TSSM Specialist Maths Units 3 & 4 2009 Trial Exam 2

16. A circle has a diameter of 3 cm, a square
has a side length of 3 cm, and an equilateral triangle has a side length of 3 cm. Which of the following lists the shapes in increasing order of circumference or perimeter?
SAMPLE QUESTION: 1,567 – 382 = _____ (A) 1,075 (B) 1,083 (C) 1,185 (D) 1,195 (E) 1,243 The correct answer is 1,185, so choice C is darkened. Sample Answer (A) (B) (C) (D) (E)
(A) (B) (C) (D) (E) 3. Which of the following gives the total
number of seconds in hours, minutes, and seconds?
(A) (B) (C) (D) (E) 6. If the points (–1, 4) and (1, –2) are on a
line that is perpendicular to the line , what is the value of ?

(A) (B) (C) (D) (E) 3
方隅留美---真题最全的SSAT培训机构
3
Upper #1 - QS #1
7. If 20% of is 18, what is 5% of (A) 9 (B) 18 (C) 36 (D) 45 (E) 90

NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENT Unit 3:Mathematics in Construction andthe Built EnvironmentNationalNQF Level 3: BTECGuided learning hours: 60Unit abstractConstruction, civil engineering and building services engineering are technical disciplines which require the collection, processing and use of numerical data. For example, in a simple construction project, the dimensions of a structure are designed and specified by the architect or engineer, the cost of the work is determined by the cost control surveyor, the quantities of materials to be ordered are determined by the buyer, and the setting out dimensions and angles may be calculated by the contractor. In more complex situations, design engineers use various formulae to calculate properties such as the rate of flow of water through pipes for drainage calculations, or the levels of bending moments in beams for sizing structural elements.It is therefore essential that learners develop an acceptable understanding of the mathematical methods and techniques required for these key activities, and of how to apply them correctly.The unit explores the rules for manipulation of formulae and equations, calculation of lengths, areas and volumes, determination of trigonometric and geometric properties, and the application of graphical and statistical techniques.Upon completion learners will be able to select and apply appropriate mathematical techniques to address a wide variety of standard, practical, industry-related problems.Learning outcomesOn completion of this unit a learner should:1 Know the basic underpinning mathematical techniques and methods used tomanipulate and/or solve formulae, equations and algebraic expressions2 Be able to select and correctly apply mathematical techniques to solve practicalconstruction problems involving perimeters, areas and volumes3 Be able to select and correctly apply a variety of geometric and trigonometrictechniques to solve practical construction problems4 Be able to select and correctly apply a variety of graphical and statisticaltechniques to solve practical construction problems.NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENTUnit content1Know the basic underpinning mathematical techniques and methods used to manipulate and/or solve formulae, equations and algebraic expressionsMathematical techniques and methods: mathematical operators; factorization;expansion; transposition; substitution and elimination; rounding; decimal places;significant figures; approximation; truncation errors and accuracy; calculatorfunctions and useFormulae, equations and algebraic expressions: linear; simultaneous; andquadratic equations; arithmetic progressions; binomial theorem2 Be able to select and correctly apply mathematical techniques to solvepractical construction problems involving perimeters, areas and volumesPerimeters, areas and volumes: calculations both for simple and compoundshapes, eg rectangles, trapeziums, triangles, prisms, circles, spheres, pyramids, cones and both regular and irregular surface areas and volumesMathematical techniques: simple mensuration formulae and numerical integration methods (mid-ordinate rule; trapezoidal rule; Simpson’s rule)3Be able to select and correctly apply a variety of geometric and trigonometric techniques to solve practical construction problemsGeometric techniques: properties of points, lines, angles, curves and planes;Pythagoras’ rule; radians; arc lengths and areas of sectors.Trigonometric techniques: sine, cosine, tangent ratios; sine rule; cosine rule;triangle area rules4Be able to select and correctly apply a variety of graphical and statistical techniques to solve practical