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Everything posted by mpcTutor

  1. Download detail pdf solution: Train word problem Best regards. Mohan Pawar http://www.mpclasses.com/ContactUS.htm US Central Time:5:14 PM 9/27/2010
  2. Please verify. I am getting Westward speed = 5 mph ( same as 5 miles per 60 min) Eastward speed = 7 mph (same as 7 miles per 60 min) I will try to post detail answer later if anyone interested. I have to go. Best regards. mpcTutor http://www.mpclasses.com/ContactUS.htm US Central Time:2:28 PM 9/27/2010
  3. For solution see: How to represent a recurring decimal number as a rational number. Best regards. MPCtutor http://www.mpclasses.com/ContactUS.htm ---------------------------------------------------------- AP Calculus, AP Physics, IIT JEE Test Prep. ---------------------------------------------------------- US Central Time:1:28 PM 9/17/2010
  4. The previous poster already gave the solution. Here are details. Simply follow the same logic that you used for other problems solved correctly. If P = Present amount = 55000 i% = % interest rate per period (Note that I deliberately wrote per period and not per year ) = 8%/4 = 2% n = No. of periods for which P is in the saving account = 2 years x 4 period per year = 8 S = Lump sum amount yielded at the end of n period = To be found yield = interest paid on investment Then S = P( 1 + i%)^n (One can easily derive this formula with 7th grade algebra background. Note 2% = 2 per cent = 2/100 = 0.02)) = 55000 ( 1 + 0.02)^8 = 64441.27 Yield = 64441.27 - 55000 = 9441.27 (Answer) Best regards. mpcTutor http://www.mpclasses.com/ContactUS.htm ---------------------------------------------------------- SAT/ACT, AP Calculus, AP Physics, IIT JEE Test Prep. ---------------------------------------------------------- US Central Time:1:49 PM 9/16/2010
  5. Your son is right and I don't see anything wrong with his proof. Although, problem asks to prove CA > CO, the zipped figure to me showed CA significantly shorter than CO without making any actual measurements. Also, triangles should appear to be congruent without actually measuring any sides or angles. So I am assuming the original diagram could be different from diagram in your attachment. Short Proof: ------------- Given: OCE & ANE as congruent triangles Consider triangle OCE, OC < CE + EO (due to triangle inequality) OC < CE + EA (due to Given, EA = EO) OC < CA (due to betweeness of points CA = CE + EA ) QED Best regards. mpcTutor www.mpclasses.com -------------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 -------------------------------------------------------------------------------- Note: If you replied to my post but didn't get an answer from me in reasonable time, I ask you to check the assumptions in your question. Thank you US Central Time: 11:30 AM 7/29/2010
  6. (Note: Underlined words are links) I am not sure if I fall in any groups that you expected to respond. But I am not surprised that there has been no reply to your post yet. I volunteered to provide solutions to problems from AP Calculus and AP Physics on Feb 3, 2010. Note that Feb to May is THE most critical time for AP student's life cycle of AP test preparation but not a single problem from AP Calculus/Physics has yet been posted. Looks like not many students do calculus with a goal to take AP Calculus test given annually in May. There was a little change in Free Response Questions (FRQ) type problems. In the past, almost always there has been a problem from kinematics which was missing in the recent AP Calculus test and it might have surprised some students and teachers. Since you are looking for preparatory material, consider the current trends in test pattern. New trend suggests that one cannot count just on the word-based familiarity with known AP problems. The same problem from kinematics can be presented under different wrapping. To answer your question, see the list of books that College board has given on their web site. College Board does give student and teacher lot of freedom in choosing material by stating "Not using a book from this list does not mean that a course will not receive authorization". After citing all this information, I must say that I myself have not yet adopted any of the books from above list of books. But I do recommend to get AP Calculus test problems from the College Board itself. I don't represent College Board and have no business gains or losses from their sales or no sales. My recommendation is based entirely on common sense: if certain universities need a good score in AP Calculus test, it makes sense for student family to know what the AP Calculus test is from the body that administers it. Certainly