There Is An Infinite Staircase Constructed From Cubes . Find The Total Volume Of The Staircase , Given That The Largest Cube Has A Side Of Length 1 And Each Successive Cube Has A Side Whose Length Is Half That Of The Preceding Cube. Does Anybody Know The C O R R E C T Answer? Tnx

Stepping Up To The Plate, to use that ghastly cliche... This is a straightforward Sum of a Geometric Series Q! Side of Cube 1, s1 = 1 => V1 = 1 Side of Cube 2, s2 = 0.5 => V2 = 0.125 Side of Cube 3, s3 = 0.25 => V3 = 0.015625 ... Sum of Volumes of the Infinite Cubes, S = V1 + V2 + V3 +... = 1 + 0.125 + 0.015625 + ... [~ Geometric Series: a1 = 1, common ratio, r = 0.125 => Sum, S = a1/(1-r)] = 1/(1 - 0.125) = 8 I'm just curious: Did this ACTUALLY appear as a Subtest III Q? Jay innovationguy@yahoo.com

No, it didn't but something similar did: There is an infinite series of half circles. In the first row you have 2 half circles and their radius is 4. Every row has double half circles but their radius is Half That Of The Preceding row. What is the total area of the infinite series? Tnx 4 the solution...I wasn't sure if I did right

Yes, it IS 1.1428 (~ 8/7) ...!! I don't know what I punched into my calculator IN ERROR!! SORRY! Jay.

hey guys Well, Thanks for all the help, the test was good, and I will take the geometry next. Algebra makes me less happy. I guess that most of you are Math majors and you've been doing this quickly. I am a business major, but I think I am kind of good with practical math. The thing is , I am not originally from the US and M math classes were in a different language. I had to study everything by the new terminilogy of english. Thank god that number stayed the same I would really appriciate if you know some good, easy to study books for Algebra and Geometry. The LA public libraries don't have most of the text books suggested in the General Examination Information Booklet. Tnx

Books for beginners might work well for you - not because you need the content, but because the terminology will get spelled out for you in ways that will make it easier to connect to what you already know. Try going to your local big bookstore and rummaging among the math books and math study books - most of them are in the math section at both Borders and Barnes & Noble. Look for books that you think make sense - both for helping you learn the terms, and for helping your future students learn the concepts. Whether you then buy any is up to you... but you're likely to find some or all in the library. I think Jay (innovation_guy) had some suggestions of specific books as well. You might try searching for his posts.

tnx a lot for all your help. I have a local barnes & nobles here in calabasas and I hope they carry the books that jay suggested. keep me posted if you have another idea. Ziv

I'm sorry but your message befuddles me just a smidgen! You write: Quote. Thanks for all the help, the test was good, and I will take the geometry next. Algebra makes me less happy. ... I would really appriciate if you know some good, easy to study books for Algebra and Geometry. Unquote. Um, so what test did you take?! Was it ACTUALLY Subtest III?! Of course, this IS the Subtest III forum and all that balderdash, but I haven't encountered a fellow that appeared the 3rd Subtest FIRST: hence, my embarassing incredulity! If I were the irrepressible Jon Stewart from The Daily Show, I'd be rubbing my eyes RIGHT ABOUT NOW! Anyway, if you're done with Trigonometry/Calculus, then BRAVO! (Usually, candidates sink their fangs into this at the culmination of the other 2 Subtests, and ONLY if their school districts demand it!) But seeing that you've surmounted that hurdle - and yet regard Algebra to be challenging (again, it's usually the other way around!), here are some user-friendly 'non'-textbooks for the 2 subtests: * Algebra the Easy Way * Geometry the Easy Way Pub: BARRON'S Together, they're available at Amazon for $20.34 (don't forget the 34 cents!) This is the book description from the back cover of the 1st book (so you'll know that it is unbiased and reliable...Oh, just kidding around!): ----------------------------------------------------------------- Back Cover Copy ALL THE ESSENTIALS IN ONE CLEAR VOLUME # High school-level algebra in the form of a fantasy novel # Solving practical problems with algebra # Hundreds of problems solved and explained # Diagrams and amusing line illustrations # Equations # Exponents # Polynomials # Permutations and Combinations # Matrices and Determinants # Mathematical Induction . . . and much more ----------------------------------------------------------------- Bottomline: I've examined both books and unhesitatingly vouchsafe my earnest seal of approval (and everyone knows how priceless that is!?!) And just in case the whim seizes you, let me issue a peremptory caution: I've scrutinized BOTH Geometry for Dummies and Algebra for Dummies, and neither passed muster: they're just too elementary for the CSET! On the other hand, I found The Complete Idiot's Guide to Precalculus (Paperback) by W. Michael Kelley to be quite serviceable. You may want to employ this in conjunction with Complete Idiot's Guide to Algebra by the same author, this latter to reinforce your intermediate Algebra foundations. (Mr. Kelley, you shall, of course, remember me in your will?...) All the books I've suggested, you are likely to find in your neighborhood BORDERS / Barne's and Noble book stores. Or get them online from http://www.Amazon.com or http://www.Half.com. Finally, a very VITAL CAVEAT: these books can be used ONLY as a primer for the CSET curriculum: by themselves, they're laughably inadequate for a rigorous CSET preparation. Use them only as a springboard for more 'conventional' college texts after familiarizing yourself with basic concepts/terminology! The level of Math sophistication on the CSET exceeds that of the aforementioned texts! For a detailed list of 'regular' books for both Subtest I and Subtest II, check out my exhaustive posts in other threads: CSET Math Test This Past Saturday, CSET Math Test This Past Saturday (PART 2) and CSET Mathematics Test Prep A tip: check out those posts regularly for Tips and Suggestions! You should be done with this thread (hopefully!)...Also, don't forget to check out the site http://innovationguy.easyjournal.com for CSET resources, practice Qs and what not! Jay. innovationguy@yahoo.com PS. Assuming that you shall indeed buy the 'Easy Way' volumes I suppose I can expect my McGrawHill investments to appreciate just a tad? (34 cents perhaps?!)