construction problemsGraphical techniques: Cartesian and Polar co-ordinates; intersections of graph lines with axes; gradients of straight lines and curves; equations of graphs; areas under graphs; solution of simultaneous and quadratic equationsStatistical techniques: processing large groups of data to achieve mean, median, mode and standard deviation; cumulative frequency, quartiles, quartile range;methods of visual presentationU N I T 3: M A T H E M A T I C S I N C O N S T R U C T I O N A N D T H E B U I L T E N V I R O N M E N TE d e x c e l L e v e l 3 B T E C N a t i o n a l s i n C o n s t r u c t i o n – I s s u e 1 – A p r i l 2007 © E d e x c e l L i m i t e d 20073G r a d i n g g r i dI n o r d e r t o p a s s t h i s u n i t , t h e e v i d e n c e t h a t t h e l e a r n e r p r e s e n t s f o r a s s e s s m e n t n e e d s t o d e m o n s t r a t e t h a t t h e y c a n m e e t a l l o f t h e l e a r n i n g o u t c o m e s f o r t h e u n i t . T h e c r i t e r i a f o r a p a s s g r a d e d e s c r i b e t h e l e v e l o f a c h i e v e m e n t r e q u i r e d t o p a s s t h i s u n i t .G r a d i n g c r i t e r i aT o a c h i e v e a p a s s g r a d e t h e e v i d e n c e m u s t s h o w t h a t t h e l e a r n e r i s a b l e t o :T o a c h i e v e a m e r i t g r a d e t h e e v i d e n c e m u s t s h o w t h a t , i n a d d i t i o n t o t h e p a s s c r i t e r i a , t h e l e a r n e r i s a b l e t o :T o a c h i e v e a d i s t i n c t i o n g r a d e t h e e v i d e n c e m u s t s h o w t h a t , i n a d d i t i o n t o t h e p a s s a n d m e r i t c r i t e r i a , t h e l e a r n e r i s a b l e t o :P 1u s e t h e m a i n f u n c t i o n s o f a s c i e n t i f i c c a l c u l a t o r t o p e r f o r m c a l c u l a t i o n s a n d a p p l y m a n u a l c h e c k s t o r e s u l t sM 1 s e l e c t a n d a p p l y a v a r i e t y o f a l g e b r a i c m e t h o d s t o s o l v e l i n e a r , q u a d r a t i c a n d s i m u l t a n e o u s l i n e a r a n d q u a d r a t i c e q u a t i o n sD 1i n d e p e n d e n t l y u n d e r t a k e c h e c k s o n c a l c u l a t i o n s u s i n g r e l e v a n t a l t e r n a t i v e m a t h e m a t i c a l m e t h o d s a n d m a k e a p p r o p r i a t e j u d g m e n t s o n t h e o u t c o m eP 2u s e s t a n d a r d m a t h e m a t i c a l m a n i p u l a t i o n t e c h n i q u e s t o s i m p l i f y e x p r e s s i o n s a n d s o l v e a v a r i e t y o f l i n e a r f o r m u l a e P 3u s e g r a p h i c a l m e t h o d s t o s o l v e l i n e a r a n d q u a d r a t i c e q u a t i o n sM 2 e x t r a c t d a t a , s e l e c t a n d a p p l y a p p r o p r i a t e a l g e b r a i c m e t h o d s t o f i n d l e n g t h s , a n g l e s , a r e a s a n d v o l u m e s f o r o n e 2D a n d o n e 3D c o m p l e x c o n s t r u c t i o n i n d u s t r y r e l a t e d p r o b l e m s P 4p r o d u c e c l e a r a n d a c c u r a t e a n s w e r s t o a v a r i e t y o f p r o b l e m s a s s o c i a t e d w i t h s i m p l e p e r i m e t e r s , a r e a s a n d v o l u m e sP 5p r o d u c e c l e a r a n d a c c u r a t e a n s w e r s t o a v a r i e t y o f s i m p l e 2D t r i g o n o m e t r i c p r o b l e m sM 3 u s e s t a n d a r d d e v i a t i o n t e c h n i q u e s t o c o m p a r e t h e q u a l i t y o f m a n u f a c t u r e d p r o d u c t s u s e d i n t h e c o n s t r u c t i o n i n d u s t r y .D 2i n d e p e n d e n t l y d e m o n s t r a t e a n u n d e r s t a n d i n g o f t h e l i m i t a t i o n s o f c e r t a i n s o l u t i o n s i n t e r m s o f a c c u r a c y , a p p r o x i m a t i o n s a n d r o u n d i n g e r r o r s .U N I T 3: M A T H E M A T I C S I N C O N S T R U C T I O N A N D T H E B U I L T E N V I R O N M E N T4E d e x c e l L e v e l 3 B T E C N a t i o n a l s i n C o n s t r u c t i o n – I s s u e 1 – A p r i l 2007 © E d e x c e l L i m i t e d 2007G r a d i n g c r i t e r i aT o a c h i e v e a p a s s g r a d e t h e e v i d e n c e m u s t s h o w t h a t t h e l e a r n e r i s a b l e t o :T o a c h i e v e a m e r i t g r a d e t h e e v i d e n c e m u s t s h o w t h a t , i n a d d i t i o n t o t h e p a s s c r i t e r i a , t h e l e a r n e r i s a b l e t o :T o a c h i e v e a d i s t i n c t i o n g r a d e t h e e v i d e n c e m u s t s h o w t h a t , i n a d d i t i o n t o t h e p a s s a n d m e r i t c r i t e r i a , t h e l e a r n e r i s a b l e t o :P 6p r o d u c e c l e a r