tests don't substitute the textbook but still I don't have recommendation for textbook. Students that I have been tutoring do use 900-1100 page textbooks which they never have time to read. It is understandable that teachers use the textbook mostly to assign problems and the publisher has teacher's solution manual. Most of these books will give indiscriminately overwhelming number of problems at the end of each chapter that even when student has access to solution manual or to online solutions, there is never enough time to master the concepts in sufficient depth to be able to solve similar problems if seen on test. Unusual as it may sound but do consider physical weight of the calculus textbook before you buy one. Best regards. mpcTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- Note: If you replied to my post but didn't get an answer from me in reasonable time, I ask you to check the assumptions in your question. Thank you US Central Time: 12:15 PM 5/21/2010 Edited at US Central Time: 12:15 PM 5/21/2010
  7. Solution: Given:3x + y + z = 2 ----------(1) 4x + 2z = 1----------(2) 5x - y + 3z = 0----------(3) If y is eliminated from (1) and (3) we get 8x + 4z = 2 ----------(4) The resulting system now has Eq (2) and (4) which represent only one straight line. These equations are called as "dependent equations* in x and z". Values of x and z will depend on y and can be infinitely many depending on value of y. Thus, The strategy is not to eliminate y but eliminate x or z. (1) x 3 - (3) gives 2x + 2y = 3 Thus x = (3 -2y)/2 ----------------(Answer1) Substituting x from Answer1 in (2) 4(3 -2y)/2 + 2z = 1 Thus, z = -5/2 + 2y ---------------(Answer2) and y = y ------------------------ (Answer3) Now for any given value of y the given eqns (1), (2) and (3) will be uniquely satisfied. Dependent Equations: ------------------------- See Eq (2) & (4). 4x + 2z = 1 and 8x + 4z = 2 are dependent because (4) depends on (2) and vice versa. Such equations are ignored when solving system of simultaneous equations and that's what is done above. Best regards. mpcTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 10:58 PM 5/18/2010 Edited at US Central Time: 7:12 AM 5/19/2010
  8. I gave this solution in hurry, please wait for someone to point out if any errors. Your book formula is correct. Use V for volts, N for turns, subscript p for primary and subscript s for secondary. Rewrite the formula as below: Vs/Vp = Ns/Np Hence Ns = Np (Vs/Vp) --------> (1) Given: Vp = 120,000 volts Vs = 120 volts Np = 1000 turns Substituting above quantities in (1) Ns = 1000 (120/120000) = 1 Current in secondary Is = Vs/Rs = 120/10 = 12 ampere c. what is the power in the secondary coil? Power in Watts Ps = Vs x Is = 120 volts x 12 ampere = 1440 watts Power in primary coil = Power in secondary coil Ip x Vp = Is x Vs = 1440 Ip = 1440/120000 = 0.012 ampere (which is comparatively low amperage) P ower loss = (I^2) R. Thus, power loss increases in square proportion of current I for a given resistance R. By reducing I to low level such as 0.012, the power companies avoid power loss during power delivery from power station which is far away fro home or place of power consumption. Rigorous solution to similar question is in math forum . ( See the link ) Best regards. mpcTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 2:43 PM 5/18/2010
  9. Reference to Saxon algebra-II automatically assumes two more separate books as part of curriculum - i) Algebra-I and ii) Geometry. The switch from New Elementary Math (NEM) to Saxon is tricky unless one has already taught before the entire high school math including pre-calculus. The difficulty is due to Geometry/Co-Ordinate Geometry, Trigonometry and Algebra-II being covered all along in the NEM up to book 4A. On the other hand, NEM 1, 2, 3 and 4A should be more than adequate for ACT + SAT and sufficient for subjects tests SAT Math Levels 1 & 2. For a brief inside view of Saxon's Advanced Math you may want to visit Amazon. Best regards. MPCTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 9:58 AM 5/17/2010
  10. That's odd -- I was able to find the table of contents and sample pages for the Singapore books here:Book 3A http://www.singaporemath.com/ProductDetails.asp?ProductCode=NEMT3A&Show=TechSpecs Book 3B http://www.singaporemath.com/ProductDetails.asp?ProductCode=NEMT3B&Show=TechSpecs Book 4A http://www.singaporemath.com/ProductDetails.asp?ProductCode=NEMT4A&Show=TechSpecs Book 4B http://www.singaporemath.com/ProductDetails.asp?ProductCode=NEMT4B&Show=TechSpecs If you were referring to the Saxon math books, then I would agree: I couldn't find similar info on their website. 69 Thanks for the links in support. Best regards. MPCTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 9:46 AM 5/17/2010
