
partial fraction
126
部分分式
D any one of a set of simpler fractions, the sum of which composes a more complex fraction
E Partial fraction decomposition is often useful in integration.
部分分式分解在积分中经常用到。