a n d a c c u r a t e a n s w e r s t o a v a r i e t y o f s i m p l e g e o m e t r i c p r o b l e m sP 7d e s c r i b e a n d i l l u s t r a t e t h e u s e o f s t a t i s t i c s i n t h e c o n s t r u c t i o n i n d u s t r y .NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENT Essential guidance for tutorsDeliveryIt is important that learners possess the basic tool kit for simplifying and solving a variety of formulae and expressions. Practical mathematics has at its core some fundamental techniques and methods which must become second nature to the learner. To achieve this the learners need time to follow through worked examples under the guidance of the tutor and then practise this work at their own pace. The work should not be seen as a rote memory exercise but as the application of basic rules as part of a structured and logical procedure. In this way they will be able to cope with a variety of numerical problems that come their way in the course of their studies and later on during their professional career.Learning outcome 1 forms the basis for all the following outcomes and should therefore be covered first. The following two learning outcomes reflect the application of important mathematical skills and techniques in the solution of spatial problems using mensuration, geometry and trigonometric methods and techniques. The final learning outcome covers the separate topic of statistics and their presentation, analysis and interpretation. This structure would therefore indicate at least three assessment instruments.Teaching and learning strategies designed to support delivery of this unit should involve theory, worked examples and then, most importantly, practice. Practice is the key word and the learners must be given many opportunities to practise the relevant techniques. The use of formative tests and coursework will help the learner to see where they may be going wrong. Within the scheme of work there should be time allowed for regular workshops and/or tutorials to reinforce the learning process. It would also be beneficial to provide additional support and tutoring for the weaker learner through the provision of qualified classroom assistants or other forms of learning support. Delivery should stimulate, motivate, educate and enthuse the learner.It is anticipated that this unit will be delivered in the first year of the programme to enable an early foundation to be established for the technical and numerically-based units that are to follow.Group activities are permissible, but tutors will need to ensure that individual learners are provided with equal experiential and assessment opportunities. Health, safety and welfare issues are paramount and should be strictly reinforced through close supervision of all workshops and activity areas, and risk assessments must be undertaken prior to practical activities. Centres are advised to read the Delivery approach section on page 24, and Annexe G: Provision and Use of Work Equipment Regulations 1998 (PUWER).NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENTAssessmentEvidence for this unit may be gathered from short time-controlled phase tests, tutor-provided practical construction scenarios, case studies, practical work or traditional example-based methods.There are many suitable forms of assessment that could be employed. Some examples of possible assessment approaches are suggested below. However, these are not intended to be prescriptive or restrictive, and are provided as an illustration of the alternative forms of assessment evidence that would be acceptable. General guidance on the design of suitable assignments is available on page 19 of this specification. Some criteria can be assessed directly by the tutor during practical activities. If this approach is used, suitable evidence would be observation records or witness statements. Guidance on the use of these is provided on the Edexcel website.A variety of assessment instruments should be used. For the earlier work involving the basic rules of algebra it is suggested that a short time-controlled assignment is given with some degree of revision coaching provided. This will stimulate knowledge and understanding of the basic techniques and methods, as well as developing mental agility. The assessments involving applied mensuration, geometry and trigonometry could be written into practical scenario-based problems that reflect the vocational pathway being studied. The final section on statistics could be in the