  11. I have not seen Saxon math beyond Algebra 1/2 so it is difficult for me to compare. Like Singapore math very few textbooks make their basic information such as table of contents and a sample topic pages available on their websites for the buyer to evaluate the book. Most of word problems in the placement test are comparable to those in New Elementary Math (NEM). In fact, majority of challenging problems from "Challenging Word Problems (CWP) - Primary 6" from Singapore Math are harder than SAT/ACT word problems if one has do them in limited time. But CWP is another book. There are many many problems in NEM so I have not used any additional NEM workbooks. NEM could be too much as supplement. ------------------------------------------- NEM volume 3 & 4 are actually 4 separate books - 3A/3B and 4A/4B with respectively 220, 240, 129 and 255 pages (i.e. a total of almost 850 pages). 4B with 255 pages is entirely problems for practice covering almost all important elementary, middle and high school math. Along with Saxon say, Algebra 1/2 which requires one to do all 30 problems per lesson, the NEM as supplement could be lot of work. Currently, I am using Singapore Math for 6th grade for students with Saxon Algebra 1/2 as their regular curriculum and it is lot of work for them. Unless criterion of evaluation of curriculum effectiveness is known, choosing a curriculum is going to be rather subjective. One can choose any of the NATIONAL level standardized tests as criterion. Most colleges use them as criterion for admissions. So why not use test prep books as supplement? For example, A book titled "Real ACT prep guide" will give almost 180 math problems that once were on real ACT. Similarly, one can choose SAT prep books from College Board or from some other publisher. Best regards. MPCTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 10:18 AM 5/15/2010
  12. Concept is nothing but certain concrete idea (as against a vague notion). It doesn't matter if the concept is in mathematics or not, the success in identifying "the" concept from all other seemingly similar concepts is needed in understanding that particular concept. Example 1: Explain "All squares are rectangles but all rectangles are not squares." The beginning of above explanation is sometime when a child learns to differentiate a table from a chair and learns to ignore the fact that they both have four legs which in fact are not important in differentiating a chair from a table. The same child will however identify both chair and table as furniture distinctly different from say a car. Use of pictures, verbal description and constant acquaintance with these objects make these non-mathematical concepts pretty clear for most children. Unfortunately, with respect to most mathematical concepts, making the child aware of say, number 3 is not that easy. We can show 3 cars, 3 apples and 3 dogs but identifying the common three-ness in the pictures of cars, apples and dogs is largely left to the child. There is not an easy way to tell the child that the "three" is common to 3 cars, 3 apples and 3 dogs. If the child sees them as "things" then he/she missed the concept of "three". Also, important thing to remember is that even grown ups don't always see everything that is shown. So every child doesn't have to see the idea right after it is explained. There could be several valid reasons for a child not see your point including barriers in communication, child's willingness to be attentive etc. Example 2: The commutative law of addition a + b = b + a is introduced to the child by dividing 15 marbles in to two groups say 10 marbles and 5 marbles and then adding 1st group in the 2nd group and vice versa and then counting to show that the result is 15 marbles. The concept here is the sum of two numbers is not affected by the order in which they are added. If this "concept of commutation" is understood then the child doesn't need to be shown 20 + 30 = 30 + 20 again with the help of marbles. Example 3: The commutative law in Example 2 above is normally not questioned with "why" but simply accepted and its reason is known in later grades when field axioms for real numbers are taught only to learn that highly fundamental facts don't have reason. A new concept called "axiom". Bottom line: In earlier years certainly one could learn the basic facts through manipulative and by solving select problems. Particularly after 4th - 5th grades it is through the practice of solving well chosen problems that many hidden concepts can be understood. In my experience, that's the way the mathematics and physics are: not only for reading but largely for solving problems (with paper and pencil). In doing all of these activities a wise goal is to keep the child interested in mathematics and the sought after math mastery will come as consequence in due time. Best regards. MPCTutor www.mpclasses.com --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 2:11 PM 5/14/2010
