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Words 1708

Pages 7

Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Tracing paper may be used.

Instructions to Candidates_____________________________________________________

Check that you have the correct brain power required to attempt this question paper.

Answer ALL the questions. Write your answers in the spaces provided in this question paper.

You must NOT phone a friend or ask the audience.

Anything you write on the formulae page will gain NO credit.

If you need more space to complete your answer to any question, write smaller.

Information for Candidates____________________________________________________

The marks for individual questions and the parts of questions are shown in round brackets: e.g. (2).

There are 23 questions in this question paper. The total mark for this paper is 110.

Calculators must not be used unless the symbol appears

Advice to Candidates__________________________________________________________

Show all stages in any calculations – A* questions often require you to explain or prove something.

Work steadily through the paper. Do not spend too long on one question.

If you cannot answer a question, leave it, attempt the next one and try not to cry.

Return at the end to those you have left out.

Have a lie down afterwards to help recover.

GCSE A* Questions

Skill: Manipulate expressions containing surds

Question 1

(a) Rationalise [pic]

.....................................

(2)

(b)(i) Expand and simplify…...

...Science and math integration unit I chose a culminating activity to use after the students had completed learning about fractions, ratios and percentages in math and in life science learning about the ecosystems and inquiry and observations to solve problems. The activity I chose has students looking at trees within a forest near the school. My rationale for selecting this project is that students in this area do a lot of hunting this time of year and are outside in the wilderness a lot during the month of October. I thought that this lesson would make them more aware of their environment and provide them a different way to look at their surroundings before they went off to the mountains for hunting elk and deer. I believe the students will be very interested in this unit of study and also it will help them to be more observant as they are hunting this next month. I tried to write a unit of study that students in this area would enjoy doing, one that would fit with their lifestyle and have a meaningful positive outcome upon completion. This is a summary of a culminating unit for science and math. Students will measure off a section of the forest and count quaking aspen trees and lodge pole pine trees within the measured off area. Students will then use the 12 processes of science and math skills to answer questions and complete investigations to solve the science question. The students need to collect data, chart it and analyze it to answer questions using math skills......

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...had taught me math for three years in a row, so I think that I have a good grasp on his approaches to the lessons that he would teach. He would assign many homework assignments, as well as in-class assignments, which helped me and other students understand and get practice with the lesson that we were learning. I think that with math having a lot of homework is a good thing. In my mind, the only way to learn how to do math is plenty of practice. The more you practice, the easier it will be. Mr. G would also have the students do some math problems on the chalk board or smart board to show the class and go over the corrections with the whole class so that everyone would understand the problem. Playing “racing” games also helped and added fun to the class. With the “racing” games, the students would get into groups and have to take turns doing problems on the chalk board and see who could get the correct answer first. It added fun and a little friendly competition to the class. It also helped the students want to try to understand and get the problem correct. One year that I had Mr. G, we had a one student that was considered “special”. The “special” student was considered special because he learned the lessons a little slower than the other students and had to be given a slightly simpler test or had to have someone walk him through the test and explain everything more into detail. Mr. G did a very good job at including him all activities and let him answer questions when......

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...what amount in one year? b. Having $200 in one year is equivalent to having what amount today? c. Which would you prefer, $200 today or $200 in one year? Does your answer depend on when you need the money? Why or why not? 7. You have an investment opportunity in Japan. It requires an investment of $1 million today and will produce a cash flow of ¥ 114 million in one year with no risk. Suppose the risk-free interest rate in the United States is 4%, the risk-free interest rate in Japan is 2%, and the current competitive exchange rate is ¥ 110 per $1. What is the NPV of this investment? Is it a good opportunity? 8. Your firm has a risk-free investment opportunity where it can invest $160,000 today and receive $170,000 in one year. For what level of interest rates is this project attractive? Present Value and the NPV Decision Rule 9. You run a construction firm. You have just won a contract to build a government office building. Building it will take one year and require an investment of $10 million today and $5 million in one year. The government will pay you $20 million upon the building’s completion. Suppose the cash flows and their times of payment are certain, and the risk-free interest rate is 10%. a. What is the NPV of this opportunity? b. How can your firm turn this NPV into cash today? 10. Your firm has identified three potential investment projects. The projects and their cash flows are shown here: Project A B C Cash Flow Today ($) -10 5 20 Cash Flow in One Year ($)...