form of a seminar or oral presentation including the production of visual aids and the use of spreadsheets. There could also be useful opportunities for self- and peer-assessment in this type of situation, but this would need to be carefully balanced against tutor assessment to ensure the validity of the evidence.To achieve a pass grade learners must meet the seven pass criteria listed in the grading grid.For P1, learners must be able to use the main functions of a scientific calculator with confidence and efficiency and be able to produce rough mental and manual checks on the answers achieved. They should give their answers in the appropriate form taking into account truncation, rounding and standard form. In all industry-related problems the correct units should be used.For P2, learners must set out the solutions using the correct mathematical conventions. All solutions to formulae should be re-substituted back to check answers. Minor oversights are acceptable when simplifying expressions provided that the majority of the work and methods are correct.For P3, for simple linear solutions learners will be expected to plot graphs by appropriate selection of a range of x-variables. For more complex types such as simultaneous equation or those including powers the range of values can be provided. All graphs should be correctly annotated and labelled.For P4, learners should provide solutions which clearly show how they have approached the mensuration problem and collated the data, eg the appropriate use of labelled diagrams. The solutions should be set out methodically and clearly using the correct mathematical conventions. Units should be clearly stated for the problems involving physical properties.NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENT For P5, learners should provide solutions which clearly show how they have approached the trigonometric problem and collated the data, eg the appropriate use of labelled diagrams. The solutions should be set out methodically and clearly using the correct mathematical conventions. Units should be clearly stated for the problems involving physical properties.For P6, learners should provide solutions which clearly show how they have approached the geometric problem and collated the data, for example the appropriate use of labelled diagrams. The solutions should be set out methodically and clearly using the correct mathematical conventions. Units should be clearly stated for the problems involving physical properties.For P7, learners need to demonstrate how industry-related data is calculated and presented. The calculation of values and their representation can be integrated within spreadsheet work. Learners should interpret the results and draw relevant conclusions. To achieve a merit grade learners must meet all of the pass criteria and the three merit grade criteria.For M1, learners, with minimal tutor support, should demonstrate how to solve linear, quadratic and simultaneous linear and quadratic equations equations using solution by: formula, by factorisation and by the ‘perfect squares’ method. The structure and layout of the solutions should show a correct and methodical progression through the various stages of the calculations.For M2, learners, with minimal tutor support, should be able to extract data from complex industry-related problems: one 2D and one 3D. They should present and apply the data to suitable mathematical models and perform the necessary calculations. The solutions should be set out methodically and clearly using the correct mathematical conventions. The units should be clearly stated throughout. For M3, learners, with minimal tutor support, should be able to use standard deviation techniques to compare and comment on the material properties of manufactured products, eg cube test strength and steel tensile strength. Access to secondary research data will be sufficient to cover this criterion.To achieve a distinction grade learners must meet all of the pass criteria and merit grade criteria and the two distinction grade criteria.For D1, learners should independently undertake alternative mathematical methods to check solutions, using appropriate and relevant techniques A high level of clarity and presentation should be displayed. For example, this could include the learner independently developing and using spreadsheets for complex multi-stage calculation to confirm manually-generated results. Learners would also be expected to draw suitable conclusions from the