  13. The same notation that you are referring to can be written as C(n.r) or specifically C(6,2) and C(8, 4) for ease of typing (which is accepted method of representation in many textbooks) C(n.r) means number of distinct combination (or groups) possible when each group contains r things out of n things. Please feel free to write back if you need detail answer. But in short, C(6,2) = 6!/[2!(6-2)!] = 15 C(8,4) = 8!/[4!(8-4)!] = 70 Thus, total ways = 15 x 70 = 1050 The topic to look for further information on notation is "Permutation and combination from pre-calculus" . We are currently registering students for online class for Pre-Calculus at our website. Sample of topic/chapter wise DVDs may also be available. Please send your request if you are interested. Best regards. MPCTutor www.mpclasses.com Contact for Additional Info --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 11:06 AM 5/7/2010
  14. This is purely math problem - No electricity/No Physics. (except use of P = V x I) I will rewrite the question and solve it. If interpreted problem is same as the original problem, use the solution, otherwise please post original problem as it is in the original source. Problem: 1) How much power does a light bulb connected to a 120V outlet use if it draws 0.5A of current? 2) One kilowatt-hour is a measure of energy which is equal to 3,600,000J. How many hours would you have to leave on the light bulb from the above problem in order to expend one kilowatt-hour? (remember that 1W=1J/s) The information in blue is not needed. 3) If one kilowatt-hour costs $.10, how long would you have to leave the light bulb on from the above problem in order to spend $1.00 on electricity? Solution: 1) Power = 120 V x 0.5 A = 60 Watts = 0.06 KW 2) Let t = time in hours Power consumed = 1 KWH = (0.06 KW) ( t hour) -----------(1) Solving (1) for t t = 1 KWH / 0.06 KW = 16.67 hours ----------(Answer) 3) Given Rate = 0.1 $/KWH Total bill = $1.00 Hence Total KWH = 1/0.1 = 10 KWH So required time = 10 KWH / 0.06 KW = 166.67 hours ---------(Answer) Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, IIT-JEE, Singapore Math --------------------------------------------------------------------------- US Central Time: 1:19 PM 5/6/2010
  15. Agree with other poster. F = 2.304 x 10^-28 N (Force of Repulsion) MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math (7-12) --------------------------------------------------------------------------- US Central Time: 11:58 AM 5/6/2010
  16. If she is getting 19 correct out of 20 then she most likely is not making computational errors. She simply has not been shown how a cylinder can be cut open into a rectangle and how same idea can be extended to a little more unusual shapes. The Saxon problems fall into distinctly two categories: 1) Given a regular cross section and height, find volume and 2) Find lateral area from perimeter and height Also, check if she is using area formulas for triangle and circle correctly. On a side note my suggestion is that she should do all required construction in the book diagram itself. By not drawing additional lines, angles etc. in the given figure, students don't see the solution. Most students will not draw their own diagram if it is not allowed to do the work in the text diagram itself. How important is this?: Almost certainly, there will be at least one and sometimes 2 similar questions on ACT. In addition, there are more than two questions on ACT that will need the background in above area. Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 4:13 PM 4/30/2010
  17. One cannot reach the chapter on two column proofs in geometry without studying several theorems in geometry (and knowing their _formal_ proofs.) Geometrical proofs are introduced as deductive proofs and deductive reasoning requires them to be formal all along - whether in column form or not. Outside United States, one will rarely find textbooks describing proofs in two column form. For example, consider the introductory theorem on intersecting lines. Theorem: If two lines intersect each other, then vertically opposite angles are congruent. Traditionally, this is proved in one of the the first 2-3 chapters without the two column format. Yet the proof is formal and rigorous. Most kids understand such proof but when they are asked to reproduce it they themselves will find that they made errors. Certainly, putting proofs in column form with statements in the right hand side and reasons in the left hand side has greatly helped in visualizing the logic in the arguments. So I would teach column form proof even in the beginning if the theorem required it. Sometimes proof in the column form is not even needed since traditional form is sufficient for understanding and easy for writing. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 9:57 AM 4/30/2010
