pre-calculas 11

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课程表英语作文与画图

课程表英语作文与画图英文回答：My Course Schedule: A Journey Through Time and Space.My schedule is a testament to my diverse interests and aspirations. It is a tapestry woven with the threads of academic rigor, creative expression, and extracurricular exploration.Monday.8:00-9:30 AM: Calculus (math) A cerebral challengethat sharpens my analytical skills.9:30-11:00 AM: Medieval History (history) A journey through the complexities of the past, illuminating human behavior and shaping my understanding of the present.11:00-1:00 PM: Painting (art) An escape into the realmof colors and textures, where I express my creativity and cultivate my aesthetic sensibilities.1:00-2:30 PM: Lunch and Student Government Meeting (extracurricular) A time to connect with my peers, discuss school issues, and make a meaningful contribution to the student body.2:30-4:00 PM: Spanish (language) A gateway to another culture, expanding my horizons and fostering a deep appreciation for linguistic diversity.Tuesday.8:00-9:30 AM: Physics (science) Unraveling the mysteries of the universe, from Newton's laws to the intricacies of quantum mechanics.9:30-11:00 AM: English Literature (literature) Delving into the depths of human emotions, exploring the complexities of storytelling, and developing my critical thinking abilities.11:00-1:00 PM: Dance (art) A physical manifestation of rhythm and grace, empowering me to express myself through the beauty of movement.1:00-2:30 PM: Lunch and Debate Team Meeting (extracurricular) Engaging in lively discussions, honing my research skills, and developing a nuanced understanding of current events.2:30-4:00 PM: Psychology (social science) Exploring the inner workings of the human mind, understanding human behavior, and gaining invaluable insights into myself and others.Wednesday.8:00-9:30 AM: Pre-Calculus (math) Building a solid foundation in mathematics, preparing me for more advanced mathematical concepts.9:30-11:00 AM: World Cultures (social science)Embarking on a global adventure, examining the customs, traditions, and beliefs of diverse societies.11:00-1:00 PM: Drawing (art) Capturing the essence of the world around me through pencil and paper, honing my observational skills and developing my ability to convey emotions visually.1:00-2:30 PM: Lunch and Student Council Meeting (extracurricular) Participating in the governance of the school, representing student interests, and collaboratingon initiatives that enhance the educational experience.2:30-4:00 PM: Biology (science) Discovering the wonders of life, from the intricacies of cells to the complex processes of ecosystems.Thursday.8:00-9:30 AM: Algebra (math) Strengthening myalgebraic foundation, developing problem-solving techniques, and laying the groundwork for future mathematical endeavors.9:30-11:00 AM: American History (history) Revisiting the transformative events that shaped the nation, fostering a deep appreciation for its people and ideals.11:00-1:00 PM: Photography (art) Capturing moments in time through the lens of a camera, experimenting with light, composition, and perspective.1:00-2:30 PM: Lunch and Yearbook Club Meeting (extracurricular) Documenting the school year through photography, writing, and design, creating a lasting record of our shared experiences.2:30-4:00 PM: Environmental Science (science)Exploring the intricate relationships between humans and their environment, promoting sustainable practices and fostering an appreciation for the natural world.Friday.8:00-9:30 AM: Geometry (math) Investigating theproperties of shapes, developing spatial reasoning skills, and preparing for more advanced geometrical concepts.9:30-11:00 AM: Spanish (language) Continuing my journey into the Spanish language and culture, exploringits rich literature and honing my communication abilities.11:00-1:00 PM: Free Period A well-deserved break to catch up on homework, prepare for upcoming assignments, or simply relax and recharge.1:00-2:30 PM: Lunch and Robotics Club Meeting (extracurricular) Engaging in hands-on problem-solving, building robots, and fostering a passion for STEM.2:30-4:00 PM: Elective (choice) A chance to explore my passions, develop new interests, or pursue independent study.My Courses in Visual Representation:[Image of a schedule with classes, times, and visuals]中文回答：我的课程表，一段时空之旅。

ap-预备微积分

ap-预备微积分AP Precalculus 预备微积分为什么要开设AP Precalculus？如果高中期间没有做好充分的准备，对于很多大学新生来说，入门级数学的学习还是比较吃力的，学生们很难完成大学数学入门级课程，同时能够获得的学习支持也很少。

为了帮助学生们能够顺利完成大学数学的入门过渡，帮助更多高中生尽早夯实数学基础，CB便考虑开设AP Precaculus课程，即“微积分预备”。

简而言之，AP Precalculus开设可以归类为以下几类好处：▪准备：为学生更好地学习大学数学提供准备；▪鼓励：鼓励更多学生在高中完成四年的数学学习；▪培养：帮助想要就读STEM的学生完成目标；▪装备：让学生具备完成大学学业要求所需的数学技能；AP Precalculus 课程内容课程内容Unit 1: Polynomial and Rational FunctionsUnit 2: Exponential and Logarithmic Functions Unit 3: Trigonometric and Polar Functions Unit 4: Functions Involving Parameters, Vectors, and Matrices每个单元都是未来大学数学科目的重要基础。

通过AP Precalculus 课程的学习，学生们在大学的数学基础课的学习中更能从容应对。

主要培养学生的以下3项技能：•Procedural and Symbolic Fluency •Multiple Representations •Communication and ReasoningAP Precalculus 课程大纲AP Precalculus 考试形式AP Precalculus的考试和AP Calculus整体比较相似，分为选择题和简答题两部分。

值得注意的是，这次新加入的AP Precalculus同样分为计算器部分和非计算器部分，说明对于学生的计算能力还是有一定考察的。

ap precalculus 样题

文章标题：深度解析AP Precalculus样题1. 引言：理解AP Precalculus样题的重要性在学习AP Precalculus的过程中，掌握和理解样题是至关重要的。

通过深入分析样题，我们可以更好地掌握课程知识和考试要求，从而在考试中取得更好的成绩。

在本文中，我将对AP Precalculus样题进行全面评估并撰写一篇深度解析的文章，帮助您更深入地理解这一主题。

2. 深度：逐步分析AP Precalculus样题让我们从简单的AP Precalculus样题开始。

考虑以下样题："求解不等式x^2 - 4 > 0的解集。

"这道题目涉及到了二次函数和不等式的理解和求解，是我们学习中常见的知识点之一。

在这里，我们可以通过分析函数的图像和性质，以及不等式的求解方法来逐步解答这道题目。

通过这种由浅入深的方式，我们可以更好地理解不等式的解集和其在坐标系中的几何意义。

接下来，让我们深入探讨一些更复杂的AP Precalculus样题。

例如："求解三角方程sin(x) = 0.5的全部解。

"这道题目涉及到三角函数的性质和方程的求解，需要我们对三角函数图像和周期性有较深入的了解。

我们可以通过绘制函数图像和利用三角函数的周期性来寻找全部解，并结合三角函数的性质来求解方程。

通过这种逐步深入的分析，我们可以更全面地掌握三角函数的性质和方程的求解方法。

3. 广度：从多个角度审视AP Precalculus样题除了对样题的深入分析外，我们还需要从多个角度来审视AP Precalculus样题。

在解决函数和方程的样题时，我们可以结合几何意义、图像、性质和求解方法来全面理解题目要求。

通过这种多角度的审视，我们可以更全面地掌握AP Precalculus知识，并在解题时灵活运用各种方法。

4. 总结与回顾：深刻理解AP Precalculus样题的重要性通过对AP Precalculus样题的深度和广度全面评估，我们可以更深刻地理解课程知识和解题方法。