resultant outcomes that relate to industrial situations. For D2, learners should independently demonstrate an understanding of the accuracy and rounding of data, and its effect on calculated outcomes. This includes the application of binomial theory to small errors. Suitable conclusions should be made on the resultant outcomes, in an industrial context.NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENTLinks to National Occupational Standards, other BTEC units, other BTEC qualifications and other relevant units and qualificationsIt is anticipated that this unit will be delivered within the early stages of the programme. This will enable the learner to apply the underpinning knowledge, skills and understanding gained in this unit to the study of other, more specialised units. This unit builds upon the knowledge, understanding and skills gained through the Mathematics taught at Key Stage 4, and underpins progression to the numerically-based units within the BTEC National Diploma, including: Unit 4: Science and Materials in Construction and the Built Environme nt; Unit 13: Environmental Science in Construction; Unit 14: Structural Mechanics in Construction and Civil Engineering, Unit 19: Further Mathematics in Construction and the Built Environment, and various building services units.The unit has no direct mapping links to the CIC Occupational Standards at Level 3. The unit provides opportunities to gain Level 3 key skills in: application of number; and information and communication technology. Opportunities for satisfying requirements for Wider Curriculum Mapping are summarised in Annexe F: Wider curriculum mapping.Essential resourcesThe application of mathematical techniques requires little in the way of resources other than scientific calculators and drawing equipment. Both of these are implicit requirements of many other units and, therefore, no additional extra resources are required for this unit, other than a range of industry-contextualised, realistic and feasible project material appropriate to the application of a range of mathematical methods.Where spreadsheets are incorporated into the delivery or assessment scheme, learners should be provided with the appropriate access to suitable software. Indicative reading for learnersTextbooksBird and May — Technician Mathematics 2, 3rd Edition (Pearman, 1994)ISBN 0582234271Greer and Taylor — BTEC National NII: Mathematics for Technicians (Nelson Thornes, 1994) ISBN 0748717013Tourret A — Applying Maths in Construction: Student Book (Architectural Press, 1997) ISBN 0340652950Tourret A and Humphreys — Applying Maths in Construction: Teacher’s Pack (Architectural Press, 1997) ISBN 0340652969NIT ATHEMATICS IN ONSTRUCTION AND THE UILT NVIRONMENT Key skillsAchievement of key skills is not a requirement of this qualification but it is encouraged. Suggestions of opportunities for the generation of Level 3 key skill evidence are given here. Staff should check that learners have produced all the evidence required by part B of the key skills specifications when assessing this evidence. Learners may need to develop additional evidence elsewhere to fully meet the requirements of the key skills specifications.Application of number Level 3When learners are:They should be able to develop the followingkey skills evidence:•performing standardcalculations associated withmensuration, trigonometry orgeometry•selecting appropriateformulae to solve industry-related problems•using appropriate formulae to solve industry-relatedproblems•interpreting, presenting and justifying the results ofcalculations. N3.1 Plan an activity and get relevantinformation from relevant sources.N3.2 Use your information to carry out multi-stage calculations to do with:a amounts or sizesb scales or proportionc handling statisticsd using formulae.N3.3 Interpret the results of your calculations, present your findings and justify yourmethods.Information and communication technology Level 3When learners are:They should be able to develop the followingkey skills evidence:•researching industry data to analyse statistical trends andmeans•manipulating and presenting data using spreadsheets •undertaking checks onmanual calculations bydeveloping and usingrelevant spreadsheets. ICT3.1 Search for information, using different sources, and multiple search criteria in atleast one case.ICT3.2 Enter and develop the information and derive new information.ICT3.3 Present combined information such as text with image, text with number,image with number.。

