For all questions, answer choice E) NOTA" means none of the above answers is correct. A) 50,500 B) 500,000 C) 500,500 D) 1,001,000 E) NOTA

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1 For all questos, aswer choce " meas oe of the above aswers s correct.. What s the sum of the frst 000 postve tegers? A) 50,500 B) 500,000 C) 500,500 D),00,000. What s the sum of the tegers betwee 00 ad 99, clusve? A) 4,950 B) 5,000 C) 5,050 D) 5, Evaluate: A) 3 B) 3 4 C) 8 9 D) Evaluate: s s s3...s... s360 A) 90 B) 0 C) 45 D) Cosder the sequece formed by the dgts of the cocateato of the postve tegers, lsted order: What s the 0th dgt of ths sequece? A) 0 B) C) 6 D) 7 6. Let s be the sum of the seres cotas s?. Whch oe of the followg ope tervals A), 3 B), 7 3 C) 7, 5 6 D) 5, Evaluate the double sum: m m A) B) C) 4 D) e 8. If, fd the value of the sum A) B) C) D)

2 9. Steve takes a arthmetc sequece wth commo dfferece d ad a geometrc sequece wth commo rato r ad adds them together, term by term, to form a ew sequece (.e., the frst term of the ew sequece s the sum of the frst terms of the arthmetc ad geometrc sequeces, etc.). If the frst three terms of the ew sequece are, order, 3, 8, ad 5, ad d ad r are both kow to be postve tegers, what s the sum of the possble values of d? A) 3 B) 7 C) 0 D) 5 0. Defe a sequece a by a0 ad a for all tegers a. What value do the terms of ths sequece approach as becomes large wthout boud? I other words, fd the value of the cotued fracto.... A) 0 B) C) 5 D) 5. Frst dscovered by Euler, the exact value of the sum of the recprocals of the perfect squares,, s. What s the value of 6 recprocals of the odd perfect squares?, whch s the sum of the A) B) C) 9 D) 8 6 a a. Defe a sequece a by a0 0, a, ad a a for all tegers. What value do the terms of ths sequece approach as becomes large wthout boud? A) 3 B) 4 C) 8 D) the sequece does ot approach ay umber 3. If, fd the value of the sum 0 log log... log... log0. A) B) log3840 log755 C) 4 5 log log 5 7 D) log6 log 4

3 4. Defe S. Fd the value of 0 S. A) B) C) 005 D) Smplfy the followg product: 0 0 A) 00 B) 0 C) 00! D) 0! 6. A partto of a postve teger s a way of wrtg as the sum of oe or more postve tegers wrtte o-creasg order. For example, all parttos of the umber 4 are 4, 3,,, ad. How may parttos of 0 express 0 as the sum of exactly 007 postve tegers? A) 4 B) 5 C) 35 D) Three of the frst fve terms of a creasg arthmetc sequece are 5,, ad 3. What s the 0th term of the sequece? A) 38 B) 4 C) 43 D) A busess eeds to hre three people to eter data to a database. Applcats must take a short exam, ad the busess mmedately hres the frst three people who meet a predetermed mmum score o the exam. If t takes a total of eght applcats utl all three spots are flled, how may possble sequeces are there for the way the applcats passed or faled the exam? A) B) 4 C) 8 D) Cosder the fucto examples, k l p, f p for some prme p ad postve teger k. As 0, otherwse 6 0 ad 69 3 l3. Fd the sum of the seres, where takes o oly the postve tegers whch dvde evely to A) l30 B) l5400 C) l D) l5400!

4 0. Suppose that to each postve teger we assg a uque, fte sequece whose terms cosst oly of 0 s ad s. For example, the followg table llustrates a possble choces of sequeces: Sequece assged to Sequece assged to Sequece assged to 3,0,,0,,0,,0,, 0,,0,0,,0,0,0,,,,0,,0,0,0,,0, What fte sequece cosstg oly of 0 s ad s ca be guarateed to dffer from every oe of ths fte umber of fte sequeces we have chose? A) the oe whose th term s the same as the th term of the sequece assged to B) the oe whose th term s the opposte of the th term of the sequece assged to C) the oe whose th term s the same as the frst term of the sequece assged to D) o such sequece s guarateed to exst. Evaluate: 3 A).5 B).75 C) D).5. The frst three terms of a quadratc sequece are, 3, ad. Fd the 4th term the sequece. A quadratc sequece s a sequece whose th term s gve by for fxed costats a, b, ad c. A) 7 B) C) 0 D) 3 a b c 3. Aaya couts to 00 a strage way. She couts,,,,, 3,,, 3, 4,,, 3, 4, 5,, startg over after each tme she reaches a umber she has ot prevously sad. She does ths utl she couts 00 for the frst tme. How may umbers, cludg repettos, does Aaya actually cout? A) 000 B) 4950 C) 5000 D) A sequece has frst term, ad each successve term the sequece s the sum of all the prevous terms. What s the 0th term ths sequece? A) 0 B) 00 C) 0 D) 009

5 5. A sequece of postve tegers startg wth 0 satsfes the followg codtos: ) the terms alteratve betwee odd ad eve; ) o teger appears twce; ad 3) the sum of ay two cosecutve terms s a multple of 3. What s the sum of the four smallest postve tegers that could ever belog to such a sequece? A) 0 B) 8 C) 4 D) A 0-dmesoal mouse scurres 4 meters ahead, turs left ad scurres meters ahead, the turs left aga ad scurres meter ahead, ad so o, always turg to ts left ad scurryg half the dstace t just prevously scurred. If the mouse cotued ths patter deftely, how far away from where t started would the mouse ultmately wd up? Assume the mouse makes 90 turs. A) 8 meters B) 4.75 meters C) 8 5 meters 5 D) 3 5 meters, fd the value of the sum If 0. A) 3 33 B) 3 C) 3 3 D) 8. The product of three cosecutve terms a geometrc sequece of real terms s 7. What s the value of the mddle of these three terms? A) 7 8 B) 3 C) 9 D) Approxmate to the earest thousadth. A).66 B).89 C).0 D) Let z,the th term of a sequece of complex umbers, be defed by z 5. Let S be the tersecto of the closed ut dsk cetered at the org ad the fourth quadrat the complex plae. What s the smallest value of such that z les S? A) 4 B) 5 C) 6 D) 7