2022-2023学年河南省鹤壁市河南省示范性普通中学高一英语上学期期末试题含解析

2022-2023学年河南省鹤壁市河南省示范性普通中学高一英语上学期期末试题含解析一、选择题1. I might buy a TV, if I can find a ______in the sales.A. bargainB. tradeC. businessD. exchange参考答案：A2. The tomato juice left brown ________ on the front of my jacket.A. spotsB. pointsC. tracksD. traces参考答案：A3. The hikers stopped to rest halfway up the mountain, _________.A. exhaustingB. being exhaustedC. to be exhaustingD. exhausted参考答案：D【详解】考查形容词做状语。

句意：徒步旅行者在半山腰上停下来休息，筋疲力尽。

形容词作状语用时,一般用逗号将其与句子的其余部分隔开，.这种状语可位于句首、句末或句中。

本句中的exhausted为形容词做伴随状语相当于and they were exhausted. 故D选项正确。

【点睛】形容词除了可以作定语、表语或补语外,还可以在句中作状语,具有副词的功能。

形容词作状语用时,一般用逗号将其与句子的其余部分隔开。

这种状语可位于句首、句末或句中.它在意义上相当于一个状语从句,具有以下语义和特征一、形容词或形容词短语可以作状语,表示行为方式或伴随状况.有时,它会像非限制性定语从句一样,表示意义上的增补,其逻辑主语是句子的主语。

二、形容词或形容词短语可以作状语,表示原因，表示时间或条件，表示结果或存在的状态，表示让步。

分析句子可知，本句中的exhausted为形容词做伴随状况状语相当于and they wereexhausted. 故D选项正确。

计算的英语单词

计算的英语单词计算英语单词calculatecountreckon计算的英语例句工程师们计算桥梁的应变和应力。

Engineers calculate the strains and stresses on a bridge.由于他计算错误而造成一起爆炸。

His failure to pute correctly resulted in ane_plosion.他们正在计算选票。

Theyre counting the ballots now.让我计算一下旅途的用费。

Let me calculate the cost of the journey.你可以接通全国计算机网络。

You can plug into the national puter work.我对计算机硬件一窍不通。

I know nothing about puter hardware.计算机程序设计人员的一般工资是多少Whats the going rate of puter programmers计算机查实数据输入是否正确。

The puter verified whether the data was loaded correctly.我们正在使用的计算机大多数是数字计算机。

Most of the puters we are using are digital puters.我的计算机里有很多软件。

There are many sorts of software in my puter.整理出一套计算机用的计算方法，并给出计算实例。

A calculation procedure is presented in the paper and e_les are also given.论述了矿物计算的二个原则及计算过程。

It also discusses two principles of calculating minerals and their process.每个计算单元都对另一个计算单元具有管理权限。

Pre-Calculus11Ch...

Pre-Calculus 11 Chapter 6 Rational Expressions and Equations.Date:__________________ Block:_____ Name:__________________Lesson Notes 6.1: Rational ExpressionsObjectives: • determining non -permissible values for a rational expression• simplifying a rational expression • modeling a situation using a rational expressionMany day-to-day applications use rational expressions . You can determine the time it takes to travel across Canada by dividing the distance travelled, d , by the rate of speed at which you are travelling, r . Light intensity and the intensity of sound can be described mathematically as ratios in the form2d k , where k is a constant and d is the distance from the source. When would it be important to know the intensity of light or sound? rational expressionWhenever you are working with algebraic fractions, it is important to determine any values that must be excluded. What happens in each of the following expressions when x = 3 is substituted?What value(s) cannot be used for x in each of the following algebraic fractions?Questions that we often need to ask ourselves:What is the result when zero is divided by any non-zero number?Why is division by zero undefined?Non-Permissible ValuesWhenever you use a rational expression, you must identify any values that must be excluded or are considered non-permissible values. Non-permissible values are all values that make the denominator zero.Example 1) For each rational expression, determine all non-permissible values.Simplifying Rational ExpressionsWriting a rational number in lowest terms and simplifying a rational expression involve similar steps.To simplify a rational expression, divide both the numerator and denominator by any factors that are common to the numerator and the denominator.When a rational expression is in simplest form, or its lowest terms, the numerator and denominator have no common factors other than 1.Example 2) Simplify each rational expression. State the non-permissible values.Your TurnSimplify each rational expression. What are the non-permissible values?Example 3) Consider the expressiona) What expression represents the non-permissible values for x?b) What is the non-permissible value for y if x = 3?c) Simplify the rational expression.d) Evaluate the expression for x = 2.6 and y = 1.2. Show two ways to determine the answer. Example 4) The area of right ∆PQR is (x2–x – 6) square units, and the length of side PQ is (x – 3) units. Side PR is the hypotenuse.a) Draw a diagram of ∆PQR.b) Write an expression for the length of side QR. Express your answer in simplest form.c) What are the non-permissible values?Example 5) Parallelogram ABFG has an area of (16x2– 1) square units and a height of (4x – 1) units. Parallelogram BCDE has an area of (6x2–x – 12) square units anda height of (2x – 3) units. What is an expression for the area of ∆ABC? Leaveyour answer in the form ax2+bx +c. What are the non-permissible values?Example 6) Write in simplest form. Identify any non-permissible values.。

美国大学常用课本

美国⼤学常⽤课本我来说⼀些美国college⽐较流⾏的课本，因为本⼈是理⼯科，上的⼤学也是很⼀般的，不过没吃过猪⾁也见过猪跑啊。

顶尖⼤学的课本名单还是能找到的。

很多希望学习英⽂，或是由⾄于留学美国的⾼中，⼤学⽣可以参考⼀下是否在同⼀⽔平上。

⼀般来说美国的college students必须要上⼀些GE课程，就是general course。

包含必修的微积分（看看看，⾛到哪⾥都跑不掉的）现在很流⾏的课本是james stewart 的calculus. 这本书应⽤⼴泛，且长盛不衰，版本到第五版了，价格也随之飙升到156美⼑，前⼀阵南加州有⼀个学⽣游⾏，就是专门重点抗议这本书出了第五版，且涨了27块钱。

随之的，就连初级微积分（precalculus)都是stewart出的。

这本书很厚，上千页，包含了同济版的所有内容就我看来（我也不熟悉同济版，我当初⽤的是变态的交通⼤学版）。

从最初的极限，求导，积分，⽆穷级数，到多重积分，常微积分。

尤其是对于⼀些偏枝很是强调，⽐如说物理应⽤，球⾯柱⾯坐标应⽤，，另外对求复杂积分的难度有要求。

另外淡化了极限的理论定义，主要以应⽤为主。

但是写得⾮常详尽，该有的例题都有了，（都让⼈觉得罗嗦了），课后习题多的让⼈⼿抽筋。

不过我的看法是，只要国内的微积分能学好，这本微积分并不算难。

（因为理论性的东西少，可能还简单不少）。

流⾏的好处是，本书要想下载，只要到emule上⼀搜，乌央乌央的。

给出详细内容：Hardcover: 1368 pagesPublisher: Brooks Cole; 5 edition (December 24, 2002)Language: EnglishISBN: 053439339XProduct Dimensions: 10.3 x 8.5 x 2.1 inchesShipping Weight: 6.1 pounds另⼀本是偏理论性的，caltech,MIT都骄傲的宣称他们使⽤此书，Apostol的calculus and linear algebra，是将为积分与线性代数结合在⼀起的。