数学专业英语3—A符号指示集一组的概念如此广泛利用整个现代数学的认识是所需的所有大学生。

集是通过集合中一种抽象方式的东西的数学家谈的一种手段。

集，通常用大写字母：A、B、C、进程运行·、X、Y、Z ；由小写字母指定元素：a、 b 的c、进程运行·，若x、y z.我们用特殊符号x∈S 意味着x 是S 的一个元素或属于美国的x如果x 不属于S，我们写xS.≠当方便时，我们应指定集的元素显示在括号内；例如，由符号表示的积极甚至整数小于10 集{2,468} {2，4.6，进程运行·} 作为显示的所有积极甚至整数集，而三个点等的发生。

点的和等等的意思是清楚时，才使用。

上市的大括号内的一组成员方法有时称为名册符号。

涉及到另一组的第一次基本概念是平等的集。

DEFINITIONOFSETEQUALITY。

两组A 和B，据说是平等的（或相同的）如果它们包含完全相同的元素，在这种情况下，我们写A = B。

如果其中一套包含在另一个元素，我们说这些集是不平等，我们写A = B。

EXAMPLE1。

根据对这一定义，由于他们都是由构成的这四个整数2，4.6 和8 两套{2,468} 和{2,864} 一律平等。

因此，当我们用来描述一组的名册符号，元素的显示的顺序无关。

动作。

集{2,468} 和{2,2,4,4,6,8} 是平等的即使在第二组，每个元素2 和4 两次列出。

这两组包含的四个要素2,468 和无他人；因此，定义要求我们称之为这些集平等。

此示例显示了我们也不坚持名册符号中列出的对象是不同。

类似的例子是一组在密西西比州，其值等于{M、我、s、p} 一组单词中的字母，组成四个不同字母M、我、s 和体育3 —B子集S.从给定的集 S，我们可能会形成新集，称为.的子集例如，组成的那些正整数小于 10 整除 4 （集合{8 毫米}）的一组一般是的所有甚至小于 10.整数集的一个子集，我们有以下的定义。

那你就得了解各种数学名称了，比如“y分之x”是“x over y”，“x乘以y”是“x times y”，“除以”是“divided by”，加plus, 减minus；“x的y次方”是“x to the power of y”，“根”是“root”，几次跟就是几的英语序数形式，6次根=6th root。