jay, you are a very funny guy...you are probably a very very good teacher. Anyway, I used the idiot's guide for the subtest III and I passed , it's not enough though, so I also used the new horizon book by adward anton. it had plenty of Cset Q's. I found some in the Woodland Hills branch (LAPL) and also in the Calabasas Library (connect to the Cojeho Valley). For the Statistics I found Nothing so far, Even any of your suggestion, so , do you have any other ideas for the statistics and probability books? keep up with the good work. I mean, keeping us alive... Ziv

Dear Ziv: Thank you for your kind and gracious words! Re "you are a very funny guy...you are probably a very very good teacher...", I sometimes wonder which of them is true, and more darkly, if neither was! I'm not terribly surprised that your local Public Library branch is not stocked with the books I suggested: for simple reasons of supply and demand, tax-payer supported libraries are likelier to stock 17 copies of regurgitated garbage by Robert Ludlum than a Math text. Anyway, for Statistics, as I've said before, ANY college book of reasonably recent vintage - say, published during the post-Reagan era! - should be adequate, especially those with BASIC, ELEMENTARY and INTRODUCTORY in their titles. For a useful syllabus visit the site I've mentioned in my earlier posts! (I've always regarded the CSET site itself as blandly objective and as animated as a couple of porcupines in heat: since it only lists a cavalcade of topics, there is no indication of 'emphasis' or focus...you need someone resolutely opiniated - like I wonder who?! - to cut throught the blather...!) Thank you for your hospitable words, again! Cheerio! Jay. innovationguy@yahoo.com PS. The gag I reference above runs: How do 2 porcupines make love? Very carefully! PPS. Of course, you can choose to BUY those books new, or used...

Ziv, have you looked just at your two local library branches? The library system holds many more books, among which might well be some of Jay's suggestions, and in that case you should be able to get them through inter-library loan. In fact, the system might also be able to get you books from Cal State Northridge. Try asking the librarian. Another good resource for buying books used, in addition to Half.com, is Powell's bookstore in Oregon, http://www.powells.com - this is the West Coast's nearest equivalent to England's Heffers or Blackwells, and it does a lively mail-order business in new and used books of all descriptions. Alternatively, visit your local community college - I'm thinking Pierce LA College, but there's probably something nearer - and find a student who's selling off last term's math books. It is slightly late in the season for that, but not horribly. Jay hasn't vetted Alan Axelrod's ACE YOUR MIDTERMS AND FINALS: FUNDAMENTALS OF MATHEMATICS (McGraw-Hill), but it might help you get a sense of what mathematics exam answers in American English are supposed to look like.

Oh, I just want to echo teachergroupie's sage words: try the Inter-Library loan/transfer (NOW I know what I'd missed writing: the infernal thing was chafing me like a boil on one's posteriors on my drive to work!!). First, of course, you shall have to unearth the library in your constellation of branches in which the required books repose. Use their computer catalogs - this is often PUBLIC access (~ accessible from home!) - or get assistance from a comely librarian starved for company (?!!). Again, don't work with one book alone: having myriad texts broadens your perspective and bolsters comprehension! Cheerio! Jay. innovationguy@yahoo.com