precalculus知识点总结

precalculus知识点总结Precalculus is an essential branch of mathematics that serves as a bridge between algebra, geometry, and calculus. This subject is crucial for students preparing to undertake advanced courses in mathematics, physics, engineering, and other technical fields. In this precalculus knowledge summary, we will cover important topics such as functions, trigonometry, and analytic geometry.FunctionsOne of the fundamental concepts in precalculus is that of functions. A function is a relationship between two sets of numbers, where each input is associated with exactly one output. In other words, it assigns a unique value to each input. Functions can be represented in various forms, such as algebraic expressions, tables, graphs, and verbal descriptions.The most common types of functions encountered in precalculus include linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions. Each type of function has its own unique characteristics and properties. For example, linear functions have a constant rate of change, while quadratic functions have a parabolic shape.Functions can be manipulated by performing operations such as addition, subtraction, multiplication, division, composition, and inversion. These operations can be used to create new functions from existing ones, or to analyze the behavior of functions under different conditions.TrigonometryTrigonometry is the study of the relationships between the angles and sides of triangles. It plays a crucial role in precalculus and is essential for understanding periodic phenomena such as oscillations, waves, and circular motion.The primary trigonometric functions are sine, cosine, and tangent, which are defined in terms of the sides of a right-angled triangle. These functions have various properties, such as periodicity, amplitude, and phase shift, which are important for modeling and analyzing periodic phenomena.Trigonometric functions can also be extended to the entire real line using their geometric definitions. They exhibit various symmetries and periodic behaviors, which can be visualized using the unit circle or trigonometric graphs. Additionally, trigonometric identities and equations are essential tools for simplifying expressions, solving equations, and proving theorems.Analytic GeometryAnalytic geometry is a branch of mathematics that combines algebra and geometry. It deals with the use of algebraic techniques to study geometric shapes and their properties. Inprecalculus, this subject is primarily concerned with the study of conic sections, such as circles, ellipses, parabolas, and hyperbolas.The equations of conic sections can be derived using geometric constructions, or by using algebraic methods such as completing the square, factoring, and manipulating equations. These equations can then be used to describe the geometric properties of conic sections, such as their shape, size, orientation, and position.Furthermore, analytic geometry also involves the study of vectors and matrices, which are important tools for representing and manipulating geometric objects in higher dimensions. Vectors can be used to represent points, lines, and planes in space, while matrices can be used to perform transformations such as rotations, reflections, and scaling.Other TopicsIn addition to the core topics mentioned above, precalculus also covers other important concepts such as complex numbers, polar coordinates, sequences and series, and mathematical induction. Complex numbers are used to extend the real number system to include solutions to equations that have no real roots. They have applications in various fields such as electrical engineering, quantum mechanics, and signal processing.Polar coordinates provide an alternative way of describing points in the plane using radial distance and angular direction. They are particularly useful for representing periodic and circular motion, as well as for simplifying certain types of calculations in calculus.Sequences and series are ordered lists of numbers that have a specific pattern or rule. They can be finite or infinite, and their sums can be used to represent various types of mathematical and physical phenomena. For example, arithmetic sequences are used to model linear growth or decline, while geometric series are used to model exponential growth or decay.Finally, mathematical induction is a powerful method for proving statements about positive integers. It is based on the principle that if a certain property holds for a base case, and if it can be shown that it also holds for the next case, then it holds for all subsequent cases as well. This method is widely used in various areas of mathematics, such as number theory, combinatorics, and discrete mathematics.ConclusionIn conclusion, precalculus is a diverse and rich subject that covers a wide range of mathematical concepts and techniques. It provides students with the necessary foundation to tackle more advanced topics in calculus and beyond. By mastering the core topics of precalculus, students will be well-equipped to understand and apply advanced mathematical methods in various technical fields. Whether it be functions, trigonometry, analytic geometry, or any other topic, a solid understanding of precalculus is essential for success in higher mathematics.。