1.(A的三次方+B的立方根-CXD的五次方)/E=F 读做:A cube plus the cube root ofB minusC multiplied by the 5th power of D, all divided by E equals F.2.(6+3+7/12-4.35X5)/(9*1/3) 读做: Six plus three and seven twelfths minus four decimal three five multiplied by fiv e, all divided by nine and a third.3. 基本术语：数学 mathematics 数字 number 双数 even number 单数 odd number 计算 calculate口算calculate mentally 笔算calculate using pen-and-paper 竖式vertical form 一位数1-digit number两位数2-digit number 文字题word problem 应用题story problem4、常用符号： ＋ plus、 － minus、 ＝ equal(s)、＞ is greater/more than、＜ is less than ( ) brackets5、加减法及各部分名称：加法 addition 加数 addend 和 sum 减法 subtraction被减数 minuend 减数 subtrahend 差 difference6、数位知识：数位表place value chart 个 Units/Ones 十 Tens 百 Hundreds7、图形名称：长方体 cuboid 正方体 cube 圆柱 cylinder球 sphere长方形 rectangle 正方形 square三角形 triangle 圆 circle边 side 角 angle 面 face专业英语中常用符号和数学表达式1．数的分类complex number 复数zero; naught;0 零real number 实数imaginary number 虚数relational number 有理数irrational number 无理数integer number 整数positive integer number 正整数natural number 自然数negative integer number 负整数fraction 分数decimal 小数odd number 奇数even number 偶数cardinal number 基数ordinal number 序数approximate number 近似数significant number 有效数2．整数addition 加法subtraction 减法addend 加数subtrahend 减数augend 被加数minuend 被减数plus sign 加号minus sign 减号sum 和difference（diffa）差plus; add; and; increase 加minus; decrease; subtract 减is; equal 等division 除法multiplication 乘法divide 除multiply; multiplied by; times 乘divisor 除数multiplier 乘数dividend 被除数multiplicand 被乘数quotient 商product 积remainder 余数positive 正negative 负3．小数和分数numerator 分子denominator 分母decimal point 小数点naught point four 零点四fraction stroke 分数线recurring decimal 循环小数4．百分数percent 百分比interest 利息average 平均数round off 舍入discount 折扣5．幂与指数power 幂; 乘方root-extracting 开方exponent 指数logarithms 对数X squared 某数的平方cube 三次方three cubed 三次方的four 乘四次方cube root 立方根square root 平方根to rise to the power of five 使乘五次方radical sign根号6．代数algebra 代数equation 等式; 方程式inequality 不等式unknown number 未知数absolute value绝对值simple equation 一次方程quadratic equation 二次方程cubic equation 三次方程monomial 单项式polynomial 多项式variable 变量coefficient 系数differential 微分integral 积分derivative 导数function 函数ratio 比proportion 比例sign of equality等号sign of inequality不等号interval 区间matrix 矩阵theorem 定理lemma 引理definition 定义7．常用数学表达式1/2a half; one halfl/3 a third; one third2/3 two thirds1/4 a quarter; one quarter; a fourth; one fourthl/100 a（one）hundredthl/1,000 a（one）thousandth113/324 one hundred and thirteen over three hundred and twenty-four four and two-thirdsforty-five and eighty-nine over twenty-three0.1 one tenth; point one0.01 one hundredth; point zero one0.001 one thousandth; point zero zero one; point two zero one 2050.0357 two thousand and fifty point zero three five seven0.25 zero point two fivepoint two five repetend fivezero point two five recurringzero point three seven twenty-five recurring对483579四舍五入到千位round off 483579 to nearest thousand 108 one followed by eighteen zeros-30.8 negative thirty point eight2-3i two minus three i; two minus three times i2％two per cent; two percent5‰ five per mill; five permill∞infinityx＋y＝zx plus y is z; add x to y is z; x and y is z(x＋y) bracket x plus y bracket closedx-y x minus y; subtract y from x; y from x; x subtracts yx±y x plus or minus yx×y; xy xy; multiply x by y; x multiplied by y; x by y; x times y;x÷ydivide x by y; y into xx over yx : y the ration of x to yx∝y x varies as y; x is in direct proportion to yx＝y x equals y; x is equal to y; x is yx≠y x is not equal to y; x is not yx≡y x is identical to y; x is equivalent to y; x is equivalent to y;x≈y x is approximately equal to y; x approximately equals yx＞y x is greater than y; x is more than yx>>y x is much greater than y; x is far greater than yx≥y x is greater than or equal to yx＜y x is less than yx<<y x is much less than yx≤y x is less than or equal to y0＜x＜1 zero is less than x is less than 1; x is greater than zero and less than 1 0≤x≤1 zero is less than or equal to x is less than or equal to 1x2 x square; x squared; the square of x;the second power of x; x to second powerx3 x cube; x cubed; the cube of x;the third power of x; x to the third powerxn the nth power of x; x to the nth power; x to the power nthe square root of x; x squaredthe cube root of xthe nth root of xx-n x to the (power) minus n(x+y)2x plus y all squaredx over y all squaredx i x i; x subscript i; x suffix i; x sub ilognxlog x to the base n; log of x to the base nlog10x log x to base 10; common logarithmlogex; lnx log x to the base e; log to