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...“Memorizing math facts is the most important step to understanding math. Math facts are the building blocks to all other math concepts and memorizing makes them readily available” (EHow Contributor, 2011). To clarify, a math fact is basic base-10 calculation of single digit numbers. Examples of basic math facts include addition and multiplication problems such as 1 + 1, 4 + 5, 3 x 5 and their opposites, 2 – 1, 9 – 4, 15/5(Marques, 2010 and Yermish, 2011). Typically, these facts are memorized at grade levels deemed appropriate to a student’s readiness – usually second or third grade for addition and subtraction and fourth grade for multiplication and division. If a child can say the answer to a math fact problem within a couple of seconds, this is considered mastery of the fact (Marques, 2010). Automaticity – the point at which something is automatic- is the goal when referring to math facts. Students are expected to be able to recall facts without spending time thinking about them, counting on their fingers, using manipulatives, etc (Yermish, 2011). . In order to become a fluent reader, a person must memorize the sounds that letters make and the sounds that those letters make when combined with other letters. Knowing math facts, combinations of numbers, is just as critical to becoming fluent in math. Numbers facts are to math as the alphabet is to reading, without them a person cannot fully succeed. (Yermish, 2011 and Marquez, 2010). A “known” fact is one that is......

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...1 Assignment. Note: For these questions you need to cite a reliable source for information, which means you cannot use sites like Wikipedia, Ask.com®, and Yahoo® answers. If you do use those sites the instructor may award 0 points for your response. The Assignment problems must have the work shown at all times. The steps for solving the problems must be explained. Failure to do so could result in your submission being given a 0. If you have any questions about how much work to show, please contact your instructor. Assignments must be submitted as a Microsoft Word® document and uploaded to the Dropbox for Unit 6. Please type all answers directly in this Assignment below the question it applies to. All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit. Note: All interest rates are to be assumed to be yearly interest rates. Question 1 (10 points) 1. You decide to invest $15000 into a bank account that that is compounding its interest monthly. Assuming the bank is paying out an interest rate of the current prime rate - 1% (In the event that prime - 1% is less than 1%, use 1%), and the investment is for 5 years a) How much money (total) do you have after the 5 years pass? Total = A(1+r/n)nt A = $15,000, r = 0.01 , n = 12, t = 5 Total = $ 15,000(1+0.01/12)60 = $ 15,768.74 b) How much do you earn in interest over the 5 years? Interest = $15,768.74 - $15,000 = $ 768.74 Question 2 (10 points) 2. You wish to......

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...Dec 4 | 11.5: Alternating Series | | 12 | Dec 7 – Dec 11 | 11.6: Absolute Convergence and the Ratio and Root Tests Review for Midterm Exam 2Midterm Exam 2 | Exam 2 : Wed, Dec 10, 5:30-7:00pm Sections: 10.1-10.4, 11.1-11.5 | 13 | Dec 14 – Dec 18 | 11.8: Power Series11.9: Representation of Functions as Power Series | | 14 | Jan 4 – Jan 8 | 11.10: Taylor and Maclaurin Series 11.11: Applications of Taylor PolynomialsComplex Numbers | | 15 | Jan 11 – Jan 15 | Review for Final Exam | Final Exam (comprehensive) | Math Learning Center (NAB239) The Department of Mathematics and Statistics offers a Math Learning Center in NAB239. The goal of this free of charge tutoring service is to provide students with a supportive atmosphere where they have access to assistance and resources outside the classroom. No need to make an appointment-just walk in. Your questions or concerns are welcome to Dr. Saadia Khouyibaba at skhouyibaba@aus.edu or cas-mlc@aus.edu Math 104 Suggested Problems TEXTBOOK: Calculus Early Transcendentals, 7th edition by James Stewart Section | Page | Exercises | 7.1 | 468 | 3, 4, 7, 9, 10, 11, 13, 15, 18, 24, 26, 32, 33, 42 | 7.2 | 476 | 3, 7, 10, 13, 15, 19, 22, 25, 28, 29, 34, 39, 41, 55 | 7.3 | 483 | 1, 2, 3, 5, 8, 9, 13, 15, 23, 24, 26, 27 | 7.4 | 492 | 1, 3, 6, 7, 9, 11, 15, 17, 22, 23, 31, 43, 45, 47, 49, 54 | 7.5 | 499 | 3, 7, 8, 15, 17, 33, 37, 41, 42, 44, 45, 49, 58, 70, 73, 76, 80 | 7.8 | 527 | 1, 2, 5, 7, 10, 12, 13, 17, 19, 21, 25,......