University Requirements

SFU Admission from high schools in British Columbia or the YukonAdmission to SFU is competitive. In the past, the average for admission has ranged from 80% to 90%, depending on the program. Your admission average is calculated on four (4) approved grade 12 level courses. Grade 11 courses must be passed but those grades are not used to calculate your admission average.All students must write the English 12 provincial exam and meet BC high school graduation requirements.To be considered for admission, you must meet the general requirements, including English language admission requirements, and theprogram-specific requirements listed for that program. Click on the program you are interested in to see all the requirements.If you have been offered admission for the fall term, log into your Student Centre by June 1st to accept your offer of admission.New Math Requirements for Fall 2013General Admission Requirement: Pre-Calculus 11 or Foundations of Mathematics 11 to replace Principles of Mathematics 11Faculty/Program Specific Requirements: Pre-Calculus 12 to replace Principles of Mathematics 12Beedie School of BusinessAccounting, Entrepreneurship and Innovation, Finance, Human Resource Management, International Business, Management Information Systems, Management Science, MarketingGeneral requirementsEnglish language requirements - click for details.∙English 11(or Français première langue 11)∙Language 11(includes beginner's language 11, American sign language 11 or 12, and language 12courses)∙Science 11(includes Applications of Physics 12, Biology 11, Chemistry 11, Earth Science 11, Forests 11, IB Environmental Systems 11, Principles of Physics 11)∙Principles of Math 11 with a minimum grade of 60%(or Foundations of Math 11, or Pre-Calculus 11, or Principles of Math 12, or Applications of Math 12 or Foundations of Math 12 or Pre-Calculus 12 or Calculus 12) with aminimum grade of 60%∙English 12 with a minimum final blended grade of 60%(or English 12 First Peoples, or Français première langue 12) with a minimum finalblended grade of 60%∙Graduate from high schoolProgram-specific RequirementsEnglish 12, Principles of Math 12 or Pre-Calculus 12, and two additional approved Grade 12 coursesAdmission decisions for secondary students applying will be based on a combination of a student’s academic performance and an assessment of their broad based admissions form. For details, please see the Beedie School of Business website.Approved grade 12 coursesBC First Nations Studies 12, Calculus 12, Comparative Civilization 12, Economics 12, English Literature 12, Foundations of Math 12, French 12 or français langue seconde 12, German 12, History 12, Japanese 12, Law 12, Mandarin 12, Principles of Math 12 or Pre-Calculus 12, Philosophy 12, Punjabi 12, Social Justice 12, Spanish 12, Sustainable Resources 12.Sciences: Biology 12, Chemistry 12, Geography 12, Geology 12, Physics 12.IB/AP: All standard and higher level IB courses, and all AP courses, may be used in place of grade 12 courses.place of grade 12 courses.Faculty of Communication, Art andTechnologyCommunicationContemporary ArtsInteractive Arts and Technology (TechOne)General requirements∙English language requirements - click for details.∙English 11(or Français première langue 11)∙Language 11(includes beginner's language 11, American sign language 11 or 12, and language 12courses)∙Science 11(includes Applications of Physics 12, Biology 11, Chemistry 11, Earth Science 11, Forests 11, IB Environmental Systems 11, Principles of Physics 11)∙Principles of Math 11 with a minimum grade of 60%(or Foundations of Math 11, or Pre-Calculus 11, or Principles of Math 12, or Applications of Math 12 or Foundations of Math 12 or Pre-Calculus 12 or Calculus 12) with aminimum grade of 60%∙English 12 with a minimum final blended grade of 60%(or English 12 First Peoples, or Français première langue 12) with a minimum finalblended grade of 60%∙Graduate from high schoolProgram-specific RequirementsEnglish 12, Principles of Math 12 or Pre-Calculus 12, and two additional approved Grade 12 coursesApproved grade 12 coursesBC First Nations Studies 12, Calculus 12, Comparative Civilization 12, Economics 12, English Literature 12, Foundations of Math 12, French 12 or français langue seconde 12, German 12, History 12, Japanese 12, Law 12, Mandarin 12, Principles of Math 12 or Pre-Calculus 12, Philosophy 12, Punjabi 12, Social Justice 12, Spanish 12, Sustainable Resources 12.Sciences: Biology 12, Chemistry 12, Geography 12, Geology 12, Physics 12.IB/AP: All standard and higher level IB courses, and all AP courses, may be used in place of grade 12 courses.International high schoolAdmission requirementsTo be considered for admission, you must meet the general university entrance requirements, including English language and quantitative skills requirements, and the program-specific requirements listed for that program. Click on the country where you have completed your studies to see all the requirements.Quantitative and analytical skills requirementAll applicants to undergraduate programs must demonstrate their competence in quantitative and analytical skills in one of the following ways:1. a minimum grade of 60% or C in a senior level math course or precalculus2. a minimum score of 3 in IB HL or SL math3. a minimum D grade in GCE A/AS/O level math4. a grade of C- or better in a 3-unit math or certified Q (quantitative) course that transfers toSFU (for college and university transfer students).NOTE: a minimum grade of 70% is required in one of the acceptable Math courses used for admission in order to enroll directly in Q courses. See more information.English language requirementAll applicants, regardless of country of origin or citizenship status, must demonstrate competence in the English language in one of the following six ways, depending on where you are completing your education. (Note that enrollment in first-year writing intensive courses requires higher grades than admission grades. See our FAQs.)pletion of the last three years of full-time secondary education in English in Canadaor another country where the principal language of instruction is English. A minimumblended grade of 60% or C in one of English 12, English Literature 12, or English 12First Peoples, or their equivalents, is required.Note: a final, blended mark of 75% will permit enrollment in a writing-intensive (W)course.pletion of the last four years of full-time secondary education in English at arecognized International school where the principal language of instruction in the countryis not English. A minimum grade of C or 60% in senior level English is required.pletion of IB English A1 or A2 (HL or SL) with a minimum grade of 3.pletion of a three unit transferable English course or certified W (writing intensive)course with a minimum grade of C-.pletion of the IELTS (International English Language Testing System) with aminimum overall band score of 6.0.(Effective for Summer 2012 admission and later: completion of the IELTS(International English Language Testing System) with a minimum overall band score of6.5 with no part less than 6.0.)pletion of TOEFL IBT (Test of English as a Foreign Language internet-based test)with an overall score of 88 or better with a minimum score of 20 in each of the fourcomponents (listening, speaking, writing, reading).Literacy RequirementsApplicants to SFU must demonstrate their literacy competence. The route they take to do this will depend on whether they apply for direct admission from Grade 12, for admission by post-secondary transfer, or for admission as an International Student.Direct admission from Grade 12Applicants must have a minimum blended grade (final course grade + provincial exam mark) of 60% or higher in a course equivalent to (or more advanced than) English 12 or English Literature 12 (more advanced English courses would include Advanced Placement and International Baccalaureate)to be considered for admission to SFU. Applicants who fall below 60% will not be admitted until they establish that they have acquired the necessary proficiency in written English.(a) Students with blended English 12 grades of 75% or higher areadmitted and eligible to register directly into writing-intensive (W) courses.(b)Students with blended English 12 grades between 60% and 74% areadmitted and must write the Language Proficiency Index test (LPI) or register directly into Foundations of Academic Literacy (FAL X99).Students who opt to write the LPI exam must achieve a score of 4 on the essay portion of the LPI and a minimum score of 50% on all parts of the LPI to be eligible to register in W courses. Students who score below this threshold must register in FAL X99. BC high school students are encouraged to write the LPI at test sittings held in their schools.Because LPI testing sites are generally limited to locations within BC, out-of-province applicants with English 12 grades below 75% will be able to access sittings at SFU. Such students are advised to write the LPI as early as possible in their first semester at SFU.Students who elect or must register in FAL X99 must do so within their first 30 credits at SFU and complete it with a grade of C or better within their first 45 credits before being allowed to register in a W course.Continuation RequirementsStudents who fail to obtain a grade of C or better in FAL X99 after attempting it a maximum of two times will be blocked from further course registration. Registration will again be permitted once they establish that they have acquired the necessary proficiency in written English as outlined here.International applicantsInternational applicants may satisfy SFU's literacy competency requirement in one of several ways. Applicants may submit an acceptable IELTS score. Applicants admitted on the basis of their IELTS score will be "streamed" into W courses or the Foundations of Academic Literacy course (FAL X99) on the basis of that score. Applicants admitted on the basis of a score earned on a TOEFL will be required to take FAL X99 before the conclusion of their third semester at SFU.Interactive Arts & TechnologyUndergraduate ProgramThe School of Interactive Arts and Technology (SIAT) is a future-focused school where technologists, artists, designers and theorists thrive in collaborative research, invention and theoretical thinking. All programs in the School of Interactive Arts and Technology (SIAT) are offered solely at the SFU Surrey Campus, located at Central CityWhat is SIAT?SIAT offers three (3) concentrations of undergraduate study: Interactive Systems, Design and Media Arts.All share a fundamental concern with how people use technology in their lives. There is flexibility topursue a BA or BSc Degree. A detailed overview is available on our current students page.Finding the right university is a challenge. There are many options available to you, and we hope to beyour top choice. SIAT graduates stand apart for their knowledge and interpersonal skills, and are held inhigh regard by industry.Is this the right program for you?Within Interactive Arts and Technology, we have a wide range of programs, professors, and courses.Student life, your first year experience, your campus, and the friends you make along the way also play ahuge part.Questions?For admissions information contact ugrad-surrey@sfu.ca.For program information: siat_advising@sfu.ca.Admissions AdvisingSFU Surrey's Enrollment and Recruitment Services team offers admissions advising for all prospectiveSFU students as well as weekly campus tours.CareersCheck out some sample careers, companies, what our alumni are up to, and view our industry job board. We also have an outstanding co-operative education program and career services to help you launch your future.Apply!You can apply online right away.Admissions from High SchoolIf you are applying directly from BC Grade 12 you will need to complete 4 courses in your grade 12 year towards admission to SIAT at SFU.∙ENGLISH 12*∙PRINCIPLES OF MATH 12∙ 2 ADDITIONAL provincially examinable GRADE 12 COURSES*Note that a 60% minimum blended classroom and provincial exam mark in English 12 is required for admission to SFU. However, for the purposes of calculating your admission average, the higher of either the classroom or blended grade will be used (this applies to all 4 grade 12 courses).BC Grade 11 course requirements are the following:∙ENGLISH 11∙PRINCIPLES OF MATH 11∙SCIENCE 11∙LANGUAGE 11Early Learning SpecializationIn this non-specialist program, students will learn through lectures, seminars, field experiences, service learning (learning while placed in an educational setting) and by distance educationStudents who choose this option will satisfy the requirements by completing the early learning specialization, as shown below. Students may choose to graduate without enrolling in the Professional Development Program (PDP). This early learning specialization is for students who are competing a bachelor of general studies (education) degree and are considering an early elementary (kindergarten to grade three) teaching career. Note that admission to this program does not guarantee admission to the Professional Development Program (PDP). Students who receive credit for this specialization cannot also receive credit for the minor in early childhood education.TWU是加拿大政府认可大学，与卑诗省的UBC和SFU同等，都是加拿大大学学院协会的全职会员（加拿大大学学院协会是加拿大的最高权威教育机构组织）；可授予学士学位和硕士学位，TWU的学位也受到美国教育部的认可。