the base e of y; natural log (of) yex; exp(x) exponential function of x, e to the power xthe summation of x sub i, where i goes from 1 to n;the sum from i equals one to n x i;the sum as i runs from one to n of the x ithe product of x sub i, where i goes from one to nthe product of all x i from i equals one to nthe product of all xi from i equals one to infinitythe absolute value of x; mod x; modulus xthe mean value of x; x barx hatx tildex* x asteriskx primex double primex double prime sub mf(x) f x; f of x; the function f of xa function f from S to Tf&cent;(x) f prime x; f dash x; the (1st) derivative of f with respect to xf&sup2;(x) f double–prime x; f double–dash x; the second derivative of f with respect to x f&cent;&sup2;(x) f triple–prime x; f triple–dash x; the third derivative of f with respect to x f4(x) four x; the fourth derivative of f with respect to xx! n factorial△finite difference or increment△x,δx the increment of xdx dee x; dee of x; differential xdel; nablanth del (nabla)the differential coefficient of y with respect to x;the first derivative of y with respect of xthe second derivative of y with respect of xthe nth derivative of y with respect of xthe partial (derivative) of y with respect to uthe second partial (derivative) of y with respect to xthe partial derivation of z with respect to x of the partial derivative of z with respect to y ∫integral of∫∫double Integral of∫…∫n-fold integral ofthe integral between limits a and b; the integral from a to bthe indefinite integral of a times x with respect to xthe integral from a to b of function of xthe double integral of f of x,ythe limit as x approaches 0the limit as x approaches 0 from abovethe limit as x approaches 0 from belowthere existsfor all∵because∴thereforex⊥y x is perpendicular to yx∥y x is parallel to yx～y the difference between x and yx∝y x varies directly as yx&THORN;y x implies y; if x, then yx&Ucirc;y x if and only if y; x is equivalent to y; x and y are equivalent { };empty setx&Icirc;A x belongs to A; x is an element (or a member) of Ax&Iuml;A x does not belong to A; x is not an element (or a member) of AA&Igrave;B A is contained in B; A is a subset of BA&Eacute;B A contains B;B is a subset of AA&Ccedil;B A cap B; A meet B; A intersection BA&Egrave;B A cup B; A join B; A union BA\B A minus B; the difference between A and BA×B A cross B; the Cartesian product of A and B(A与B的笛卡尔积)||A||the norm (or modulus) of Avector FAB; the length of the segment ABAT A transpose; the transpose of AA-1 A inverse; the inverse of Ax→y x maps into y; x is sent (or mapped) to yx→∞x approaches infinity∠xangle xx is perpendicular to yx is parallel to ysin sinecos cosinetg, tan tangentctg, cot cotangentsc, sec secantcsc, cosec cosecantsin-1, arcsin arc sinecos-1, arcos arc cosinesinh the hyperbolic sinecosh the hyperbolic cosine( ) round brackets; parentheses ;the signs of grouping [ ] square（angular）brackets; bracket< > angle bracket{} braces8．常用希腊字母字母读音字母读音字母读音alphabeta ,gamaxi ,psideltaepsilonzeta ,phiomegalambdamnnuetarho,sigmataupi9．其他数学名词line 线angle 角intersecting line 相交线parallel line 平行线triangle 三角形quadrilateral 四边形rectangle 矩形lozenge 菱形square正方形polygon多边形circle圆arc弧perimeter周长area面积diameter直径volume体积10．具体读法实例y=f(x) y is a function of x6×5＝30 six times (multiplied by) five equals (is equal to) thirty(x-y)(x+y) x minus y; x plus ythe fifth root of x squarey-10 y to the minus tenth (power)20 : 5＝16 : 4 the ratio of 20 to 5 equals the ration of 16 to 4 (20 is to 5 as 16 is to 4) e=1.6×10-19 e equals one point multiplied by ten to minus nineteenth power10-n ten to the minus none over n squareone over one minus n times z reversef(x)=ax2+bx+c the function of x equals a times the square of x plus b times x plus c |a|=b the absolute value of a equals that of bmax f(x) the maximum value of f(x)min f(x) the minimum value of f(x)∞ a sub n approaches / tends to infinity◊anthe limit of Sn as n gets arbitrarily large is one thirdx to the fifth power plus A over (divided by) the quantity x squared plus B, to the two-thirds power (A+B)C the quantity A plus B times CA+B=C A plus B equals CA-B=C A minus B equals CA×B=C A multiplied by B equals CA/B=C A divided by B equals CA : B=C : D A is toB of A to B asC is to D11．数学问题求解的一般表示Solve the following system of equationsSolution: multiply equation (1) by (2) and getSubtract equation (2) from equation (4), and getSubtract equation (3) from equation (2), and getfrom equation (5) from equation (6),obtain x and y.。