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...Week 1 DQ 1 Response 1) Given the enumeration methods; sum rule, product rule, permutations, combinations along with enumeration methods for indistinguishable objects, how can we devise a strategy to solve problems requiring these methods? A basic concept in the branch of the theory of algorithms called enumeration theory, which investigates general properties of classes of objects numbered by arbitrary constructive objects (cf. Constructive object). Most often, natural numbers appear in the role of the constructive objects that serve as numbers of the elements of the classes in question ("Enumeration", 2013). The Sum/Difference Rules refer to the derivative of the sum of two functions is the sum of the derivatives of the two functions ("Basic Derivative Rules", 2013). The product rule is one of several rules used to find the derivative of a function. Specifically, it is used to find the derivative of the product of two functions. It is also called Leibnitz's Law, and it states that for two functions f and g their derivative (in Leibnitz notation, ). The derivative of f times g is not equal to the derivative of f times the derivative of g: .The product rule can be used with multiple functions and is used to derive the power rule. The product rule can also be applied to dot products and cross products of vector functions. The Leibnitz Identity, a generalization of the product rule, can be applied to find higher-order derivatives ("Definition Of Product Rule", 2013). A......

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...Math 1P05 Assignment #1 Due: September 26 Questions 3, 4, 6, 7, 11 and 12 require some Maple work. 1. Solve the following inequalities: a) b) c) 2. Appendix D #72 3. Consider the functions and . a) Use a Maple graph to estimate the largest value of at which the graphs intersect. Hand in a graph that clearly shows this intersection. b) Use Maple to help you find all solutions of the equation. 4. Consider the function. a) Find the domain of. b) Find and its domain. What is the range of? c) To check your result in b), plot and the line on the same set of axes. (Hint: To get a nice graph, choose a plotting range for bothand.) Be sure to label each curve. 5. Section 1.6 #62 6. Section 2.1 #4. In d), use Maple to plot the curve and the tangent line. Draw the secant lines by hand on your Maple graph. 7. Section 2.2 #24. Use Maple to plot the function. 8. Section 2.2 #36 9. Section 2.3 #14 10. Section 2.3 #26 11. Section 2.3 #34 12. Section 2.3 #36 Recommended Problems Appendix A all odd-numbered exercises 1-37, 47-55 Appendix B all odd-numbered exercises 21-35 Appendix D all odd-numbered exercises 23-33, 65-71 Section 1.5 #19, 21 Section 1.6 all odd-numbered exercises 15-25, 35-41, 51, 53 Section 2.1 #3, 5, 7 Section 2.2 all odd-numbered exercises 5-9, 15-25, 29-37 Section 2.3 all odd-numbered exercises 11-31...