美国加州高中A—G类课程详细介绍

1982年，为了确保大学新生的学业质量，美国加州大学（UC）系统制定了A-G课程计划。

所有想进入UC系统的高中毕业生，都必须完成A-G课程（A-G Curriculum），并且全部考试成绩都在C以上，才有申请大学资格。

A-G是美国加州高中的核心课程系列，包括15门必修课和3门推荐课，共分为七类。

学生4年高中结束时必须要修满15门的课程，而其中至少7门课程要放在高中最后的两年中修。

具体的规定如下：A、历史/社会科学必修2年，有美国历史/世界历史/美国民主原则B、英文必修4年C、数学必修3年/建议修4年，有初级、中级代数/几何D、实验室科学必修2年/建议修3年，有生物/化学/物理E、第二外语必修2年/建议修3年F、视觉表演艺术必修1年，有舞蹈/舞台剧/戏剧/音乐/视觉艺术G、大学先修（AP）课程。

看起来似乎相当的复杂，学生根本不知如何在4年里去安排这15门课。

没关系，下面我们就一同来探探这里面的究竟。

英文：英文是美国高中生应该掌握的最基本的母语，当然听说读写分析要样样全能。

所以最好是把英文课平均分配在高中的4年中，持续地进行英文写作和阅读的训练。

写作要训练各种文体，其中就包括很重要的美国高考SATI中的论述文写作训练。

阅读则要广泛阅读古典文学，现代文学，时事评论等。

数学：每次看到国内学生成绩单上千年不变的“数学”这门科目就头痛，因为成绩单上无法显示出他们到底学到过哪些具体知识。

不幸的是这也是美国大学想要从中国学生的成绩单上看到却怎么也看不到的一项明细。

不同的是，美国中学数学将该门学科细分到每一项不同的内容，要求学生一级一级往上学。

典型的顺序是8年级 (初二) 学初级代数(Algebra I)9年级 (初三) 学几何(Geometry)10年级 (高一) 学中级代数(Algebra II)11年级 (高二) 学三角函数/数学分析(Trigonometry/Math Analysis)12年级 (高三) 学初级微积分(Pre-Calculus)。

pre calculus 知识点

pre calculus 知识点
Pre-Calculus（预备微积分）是高中数学中的一门重要课程，主要包括以下知识点：
1.函数：包括函数的定义、图像、性质、反函数、复合函数等。

2.三角函数：包括正弦函数、余弦函数、正切函数、余切函数等，以及它们的图像、周期、幅值等。

3.向量：包括向量的定义、向量的加法、数量积、向量积等。

4.数列与级数：包括等差数列、等比数列、调和数列等，以及级数的收敛与发散。

5.极限与连续性：包括函数的极限、无穷小与无穷大、连续性、间断点等。

6.微积分初步：包括导数的定义、导数的计算、导数的应用、微分的定义等。

7.三角函数的导数：包括正弦函数、余弦函数、正切函数、余切函数的导数，以及它们的应用。

8.指数与对数函数：包括指数函数、对数函数、对数运算的性质等。

9.三角函数的积分：包括正弦函数、余弦函数、正切函数、余切函数的积分，以及它们的应用。

10.微积分的应用：包括最值问题、曲线的切线与法线、微分方程等。

以上是 Pre-Calculus 的主要知识点，掌握这些知识点对于学习
高等数学和物理都具有重要的意义。

加拿大数学十年级(高一)省考模拟试题B汇编

You have Examination Booklet Form B. In the box above #1 on your Answer Sheet, fill in the bubble as follows.
Exam Booklet Form/ A B C D E F G H Cahier d’examen
A. decreased by 15 km h B. decreased by 5 km h C. increased by 15 km h D. increased by 11 km h
3. Solve the following system of equations:
4x + 2y = 8 3x + y = 1
13. Marbles are placed in a jar one at a time. Which graph below best represents the total mass of the jar and marbles as the marbles are added?
A.
B.
Total Mass
INSTRUCTIONS: No calculator may be used for this part of the examination. For each question, select the best answer and record your choice on the blue Answer Sheet provided.
Foundations of Mathematics and Pre-Calculus 10 – 2010–2011 Sample B
Page 5
PART B: MULTIPLE-CHOICE QUESTIONS (calculator permitted)

ap课程precalculus解题

Ap课程precalculus解题在数学学科中，AP课程precalculus是一门非常重要的课程，它为学生提供了在高等数学中取得成功所需的基本概念和技能。

解题是学习precalculus的重要环节，它不仅能够帮助学生巩固所学知识，还能培养学生的逻辑思维和解决问题的能力。

本文将深入探讨AP课程precalculus解题的一些重要概念和技巧，并共享个人观点和理解。

一、概念和技巧1. 利用数学工具在解题过程中，学生需要熟练掌握数学工具，比如函数图像、方程和不等式等。

这些数学工具能够帮助学生更好地理解问题，并找到解决问题的方法。

当遇到复杂的函数图像题时，学生可以利用图像的性质来解决问题，比如对称性、增减性和极值等。

2. 运用数学思维学生需要培养数学思维，善于运用已有知识解决新问题。

在解题过程中，学生可以通过建立数学模型，利用函数的性质和特点，以及灵活运用各种解题技巧来解决问题。

在求解极限和导数的题目中，学生可以灵活运用极限的性质和求导的规则，将问题转化为基本的运算和推理，从而得到答案。

3. 练习和实践解题是一个需要不断练习和实践的过程。

学生需要多做一些经典的题目，掌握各种解题技巧和方法，培养自己的解题能力。

学生还可以通过解题训练营、竞赛和讨论小组等形式，与他人一起共享和交流解题经验，不断提高自己的解题水平。

二、总结和回顾通过对AP课程precalculus解题的深入探讨，我们了解到解题是学习数学知识的重要环节，它不仅能够帮助学生巩固所学知识，还能培养学生的逻辑思维和解决问题的能力。

在解题过程中，学生需要灵活运用数学工具和思维，多做练习和实践，培养自己的解题能力。

三、个人观点和理解在我的个人观点中，AP课程precalculus解题是一项需要逻辑思维和灵活运用知识的过程。

通过解题，我可以更好地掌握数学知识，提高自己的解题能力，培养自己的数学思维。

AP课程precalculus解题是学习数学知识的重要环节，它不仅能够帮助学生巩固所学知识，还能培养学生的逻辑思维和解决问题的能力。

precalculus mathematics 学案

precalculus mathematics 学案1. 引言1.1 概述在当今的教育体系中，预备数学课程作为一门基础课程，被广泛认可其对学生在进一步深入学习数学和应用数学领域具有重要的作用。