  18. The problem is confusing the reader with trivial data. Simplified version of above problem is: under condition A wind chill -16 but under condition B the wind chill is 4 times that under A. So what is wind chill under B? Ans. is obviously -64 deg F MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 12:48 PM 4/20/2010
  19. Please see solution at http://www.welltrainedmind.com/forums/showthread.php?p=1541594#post1541594 Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 8:35 PM 3/5/2010
  20. Problem 1 ----------- Away from earth we know that there is loss in weight. The question is asking to find how much will astronaut weigh in Newtons the space station up there. So astronaut with mass 81 kg has weight (81 kg) x (10 m/s^2) = 810 N when on earth. So expect answer to be much less than 810 N. By Newton's law of gravitation F = (GMm)/d^2 = ma ----------> (1) Where G = 6.67 x 10^(-11) Nm^2/kg^2 = constant of gravitation M = 5.98 x 10^24 kg = Mass of earth m = 81 kg = astronaut's mass R = 6.37 x 10^6 m =radius of earth d = 3R = distance between center of earth and the astronaut Substitute relevant variable in (1) Force in Newton = [6.67 x 10^(-11)] * [5.98 x 10^24] * [81] / (3 * 6.37 x 10^6)^2 = 88.47 N ( which on earth is 810 N so we are doing ok) 2. The astronaut in the above was launched into space by a Saturn rocket. The upward acceleration of a Saturn rocket shortly after blast-off in 80m/s^2. When the Saturn rocket is accelerating, what is the apparent weight of astronaut, that is, what does the astronaut experience as the weight of his body?(Hint: Keep in mind the definition of weight and that more than acceleration due to gravity is acting on the astronaut.) Answer must be in Newtons. Problem 2 ------------ When astronaut is sitting in the seat while rocket is still on ground his seat is pushing him/her upward with 810 N force which is the weight. When rocket itself has acceleration in upward direction there will be additional force of (80 m/s^2) * (81 kg) = 6480 N So, net upward force experienced by astronaut = 6480 + 810 = 7290 N You can imagine astronaut's upward force on a moderate scale when you go upwards in a very high speed elevators in tall buildings. You are welcome. Please check answers in your book if you can. I did these problems in a bit of hurry. If my solutions are incorrect, please post your feedback. Thanks. Also, if you had posted the question under http://www.welltrainedmind.com/forums/showthread.php?t=153209 I would have received email from forum admin about your post and I would have known about your questions a little earlier. Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 8:31 PM 3/5/2010
  21. Answer (a) Tangential speed = radius x rotational speed. (Recall v = r*w) Since w (omega) is constant the tangential speed will vary directly with radius alone. Half way from axis of rotation means half tangential speed. Answer (b) Angular momentum = Moment of inertia x angular velocity. With 3 kg bag Moment of inertia increases and hence angular momentum increases proportionately. The problem must assume that angular velocity is constant.) Answer (d)Angular momentum = Moment of inertia x angular velocity. = (25 kg x 225 m^2) x (10 Pi/60) = 2945.24 kg*m^2/s = approx. 3000 kg*m^2/s (Recall I =m*r^2) Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 2:25 PM 2/23/2010
  22. In my experience, the best test prep material for AP Calculus is the question bank from College Board itself. Nothing can come closer to it in matching level of difficulty and question pattern. These are PDF files for download of previously appeared questions on actual AP Calculus tests. One has to buy them online at College Board's online store. I believe you probably are looking for commercial off the shelf prep books from local bookstores. Three years back I chose Princeton Review 2006-2007 for following 2 reasons: a) It was easily accessible to look at its content in the local bookstores. This was very important for me so I knew what I was buying. b) In comparison with then available similar books, I found it had chapters with briefly revised topics. It had 5 practice tests. Other titles were introduced in the market after I chose Princeton Review and I don't know how Princeton Review compares with say "5 steps to a 5" or the Barron's Test Prep. Recently, I know some teachers have recommended following book which I have not used or seen in local bookstores. http://www.dsmarketing.com/books_calcBC.html If you already have a good textbook but want only practice tests, consider College Board's set of past tests as a PDF file that also contains brief solutions. Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 4:34 PM 2/20/2010