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...Math. Questions for Bank and Other Competitive Exam 1) What is 30% of 450? (1) 150 (2) 135 (3) 180 (4) 1350 3) Ten men can finish construction of a wall in eight days. How much men are needed to finish the work in half-a-day? (1) 80 (2) 100 (3) 120 (4) 160 4) Find the next number in the series. 1, 2, 9, 28, 65, _________. (1) 126 (2) 182 (3) 196 (4) 245 5) A shop gives 10% discount on the purchase of an item. If paid for in cash immediately, a further discount of 12% is given. If the original price of the item is Rs. 250, what is the price of the article if a cash purchase is made? (1) Tk. 200 (2) Tk. 195 (3) Tk. 198 (4) Tk. 190 6) It was Wednesday on July 15, 1964. What was the day on July 15, 1965? (1) Thursday (2) Tuesday (3) Friday (4) None of these 7) The average of x1 x2 x3 and x4 is 16. Half the sum of x2 x3 x4 is 23. What is the value of x1? (1) 18 (2) 19 (3) 20 (4) 17 8) If March 1 of a leap year fell three days after Friday, what day of the week will dawn on November 22? (1) Saturday (2) Sunday (3) Thursday (4) None of these 9) How is 1/2 % expressed as a decimal fraction? (1) 0.5 (2) 0.05 (3) 0.005 (4) 0.0005 10) Find the next number in the series : 235, 346, 457…… (1) 578 (2) 568 (3) 468 (4) 558 11) A sofaset carrying a sale-price ticket of Rs. 5,000 is sold at a discount of 4%, thereby the trader earns a profit of 20%. The trader’s cost price of the sofaset is: (1) Tk. 4,200 (2) Tk. 4,000 (3)...

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...x^2 表示 x 的平方，=！表示不等于。pi 表示圆周率 类型 1： 20. The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? (A) 25 (B) 26 (C) 50 (D) 51 (E) 52 14. Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible? 16. Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the following represents the number of members in set Z ? (A) x + y + k (B) x + y - k (C) x + y + 2k (D) x + y - 2k (E) 2x + 2y - 2k 20. There are 75 more women than men enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men? 1 / 18 17. A merchant sells three types of clocks that chime as indicated by the check marks in the table above. What is the total number of chimes of the inventory of clocks in the 90-minute period from 7:15 to 8:45 ? 18. If the 5 cards shown above are placed in a row so is never at eithe end, how many different arrangements are possible? 20. When 15 is divided by the positive integer k, the remainder is 3. For how many different values of k is this true? (A) One (B) Two (C) Three (D) Four (E) Five 17. On the number line above, there are 9 equal intervals between 0 and 1. What is the value of...

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...Edexcel Maths FP3 Past Paper Pack 2009-2013 PhysicsAndMathsTutor.com PhysicsAndMathsTutor.com Surname Centre No. Initial(s) Paper Reference 6 6 6 9 Candidate No. 0 1 Signature Paper Reference(s) 6669/01 Examiner’s use only Edexcel GCE Team Leader’s use only Further Pure Mathematics FP3 Advanced/Advanced Subsidiary Tuesday 23 June 2009 – Morning Time: 1 hour 30 minutes Question Leave Number Blank 1 2 3 4 Materials required for examination Mathematical Formulae (Orange) Items included with question papers Nil Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. 5 6 7 8 Instructions to Candidates In the boxes above, write your centre number, candidate number, your surname, initials and signature. Check that you have the correct question paper. Answer ALL the questions. You must write your answer to each question in the space following the question. When a calculator is used, the answer should be given to an appropriate degree of accuracy. Information for Candidates A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. Full marks may be obtained for answers to ALL questions. The marks for individual questions and the parts of questions are shown in round......

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...http://sahatmozac.blogspot.com ADDITIONAL MATHEMATICS MODULE 1 FUNCTIONS Organized by Jabatan Pelajaran Pulau Pinang 2006 http://mathsmozac.blogspot.com http://sahatmozac.blogspot.com CHAPTER 1 : FUNCTIONS Contents 1.1 Concept map Page 2 1.2 Determine domain , codomain , object, image and range of relation 3 1.3 Classifying the types of relations 3 2.1 Recognize functions as a special relation. 2.2 Expressing functions using function notation. 2.3 Determine domain , object , image and range 4-5 3.0 Composite Functions 6 -9 4.0 SPM Questions 9 – 10 5.0 Assessment test 11 – 12 6.0 Answers 13 – 14 http://mathsmozac.blogspot.com 1 http://sahatmozac.blogspot.com CONCEPT MAP FUNCTIONS Relations Object images ………….,, …………… …………… Functions Function Notation Type of relation y Or ……………… Composite Functions Inverse Functions f: x One to one Many to one ……….. fg ( x ) = ……………. Object f(x)=y ……………… http://mathsmozac.blogspot.com 2 http://sahatmozac.blogspot.com 1.1 Functions Express the relation between the following pairs of sets in the form of arrow diagram, ordered pair and graph. Arrow diagram Ordered pair Graph a ) Set A = Kelantan, Perak , Selangor Set B = Shah Alam , Kota Bharu ,Ipoh Relation: ‘ City of the state in Malaysia ‘ b )Set A = triangle,rectangle, pentagon Set B = 3,4,5 Relation : ‘......