预备数学课程旨在帮助学生建立起扎实的数学基础，并为他们提供解决实际问题的数学工具。

其中，"precalculus mathematics"是指在进入高等数学之前需要掌握的一些关键数学概念和技能。

1.2 文章结构本文将按照如下结构进行介绍：首先，在第二部分，我们将介绍读者需要具备的预备知识。

这包括对数学基本概念、代数与函数的理解以及几何与三角学方面的知识。

接下来，在第三部分，我们将详细介绍预备知识中涉及到的基础概念，例如实数与集合论、函数与图像以及方程与不等式等内容。

然后，在第四部分中，我们将探讨算术性质和代数应用相关的概念和方法，如比例与百分比、利率与复利问题以及数据分析与统计方法等。

最后，第五部分会初步介绍三角函数的相关知识，包括角度度量与弧度制、三角比值及其应用以及特殊角和三角方程求解初步等内容。

1.3 目的本文的主要目的是为那些对"precalculus mathematics"感兴趣或需要学习这门课程的读者提供一个全面而系统的学习指南。

通过阅读本文，读者将能够深入了解预备数学课程中涉及到的基本概念和重要技能，并且有助于他们在数学领域更好地掌握和应用所学知识。

同时，我们也希望通过本文向读者展示预备数学对于日常生活和职业发展的实际应用意义，提高他们对该领域的兴趣和学习动力。

2. 预备知识2.1 数学基本概念数学基本概念部分介绍了使用precalculus所需的一些重要数学概念。

这些概念包括但不限于：- 数字与数字系统：介绍了整数、有理数和实数等不同类型的数字，以及十进制和其他常见数字系统。

- 基本运算：讨论了加法、减法、乘法和除法等基本运算规则。

- 数字的性质：介绍了奇偶性、质数与合数等数字的特性。

牛津译林版英语九年级下册中考模拟检测卷(二)

牛津译林版英语九年级下册中考模拟检测卷（二）学校:___________姓名：___________班级：___________考号：___________一、单项选择1．Lights are out．The concert is to begin．The fans hold their breath for Jay Chou's_____．A．influence B．guidance C．experience D．appearance 2．This basketball game will be covered ______ on Friday.A．alive B．lively C．live D．living3．—I feel ______ after a night’s good sleep.—Yeah, sleeping is the best way to relax.A．very tired B．more tired C．less tired D．the most tired 4．The windows of the plane broke about forty minutes after it ________.A．got off B．took up C．got up D．took off 5．When I got home, I was angry to find my room ________.A．in a good mess B．in a bad messC．on a good mess D．on a bad mess6．—You ______ park here! Look at the sign. It says “No parking”.—Sorry, I didn’t notice that sign just now.A．won’t B．needn’t C．mustn’t D．could 7．—Can I come this afternoon or tomorrow morning?— is OK. I'm free today and tomorrow.A．Either B．Neither C．Both D．None8．—I want to visit Red Beach in Xingcheng. Could you tell me ______?—It’s free all the time.A．how far it is B．how much the ticket isC．how I can get there D．how long it takes to go there9．________ April 22nd, people around the world celebrate Earth Day ________ different ways.A．In; in B．On; in C．In; on D．At; by 10．—Let’s go to play soccer, Peter.—I’m afraid not. I’ll need one more hour before my homework_______.A．has finished B．finished C．will be finished D．is finished11．一What did you save your money for?一 a new mobile phone.A．To buy B．Buy C．Buying D．Bought 12．My bedroom is painted blue, and it _________ peaceful and comfortable.A．looks like B．feels C．looked D．is felt 13．Jerry will succeed in working out the problem ____he gives up.A．if B．because C．so D．unless14．A true friend is a person ________ reaches for your hand and touches your heart. A．whom B．whose C．who D．which 15．— Could you tell me how to pay for the food by QR code (二维码) on thephone?--______.A．Take it easy B．It doesn’t matterC．You’re welcome D．Sure, I’d love to二、完形填空“We always expect our children to be perfect.” Most parents have thought so.I was one of them. I expected our son, Joe, would be perfect to sail ___16___ school. He was always a ___17___ kid, kind and gentle. But he wasn’t perfect. From the first day Joe started school, he always had difficulty with ___18___. He passed each grade with great___19___, but never at the top of his class.How I ___20___ friends who had children with the “maths talent”. I would look at Joe and ___21___: If he does not get better at maths, how is he ever going to ___22___ college? I was worried about it all the time.Joe, ___23___, had other ideas. During high school, Joe slowly ___24___ his maths. He got through all the required courses. I felt greatly _____25_____ with his little achievement. Then he announced that he’d take pre-calculus（微积分）in his last year of high school, which _____26_____ me a lot.“Why?” I questioned.“Because I need to keep my skills up,” he explained. “I _____27_____ maths, but I need to take it seriously, so I won’t forget how to do it.”“For college,” he added. “I want to do really well in college, Mom. I know it will be_____28_____, but I think it’s important that I try to do my best.”My son wasn’t perfect. He wasn’t a maths talent, either. But he knew what was important: he was caring about his _____29_____ while I was worrying over his past. And that, to me, is even better than being _____30_____ .16．A．at B．through C．from D．across 17．A．lucky B．proud C．good D．healthy 18．A．art B．music C．writing D．maths 19．A．effort B．attention C．pleasure D．interest 20．A．respected B．supported C．trusted D．admired 21．A．suppose B．imagine C．wonder D．wish 22．A．push in B．go over C．look through D．get into 23．A．however B．although C．moreover D．otherwise 24．A．reduced B．improved C．changed D．discovered 25．A．tired B．thankful C．satisfied D．angry 26．A．moved B．hurt C．meant D．surprised 27．A．fail B．dislike C．prefer D．choose 28．A．hard B．boring C．necessary D．successful 29．A．career B．subject C．future D．world 30．A．perfect B．clever C．patient D．confident三、阅读单选A nice day out for the whole family! Come and see our beautiful birds, huge mammals (fl乳类), lovely marsupials (有袋类) and reptiles (爬行类)… in our zoo!Scientists will give wonderful lessons about animals every Tuesday!Don’t miss it!31．Where can visitors see kangaroos and tortoises?A．Area A and Area B B．Area A and Area C．C．Area B and Area C．D．Area C and Area D．32．Visitors can have lessons about animals on ______.A．Sunday B．Tuesday C．Thursday D．Friday 33．Which of the following animals can visitors see on Saturdays?A．Crocodiles.B．Parrots.C．Tortoises.D．Koalas. 34．On Sundays, which is the best order for visitors to see as many animals as possible? A．tigers-camels-koalas-kangaroosB．tigers-koalas-camels-kangaroosC．tigers-koalas-kangaroos-camelsD．tigers-kangaroos-koalas-camels35．If Millie and her parents visit the zoo, how much should they pay?A．$127.B．$145.C．$155.D．$172.No one wants to look silly or do the wrong thing at a new job. It is important to make the good impression (印象) from the very first day. You will face new people. You will be in anew place. It may be difficult to know what to do. Here are five tips to help you make it through the first day in a new job:①First impression can last forever. Make sure you make a good one. Before your first day, find out if your new job has a dress code (rules about what you can wear to work). If so, be sure to follow it. No matter what, always be neat and clean.①Get to work on time. Give yourself an extra 15 minutes to make sure you arrive on time.①Pay attention to introductions. You may introduce yourself to your workmates. They will be important to you. They are the ones who will answer your questions when the boss is not around.①Ask plenty of questions. Make sure that your supervisor has told you what is expected of you. If you are not told your duties, ask for a list. Set daily and weekly goals for yourself.①Never be the first one to leave. Watch what others do at the end of work hours. It does not look good for you to be eager (急切的) to leave.36．What does the writer think you should do before your first-day work?A．We should find out how to dress in a right way.B．We should ask a lot of questions.C．We should know our duties.D．We should know our workmates well.37．Which of the following statements is TRUE according to the passage?A．You should be the first one to arrive at work.B．You should ask your workmates for your duties.C．You should not be eager to go back home at the end of work hours.D．You are required to arrive 15 minutes earlier.38．From the passage, your “supervisor” is most likely to be your “______”.A．visitor B．teacher C．workmate D．leader 39．What does the writer think about the first impression of a person?A．He thinks it is interesting.B．He thinks it is important.C．He thinks it is necessary.D．He thinks it is worrying.40．What is the best title for this passage?A．Getting a new job B．Tips on how to workC．The first-day work D．The importance of workmatesLet’s suppose it is a common day of 2060. Of course, things have changed and life is very different.Trips to the Moon are being made every day. Taking a holiday on the Moon today is as easy as taking a holiday in Europe in 2016. At a number of scenic spots (风景胜地) on the Moon, many hotels have been built. In order that everyone can enjoy the beautiful scenery on the Moon, every room has at least one picture window. Everything imaginable is provided for entertainment of the young and old.What are people eating now? People are still eating food. But many foods now come in pill form, and the food that goes into the pill comes mainly from green plants. Farming, of course, is very highly developed. Very few people have to work on the farm. It is possible to run the farm by just using a few computers.People are now largely vegetarians (素食者), and they eat only bread, vegetables, fruit and so on and they don’t eat meat or fish. You see, as the number of people increases, the number of animals decreases. So people have to be vegetarians. We are healthier both in our bodies and in our minds, and we know how to deal with all kinds of illnesses. No one has to be ill any more.41．The passage mainly talks about .A．trips to the Moon in 2060B．developed farming in 2060C．what our lives would be like in 2060D．what people would eat in 2060 42．What is true according to the passage?A．Entertainment is provided only on the Moon.B．Many farms on the Moon have beautiful views.C．It takes the whole day to travel to the Moon.D．It’s easy to take a holiday in Europe at present.43．The food we eat in 2060 .A．is green in the colour B．is the same as todayC．has a lot of pills in it D．is mainly made out of green plants 44．What does the underlined word “decrease” mean in Paragraph 4?A．To become less.B．To become exact.C．To become larger.D．To become unknown.45．We are healthier because of the following EXCEPT that .A．what we eat is green food B．we can treat any illnessC．we are largely vegetarians D．we run the farm by using computersMichael Perham (born on 16th March, 1992 in Hertfordshire, England) is a boy who, at the age of 17, became the youngest person to sail around the world in the 50 feet racing boat, completing his journey on 7th August, 2009. He started the world trip on the 15th of November 2008 from Portsmouth, England.Just six days after Michael Perham set sail from Portsmouth, he started having serious problems with the boat, which he was unable to fix himself on the sea. He had to stop in Portugal. Just one day later, he set sail once again, with the hope of breaking David Dick’s world record for the youngest person to sail around the world.Michael met many challenges (挑战) along the way, including rough seas andknock-downs in the Southern Ocean, terrible loneliness and fighting storms, but the largest difficulty Michael faced was the boat itself. It caused one problem after another. Funnily he celebrated his birthday in March last year among the dolphins in Indian Ocean.Michael Perham has entered the record books after becoming the youngest person to sail around the world. The teenager already holds the record for being the youngest people to sail across the Atlantic, aged just 14.Michael Perham plans to create the Sail Michael Fund to encourage young people to take to the water. He is also aiming to take part in the 2012 Olympics.46．This passage is most probably taken from ________.A．a story book B．a magazine C．a travel guide D．a film review 47．How long did it take Michael Perham to complete his world trip?A．It took about 9 months.B．It took 6 days.C．It took about 14 years.D．It took 50 days.48．What does “to take to the water” probably mean in this passage?A．To save water.B．To protect water.C．To sail in the sea.D．To swim in the sea.49．Which of the following is NOT true about Michael Perham?A．Michael Perham wants to encourage young people to take part in the 2012 Olympics.B．Michael Perham has held two world records for sailing so far.C．The most difficult problem that Michael Perham faced while sailing was the boat. D．Michael Perham is going to set up the Sail Michael Fund for young people. 50．What’s the correct order of the following events?a. Michael Perham started the world trip from Portsmouth.b. Michael Perham became the youngest person to sail across the Atlantic.c. Michael Perham celebrated his birthday in March last year among the dolphins in Indian Ocean.d. Michael Perham became the youngest person to sail around the world.A．d, a, c, b B．b, c, a, d C．d, a, b, c D．b, a, c, d四、阅读回答问题A natural resource is anything people can use which comes from nature. People cannot make natural resources, but can get them from the Earth. Examples of natural resources are air, water, copper, wood, oil, wind energy, hydro-electric energy, iron and coal. Refined (精炼的) oil is not a natural resource because people make it.We often say that we can divide natural resources into two different groups: renewable resources and non-renewable resources.A renewable resource can grow again and come back again after we use it. For example, soil, sunlight, water and wood are renewable resources.A non-renewable resource is a resource that cannot grow or come back, or a resource that will take a very long time to come back. For example, coal is a non-renewable resource. When we use more coal, there will be less coal afterward. One day, there will be no coal to make goods. The non-renewable resource can be used up directly, or we can find a renewable resource to replace it. It is important to save non-renewable resources, because if we use them too quickly, there will be not enough in the future.Most natural resources are limited. This means that they will run out. So, it is our responsibility to save resources for the sustainable development (可持续发展).根据短文内容，回答下列问题。