  23. In response to WTM 4 8: =============== While there is still time, could you download information manual from College Board and read page 24 Link is: http://professionals.collegeboard.com/profdownload/ap-coordinators-manual.pdf Page 24 in the above manual refers to "Homeschooled Students and Students Whose Schools Do Not Offer AP Exams" I am quoting 2 guidelines from page 24: 1) "Students should contact AP Services no later than March 1 to get the names and telephone numbers of local AP Coordinators whose schools are administering the AP Exams they plan to take. Prior to calling, students should prepare a list of the exams they plan to take so that the schools and AP Coordinators can be easily identified." 2) "Students should contact the AP Coordinators identified by AP Services no later than March 15. Students should inform the Coordinator they contact that they want to locate a school willing to administer the AP Exams they plan to take. They will be using their own school’s code or the state homeschool code, ensuring that their exam grade(s) will be reported separately from the school at which they test." It appears that you already have done things that you need to do, yet if you could browse other relevant pages that might be useful. I know from other forums that College Board supports the idea of kids taking AP tests. My best wishes for you and your child. Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 7:05 PM 2/18/2010
  24. I have personally not seen TIMSS test papers and I don't know if students are allowed to use calculator or not. Whenever calculator is not allowed, kids in USA will find overseas students having certain advantage in being able to do math without calculator. This in itself is another point of debate which I don't want to start. Again, point here is not about calculator use but I am trying to make sure that we are comparing apples to apples. Comparing US and Singapore curricula, I would say Singapore is more traditional than US. We are always experimenting. In US, the goal for all round development of child results in sacrifice in other areas such as math. In Singapore and in most Asian countries academic competition is so intense that kids cannot afford time for other activities during 10th, 11th and 12th grade years. These are the kids who have competed in TIMSS. So one can attribute their success in TIMSS to curriculum sequence or to their effort or to both. I think it is largely the effort put in by students that makes the difference. Singapore curriculum was introduced only recently in US schools with history of less than 12-13 years. If you are leaning towards Singapore math, my suggestion is to aim for finishing "New additional syllabus math" by end of summer after which your child enters 11th grade. One could accelerate and go faster but I have yet not seen any real benefit in acceleration. Again, success or benefit in any curriculum must be measured only by a national level standardized test such as AP/SAT/ACT/CLEP. Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 2:26 PM 2/17/2010
  25. New Elementary Mathematics (NEM) Volume 1 which is the first book in Singapore Math series for 7th graders has chapters 9 through 14 related exclusively to geometry. Almost 50% content in the book is geometry. So Singapore math does contain adequate geometry. A link to table of contents related to geometry in NEM is below: http://www.singaporemath.com/ProductDetails.asp?ProductCode=NEMT1&Show=TechSpecs Now coming to the columnar proofs, the language has certainly changed, instead of asking prove angle A = Pi/3, now most books ask you to find angle A. Whether, student proves A=Pi/3 or finds A=Pi/3, the method of solution remains same in content and rigor. The solution may not be in column form but it essentially is identical to one if written in column form. I think that's what the other poster is also saying. Best regards. MPCTutor --------------------------------------------------------------------------- AP Calculus, AP Physics, Singapore Math Grades 7-12 --------------------------------------------------------------------------- US Central Time: 10:40 AM 2/17/2010
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