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...Man, throughout his existence, is almost always confronted with different kinds of problems. What to do with these problems and how to solve them are questions which often placed him in a dilemma. Sometime he may be able to find solutions to these problems or he may not. Some solutions may be simple or may be complicated. But what is certain is that there is always a solution to every problem that man is besieging with. This solution may be outright or may go through different Mathematics process. Mathematics plays a vital role in our life to brighten up our humanly uncertainties and complexities. Mathematics is exquisitely designed to answer some of our questions, as Pythagoras said; “The world is a harmony of numbers.” Mathematics, through sometimes puzzling and complicated, is enjoyable. It is full of excitement when strong determination and constant interest is properly established and upgraded. Students feel jubilant and rewarded when correct solution is achieved. “The harder the struggle, the sweeter the victory is a common expression. This study was brought about when Mathematics, especially problem solving processes, Mathematics interest and Mathematics aptitude. Problem solving, which the National Council for Teacher in Mathematics (NCTM) 1980’s widely heralded statement in its agenda for action and problem solving has been the theme of the council. Knowledge and skills of Mathematics problem solving is believed to help school goers solve problems in their day...

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...pictures and diagrams to record their thinking. Next they must develop the skill of enquiring, asking questions to further their understanding of a problem. Finally they are able to develop their understanding of reasoning and communication. According to the Using and Applying Guidance Paper (DfES,2006) to enable a child to reason they must be ‘taught how to describe, interpret and explain what they see and how to use this to inform their thinking and reasoning’(p10). Black (2005) argues a key element of a child’s development of reasoning is the ability to think and communicate their thoughts effectively. According to the Lancashire Primary Mathematics newsletter (Lancashire County Council,2010) believes providing children with activities and dialogue which develops all of the aforementioned skills can allow them to acquire problem solving and reasoning skills. In addition Askew et al. (1997) believed developing children’s problem solving skills will also generate a deeper understanding of mathematical concepts, as children are able to form connections in their mathematical learning. In addition some mathematic advisors believe (Lancashire County Council,2010;DfES,2006)to develop high-quality mathematical dialogue; which elevates children’s skills of reasoning , the teacher holds a pivotal role and has a ‘significant impact on the quality of communication and reasoning within maths’ (DfES,2010.p3) Saljo and Wyndham (1997) argue that reasoning activities allow children to......

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...Math was always the class that could never quite keep my attention in school. I was a daydreamer and a poor student and applying myself to it was pretty much out of the question. When I would pay some attention I would still forget the steps it had taken me to find the solution. So, when the next time came around I was lost. This probably came about because as a kid I wasn’t real fond of structure. I was more into abstract thought and didn’t think that life required much more than that at the time. I was not interested in things I had to write down and figure out step by step on a piece of paper. I figured I could be Tom Sawyer until about the age of seventy two. My thoughts didn’t need a rhyme or reason and didn’t need laws to keep them within any certain limits. The furthest I ever made it in school was Algebra II and I barely passed that. The reason wasn’t that I couldn’t understand math. It was more that I didn’t apply myself to the concepts of it, or the practice and study it took to get there. I was always more interested in other concepts. Concepts that were gathered by free thinkers, philosophers, idealists. Now I knew that a lot of those figures I read about tried their hand in the sciences, physics, and mathematics in their day, but I was more interested in their philosophical views on everyday life. It was not until I started reading on the subject of quantum physics and standard physics that I became interested in math. The fact that the laws of standard......

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