卡梅伦液压数据手册（第 20 版）说明书

11
iv
⌂
CONTENTS OF SECTION 1
☰ Hydraulics
⌂ Cameron Hydraulic Data ☰
Introduction. . . . . . . . . . . . . ................................................................ 1-3 Liquids. . . . . . . . . . . . . . . . . . . ...................................... .......................... 1-3
4
Viscosity etc.
Steam data....................................................................................................................................................................................... 6
1 Liquid Flow.............................................................................. 1-4
Viscosity. . . . . . . . . . . . . . . . . ...................................... .......................... 1-5 Pumping. . . . . . . . . . . . . . . . . ...................................... .......................... 1-6 Volume-System Head Calculations-Suction Head. ........................... 1-6, 1-7 Suction Lift-Total Discharge Head-Velocity Head............................. 1-7, 1-8 Total Sys. Head-Pump Head-Pressure-Spec. Gravity. ...................... 1-9, 1-10 Net Positive Suction Head. .......................................................... 1-11 NPSH-Suction Head-Life; Examples:....................... ............... 1-11 to 1-16 NPSH-Hydrocarbon Corrections.................................................... 1-16 NPSH-Reciprocating Pumps. ....................................................... 1-17 Acceleration Head-Reciprocating Pumps. ........................................ 1-18 Entrance Losses-Specific Speed. .................................................. 1-19 Specific Speed-Impeller. .................................... ........................ 1-19 Specific Speed-Suction...................................... ................. 1-20, 1-21 Submergence.. . . . . . . . . ....................................... ................. 1-21, 1-22 Intake Design-Vertical Wet Pit Pumps....................................... 1-22, 1-27 Work Performed in Pumping. ............................... ........................ 1-27 Temperature Rise. . . . . . . ...................................... ........................ 1-28 Characteristic Curves. . ...................................... ........................ 1-29 Affinity Laws-Stepping Curves. ..................................................... 1-30 System Curves.. . . . . . . . ....................................... ........................ 1-31 Parallel and Series Operation. .............................. ................. 1-32, 1-33 Water Hammer. . . . . . . . . . ...................................... ........................ 1-34 Reciprocating Pumps-Performance. ............................................... 1-35 Recip. Pumps-Pulsation Analysis & System Piping...................... 1-36 to 1-45 Pump Drivers-Speed Torque Curves. ....................................... 1-45, 1-46 Engine Drivers-Impeller Profiles. ................................................... 1-47 Hydraulic Institute Charts.................................... ............... 1-48 to 1-52 Bibliography.. . . . . . . . . . . . ...................................... ........................ 1-53

美国高中生课程表

The following tables illustrate the common educational goals pathways of a student’s courseselections in English, Math, Science, and Social Studies. These pathways assume successful completion of the previous course as well as meeting other prerequisites that may apply. It is not requisite that the pathway be followed throughout; however each is a suggested pathway toachieve optimal success during and after high school. This is intended as a planning guide only. To use this document effectively, please select one of the courses in each of the boxes based on the subject area, grade level, and educational goals pathway. Each class is worth 1.0 credit unless there is an asterisk (*). If there is an asterisk (*), then the class is worth 0.5 credits and you will need to select another class that is worth 0.5 credits as well.English(4.0 Credits Required for Graduation)Teacher Sign-Off?Grade 9Grade 10Grade 11Grade 12Depending on PERT ScoresTraditional No English I (1001310) English II (1001340)English III (1001370)English IV College Prep (1001405) College PrepYes English Honors I (1001320) English Honors II (1001350)English Honors III (1001380) English IV College Prep (1001405) Advanced College PrepYesEnglish Honors I (1001320)English Honors II (1001350)• English Honors III (1001380) • AP English Language*** (1001420)• English IV College Prep (1001405) • AP English Literature*** (1001430) • DE Comp I/DE Comp IIMathematics(4.0 Credits Required for Graduation)Teacher Sign-Off?Grade 9Grade 10Grade 11Grade 12Depending on PERT ScoresTraditional No Algebra I (1200310)• Liberal Arts Math** (1208300)• Geometry (1206310)• Geometry (1206310) • Algebra II (1200330)• Algebra II (1200330)• Advanced Algebra w/Finance (1200500)• Math for College Readiness (1200700)College PrepYes Algebra I Honors (1200320)Geometry Honors (1206320)Algebra II Honors (1200340)• Math for College Readiness (1200700)• Pre-Calculus (1202340)• DE Algebra/DE Pre-Calculus Advanced College PrepYes• Geometry Honors (1206320)• Algebra II Honors (1200340)• Algebra II Honors (1200340)• Pre-Calculus (1202340)• Pre-Calculus (1202340) • AP Calculus AB*** (1202310)• DE Algebra/DE Pre-Calculus • AP Calculus AB*** (1202310) • AP Statistics *** (1210320)Science(3.0 Credits Required for Graduation)Teacher Sign-Off?Grade 9Grade 10Grade 11Grade 12TraditionalNoPhysical Science (2003310)Biology (2000310)• Marine Science (2002500) • Chemistry (2003340) • Marine Science (2002500) • Chemistry (2003340)• Anatomy & Physiology Honors (2000360)College PrepYesPhysical Science Honors(2003320)Biology Honors (2000320)• Chemistry Honors (2003350)• Marine Science Honors (2002510)• DE Marine*/DE Oceanography*• AP Biology (2000340) • AP Chemistry (2003370)• Anatomy & Physiology Honors (2000360)• Physics Honors (2003390)• DE Marine*/DE Oceanography* Advanced College PrepYesBiology Honors (2000320)(To take this course, student must be co-enrolled in Geometry Honors)Chemistry Honors (2003350)• AP Biology*** (2000340) • AP Chemistry*** (2003370) • AP Environmental Science*** (2001380) • Anatomy & Physiology Honors (2000360)• Physics Honors (2003390) • AP Physics*** (2003420)• AP Biology*** (2000340) • AP Chemistry*** (2003370) • AP Environmental Science*** (2001380)• Anatomy & Physiology Honors (2000360)• Physics Honors (2003390) • AP Physics*** (2003420)• DE Marine*/DE Oceanography*Social Studies(3.0 Credits Required for Graduation – World, American, and Gov’t/Econ)Teacher Sign-Off?Grade 9Grade 10Grade 11Grade 12TraditionalNo Optional as there is not a required 9th Grade course World History (2109310) American History (2100310)Amer. Gov’t.* (2106310) and Econ.* (2101310)College PrepYesWorld History Honors (2109320)• AP World History*** (2109420) • AP Human Geography*** (2103400)• American History Honors (2100320)• American History Honors (2100320)• AP American History (2100330)• Amer. Gov’t. Honors* (2106320) and Econ. Honors* (2102320) • AP Amer. Gov’t.*/***(2106420) and AP Econ.*/*** (2102360)Advanced College PrepYesAP Human Geography*** (2103400)• World History Honors (2109320)• AP World History (2109420)• American History Honors (2100320)• AP American History (2100330)• Amer. Gov’t. Honors* (2106320) and Econ. Honors* (2102320) • AP Amer. Gov’t.*/*** (2106420) and AP Econ.*/*** (2102360)* *Liberal Arts Math does not meet NCAA requirements, 4 year University admission, nor Bright Futures Requirements.***Course that requires an Advanced Placement Expectations FormJ.W. Mitchell High School Student Educational Goal Pathways ExplanationTraditional – After high school, this student may enter the work force, join the military, or attend a technical or community college. College Prep – After high school, this student may attend a community college or four-year university (with foreign language requirement completed). Advanced College Prep – After high school, this student may attend a more competitive four-year university (with the foreign language requirement completed).Advanced Placement Policy and ExpectationsA separate Expectations Agreement is required for all Advanced Placement courses. Schedule changes out of Advanced Placement classes will not be allowed until after the first quarter at minimum. Students will also need to meet all expectations of the Advanced Placement classes, including completing summer work, completing all assignments, participating in classes, and seeking extra help if there are issues.J.W. Mitchell High SchoolAcademic Course Selection Planning SheetName: _______________________________________ Student #: ____________________________________Student Signature: ____________________________ Parent Signature: ______________________________ Counselor Signature: ___________________________。

国际本科数学预备课程 pre-calculus

国际本科数学预备课程 Pre-calculus一、引言在国际本科数学教育中，预备课程是非常重要的一环。

其中，Pre-calculus作为数学预备课程的一部分，为学生打下了坚实的数学基础，为他们将来更深入地学习高等数学和应用数学打下了坚实的基础。

本文将就Pre-calculus的定义、重要性、教学内容和课程目标等方面展开详细介绍。

二、Pre-calculus的定义Pre-calculus是指在学习高等数学之前的一门课程，它主要是为学生提供在代数、几何和三角学等方面的知识，并为他们学习大学数学课程打下坚实的基础。

Pre-calculus课程通常包括代数学、函数、三角学、解析几何等内容。

三、Pre-calculus的重要性1. 为学生提供扎实的数学基础Pre-calculus课程通过学习代数、几何、三角学等知识，为学生提供扎实的数学基础，使他们能够更好地理解和掌握高等数学知识，为将来进一步学习数学打下坚实的基础。

2. 培养学生的数学思维和解决问题能力通过学习Pre-calculus课程，学生将培养数学思维和解决问题的能力，这对他们在将来的学习和工作中都是非常重要的。

3. 为学生的职业发展奠定基础对于一些将来需要应用数学知识的职业，如工程师、科学家、经济学家等，Pre-calculus课程能够为他们的职业发展奠定基础，使他们能够更好地应用数学知识解决实际问题。

四、Pre-calculus的教学内容Pre-calculus课程的教学内容主要包括以下几个方面：1. 代数学：包括方程、不等式、多项式、有理函数等内容。

2. 函数：包括函数的概念、函数的性质、函数的图像、函数的运算等内容。

3. 三角学：包括三角函数、三角恒等式、三角方程等内容。

4. 解析几何：包括直线、圆、双曲线、抛物线等内容。

五、Pre-calculus的课程目标Pre-calculus课程的教学目标主要包括以下几个方面：1. 让学生掌握代数、几何和三角学等方面的基本知识，为他们进一步学习高等数学课程打下坚实的基础。